Conservapedia - User contributions [en]

Talk:Theory of relativity

2012-04-18T21:31:23Z

Cahnkj: evidence that Mr. Schafly hates relativity

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== Mass depending on direction ==

The article states:
:''There is a logical difficulty, however, to an increase in relativistic mass. Such increase would only exist in the direction of motion, and the rest mass would remain intact with respect to a force applied in a direction orthogonal to velocity. Neither mass nor energy is a vector, and the notion of the mass of an object having different values depending on the direction of an applied force is illogical.''

As [[User:RSchlafly|RSchlafly]] on 8 July 2007 (EDT): ''This paragraph is nonsense [..] The relativistic mass applies no matter what the direction of the force is.''

[[User:AugustO|AugustO]] 15:45, 10 January 2012 (EST)

== Neutrinos now obey speed limit ==

The observation sited in the first sentence of this article has been discredited. [http://news.sciencemag.org/scienceinsider/2012/02/official-word-on-superluminal-ne.html?ref=hp] It appears that a loose fiber-optics cable is to blame for the misreadings. I suggest editing this first sentence, and any other mention of this in the article.--[[User:CarloP|CarloP]] 18:51, 2 March 2012 (EST)

:Issues concerning the neutrino experiment are not yet fully resolved. No problam: I replaced it with another counterexample.--[[User:Aschlafly|Andy Schlafly]] 19:12, 2 March 2012 (EST)

== Why does Conservapedia seek to discredit Relativity ==

Can someone explain why Conservapedia is so opposed to the Theory of Relativity?

Is there some philosophical or conservative/liberal basis for this opposition? [[User:RolandPlankton|RolandPlankton]] 18:32, 5 April 2012 (EDT)

:''Conservapedia'' seeks the truth, not merely what the [[lamestream media]] claim is the truth. Moreover, once one accepts a logical fallacy, then anything false can be proven from it.--[[User:Aschlafly|Andy Schlafly]] 23:34, 5 April 2012 (EDT)
:: Ahh.... But the fact that the conclusion is false does not necessarily render the basis false. I could say "Andy Schlafly founded Conservapedia and therefore I am a pig monkey." I am not a pig monkey, and even if I were, that has nothing to do with you founding this website. But you still did. [[User:Gregkochuconn|Gregkochuconn]] 09:58, 9 April 2012 (EDT)

:When looking around the internet, it is obvious that Conservapedia's classification of relativity as [[pseudoscience]] is a source of some amusement and contempt. Aschlafly, could you please answer the two questions I raised above? [[User:RolandPlankton|RolandPlankton]] 11:27, 9 April 2012 (EDT)

::Roland, liberal peer pressure from "around the internet" does not illuminate the truth. If what liberals on the internet said made a dime's bit of difference, then the [[Bible]] would not be the best selling book (by far) and the percentage of people who are [[conservative]] would not be growing (as it does).

::"Can someone explain why Conservapedia is so opposed to the Theory of Relativity?" Because it's false, it confuses people, it misleads people into stop reading the Bible, and its orthodoxy interferes with the advancement of science for the benefit of all. Other than that, it's not a bad theory!

::"Is there some philosophical or conservative/liberal basis for this opposition?" The only bias is by liberals who shout down any criticism of the theory. If the theory were so clearly true, then there would be no need for some liberals to rely on [[censorship]] in propping it up.--[[User:Aschlafly|Andy Schlafly]] 17:10, 9 April 2012 (EDT)

== GPS and Relativity ==

I note that anyone using a GPS is relying on the Theory of Relativity being true, since calculations derived from Relativity are used within a GPS. [[User:RolandPlankton|RolandPlankton]] 18:32, 5 April 2012 (EDT)

:GPS does '''''not''''' rely on the [[Theory of Relativity]], and this has been thoroughly explained on this site.--[[User:Aschlafly|Andy Schlafly]] 23:34, 5 April 2012 (EDT)

::Hi Aschlafly, I've located at least some of the discussion re GPS in the archives of this talk page, and there a lot of references for me to examine before I can make any further serious comments; certainly there are some references which appear to state that GPS relies on relativity. Can you perhaps draw my attention to what you consider the most important (half-dozen or so) references which indicate that the GPS system does NOT rely on relativity so that I have somewhere to start from? In the meantime I'll continue editing and improving less controversial articles as I have been doing for the last two months (my talk page lists nearly 40 articles I can usefully contribute to). [[User:RolandPlankton|RolandPlankton]] 14:17, 6 April 2012 (EDT)

:::This note 7 is on [[Counterexamples to Relativity]]:

::::Contrary to the claims of Relativists, the GPS system has never been based on Relativity. The Time Service Department, U.S. Navy, observed that "The Operational Control System (OCS) of the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein’s general theory of relativity would seem to require" in part because "the effects of relativity, where they are different from the effects predicted by classical mechanics and electromagnetic theory, are too small to matter – less than one centimeter, for users on or near the earth.”

:::The Theory of Relativity does not even assert that it would require significant adjustments to GPS timing: the small effects claimed by the special and general theories nearly cancel each other out for orbiting satellites. From an engineering perspective, it makes far more sense simply to adjust the clocks using synchronization rather than relying on (dubious) theoretical claims.--[[User:Aschlafly|Andy Schlafly]] 14:36, 6 April 2012 (EDT)

Another false claim because of sloppy reading: In the same source by The Time Service Department, U.S. Navy, you can find how the authors Fliegel and DiEsposti describe what is happening to the clocks in the satellites:
''Since GPS receivers work in the time and not in the frequency domain, they handle the velocity, gravity, and acceleration shifts differently than described above. First, each GPS space vehicle (SV) clock is offset from its nominal rate by about -4.45 × 10-10 (= -38 microseconds per day) to allow for the relativistic offsets between the differences between the SV and the ground. Of this -38 microseconds per day, about -45 are due to the gravitational potential difference between the SV at its mean distance and the earth's surface, and +7 to the mean SV speed, which is about 3.87 km/sec. (p. 193).

The text is about the necessity of ''further'' corrections by the ''operational control system'' - there are corrections ''already'' installed in the clocks!

''The Theory of Relativity does not even assert that it would require significant adjustments to GPS timing:'' This sentence is wrong. It has shown to be wrong a couple of times, so it starts to become a lie. [[User:AugustO|AugustO]] 15:12, 6 April 2012 (EDT)

:The [[Theory of Relativity]] was not used to develop GPS, nor would it be sensible to waste time and money doing so. Synchronization is cheaper, simpler, and more reliable. The above quote does not contradict this obvious truth.--[[User:Aschlafly|Andy Schlafly]] 16:32, 6 April 2012 (EDT)

::The fact that these offsets are implemented in the clocks '''in accord with the theory of relativity''' as you can read in the very source you quoted shows that the [[Theory of Relativity]] is used in the GPS - and this from the very beginning of the project! Please, start to read your sources - completely! [[User:AugustO|AugustO]] 16:37, 6 April 2012 (EDT)

Please, before we get into any more debate, could someone supply some actual references (not quotes from) which state that relativity is not used in GPS? [[User:RolandPlankton|RolandPlankton]] 16:41, 6 April 2012 (EDT)

:Aschlafly took his quote from [http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf GPS and Relativity: An Engineering Overview] by Henry F. Fliegel and Raymond S. DiEsposti (though he probably isn't aware of this). The paper is about relativistic effects due to moving GPS-'''''receivers''''' (or GPS-receivers in high altitudes) and comes to the conclusion, that at the moment, they don't have to include additional relativistic corrections.

:Aschlafly interprets this as if ''no'' relativistic corrections are implemented in the GPS.
:However, in the paper itself, you will find the section I quoted above, where the authors describe such very corrections within the clocks of the satellites.
:I'm afraid that Aschlafly won't come up with ''some actual references (not quotes from) which state that relativity is not used in GPS'' as there aren't any.
:[[User:AugustO|AugustO]] 16:53, 6 April 2012 (EDT)

Folks, the burden of proof is on anyone who claims that the [[Theory of Relativity]] was used to design GPS. That burden includes describing who, when, where, how, and why. It didn't happen. And if it did, the person who wasted time and money on such a frivolous approach should explain the mistake, because engineers can simply synchronize the clocks far more accurately than the theory ever could.--[[User:Aschlafly|Andy Schlafly]] 18:15, 8 April 2012 (EDT)

:It looks to me as if you are trying to put impossible conditions prior to any debate. To avoid a lengthy debate all you have to do is produce some actual references which support your point of view. Is this too much to ask?

:If it didn't happen then you should be able to produce some evidence of this, so '''some actual references please'''. The only 'evidence' you have produced so far is an out-of-context quote from a paper which is concerned primarily with GPS receivers (that same paper mentions the use of relativity-related adjustments to the clocks on the GPS satellite transmitters). Surely you must have more than this. Will you accept evidence from engineers and companies involved in designing and building the GPS system? If not, why not? Who would you accept evidence from? The US Department of Defense? Do you seriously expect a member of the public to be able to access internal design documents as your "who, when, where, how, and why" statement implies?

:If you care to check my contribution history you will see that I am actively contributing non-controversial information to articles. This discussion re GPS etc. is only a small part of my activities on Conservapedia. Since I've barely started on considering and consolidating what evidence there is re GPS I would rather have a week or so to look at the evidence before getting into a debate. This should give you ample time to come up with some references to support the separation of GPS and relativity. Simple searches via Google turn up numerous instances where relativity is claimed to be relevant to GPS, but I can't find anything to the contrary and '''I need your help to do so'''. I would really like to see evidence from '''both sides''' of the discussion before entering the debate, so '''some actual references please'''. [[User:RolandPlankton|RolandPlankton]] 19:15, 8 April 2012 (EDT)

::Roland, you're requesting proof that something didn't happen. Moreover, someone with an engineering background (such as myself) would not expect it to have happened. It is like asking for a reference that no green cheese was found on the Moon. No such scientific reference is likely to exist, nor would anyone expect such a reference to exist.--[[User:Aschlafly|Andy Schlafly]] 19:28, 8 April 2012 (EDT)

:: Every single article on GPS says that relativistic adjustments are made to the satellite clocks. Some give the formulas and some give quantitative data on the adjustments. Textbooks explain why the adjustments are necessary. I don't see any reason to doubt that GPS uses relativistic adjustments. [[User:RSchlafly|RSchlafly]] 20:52, 8 April 2012 (EDT)

:::GPS does make synchronizing adjustments. Call them whatever you like, but those adjustments are not made based on predictions by the [[Theory of Relativity]]. Indeed, it would be a silly waste of time and money to synchronize in such a manner.--[[User:Aschlafly|Andy Schlafly]] 21:07, 8 April 2012 (EDT)
:::: Unless you drive the flying Delorean from ''Back to the Future'', relativity would say that its effect on your car when you're driving at normal speeds is so small it need not be accounting for. The normal error for GPS (about 40 feet) is many magnitudes higher than the error relativity would cause. Now, the GPS in the Flying DeLorean would be another issue. But until that's invented, let's not worry about it, ok? Of course, if you were orienteering, your speed would be even slower than if you were driving. Indeed, if you were moving at any normal speed (even a supersonic jet), relativity would be incredibly small (assuming that it exists as scientists explain it). [[User:Gregkochuconn|Gregkochuconn]] 22:14, 8 April 2012 (EDT)

:::::''GPS does make synchronizing adjustments'' Not only simple synchronizing: read the specifications for the GPS, read the sources ''in full'' which you are quoting, and you will see that all these engineers and scientists don't give a damn that you think that they are wasting ''time and money''.
:::::Aschlafly, your position is only tenable as you are willing to ignore most of the data which is presented to you. [[User:AugustO|AugustO]] 03:12, 9 April 2012 (EDT)

::Aschlafly, please correct me if I am misunderstanding you, but it seems to me that you believe very firmly that relativity has nothing to do with GPS, even though you are unwilling to present any evidence to support this belief, and wish to put severe restrictions on what 'proof' of the relationship other folks may present. I raised some five questions above as to what sort of evidence you might consider. Could you please answer these questions.

::I'd like to ask Mr. Schafly if he could explain what the clock adjustments on GPS satellites are for, the article is not clear, and neither is anything on this talk page.--[[User:Cahnkj|Cahnkj]] 00:44, 11 April 2012 (EDT)

:::Cahnkj, herewith a summary of the clock-adjustment situation as I (RolandPlankton) see it. Newton's equations of motions say nothing about how clocks keep time. Einstein's equations of relativity imply that identical clocks will vary in their timekeeping (tick at different rates) if they are travelling at different speeds, or if they are at different heights in a gravitational field, or if they are subject to different accelerations; see [http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf GPS and Relativity: An Engineering Overview]. Now the satellites used in the GPS system require very accurate clocks which are in step with ground-based clocks. The paper just quoted provides the various relativistic equations which apply - the satellites are travelling faster than a ground-based receiver, and are at a different height in a gravitational field. Prior to launch the clocks in the GPS satellites are deliberately set to a different tick rate from ground-based clocks, so that when they are in orbit the clocks will appear to tick at the same rate; the difference in tick rates is about 38 nanoseconds per day, and this adjustment can be calculated from the relevant relativistic equations.

:::But the problem is that Aschlafly rejects the Theory of Relativity, and hence rejects any calculation based on that. The only serious argument he has put forth on this current talk page (see preceding section) is an appeal to [http://en.wikipedia.org/wiki/Wikipedia:The_Truth the truth]; the quote he provides above is also demolished above. You may wish to consult [[Counterexamples to Relativity]], which is rebutted point by point in [[Essay:Rebuttal to Counterexamples to Relativity]].

:::Hope this doesn't add too much to the confusion. [[User:RolandPlankton|RolandPlankton]] 12:07, 11 April 2012 (EDT)

::::Mr. Schlafly states above that "the burden of proof is on anyone who claims that the Theory of Relativity was used to design GPS." (This is a fair requirement, and it seems as this has been done when AugustO referred to the Fliegel and DiEsposti paper above.)

::::But really, isn't the burden of proof on anyone who claims ''anything'' on this site, since Conservapedia Commandment #1 states that "everything you post must be true and verifiable" and Commandment #2 states that users should "always cite and give credit to <nowiki>[their]</nowiki> sources?" --[[User:AndreaM|AndreaM]] 19:03, 12 April 2012 (EDT)

:::::Good point. Anyone who asserts ''on this site'' that GPS was designed based on the [[Theory of Relativity]] needs to prove the claim. Note that the claim is implausible because it is cheaper, easier, and more precise to synchronize GPS based on observations rather than theoretical speculation. Also note that no [[Nobel Prize]] has been given for verification of the [[Theory of Relativity]] with GPS.--[[User:Aschlafly|Andy Schlafly]] 19:55, 12 April 2012 (EDT)

===A Separate Question for Mr. Schlafly About References===

::Aschlafly, as a separate issue, in view of of your apparent attitude to references, could I ask you to have a look at the articles I have been working on over the last two months: [[Pi]], [[Programming language]], [[Compiler]], and the work-in-progress [[Chomsky hierarchy]]. Obviously I'm only asking you to consider the changes I have made. In particular, can you check if the references are acceptable to you, and can you also check that the general style and level of writing is in accordance with Conservapedia's aims? The next article I intend to turn my intention to is [[Context-Free Grammar]], since it seems to me that this fails to satisfy [[Conservapedia:Guidelines#Style]] "Articles on complex topics need an introduction which assumes little or no previous knowledge". [[User:RolandPlankton|RolandPlankton]] 11:03, 9 April 2012 (EDT)

:::Roland, your good edits are appreciated and I've seen no complaints about them. I agree that the [[Context-Free Grammar]] would benefit from a better introduction and look forward to reading what you add there.--[[User:Aschlafly|Andy Schlafly]] 17:39, 9 April 2012 (EDT)

== Why are adjustments needed to GPS? ==

A good question was raised above: if synchronization to GPS is not due to the [[Theory of Relativity]], then what is it due to?

And the answer is simply this: [[quantum mechanics]]. There are fundamental uncertainties, and those uncertainties will lead to clock differences. Otherwise a [[perpetual motion machine]] would be possible. It isn't.--[[User:Aschlafly|Andy Schlafly]] 22:50, 11 April 2012 (EDT)

Where to start with this. This is so bad it isn't even wrong. Could I respectfully suggest that you confine your efforts to areas you understand at least a little bit.

The impossibility of perpetual motion has nothing to do with quantum mechanics. It comes from the 2nd and 3rd laws of thermodynamics and predates quantum mechanics by at least 100 years.

The uncertainty principle is also completely irrelevant. If we imagine a 100 kg satellite moving at a velocity of approximately 100 km/s (this is three times the earth's velocity , so is a plausible and easy to handle number). If we know the satelites location to an uncertainty of 1cm then the uncertainty on its velocity implied by the uncertainty principle is 1 part in 10^39 (i.e. completely negligable).[[User:Jloveday|Jloveday]] 13:10, 14 April 2012 (EDT)

:Well, this is progress indeed. Could you please provide references to support the contention that the synchronization is required as a result of quantum mechanical effects?

:Also, as an aside, how do you say that fundamental uncertainties described by quantum mechanics relate to the impossibility of a perpetual motion machine? Not sure I follow you there. --[[User:JeromeKJ|JeromeKJ]] 23:36, 11 April 2012 (EDT)

::It's basic logic. Unless someone denies [[quantum mechanics]] and the fundamental uncertainties it describes -- and many [[Relativists]] do deny it -- then synchronization will be required as a logical result.--[[User:Aschlafly|Andy Schlafly]] 23:58, 11 April 2012 (EDT)

:::Do you have any references? --[[User:JeromeKJ|JeromeKJ]] 00:04, 12 April 2012 (EDT)

::::I haven't looked ... nor is it necessary to. I wouldn't look for references to confirm any logical statement.--[[User:Aschlafly|Andy Schlafly]] 00:14, 12 April 2012 (EDT)

:::::Really? Is it fair to say then that this contention that the synchronization is required as a result of quantum mechanical effects is not something that you have read about but rather something that you yourself concluded from your own knowledge of quantum mechanics and GPS systems? --[[User:JeromeKJ|JeromeKJ]] 00:21, 12 April 2012 (EDT)
:::::P.S. As a result of this discussion I found a couple of articles which appear to confirm that GPS satellites have their clocks adjusted by about 38,000 nanoseconds per day before launch in compliance with relitavistic predictions (both Special and General Relativity are taken into account). The articles are [http://metaresearch.org/cosmology/gps-relativity.asp here] and [http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html here]. Is there really any question that this is what is happening? I would think that if these sources are to be questioned that some sort of reference should be provided. A mere assertion that the adjustments are as a result of quantum mechanical effects and that it is a matter of logic would not usually be enough for any serious encyclopedia. --[[User:JeromeKJ|JeromeKJ]] 00:53, 12 April 2012 (EDT)

::::::The references are [[hearsay]]. Logic is far more compelling, more efficient, and more likely to lead to the correct result.

::::::To take the analogy mentioned above, if you agree that [[perpetual motion machines]] are impossible, what is the reason?--[[User:Aschlafly|Andy Schlafly]] 01:45, 12 April 2012 (EDT)

:Quantum mechanics gives a probabilistic model of phenomena. Indeed, the page you linked for quantum mechanics states:
::"If we measure such an observable, generally the wave function does not predict exactly which value we will obtain. Instead, the wave function gives us the probability that a certain value will be obtained."
:If this is the case, that means that Quantum mechanical phenomena are ''unpredictable''. How is it that clock adjustments can be made based on unpredictable events, ie, probabilities?
:I'd also like to know how the GPS system is affected by these phenomena.
:--[[User:Cahnkj|Cahnkj]] 01:51, 12 April 2012 (EDT)

Logic is a nice thing. But engineers like to calculate. So could you give us a Ballpark estimate for the quantum mechanic effects which come into play here? [[User:AugustO|AugustO]] 01:59, 12 April 2012 (EDT)

:(Edit conflict x2) Andy, as a lawyer I can assure you that hearsay is a [[legal]] concept which is of little use in this sort of scientific discussion. Whilst I understand that non-legally trained people sometimes confuse the nature and applicability of the concept, I can confirm that it has no relevance here.

:The difficulty here arises from your wanting to assert the truth of a matter without providing either references or even the basis for you own logic. Just saying "quantum mechanics" is hardly enlightening. Do you deny that GPS satellite clocks are adjusted by approximately 38,000 nanoseconds as referred to in the references that I provided? If not, do you say that there is a quantum calculation that accounts for that adjustment? What is that quantum calculation and what is it based on? I am really having difficulty in understanding the basis for all of this. --[[User:JeromeKJ|JeromeKJ]] 02:03, 12 April 2012 (EDT)

:Aschlafly, this reference [http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf GPS and Relativity: An Engineering Overview] has been pointed out to you several times already. Since it is published by folks actually working on the GPS system, I hardly think that it qualifies as 'hearsay'. It contains all the relevant relativistic equations, which are not really that complicated, and derives the 38 nanosecond figure quoted above. An assertion on scientific matters without any evidence can't really be taken seriously. Can we please see the quantum mechanical equations and calculations which come up with the same or similar result? [[User:RolandPlankton|RolandPlankton]] 09:49, 12 April 2012 (EDT)

:Aschlafly, I'm inclined to suspect that your disbelief in relativity is so strong that you are unwilling to consider any evidence which might indicate that relativity could be correct, and are hence flailing around looking for some other explanation as to what actually happens (GPS clock adjustment by 38 ns). Would you care to comment on my suspicion? [[User:RolandPlankton|RolandPlankton]] 09:49, 12 April 2012 (EDT)

Quote: "A logical statement is a declarative sentence that is either true or false." [http://www.ontotext.com/factforge/logical-statement].

So Aschlafly, why don't you need a reference to confirm a logical statement? Just because a statement is logical doesn't mean that it is true. [[User:RolandPlankton|RolandPlankton]] 16:53, 12 April 2012 (EDT)

: It would be helpful to have a more modern reference. GPS switched to a system of daily updates to the satellites. Maybe those relativistic formulas cause errors that require daily clock synchronizations to correct. Not likely. But to prove the point we ought to find a reference that says that the satellites still use the 38 ns/day relativistic adjustments, and that the daily corrections are much smaller than that. [[User:RSchlafly|RSchlafly]] 17:18, 12 April 2012 (EDT)
::The best I've found so far is [http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/GPS/Neil_Ashby_Relativity_GPS.pdf] from Physics Today, May 2002. This confirms the initial adjustment and mentions further on page 7: "Additional small frequency offsets arise from clock drift, environmental changes, and other unavoidable effects such as the inability to launch the satellite into an orbit with precisely the desired semimajor axis. The satellite clock frequencies are adjusted so that they remain as close as possible to the frequency of the Naval Observatory's clock ensemble." Unfortunately it doesn't give the actual size of the adjustments, thought the word 'small' does indicate it as being much less than the initial adjustment. I rather like the last sentence of this paper: "Ordinary users of the GPS, though they may not need to be aware of it, have thus become dependent on Einstein's conception of space and time." [[User:RolandPlankton|RolandPlankton]] 18:26, 12 April 2012 (EDT)

:::The lack of evidence, amid so much political pressure to prove it, is indicative that no proof can be found. Notice how no [[Nobel Prize]]s have been given for GPS confirming the [[Theory of Relativity]]?--[[User:Aschlafly|Andy Schlafly]] 21:01, 12 April 2012 (EDT)
:::If you want to use the [[Nobel Prize]] as evidence against relativity, might I direct you to:
:::http://www.nobelprize.org/educational/physics/relativity/
:::Where the official Nobel Prize website discusses various experiments related to relativity, and the relevant [[Nobel Prize]]s awarded for them.
:::--[[User:Cahnkj|Cahnkj]] 00:32, 13 April 2012 (EDT)

::::GPS is not even on that overly broad list.--[[User:Aschlafly|Andy Schlafly]] 00:43, 13 April 2012 (EDT)

::Aschlafly, I've tried to confine my evidence to items which not even you can claim as 'hearsay'. A simple Google search turns up hundreds of references linking GPS and relativity, but in view of your earlier dismissal of such as hearsay, I thought I'd better stick to indisputable items. At least there is some fairly convincing evidence linking GPS with relativity (including all the relevant equations and the result of applying these equations), unlike your assertion linking GPS with quantum mechanics, where you have produced precisely zero evidence. You still haven't responded to my comments and question re 'logical statements' above. So, where is the evidence for your assertion? [[User:RolandPlankton|RolandPlankton]] 02:46, 13 April 2012 (EDT)

:::There is no credible evidence that the [[Theory of Relativity]] had anything to do with the development of GPS. In addition, not even the pro-Relativity [[Nobel Prize]] [[liberals]] say that GPS proves the theory.

:::My comment about [[quantum mechanics]] was in response to a question about why synchronization is needed. Unless someone thinks that [[perpetual motion machines]] are possible (have you answered my question about that?), then synchronization will be needed.--[[User:Aschlafly|Andy Schlafly]] 11:00, 13 April 2012 (EDT)
::::Could you please clarify what the connection between synchronisation, quantum mechanics and perpetual motion machines is? From what I've learned, clock synchronisation between the satellites is necessary because any signal between them travels at a finite speed, namely the speed of light. Do you deny that? The claim is that in order to compute the signal travel time and thus to synchronize the clocks correctly, the relative velocities and the differences in gravitational potential due to the different altitudes of the satellites (and Earth's surface) have to be taken into account. Do you think that is wrong? --[[User:FrederickT3|FrederickT3]] 11:56, 13 April 2012 (EDT)

Lets stick to the subject (GPS and relativity); perpetual motion is a complete red herring, and I'm not sure how Nobel prizes come into the picture (we're debating science, not prizes).
On the basis of '''actual evidence produced''' in this discussion so far, I think that we can confidently state four facts:
#Prior to launch, the clock in a GPS satellite is set to run about 38 nanoseconds/day different from an otherwise identical clock on the earth's surface.
#When in orbit the GPS clock then appears to tick at the same rate as an identical clock on the earth's surface.
#Equations based on the theory of relativity accurately come up with this figure of around 38 nanoseconds.
#No evidence has been produced to show how quantum mechanics is involved.

If anyone disagrees with any of the above, they need to bear in mind ('''emphasis''' added):
:from Conservapedia:Commandments 1 Everything you post must be true and '''verifiable'''.
:from Conservapedia:Commandments 2 '''Always cite''' and give credit to your sources.
:from Conservapedia:Guidelines/Reliability 4 A major difference between Liberalism and Conservatism is how much each group is willing to have its pronouncements checked, its actions reviewed and evaluated.

Hope this summary helps. [[User:RolandPlankton|RolandPlankton]] 14:41, 13 April 2012 (EDT)

: That is the story as I have heard it. Except that I heard that the 38 ns/day adjustment was remotely switchable, because of relativity skeptics who did not believe that it would be necessary. I also don't agree that GPS is "dependent on Einstein's conception of space and time." The GPS system has the ability to measure the daily adjustments that it needs. So even with any relativity theory or Einstein conception, it could just make those 38 ns/day adjustments and GPS would have all the accuracy it has today. [[User:RSchlafly|RSchlafly]] 15:19, 13 April 2012 (EDT)

::In the summary I was careful to stick to facts supported by evidence, and to avoid saying "GPS is dependent on Einstein's conception of space and time", even though the two main references I have quoted do in fact say this. All I said was that the adjustment calculated according to relativity agrees with the actual adjustment, from which one might reasonably conclude, in this instance at least, that relativity is consistent with reality. [[User:RolandPlankton|RolandPlankton]] 15:44, 13 April 2012 (EDT)

::I note that no one has proposed any credible alternative theory as to why the orbiting clocks tick at a different speed from surface clocks, so until some better theory comes along I'm quite happy to stick with relativity. [[User:RolandPlankton|RolandPlankton]] 16:00, 13 April 2012 (EDT)

== Logic and the GPS ==

*Atomic watches work on the Earth quite fine
*[[Quantum mechanics]] describe the physics of ''very small length and energy scales''
*Satellites are macroscopic objects.
*Even a precision of 1cm on the surface of the Earth isn't a very small length.

So which kind of logic tells us that quantum mechanical effects influence the synchronization of the clocks? Why are not only the scientists involved lying, but also their calculations?

For me it seems to be a logical conclusion that you, Aschlafly, are even more knowledgeable of Greek than of Science! [[User:AugustO|AugustO]] 08:21, 12 April 2012 (EDT)
:He's trying to apply the Heisenburg Uncertainty principle to satellites? Are you kidding me? That principle is used for things at the ATOMIC LEVEL! Using ANYTHING with regards to quantum mechanics in an argument about satellites is absurdism and/or ignorance of the subject matter! Seriously Andy, I know you hate the Theory of Relativity, but you should really leave science to those who understand it. [[User:JanSmuts|JanSmuts]] 16:04, 12 April 2012 (EDT)
::For someone who thinks that Brownian motion is about motion at the sub-atomic level your suggestions of scientific superiority ring hollow.--[[User:DavidEdwards|DavidEdwards]] 10:15, 13 April 2012 (EDT)

== Newtonian explanation of Mercury's precession ==

I removed the phrase "[precession can be understood by] factoring in the gravitational pull due to other planets". The first sentence of that paragraph says the opposite, that the extra precession cannot be understood "even after accounting for gravitational perturbations caused all other planets". Unless I'm reading it wrong, it sounded like a contradiction. [[User:Spielman|Spielman]] 16:51, 13 April 2012 (EDT)

:Where is the contradiction? If the exponent in Newtonian gravity is slightly adjusted, then it predicts the Mercury precession.--[[User:Aschlafly|Andy Schlafly]] 18:01, 13 April 2012 (EDT)

::I'm curious as to the justification for changing a formula in Newtonian gravity. Do you change it for every situation, or just for this one special case? Can you give us the adjusted formula, and specify the exact change? For such a change in physics which has been in use for over 250 years I would like to see a reference, preferably several good references. [[User:RolandPlankton|RolandPlankton]] 18:25, 13 April 2012 (EDT)
:::The old Newcomb-Hall hypothesis. [http://books.google.at/books?id=oKGlHjDzGjQC&lpg=PA379&dq=newcomb%20hall%20precession&pg=PA379#v=onepage&q=newcomb%20hall%20precession&f=false This book] says that it contradicts the observations of the orbit of the moon, which rules out a change of exponent of of the required magnitude. --[[User:FrederickT3|FrederickT3]] 18:30, 13 April 2012 (EDT)
::The contributors to this section might be pleased to see that the issue has been discussed, at great length, right here at Conservapedia. An entire debate page was created for it: [[Debate:What is the exponent of r in Newtonian gravity%3F]] This was a discussion that spilled over from [[Essay:Quantifying Open-Mindedness]].

::Furthermore, the subject was discussed on the relativity page itself, in the section [[Theory_of_relativity#Experimental_Verification_of_Relativity]]. There is a large chart showing the precessions of the planets under the Newcomb-Hall theory and under general relativity. They are the last two columns of the chart. The actual observations match the last column very well (see [http://www.mathpages.com/rr/s6-02/6-02.htm], taking into account that it's very hard to get accurate reading on the outer planets, since their precession is so small.

::One can see that the last two columns of the chart match only for Mercury. That is, Newcomb and Hall "tweaked" the exponent to the value of 2.000000157 in order to get Mercury's precession correct.

::Under the Newcomb-Hall theory, the precession of any orbiting body would be .000000078 revolutions per orbit. This works for Mercury, but is too high for the other planets, and way too high for the Moon. This is why the theory was discarded. With modern artificial satellites, such as the International Space Station, an orbit takes only an hour and a half, and the precession would be enormous. The clearly wrong value for the Moon is why the Newcomb-Hall theory was quickly discarded.

::Under general relativity, we know that the precession per orbit is proportional to the square of the planet's orbital velocity. Mercury has the highest velocity, so it has readily measurable precession. Artificial satellites are much slower, and the Moon is slower still.

::I personally don't see accepting the possible truth of such a thoroughly discredited theory as evidence of open-mindedness, but open-mindedness is admittedly a very tricky issue. [[User:SamHB|SamHB]] 18:11, 14 April 2012 (EDT)

::::"Mathematical physicists" (an [[oxymoron]] - I'll add it to the list) insisted that it was impossible for the exponent in Newtonian gravity to be anything other than '''''precisely''''' 2 (or -2). With the political push to promote the [[Theory of Relativity]], the influence of the mathematical physicists rose too, and that is what shut down the valid inquiry into whether the Newtonian exponent should be '''''precisely''''' 2 (or -2). But any logical inquiry must admit the possibility, or even the likelihood, that it would not be exactly 2 (or -2).--[[User:Aschlafly|Andy Schlafly]] 19:31, 13 April 2012 (EDT)

The issue here is not whether the exponent is precisely two or not but that you have to have a model which explains all (or at least as many as possible) observations. To get the precision of Mercury right you produce a model which then fails to explain the observed precession of every other body in the solar system. This seems to be a good experimental demonstration that Newcomb-Hall is wrong (or least inadequate as a model). [[User:Jloveday|Jloveday]] 15:32, 15 April 2012 (EDT)

:I'm not sure how [[User:Aschlafly|Andy Schlafly]] got us on the subject of the Newtonian exponent. My comment makes no mention of it. I'll answer his original question "where's the contradiction?": I quoted two sentences, both containing the phrase "other planets". One sentence said the precession '''can''' be understood by including the effects of the other planets, whereas the other said the precession '''cannot''' be understood that way. It is just rhetoric. The contradiction has little to do with physics. [[User:Spielman|Spielman]] 12:06, 16 April 2012 (EDT)

== First sentence of article contradicted by the rest ==

Given that main body of the article now largely deals with the things GR can explain (including the precession of Mercury) should not the first sentance be changed?[[User:Jloveday|Jloveday]] 15:37, 15 April 2012 (EDT)

Yes, but you're likely to be banned if you try. Mr. Schafly hates relativity (as evidenced by this talk page), and he is the last word here, because this is ''his'' website. --[[User:Cahnkj|Cahnkj]] 17:31, 18 April 2012 (EDT)

Talk:Theory of relativity

2012-04-13T04:33:02Z

Cahnkj: indent-a-a-tion is beating me good

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== Mass depending on direction ==

The article states:
:''There is a logical difficulty, however, to an increase in relativistic mass. Such increase would only exist in the direction of motion, and the rest mass would remain intact with respect to a force applied in a direction orthogonal to velocity. Neither mass nor energy is a vector, and the notion of the mass of an object having different values depending on the direction of an applied force is illogical.''

As [[User:RSchlafly|RSchlafly]] on 8 July 2007 (EDT): ''This paragraph is nonsense [..] The relativistic mass applies no matter what the direction of the force is.''

[[User:AugustO|AugustO]] 15:45, 10 January 2012 (EST)

== Neutrinos now obey speed limit ==

The observation sited in the first sentence of this article has been discredited. [http://news.sciencemag.org/scienceinsider/2012/02/official-word-on-superluminal-ne.html?ref=hp] It appears that a loose fiber-optics cable is to blame for the misreadings. I suggest editing this first sentence, and any other mention of this in the article.--[[User:CarloP|CarloP]] 18:51, 2 March 2012 (EST)

:Issues concerning the neutrino experiment are not yet fully resolved. No problam: I replaced it with another counterexample.--[[User:Aschlafly|Andy Schlafly]] 19:12, 2 March 2012 (EST)

== Why does Conservapedia seek to discredit Relativity ==

Can someone explain why Conservapedia is so opposed to the Theory of Relativity?

Is there some philosophical or conservative/liberal basis for this opposition? [[User:RolandPlankton|RolandPlankton]] 18:32, 5 April 2012 (EDT)

:''Conservapedia'' seeks the truth, not merely what the [[lamestream media]] claim is the truth. Moreover, once one accepts a logical fallacy, then anything false can be proven from it.--[[User:Aschlafly|Andy Schlafly]] 23:34, 5 April 2012 (EDT)
:: Ahh.... But the fact that the conclusion is false does not necessarily render the basis false. I could say "Andy Schlafly founded Conservapedia and therefore I am a pig monkey." I am not a pig monkey, and even if I were, that has nothing to do with you founding this website. But you still did. [[User:Gregkochuconn|Gregkochuconn]] 09:58, 9 April 2012 (EDT)

:When looking around the internet, it is obvious that Conservapedia's classification of relativity as [[pseudoscience]] is a source of some amusement and contempt. Aschlafly, could you please answer the two questions I raised above? [[User:RolandPlankton|RolandPlankton]] 11:27, 9 April 2012 (EDT)

::Roland, liberal peer pressure from "around the internet" does not illuminate the truth. If what liberals on the internet said made a dime's bit of difference, then the [[Bible]] would not be the best selling book (by far) and the percentage of people who are [[conservative]] would not be growing (as it does).

::"Can someone explain why Conservapedia is so opposed to the Theory of Relativity?" Because it's false, it confuses people, it misleads people into stop reading the Bible, and its orthodoxy interferes with the advancement of science for the benefit of all. Other than that, it's not a bad theory!

::"Is there some philosophical or conservative/liberal basis for this opposition?" The only bias is by liberals who shout down any criticism of the theory. If the theory were so clearly true, then there would be no need for some liberals to rely on [[censorship]] in propping it up.--[[User:Aschlafly|Andy Schlafly]] 17:10, 9 April 2012 (EDT)

== GPS and Relativity ==

I note that anyone using a GPS is relying on the Theory of Relativity being true, since calculations derived from Relativity are used within a GPS. [[User:RolandPlankton|RolandPlankton]] 18:32, 5 April 2012 (EDT)

:GPS does '''''not''''' rely on the [[Theory of Relativity]], and this has been thoroughly explained on this site.--[[User:Aschlafly|Andy Schlafly]] 23:34, 5 April 2012 (EDT)

::Hi Aschlafly, I've located at least some of the discussion re GPS in the archives of this talk page, and there a lot of references for me to examine before I can make any further serious comments; certainly there are some references which appear to state that GPS relies on relativity. Can you perhaps draw my attention to what you consider the most important (half-dozen or so) references which indicate that the GPS system does NOT rely on relativity so that I have somewhere to start from? In the meantime I'll continue editing and improving less controversial articles as I have been doing for the last two months (my talk page lists nearly 40 articles I can usefully contribute to). [[User:RolandPlankton|RolandPlankton]] 14:17, 6 April 2012 (EDT)

:::This note 7 is on [[Counterexamples to Relativity]]:

::::Contrary to the claims of Relativists, the GPS system has never been based on Relativity. The Time Service Department, U.S. Navy, observed that "The Operational Control System (OCS) of the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein’s general theory of relativity would seem to require" in part because "the effects of relativity, where they are different from the effects predicted by classical mechanics and electromagnetic theory, are too small to matter – less than one centimeter, for users on or near the earth.”

:::The Theory of Relativity does not even assert that it would require significant adjustments to GPS timing: the small effects claimed by the special and general theories nearly cancel each other out for orbiting satellites. From an engineering perspective, it makes far more sense simply to adjust the clocks using synchronization rather than relying on (dubious) theoretical claims.--[[User:Aschlafly|Andy Schlafly]] 14:36, 6 April 2012 (EDT)

Another false claim because of sloppy reading: In the same source by The Time Service Department, U.S. Navy, you can find how the authors Fliegel and DiEsposti describe what is happening to the clocks in the satellites:
''Since GPS receivers work in the time and not in the frequency domain, they handle the velocity, gravity, and acceleration shifts differently than described above. First, each GPS space vehicle (SV) clock is offset from its nominal rate by about -4.45 × 10-10 (= -38 microseconds per day) to allow for the relativistic offsets between the differences between the SV and the ground. Of this -38 microseconds per day, about -45 are due to the gravitational potential difference between the SV at its mean distance and the earth's surface, and +7 to the mean SV speed, which is about 3.87 km/sec. (p. 193).

The text is about the necessity of ''further'' corrections by the ''operational control system'' - there are corrections ''already'' installed in the clocks!

''The Theory of Relativity does not even assert that it would require significant adjustments to GPS timing:'' This sentence is wrong. It has shown to be wrong a couple of times, so it starts to become a lie. [[User:AugustO|AugustO]] 15:12, 6 April 2012 (EDT)

:The [[Theory of Relativity]] was not used to develop GPS, nor would it be sensible to waste time and money doing so. Synchronization is cheaper, simpler, and more reliable. The above quote does not contradict this obvious truth.--[[User:Aschlafly|Andy Schlafly]] 16:32, 6 April 2012 (EDT)

::The fact that these offsets are implemented in the clocks '''in accord with the theory of relativity''' as you can read in the very source you quoted shows that the [[Theory of Relativity]] is used in the GPS - and this from the very beginning of the project! Please, start to read your sources - completely! [[User:AugustO|AugustO]] 16:37, 6 April 2012 (EDT)

Please, before we get into any more debate, could someone supply some actual references (not quotes from) which state that relativity is not used in GPS? [[User:RolandPlankton|RolandPlankton]] 16:41, 6 April 2012 (EDT)

:Aschlafly took his quote from [http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf GPS and Relativity: An Engineering Overview] by Henry F. Fliegel and Raymond S. DiEsposti (though he probably isn't aware of this). The paper is about relativistic effects due to moving GPS-'''''receivers''''' (or GPS-receivers in high altitudes) and comes to the conclusion, that at the moment, they don't have to include additional relativistic corrections.

:Aschlafly interprets this as if ''no'' relativistic corrections are implemented in the GPS.
:However, in the paper itself, you will find the section I quoted above, where the authors describe such very corrections within the clocks of the satellites.
:I'm afraid that Aschlafly won't come up with ''some actual references (not quotes from) which state that relativity is not used in GPS'' as there aren't any.
:[[User:AugustO|AugustO]] 16:53, 6 April 2012 (EDT)

Folks, the burden of proof is on anyone who claims that the [[Theory of Relativity]] was used to design GPS. That burden includes describing who, when, where, how, and why. It didn't happen. And if it did, the person who wasted time and money on such a frivolous approach should explain the mistake, because engineers can simply synchronize the clocks far more accurately than the theory ever could.--[[User:Aschlafly|Andy Schlafly]] 18:15, 8 April 2012 (EDT)

:It looks to me as if you are trying to put impossible conditions prior to any debate. To avoid a lengthy debate all you have to do is produce some actual references which support your point of view. Is this too much to ask?

:If it didn't happen then you should be able to produce some evidence of this, so '''some actual references please'''. The only 'evidence' you have produced so far is an out-of-context quote from a paper which is concerned primarily with GPS receivers (that same paper mentions the use of relativity-related adjustments to the clocks on the GPS satellite transmitters). Surely you must have more than this. Will you accept evidence from engineers and companies involved in designing and building the GPS system? If not, why not? Who would you accept evidence from? The US Department of Defense? Do you seriously expect a member of the public to be able to access internal design documents as your "who, when, where, how, and why" statement implies?

:If you care to check my contribution history you will see that I am actively contributing non-controversial information to articles. This discussion re GPS etc. is only a small part of my activities on Conservapedia. Since I've barely started on considering and consolidating what evidence there is re GPS I would rather have a week or so to look at the evidence before getting into a debate. This should give you ample time to come up with some references to support the separation of GPS and relativity. Simple searches via Google turn up numerous instances where relativity is claimed to be relevant to GPS, but I can't find anything to the contrary and '''I need your help to do so'''. I would really like to see evidence from '''both sides''' of the discussion before entering the debate, so '''some actual references please'''. [[User:RolandPlankton|RolandPlankton]] 19:15, 8 April 2012 (EDT)

::Roland, you're requesting proof that something didn't happen. Moreover, someone with an engineering background (such as myself) would not expect it to have happened. It is like asking for a reference that no green cheese was found on the Moon. No such scientific reference is likely to exist, nor would anyone expect such a reference to exist.--[[User:Aschlafly|Andy Schlafly]] 19:28, 8 April 2012 (EDT)

:: Every single article on GPS says that relativistic adjustments are made to the satellite clocks. Some give the formulas and some give quantitative data on the adjustments. Textbooks explain why the adjustments are necessary. I don't see any reason to doubt that GPS uses relativistic adjustments. [[User:RSchlafly|RSchlafly]] 20:52, 8 April 2012 (EDT)

:::GPS does make synchronizing adjustments. Call them whatever you like, but those adjustments are not made based on predictions by the [[Theory of Relativity]]. Indeed, it would be a silly waste of time and money to synchronize in such a manner.--[[User:Aschlafly|Andy Schlafly]] 21:07, 8 April 2012 (EDT)
:::: Unless you drive the flying Delorean from ''Back to the Future'', relativity would say that its effect on your car when you're driving at normal speeds is so small it need not be accounting for. The normal error for GPS (about 40 feet) is many magnitudes higher than the error relativity would cause. Now, the GPS in the Flying DeLorean would be another issue. But until that's invented, let's not worry about it, ok? Of course, if you were orienteering, your speed would be even slower than if you were driving. Indeed, if you were moving at any normal speed (even a supersonic jet), relativity would be incredibly small (assuming that it exists as scientists explain it). [[User:Gregkochuconn|Gregkochuconn]] 22:14, 8 April 2012 (EDT)

:::::''GPS does make synchronizing adjustments'' Not only simple synchronizing: read the specifications for the GPS, read the sources ''in full'' which you are quoting, and you will see that all these engineers and scientists don't give a damn that you think that they are wasting ''time and money''.
:::::Aschlafly, your position is only tenable as you are willing to ignore most of the data which is presented to you. [[User:AugustO|AugustO]] 03:12, 9 April 2012 (EDT)

::Aschlafly, please correct me if I am misunderstanding you, but it seems to me that you believe very firmly that relativity has nothing to do with GPS, even though you are unwilling to present any evidence to support this belief, and wish to put severe restrictions on what 'proof' of the relationship other folks may present. I raised some five questions above as to what sort of evidence you might consider. Could you please answer these questions.

::I'd like to ask Mr. Schafly if he could explain what the clock adjustments on GPS satellites are for, the article is not clear, and neither is anything on this talk page.--[[User:Cahnkj|Cahnkj]] 00:44, 11 April 2012 (EDT)

:::Cahnkj, herewith a summary of the clock-adjustment situation as I (RolandPlankton) see it. Newton's equations of motions say nothing about how clocks keep time. Einstein's equations of relativity imply that identical clocks will vary in their timekeeping (tick at different rates) if they are travelling at different speeds, or if they are at different heights in a gravitational field, or if they are subject to different accelerations; see [http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf GPS and Relativity: An Engineering Overview]. Now the satellites used in the GPS system require very accurate clocks which are in step with ground-based clocks. The paper just quoted provides the various relativistic equations which apply - the satellites are travelling faster than a ground-based receiver, and are at a different height in a gravitational field. Prior to launch the clocks in the GPS satellites are deliberately set to a different tick rate from ground-based clocks, so that when they are in orbit the clocks will appear to tick at the same rate; the difference in tick rates is about 38 nanoseconds per day, and this adjustment can be calculated from the relevant relativistic equations.

:::But the problem is that Aschlafly rejects the Theory of Relativity, and hence rejects any calculation based on that. The only serious argument he has put forth on this current talk page (see preceding section) is an appeal to [http://en.wikipedia.org/wiki/Wikipedia:The_Truth the truth]; the quote he provides above is also demolished above. You may wish to consult [[Counterexamples to Relativity]], which is rebutted point by point in [[Essay:Rebuttal to Counterexamples to Relativity]].

:::Hope this doesn't add too much to the confusion. [[User:RolandPlankton|RolandPlankton]] 12:07, 11 April 2012 (EDT)

::::Mr. Schlafly states above that "the burden of proof is on anyone who claims that the Theory of Relativity was used to design GPS." (This is a fair requirement, and it seems as this has been done when AugustO referred to the Fliegel and DiEsposti paper above.)

::::But really, isn't the burden of proof on anyone who claims ''anything'' on this site, since Conservapedia Commandment #1 states that "everything you post must be true and verifiable" and Commandment #2 states that users should "always cite and give credit to <nowiki>[their]</nowiki> sources?" --[[User:AndreaM|AndreaM]] 19:03, 12 April 2012 (EDT)

:::::Good point. Anyone who asserts ''on this site'' that GPS was designed based on the [[Theory of Relativity]] needs to prove the claim. Note that the claim is implausible because it is cheaper, easier, and more precise to synchronize GPS based on observations rather than theoretical speculation. Also note that no [[Nobel Prize]] has been given for verification of the [[Theory of Relativity]] with GPS.--[[User:Aschlafly|Andy Schlafly]] 19:55, 12 April 2012 (EDT)

===A Separate Question for Mr. Schlafly About References===

::Aschlafly, as a separate issue, in view of of your apparent attitude to references, could I ask you to have a look at the articles I have been working on over the last two months: [[Pi]], [[Programming language]], [[Compiler]], and the work-in-progress [[Chomsky hierarchy]]. Obviously I'm only asking you to consider the changes I have made. In particular, can you check if the references are acceptable to you, and can you also check that the general style and level of writing is in accordance with Conservapedia's aims? The next article I intend to turn my intention to is [[Context-Free Grammar]], since it seems to me that this fails to satisfy [[Conservapedia:Guidelines#Style]] "Articles on complex topics need an introduction which assumes little or no previous knowledge". [[User:RolandPlankton|RolandPlankton]] 11:03, 9 April 2012 (EDT)

:::Roland, your good edits are appreciated and I've seen no complaints about them. I agree that the [[Context-Free Grammar]] would benefit from a better introduction and look forward to reading what you add there.--[[User:Aschlafly|Andy Schlafly]] 17:39, 9 April 2012 (EDT)

== Why are adjustments needed to GPS? ==

A good question was raised above: if synchronization to GPS is not due to the [[Theory of Relativity]], then what is it due to?

And the answer is simply this: [[quantum mechanics]]. There are fundamental uncertainties, and those uncertainties will lead to clock differences. Otherwise a [[perpetual motion machine]] would be possible. It isn't.--[[User:Aschlafly|Andy Schlafly]] 22:50, 11 April 2012 (EDT)

:Well, this is progress indeed. Could you please provide references to support the contention that the synchronization is required as a result of quantum mechanical effects?

:Also, as an aside, how do you say that fundamental uncertainties described by quantum mechanics relate to the impossibility of a perpetual motion machine? Not sure I follow you there. --[[User:JeromeKJ|JeromeKJ]] 23:36, 11 April 2012 (EDT)

::It's basic logic. Unless someone denies [[quantum mechanics]] and the fundamental uncertainties it describes -- and many [[Relativists]] do deny it -- then synchronization will be required as a logical result.--[[User:Aschlafly|Andy Schlafly]] 23:58, 11 April 2012 (EDT)

:::Do you have any references? --[[User:JeromeKJ|JeromeKJ]] 00:04, 12 April 2012 (EDT)

::::I haven't looked ... nor is it necessary to. I wouldn't look for references to confirm any logical statement.--[[User:Aschlafly|Andy Schlafly]] 00:14, 12 April 2012 (EDT)

:::::Really? Is it fair to say then that this contention that the synchronization is required as a result of quantum mechanical effects is not something that you have read about but rather something that you yourself concluded from your own knowledge of quantum mechanics and GPS systems? --[[User:JeromeKJ|JeromeKJ]] 00:21, 12 April 2012 (EDT)
:::::P.S. As a result of this discussion I found a couple of articles which appear to confirm that GPS satellites have their clocks adjusted by about 38,000 nanoseconds per day before launch in compliance with relitavistic predictions (both Special and General Relativity are taken into account). The articles are [http://metaresearch.org/cosmology/gps-relativity.asp here] and [http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html here]. Is there really any question that this is what is happening? I would think that if these sources are to be questioned that some sort of reference should be provided. A mere assertion that the adjustments are as a result of quantum mechanical effects and that it is a matter of logic would not usually be enough for any serious encyclopedia. --[[User:JeromeKJ|JeromeKJ]] 00:53, 12 April 2012 (EDT)

::::::The references are [[hearsay]]. Logic is far more compelling, more efficient, and more likely to lead to the correct result.

::::::To take the analogy mentioned above, if you agree that [[perpetual motion machines]] are impossible, what is the reason?--[[User:Aschlafly|Andy Schlafly]] 01:45, 12 April 2012 (EDT)

:Quantum mechanics gives a probabilistic model of phenomena. Indeed, the page you linked for quantum mechanics states:
::"If we measure such an observable, generally the wave function does not predict exactly which value we will obtain. Instead, the wave function gives us the probability that a certain value will be obtained."
:If this is the case, that means that Quantum mechanical phenomena are ''unpredictable''. How is it that clock adjustments can be made based on unpredictable events, ie, probabilities?
:I'd also like to know how the GPS system is affected by these phenomena.
:--[[User:Cahnkj|Cahnkj]] 01:51, 12 April 2012 (EDT)

Logic is a nice thing. But engineers like to calculate. So could you give us a Ballpark estimate for the quantum mechanic effects which come into play here? [[User:AugustO|AugustO]] 01:59, 12 April 2012 (EDT)

:(Edit conflict x2) Andy, as a lawyer I can assure you that hearsay is a [[legal]] concept which is of little use in this sort of scientific discussion. Whilst I understand that non-legally trained people sometimes confuse the nature and applicability of the concept, I can confirm that it has no relevance here.

:The difficulty here arises from your wanting to assert the truth of a matter without providing either references or even the basis for you own logic. Just saying "quantum mechanics" is hardly enlightening. Do you deny that GPS satellite clocks are adjusted by approximately 38,000 nanoseconds as referred to in the references that I provided? If not, do you say that there is a quantum calculation that accounts for that adjustment? What is that quantum calculation and what is it based on? I am really having difficulty in understanding the basis for all of this. --[[User:JeromeKJ|JeromeKJ]] 02:03, 12 April 2012 (EDT)

:Aschlafly, this reference [http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf GPS and Relativity: An Engineering Overview] has been pointed out to you several times already. Since it is published by folks actually working on the GPS system, I hardly think that it qualifies as 'hearsay'. It contains all the relevant relativistic equations, which are not really that complicated, and derives the 38 nanosecond figure quoted above. An assertion on scientific matters without any evidence can't really be taken seriously. Can we please see the quantum mechanical equations and calculations which come up with the same or similar result? [[User:RolandPlankton|RolandPlankton]] 09:49, 12 April 2012 (EDT)

:Aschlafly, I'm inclined to suspect that your disbelief in relativity is so strong that you are unwilling to consider any evidence which might indicate that relativity could be correct, and are hence flailing around looking for some other explanation as to what actually happens (GPS clock adjustment by 38 ns). Would you care to comment on my suspicion? [[User:RolandPlankton|RolandPlankton]] 09:49, 12 April 2012 (EDT)

Quote: "A logical statement is a declarative sentence that is either true or false." [http://www.ontotext.com/factforge/logical-statement].

So Aschlafly, why don't you need a reference to confirm a logical statement? Just because a statement is logical doesn't mean that it is true. [[User:RolandPlankton|RolandPlankton]] 16:53, 12 April 2012 (EDT)

: It would be helpful to have a more modern reference. GPS switched to a system of daily updates to the satellites. Maybe those relativistic formulas cause errors that require daily clock synchronizations to correct. Not likely. But to prove the point we ought to find a reference that says that the satellites still use the 38 ns/day relativistic adjustments, and that the daily corrections are much smaller than that. [[User:RSchlafly|RSchlafly]] 17:18, 12 April 2012 (EDT)
::The best I've found so far is [http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/GPS/Neil_Ashby_Relativity_GPS.pdf] from Physics Today, May 2002. This confirms the initial adjustment and mentions further on page 7: "Additional small frequency offsets arise from clock drift, environmental changes, and other unavoidable effects such as the inability to launch the satellite into an orbit with precisely the desired semimajor axis. The satellite clock frequencies are adjusted so that they remain as close as possible to the frequency of the Naval Observatory's clock ensemble." Unfortunately it doesn't give the actual size of the adjustments, thought the word 'small' does indicate it as being much less than the initial adjustment. I rather like the last sentence of this paper: "Ordinary users of the GPS, though they may not need to be aware of it, have thus become dependent on Einstein's conception of space and time." [[User:RolandPlankton|RolandPlankton]] 18:26, 12 April 2012 (EDT)

:::The lack of evidence, amid so much political pressure to prove it, is indicative that no proof can be found. Notice how no [[Nobel Prize]]s have been given for GPS confirming the [[Theory of Relativity]]?--[[User:Aschlafly|Andy Schlafly]] 21:01, 12 April 2012 (EDT)
:::If you want to use the [[Nobel Prize]] as evidence against relativity, might I direct you to:
:::http://www.nobelprize.org/educational/physics/relativity/
:::Where the official Nobel Prize website discusses various experiments related to relativity, and the relevant [[Nobel Prize]]s awarded for them.
:::--[[User:Cahnkj|Cahnkj]] 00:32, 13 April 2012 (EDT)

== Logic and the GPS ==

*Atomic watches work on the Earth quite fine
*[[Quantum mechanics]] describe the physics of ''very small length and energy scales''
*Satellites are macroscopic objects.
*Even a precision of 1cm on the surface of the Earth isn't a very small length.

So which kind of logic tells us that quantum mechanical effects influence the synchronization of the clocks? Why are not only the scientists involved lying, but also their calculations?

For me it seems to be a logical conclusion that you, Aschlafly, are even more knowledgeable of Greek than of Science! [[User:AugustO|AugustO]] 08:21, 12 April 2012 (EDT)
:He's trying to apply the Heisenburg Uncertainty principle to satellites? Are you kidding me? That principle is used for things at the ATOMIC LEVEL! Using ANYTHING with regards to quantum mechanics in an argument about satellites is absurdism and/or ignorance of the subject matter! Seriously Andy, I know you hate the Theory of Relativity, but you should really leave science to those who understand it. [[User:JanSmuts|JanSmuts]] 16:04, 12 April 2012 (EDT)

Talk:Theory of relativity

2012-04-13T04:32:01Z

Cahnkj: /* Why are adjustments needed to GPS? */ umad?

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|'''Attention: Please review previous points on the discussion page before adding your own commentary. Many topics have been discussed many, many, times. If you have something new to add, feel free, but it is not necessary or helpful to read the same arguments over and over and over.'''

'''Raising arguments which have been discussed before wastes the time of valuable editors and repeatedly doing so violates [[90/10]].'''

For older discussions, see the archive [[Talk:Theory of relativity/index|index]]. 
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== Mass depending on direction ==

The article states:
:''There is a logical difficulty, however, to an increase in relativistic mass. Such increase would only exist in the direction of motion, and the rest mass would remain intact with respect to a force applied in a direction orthogonal to velocity. Neither mass nor energy is a vector, and the notion of the mass of an object having different values depending on the direction of an applied force is illogical.''

As [[User:RSchlafly|RSchlafly]] on 8 July 2007 (EDT): ''This paragraph is nonsense [..] The relativistic mass applies no matter what the direction of the force is.''

[[User:AugustO|AugustO]] 15:45, 10 January 2012 (EST)

== Neutrinos now obey speed limit ==

The observation sited in the first sentence of this article has been discredited. [http://news.sciencemag.org/scienceinsider/2012/02/official-word-on-superluminal-ne.html?ref=hp] It appears that a loose fiber-optics cable is to blame for the misreadings. I suggest editing this first sentence, and any other mention of this in the article.--[[User:CarloP|CarloP]] 18:51, 2 March 2012 (EST)

:Issues concerning the neutrino experiment are not yet fully resolved. No problam: I replaced it with another counterexample.--[[User:Aschlafly|Andy Schlafly]] 19:12, 2 March 2012 (EST)

== Why does Conservapedia seek to discredit Relativity ==

Can someone explain why Conservapedia is so opposed to the Theory of Relativity?

Is there some philosophical or conservative/liberal basis for this opposition? [[User:RolandPlankton|RolandPlankton]] 18:32, 5 April 2012 (EDT)

:''Conservapedia'' seeks the truth, not merely what the [[lamestream media]] claim is the truth. Moreover, once one accepts a logical fallacy, then anything false can be proven from it.--[[User:Aschlafly|Andy Schlafly]] 23:34, 5 April 2012 (EDT)
:: Ahh.... But the fact that the conclusion is false does not necessarily render the basis false. I could say "Andy Schlafly founded Conservapedia and therefore I am a pig monkey." I am not a pig monkey, and even if I were, that has nothing to do with you founding this website. But you still did. [[User:Gregkochuconn|Gregkochuconn]] 09:58, 9 April 2012 (EDT)

:When looking around the internet, it is obvious that Conservapedia's classification of relativity as [[pseudoscience]] is a source of some amusement and contempt. Aschlafly, could you please answer the two questions I raised above? [[User:RolandPlankton|RolandPlankton]] 11:27, 9 April 2012 (EDT)

::Roland, liberal peer pressure from "around the internet" does not illuminate the truth. If what liberals on the internet said made a dime's bit of difference, then the [[Bible]] would not be the best selling book (by far) and the percentage of people who are [[conservative]] would not be growing (as it does).

::"Can someone explain why Conservapedia is so opposed to the Theory of Relativity?" Because it's false, it confuses people, it misleads people into stop reading the Bible, and its orthodoxy interferes with the advancement of science for the benefit of all. Other than that, it's not a bad theory!

::"Is there some philosophical or conservative/liberal basis for this opposition?" The only bias is by liberals who shout down any criticism of the theory. If the theory were so clearly true, then there would be no need for some liberals to rely on [[censorship]] in propping it up.--[[User:Aschlafly|Andy Schlafly]] 17:10, 9 April 2012 (EDT)

== GPS and Relativity ==

I note that anyone using a GPS is relying on the Theory of Relativity being true, since calculations derived from Relativity are used within a GPS. [[User:RolandPlankton|RolandPlankton]] 18:32, 5 April 2012 (EDT)

:GPS does '''''not''''' rely on the [[Theory of Relativity]], and this has been thoroughly explained on this site.--[[User:Aschlafly|Andy Schlafly]] 23:34, 5 April 2012 (EDT)

::Hi Aschlafly, I've located at least some of the discussion re GPS in the archives of this talk page, and there a lot of references for me to examine before I can make any further serious comments; certainly there are some references which appear to state that GPS relies on relativity. Can you perhaps draw my attention to what you consider the most important (half-dozen or so) references which indicate that the GPS system does NOT rely on relativity so that I have somewhere to start from? In the meantime I'll continue editing and improving less controversial articles as I have been doing for the last two months (my talk page lists nearly 40 articles I can usefully contribute to). [[User:RolandPlankton|RolandPlankton]] 14:17, 6 April 2012 (EDT)

:::This note 7 is on [[Counterexamples to Relativity]]:

::::Contrary to the claims of Relativists, the GPS system has never been based on Relativity. The Time Service Department, U.S. Navy, observed that "The Operational Control System (OCS) of the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein’s general theory of relativity would seem to require" in part because "the effects of relativity, where they are different from the effects predicted by classical mechanics and electromagnetic theory, are too small to matter – less than one centimeter, for users on or near the earth.”

:::The Theory of Relativity does not even assert that it would require significant adjustments to GPS timing: the small effects claimed by the special and general theories nearly cancel each other out for orbiting satellites. From an engineering perspective, it makes far more sense simply to adjust the clocks using synchronization rather than relying on (dubious) theoretical claims.--[[User:Aschlafly|Andy Schlafly]] 14:36, 6 April 2012 (EDT)

Another false claim because of sloppy reading: In the same source by The Time Service Department, U.S. Navy, you can find how the authors Fliegel and DiEsposti describe what is happening to the clocks in the satellites:
''Since GPS receivers work in the time and not in the frequency domain, they handle the velocity, gravity, and acceleration shifts differently than described above. First, each GPS space vehicle (SV) clock is offset from its nominal rate by about -4.45 × 10-10 (= -38 microseconds per day) to allow for the relativistic offsets between the differences between the SV and the ground. Of this -38 microseconds per day, about -45 are due to the gravitational potential difference between the SV at its mean distance and the earth's surface, and +7 to the mean SV speed, which is about 3.87 km/sec. (p. 193).

The text is about the necessity of ''further'' corrections by the ''operational control system'' - there are corrections ''already'' installed in the clocks!

''The Theory of Relativity does not even assert that it would require significant adjustments to GPS timing:'' This sentence is wrong. It has shown to be wrong a couple of times, so it starts to become a lie. [[User:AugustO|AugustO]] 15:12, 6 April 2012 (EDT)

:The [[Theory of Relativity]] was not used to develop GPS, nor would it be sensible to waste time and money doing so. Synchronization is cheaper, simpler, and more reliable. The above quote does not contradict this obvious truth.--[[User:Aschlafly|Andy Schlafly]] 16:32, 6 April 2012 (EDT)

::The fact that these offsets are implemented in the clocks '''in accord with the theory of relativity''' as you can read in the very source you quoted shows that the [[Theory of Relativity]] is used in the GPS - and this from the very beginning of the project! Please, start to read your sources - completely! [[User:AugustO|AugustO]] 16:37, 6 April 2012 (EDT)

Please, before we get into any more debate, could someone supply some actual references (not quotes from) which state that relativity is not used in GPS? [[User:RolandPlankton|RolandPlankton]] 16:41, 6 April 2012 (EDT)

:Aschlafly took his quote from [http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf GPS and Relativity: An Engineering Overview] by Henry F. Fliegel and Raymond S. DiEsposti (though he probably isn't aware of this). The paper is about relativistic effects due to moving GPS-'''''receivers''''' (or GPS-receivers in high altitudes) and comes to the conclusion, that at the moment, they don't have to include additional relativistic corrections.

:Aschlafly interprets this as if ''no'' relativistic corrections are implemented in the GPS.
:However, in the paper itself, you will find the section I quoted above, where the authors describe such very corrections within the clocks of the satellites.
:I'm afraid that Aschlafly won't come up with ''some actual references (not quotes from) which state that relativity is not used in GPS'' as there aren't any.
:[[User:AugustO|AugustO]] 16:53, 6 April 2012 (EDT)

Folks, the burden of proof is on anyone who claims that the [[Theory of Relativity]] was used to design GPS. That burden includes describing who, when, where, how, and why. It didn't happen. And if it did, the person who wasted time and money on such a frivolous approach should explain the mistake, because engineers can simply synchronize the clocks far more accurately than the theory ever could.--[[User:Aschlafly|Andy Schlafly]] 18:15, 8 April 2012 (EDT)

:It looks to me as if you are trying to put impossible conditions prior to any debate. To avoid a lengthy debate all you have to do is produce some actual references which support your point of view. Is this too much to ask?

:If it didn't happen then you should be able to produce some evidence of this, so '''some actual references please'''. The only 'evidence' you have produced so far is an out-of-context quote from a paper which is concerned primarily with GPS receivers (that same paper mentions the use of relativity-related adjustments to the clocks on the GPS satellite transmitters). Surely you must have more than this. Will you accept evidence from engineers and companies involved in designing and building the GPS system? If not, why not? Who would you accept evidence from? The US Department of Defense? Do you seriously expect a member of the public to be able to access internal design documents as your "who, when, where, how, and why" statement implies?

:If you care to check my contribution history you will see that I am actively contributing non-controversial information to articles. This discussion re GPS etc. is only a small part of my activities on Conservapedia. Since I've barely started on considering and consolidating what evidence there is re GPS I would rather have a week or so to look at the evidence before getting into a debate. This should give you ample time to come up with some references to support the separation of GPS and relativity. Simple searches via Google turn up numerous instances where relativity is claimed to be relevant to GPS, but I can't find anything to the contrary and '''I need your help to do so'''. I would really like to see evidence from '''both sides''' of the discussion before entering the debate, so '''some actual references please'''. [[User:RolandPlankton|RolandPlankton]] 19:15, 8 April 2012 (EDT)

::Roland, you're requesting proof that something didn't happen. Moreover, someone with an engineering background (such as myself) would not expect it to have happened. It is like asking for a reference that no green cheese was found on the Moon. No such scientific reference is likely to exist, nor would anyone expect such a reference to exist.--[[User:Aschlafly|Andy Schlafly]] 19:28, 8 April 2012 (EDT)

:: Every single article on GPS says that relativistic adjustments are made to the satellite clocks. Some give the formulas and some give quantitative data on the adjustments. Textbooks explain why the adjustments are necessary. I don't see any reason to doubt that GPS uses relativistic adjustments. [[User:RSchlafly|RSchlafly]] 20:52, 8 April 2012 (EDT)

:::GPS does make synchronizing adjustments. Call them whatever you like, but those adjustments are not made based on predictions by the [[Theory of Relativity]]. Indeed, it would be a silly waste of time and money to synchronize in such a manner.--[[User:Aschlafly|Andy Schlafly]] 21:07, 8 April 2012 (EDT)
:::: Unless you drive the flying Delorean from ''Back to the Future'', relativity would say that its effect on your car when you're driving at normal speeds is so small it need not be accounting for. The normal error for GPS (about 40 feet) is many magnitudes higher than the error relativity would cause. Now, the GPS in the Flying DeLorean would be another issue. But until that's invented, let's not worry about it, ok? Of course, if you were orienteering, your speed would be even slower than if you were driving. Indeed, if you were moving at any normal speed (even a supersonic jet), relativity would be incredibly small (assuming that it exists as scientists explain it). [[User:Gregkochuconn|Gregkochuconn]] 22:14, 8 April 2012 (EDT)

:::::''GPS does make synchronizing adjustments'' Not only simple synchronizing: read the specifications for the GPS, read the sources ''in full'' which you are quoting, and you will see that all these engineers and scientists don't give a damn that you think that they are wasting ''time and money''.
:::::Aschlafly, your position is only tenable as you are willing to ignore most of the data which is presented to you. [[User:AugustO|AugustO]] 03:12, 9 April 2012 (EDT)

::Aschlafly, please correct me if I am misunderstanding you, but it seems to me that you believe very firmly that relativity has nothing to do with GPS, even though you are unwilling to present any evidence to support this belief, and wish to put severe restrictions on what 'proof' of the relationship other folks may present. I raised some five questions above as to what sort of evidence you might consider. Could you please answer these questions.

::I'd like to ask Mr. Schafly if he could explain what the clock adjustments on GPS satellites are for, the article is not clear, and neither is anything on this talk page.--[[User:Cahnkj|Cahnkj]] 00:44, 11 April 2012 (EDT)

:::Cahnkj, herewith a summary of the clock-adjustment situation as I (RolandPlankton) see it. Newton's equations of motions say nothing about how clocks keep time. Einstein's equations of relativity imply that identical clocks will vary in their timekeeping (tick at different rates) if they are travelling at different speeds, or if they are at different heights in a gravitational field, or if they are subject to different accelerations; see [http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf GPS and Relativity: An Engineering Overview]. Now the satellites used in the GPS system require very accurate clocks which are in step with ground-based clocks. The paper just quoted provides the various relativistic equations which apply - the satellites are travelling faster than a ground-based receiver, and are at a different height in a gravitational field. Prior to launch the clocks in the GPS satellites are deliberately set to a different tick rate from ground-based clocks, so that when they are in orbit the clocks will appear to tick at the same rate; the difference in tick rates is about 38 nanoseconds per day, and this adjustment can be calculated from the relevant relativistic equations.

:::But the problem is that Aschlafly rejects the Theory of Relativity, and hence rejects any calculation based on that. The only serious argument he has put forth on this current talk page (see preceding section) is an appeal to [http://en.wikipedia.org/wiki/Wikipedia:The_Truth the truth]; the quote he provides above is also demolished above. You may wish to consult [[Counterexamples to Relativity]], which is rebutted point by point in [[Essay:Rebuttal to Counterexamples to Relativity]].

:::Hope this doesn't add too much to the confusion. [[User:RolandPlankton|RolandPlankton]] 12:07, 11 April 2012 (EDT)

::::Mr. Schlafly states above that "the burden of proof is on anyone who claims that the Theory of Relativity was used to design GPS." (This is a fair requirement, and it seems as this has been done when AugustO referred to the Fliegel and DiEsposti paper above.)

::::But really, isn't the burden of proof on anyone who claims ''anything'' on this site, since Conservapedia Commandment #1 states that "everything you post must be true and verifiable" and Commandment #2 states that users should "always cite and give credit to <nowiki>[their]</nowiki> sources?" --[[User:AndreaM|AndreaM]] 19:03, 12 April 2012 (EDT)

:::::Good point. Anyone who asserts ''on this site'' that GPS was designed based on the [[Theory of Relativity]] needs to prove the claim. Note that the claim is implausible because it is cheaper, easier, and more precise to synchronize GPS based on observations rather than theoretical speculation. Also note that no [[Nobel Prize]] has been given for verification of the [[Theory of Relativity]] with GPS.--[[User:Aschlafly|Andy Schlafly]] 19:55, 12 April 2012 (EDT)

===A Separate Question for Mr. Schlafly About References===

::Aschlafly, as a separate issue, in view of of your apparent attitude to references, could I ask you to have a look at the articles I have been working on over the last two months: [[Pi]], [[Programming language]], [[Compiler]], and the work-in-progress [[Chomsky hierarchy]]. Obviously I'm only asking you to consider the changes I have made. In particular, can you check if the references are acceptable to you, and can you also check that the general style and level of writing is in accordance with Conservapedia's aims? The next article I intend to turn my intention to is [[Context-Free Grammar]], since it seems to me that this fails to satisfy [[Conservapedia:Guidelines#Style]] "Articles on complex topics need an introduction which assumes little or no previous knowledge". [[User:RolandPlankton|RolandPlankton]] 11:03, 9 April 2012 (EDT)

:::Roland, your good edits are appreciated and I've seen no complaints about them. I agree that the [[Context-Free Grammar]] would benefit from a better introduction and look forward to reading what you add there.--[[User:Aschlafly|Andy Schlafly]] 17:39, 9 April 2012 (EDT)

== Why are adjustments needed to GPS? ==

A good question was raised above: if synchronization to GPS is not due to the [[Theory of Relativity]], then what is it due to?

And the answer is simply this: [[quantum mechanics]]. There are fundamental uncertainties, and those uncertainties will lead to clock differences. Otherwise a [[perpetual motion machine]] would be possible. It isn't.--[[User:Aschlafly|Andy Schlafly]] 22:50, 11 April 2012 (EDT)

:Well, this is progress indeed. Could you please provide references to support the contention that the synchronization is required as a result of quantum mechanical effects?

:Also, as an aside, how do you say that fundamental uncertainties described by quantum mechanics relate to the impossibility of a perpetual motion machine? Not sure I follow you there. --[[User:JeromeKJ|JeromeKJ]] 23:36, 11 April 2012 (EDT)

::It's basic logic. Unless someone denies [[quantum mechanics]] and the fundamental uncertainties it describes -- and many [[Relativists]] do deny it -- then synchronization will be required as a logical result.--[[User:Aschlafly|Andy Schlafly]] 23:58, 11 April 2012 (EDT)

:::Do you have any references? --[[User:JeromeKJ|JeromeKJ]] 00:04, 12 April 2012 (EDT)

::::I haven't looked ... nor is it necessary to. I wouldn't look for references to confirm any logical statement.--[[User:Aschlafly|Andy Schlafly]] 00:14, 12 April 2012 (EDT)

:::::Really? Is it fair to say then that this contention that the synchronization is required as a result of quantum mechanical effects is not something that you have read about but rather something that you yourself concluded from your own knowledge of quantum mechanics and GPS systems? --[[User:JeromeKJ|JeromeKJ]] 00:21, 12 April 2012 (EDT)
:::::P.S. As a result of this discussion I found a couple of articles which appear to confirm that GPS satellites have their clocks adjusted by about 38,000 nanoseconds per day before launch in compliance with relitavistic predictions (both Special and General Relativity are taken into account). The articles are [http://metaresearch.org/cosmology/gps-relativity.asp here] and [http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html here]. Is there really any question that this is what is happening? I would think that if these sources are to be questioned that some sort of reference should be provided. A mere assertion that the adjustments are as a result of quantum mechanical effects and that it is a matter of logic would not usually be enough for any serious encyclopedia. --[[User:JeromeKJ|JeromeKJ]] 00:53, 12 April 2012 (EDT)

::::::The references are [[hearsay]]. Logic is far more compelling, more efficient, and more likely to lead to the correct result.

::::::To take the analogy mentioned above, if you agree that [[perpetual motion machines]] are impossible, what is the reason?--[[User:Aschlafly|Andy Schlafly]] 01:45, 12 April 2012 (EDT)

:Quantum mechanics gives a probabilistic model of phenomena. Indeed, the page you linked for quantum mechanics states:
::"If we measure such an observable, generally the wave function does not predict exactly which value we will obtain. Instead, the wave function gives us the probability that a certain value will be obtained."
:If this is the case, that means that Quantum mechanical phenomena are ''unpredictable''. How is it that clock adjustments can be made based on unpredictable events, ie, probabilities?
:I'd also like to know how the GPS system is affected by these phenomena.
:--[[User:Cahnkj|Cahnkj]] 01:51, 12 April 2012 (EDT)

Logic is a nice thing. But engineers like to calculate. So could you give us a Ballpark estimate for the quantum mechanic effects which come into play here? [[User:AugustO|AugustO]] 01:59, 12 April 2012 (EDT)

:(Edit conflict x2) Andy, as a lawyer I can assure you that hearsay is a [[legal]] concept which is of little use in this sort of scientific discussion. Whilst I understand that non-legally trained people sometimes confuse the nature and applicability of the concept, I can confirm that it has no relevance here.

:The difficulty here arises from your wanting to assert the truth of a matter without providing either references or even the basis for you own logic. Just saying "quantum mechanics" is hardly enlightening. Do you deny that GPS satellite clocks are adjusted by approximately 38,000 nanoseconds as referred to in the references that I provided? If not, do you say that there is a quantum calculation that accounts for that adjustment? What is that quantum calculation and what is it based on? I am really having difficulty in understanding the basis for all of this. --[[User:JeromeKJ|JeromeKJ]] 02:03, 12 April 2012 (EDT)

:Aschlafly, this reference [http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf GPS and Relativity: An Engineering Overview] has been pointed out to you several times already. Since it is published by folks actually working on the GPS system, I hardly think that it qualifies as 'hearsay'. It contains all the relevant relativistic equations, which are not really that complicated, and derives the 38 nanosecond figure quoted above. An assertion on scientific matters without any evidence can't really be taken seriously. Can we please see the quantum mechanical equations and calculations which come up with the same or similar result? [[User:RolandPlankton|RolandPlankton]] 09:49, 12 April 2012 (EDT)

:Aschlafly, I'm inclined to suspect that your disbelief in relativity is so strong that you are unwilling to consider any evidence which might indicate that relativity could be correct, and are hence flailing around looking for some other explanation as to what actually happens (GPS clock adjustment by 38 ns). Would you care to comment on my suspicion? [[User:RolandPlankton|RolandPlankton]] 09:49, 12 April 2012 (EDT)

Quote: "A logical statement is a declarative sentence that is either true or false." [http://www.ontotext.com/factforge/logical-statement].

So Aschlafly, why don't you need a reference to confirm a logical statement? Just because a statement is logical doesn't mean that it is true. [[User:RolandPlankton|RolandPlankton]] 16:53, 12 April 2012 (EDT)

: It would be helpful to have a more modern reference. GPS switched to a system of daily updates to the satellites. Maybe those relativistic formulas cause errors that require daily clock synchronizations to correct. Not likely. But to prove the point we ought to find a reference that says that the satellites still use the 38 ns/day relativistic adjustments, and that the daily corrections are much smaller than that. [[User:RSchlafly|RSchlafly]] 17:18, 12 April 2012 (EDT)
::The best I've found so far is [http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/GPS/Neil_Ashby_Relativity_GPS.pdf] from Physics Today, May 2002. This confirms the initial adjustment and mentions further on page 7: "Additional small frequency offsets arise from clock drift, environmental changes, and other unavoidable effects such as the inability to launch the satellite into an orbit with precisely the desired semimajor axis. The satellite clock frequencies are adjusted so that they remain as close as possible to the frequency of the Naval Observatory's clock ensemble." Unfortunately it doesn't give the actual size of the adjustments, thought the word 'small' does indicate it as being much less than the initial adjustment. I rather like the last sentence of this paper: "Ordinary users of the GPS, though they may not need to be aware of it, have thus become dependent on Einstein's conception of space and time." [[User:RolandPlankton|RolandPlankton]] 18:26, 12 April 2012 (EDT)

:::The lack of evidence, amid so much political pressure to prove it, is indicative that no proof can be found. Notice how no [[Nobel Prize]]s have been given for GPS confirming the [[Theory of Relativity]]?--[[User:Aschlafly|Andy Schlafly]] 21:01, 12 April 2012 (EDT)
:::If you want to use the [[Nobel Prize]] as evidence against relativity, might I direct you to:
:::http://www.nobelprize.org/educational/physics/relativity/
:::Where the official Nobel Prize website discusses various experiments related to relativity, and the relevant [[Nobel Prize]]s awarded for them.
--[[User:Cahnkj|Cahnkj]] 00:32, 13 April 2012 (EDT)

== Logic and the GPS ==

*Atomic watches work on the Earth quite fine
*[[Quantum mechanics]] describe the physics of ''very small length and energy scales''
*Satellites are macroscopic objects.
*Even a precision of 1cm on the surface of the Earth isn't a very small length.

So which kind of logic tells us that quantum mechanical effects influence the synchronization of the clocks? Why are not only the scientists involved lying, but also their calculations?

For me it seems to be a logical conclusion that you, Aschlafly, are even more knowledgeable of Greek than of Science! [[User:AugustO|AugustO]] 08:21, 12 April 2012 (EDT)
:He's trying to apply the Heisenburg Uncertainty principle to satellites? Are you kidding me? That principle is used for things at the ATOMIC LEVEL! Using ANYTHING with regards to quantum mechanics in an argument about satellites is absurdism and/or ignorance of the subject matter! Seriously Andy, I know you hate the Theory of Relativity, but you should really leave science to those who understand it. [[User:JanSmuts|JanSmuts]] 16:04, 12 April 2012 (EDT)

Talk:Theory of relativity

2012-04-13T04:30:46Z

Cahnkj: /* Why are adjustments needed to GPS? */ umad?

{| style=" width:95%; text-align:left; background:{{{background}}}; color:{{{color|black}}}; border:3px solid black; clear:both " align="center"
|-
|width="2%" style="text-align:center" cellpadding="5"|'''!'''
|'''Attention: Please review previous points on the discussion page before adding your own commentary. Many topics have been discussed many, many, times. If you have something new to add, feel free, but it is not necessary or helpful to read the same arguments over and over and over.'''

'''Raising arguments which have been discussed before wastes the time of valuable editors and repeatedly doing so violates [[90/10]].'''

For older discussions, see the archive [[Talk:Theory of relativity/index|index]]. 
|valign="top" style="text-align:right"|[[Image:Conservlogo.png|65px]]
|}


== Mass depending on direction ==

The article states:
:''There is a logical difficulty, however, to an increase in relativistic mass. Such increase would only exist in the direction of motion, and the rest mass would remain intact with respect to a force applied in a direction orthogonal to velocity. Neither mass nor energy is a vector, and the notion of the mass of an object having different values depending on the direction of an applied force is illogical.''

As [[User:RSchlafly|RSchlafly]] on 8 July 2007 (EDT): ''This paragraph is nonsense [..] The relativistic mass applies no matter what the direction of the force is.''

[[User:AugustO|AugustO]] 15:45, 10 January 2012 (EST)

== Neutrinos now obey speed limit ==

The observation sited in the first sentence of this article has been discredited. [http://news.sciencemag.org/scienceinsider/2012/02/official-word-on-superluminal-ne.html?ref=hp] It appears that a loose fiber-optics cable is to blame for the misreadings. I suggest editing this first sentence, and any other mention of this in the article.--[[User:CarloP|CarloP]] 18:51, 2 March 2012 (EST)

:Issues concerning the neutrino experiment are not yet fully resolved. No problam: I replaced it with another counterexample.--[[User:Aschlafly|Andy Schlafly]] 19:12, 2 March 2012 (EST)

== Why does Conservapedia seek to discredit Relativity ==

Can someone explain why Conservapedia is so opposed to the Theory of Relativity?

Is there some philosophical or conservative/liberal basis for this opposition? [[User:RolandPlankton|RolandPlankton]] 18:32, 5 April 2012 (EDT)

:''Conservapedia'' seeks the truth, not merely what the [[lamestream media]] claim is the truth. Moreover, once one accepts a logical fallacy, then anything false can be proven from it.--[[User:Aschlafly|Andy Schlafly]] 23:34, 5 April 2012 (EDT)
:: Ahh.... But the fact that the conclusion is false does not necessarily render the basis false. I could say "Andy Schlafly founded Conservapedia and therefore I am a pig monkey." I am not a pig monkey, and even if I were, that has nothing to do with you founding this website. But you still did. [[User:Gregkochuconn|Gregkochuconn]] 09:58, 9 April 2012 (EDT)

:When looking around the internet, it is obvious that Conservapedia's classification of relativity as [[pseudoscience]] is a source of some amusement and contempt. Aschlafly, could you please answer the two questions I raised above? [[User:RolandPlankton|RolandPlankton]] 11:27, 9 April 2012 (EDT)

::Roland, liberal peer pressure from "around the internet" does not illuminate the truth. If what liberals on the internet said made a dime's bit of difference, then the [[Bible]] would not be the best selling book (by far) and the percentage of people who are [[conservative]] would not be growing (as it does).

::"Can someone explain why Conservapedia is so opposed to the Theory of Relativity?" Because it's false, it confuses people, it misleads people into stop reading the Bible, and its orthodoxy interferes with the advancement of science for the benefit of all. Other than that, it's not a bad theory!

::"Is there some philosophical or conservative/liberal basis for this opposition?" The only bias is by liberals who shout down any criticism of the theory. If the theory were so clearly true, then there would be no need for some liberals to rely on [[censorship]] in propping it up.--[[User:Aschlafly|Andy Schlafly]] 17:10, 9 April 2012 (EDT)

== GPS and Relativity ==

I note that anyone using a GPS is relying on the Theory of Relativity being true, since calculations derived from Relativity are used within a GPS. [[User:RolandPlankton|RolandPlankton]] 18:32, 5 April 2012 (EDT)

:GPS does '''''not''''' rely on the [[Theory of Relativity]], and this has been thoroughly explained on this site.--[[User:Aschlafly|Andy Schlafly]] 23:34, 5 April 2012 (EDT)

::Hi Aschlafly, I've located at least some of the discussion re GPS in the archives of this talk page, and there a lot of references for me to examine before I can make any further serious comments; certainly there are some references which appear to state that GPS relies on relativity. Can you perhaps draw my attention to what you consider the most important (half-dozen or so) references which indicate that the GPS system does NOT rely on relativity so that I have somewhere to start from? In the meantime I'll continue editing and improving less controversial articles as I have been doing for the last two months (my talk page lists nearly 40 articles I can usefully contribute to). [[User:RolandPlankton|RolandPlankton]] 14:17, 6 April 2012 (EDT)

:::This note 7 is on [[Counterexamples to Relativity]]:

::::Contrary to the claims of Relativists, the GPS system has never been based on Relativity. The Time Service Department, U.S. Navy, observed that "The Operational Control System (OCS) of the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein’s general theory of relativity would seem to require" in part because "the effects of relativity, where they are different from the effects predicted by classical mechanics and electromagnetic theory, are too small to matter – less than one centimeter, for users on or near the earth.”

:::The Theory of Relativity does not even assert that it would require significant adjustments to GPS timing: the small effects claimed by the special and general theories nearly cancel each other out for orbiting satellites. From an engineering perspective, it makes far more sense simply to adjust the clocks using synchronization rather than relying on (dubious) theoretical claims.--[[User:Aschlafly|Andy Schlafly]] 14:36, 6 April 2012 (EDT)

Another false claim because of sloppy reading: In the same source by The Time Service Department, U.S. Navy, you can find how the authors Fliegel and DiEsposti describe what is happening to the clocks in the satellites:
''Since GPS receivers work in the time and not in the frequency domain, they handle the velocity, gravity, and acceleration shifts differently than described above. First, each GPS space vehicle (SV) clock is offset from its nominal rate by about -4.45 × 10-10 (= -38 microseconds per day) to allow for the relativistic offsets between the differences between the SV and the ground. Of this -38 microseconds per day, about -45 are due to the gravitational potential difference between the SV at its mean distance and the earth's surface, and +7 to the mean SV speed, which is about 3.87 km/sec. (p. 193).

The text is about the necessity of ''further'' corrections by the ''operational control system'' - there are corrections ''already'' installed in the clocks!

''The Theory of Relativity does not even assert that it would require significant adjustments to GPS timing:'' This sentence is wrong. It has shown to be wrong a couple of times, so it starts to become a lie. [[User:AugustO|AugustO]] 15:12, 6 April 2012 (EDT)

:The [[Theory of Relativity]] was not used to develop GPS, nor would it be sensible to waste time and money doing so. Synchronization is cheaper, simpler, and more reliable. The above quote does not contradict this obvious truth.--[[User:Aschlafly|Andy Schlafly]] 16:32, 6 April 2012 (EDT)

::The fact that these offsets are implemented in the clocks '''in accord with the theory of relativity''' as you can read in the very source you quoted shows that the [[Theory of Relativity]] is used in the GPS - and this from the very beginning of the project! Please, start to read your sources - completely! [[User:AugustO|AugustO]] 16:37, 6 April 2012 (EDT)

Please, before we get into any more debate, could someone supply some actual references (not quotes from) which state that relativity is not used in GPS? [[User:RolandPlankton|RolandPlankton]] 16:41, 6 April 2012 (EDT)

:Aschlafly took his quote from [http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf GPS and Relativity: An Engineering Overview] by Henry F. Fliegel and Raymond S. DiEsposti (though he probably isn't aware of this). The paper is about relativistic effects due to moving GPS-'''''receivers''''' (or GPS-receivers in high altitudes) and comes to the conclusion, that at the moment, they don't have to include additional relativistic corrections.

:Aschlafly interprets this as if ''no'' relativistic corrections are implemented in the GPS.
:However, in the paper itself, you will find the section I quoted above, where the authors describe such very corrections within the clocks of the satellites.
:I'm afraid that Aschlafly won't come up with ''some actual references (not quotes from) which state that relativity is not used in GPS'' as there aren't any.
:[[User:AugustO|AugustO]] 16:53, 6 April 2012 (EDT)

Folks, the burden of proof is on anyone who claims that the [[Theory of Relativity]] was used to design GPS. That burden includes describing who, when, where, how, and why. It didn't happen. And if it did, the person who wasted time and money on such a frivolous approach should explain the mistake, because engineers can simply synchronize the clocks far more accurately than the theory ever could.--[[User:Aschlafly|Andy Schlafly]] 18:15, 8 April 2012 (EDT)

:It looks to me as if you are trying to put impossible conditions prior to any debate. To avoid a lengthy debate all you have to do is produce some actual references which support your point of view. Is this too much to ask?

:If it didn't happen then you should be able to produce some evidence of this, so '''some actual references please'''. The only 'evidence' you have produced so far is an out-of-context quote from a paper which is concerned primarily with GPS receivers (that same paper mentions the use of relativity-related adjustments to the clocks on the GPS satellite transmitters). Surely you must have more than this. Will you accept evidence from engineers and companies involved in designing and building the GPS system? If not, why not? Who would you accept evidence from? The US Department of Defense? Do you seriously expect a member of the public to be able to access internal design documents as your "who, when, where, how, and why" statement implies?

:If you care to check my contribution history you will see that I am actively contributing non-controversial information to articles. This discussion re GPS etc. is only a small part of my activities on Conservapedia. Since I've barely started on considering and consolidating what evidence there is re GPS I would rather have a week or so to look at the evidence before getting into a debate. This should give you ample time to come up with some references to support the separation of GPS and relativity. Simple searches via Google turn up numerous instances where relativity is claimed to be relevant to GPS, but I can't find anything to the contrary and '''I need your help to do so'''. I would really like to see evidence from '''both sides''' of the discussion before entering the debate, so '''some actual references please'''. [[User:RolandPlankton|RolandPlankton]] 19:15, 8 April 2012 (EDT)

::Roland, you're requesting proof that something didn't happen. Moreover, someone with an engineering background (such as myself) would not expect it to have happened. It is like asking for a reference that no green cheese was found on the Moon. No such scientific reference is likely to exist, nor would anyone expect such a reference to exist.--[[User:Aschlafly|Andy Schlafly]] 19:28, 8 April 2012 (EDT)

:: Every single article on GPS says that relativistic adjustments are made to the satellite clocks. Some give the formulas and some give quantitative data on the adjustments. Textbooks explain why the adjustments are necessary. I don't see any reason to doubt that GPS uses relativistic adjustments. [[User:RSchlafly|RSchlafly]] 20:52, 8 April 2012 (EDT)

:::GPS does make synchronizing adjustments. Call them whatever you like, but those adjustments are not made based on predictions by the [[Theory of Relativity]]. Indeed, it would be a silly waste of time and money to synchronize in such a manner.--[[User:Aschlafly|Andy Schlafly]] 21:07, 8 April 2012 (EDT)
:::: Unless you drive the flying Delorean from ''Back to the Future'', relativity would say that its effect on your car when you're driving at normal speeds is so small it need not be accounting for. The normal error for GPS (about 40 feet) is many magnitudes higher than the error relativity would cause. Now, the GPS in the Flying DeLorean would be another issue. But until that's invented, let's not worry about it, ok? Of course, if you were orienteering, your speed would be even slower than if you were driving. Indeed, if you were moving at any normal speed (even a supersonic jet), relativity would be incredibly small (assuming that it exists as scientists explain it). [[User:Gregkochuconn|Gregkochuconn]] 22:14, 8 April 2012 (EDT)

:::::''GPS does make synchronizing adjustments'' Not only simple synchronizing: read the specifications for the GPS, read the sources ''in full'' which you are quoting, and you will see that all these engineers and scientists don't give a damn that you think that they are wasting ''time and money''.
:::::Aschlafly, your position is only tenable as you are willing to ignore most of the data which is presented to you. [[User:AugustO|AugustO]] 03:12, 9 April 2012 (EDT)

::Aschlafly, please correct me if I am misunderstanding you, but it seems to me that you believe very firmly that relativity has nothing to do with GPS, even though you are unwilling to present any evidence to support this belief, and wish to put severe restrictions on what 'proof' of the relationship other folks may present. I raised some five questions above as to what sort of evidence you might consider. Could you please answer these questions.

::I'd like to ask Mr. Schafly if he could explain what the clock adjustments on GPS satellites are for, the article is not clear, and neither is anything on this talk page.--[[User:Cahnkj|Cahnkj]] 00:44, 11 April 2012 (EDT)

:::Cahnkj, herewith a summary of the clock-adjustment situation as I (RolandPlankton) see it. Newton's equations of motions say nothing about how clocks keep time. Einstein's equations of relativity imply that identical clocks will vary in their timekeeping (tick at different rates) if they are travelling at different speeds, or if they are at different heights in a gravitational field, or if they are subject to different accelerations; see [http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf GPS and Relativity: An Engineering Overview]. Now the satellites used in the GPS system require very accurate clocks which are in step with ground-based clocks. The paper just quoted provides the various relativistic equations which apply - the satellites are travelling faster than a ground-based receiver, and are at a different height in a gravitational field. Prior to launch the clocks in the GPS satellites are deliberately set to a different tick rate from ground-based clocks, so that when they are in orbit the clocks will appear to tick at the same rate; the difference in tick rates is about 38 nanoseconds per day, and this adjustment can be calculated from the relevant relativistic equations.

:::But the problem is that Aschlafly rejects the Theory of Relativity, and hence rejects any calculation based on that. The only serious argument he has put forth on this current talk page (see preceding section) is an appeal to [http://en.wikipedia.org/wiki/Wikipedia:The_Truth the truth]; the quote he provides above is also demolished above. You may wish to consult [[Counterexamples to Relativity]], which is rebutted point by point in [[Essay:Rebuttal to Counterexamples to Relativity]].

:::Hope this doesn't add too much to the confusion. [[User:RolandPlankton|RolandPlankton]] 12:07, 11 April 2012 (EDT)

::::Mr. Schlafly states above that "the burden of proof is on anyone who claims that the Theory of Relativity was used to design GPS." (This is a fair requirement, and it seems as this has been done when AugustO referred to the Fliegel and DiEsposti paper above.)

::::But really, isn't the burden of proof on anyone who claims ''anything'' on this site, since Conservapedia Commandment #1 states that "everything you post must be true and verifiable" and Commandment #2 states that users should "always cite and give credit to <nowiki>[their]</nowiki> sources?" --[[User:AndreaM|AndreaM]] 19:03, 12 April 2012 (EDT)

:::::Good point. Anyone who asserts ''on this site'' that GPS was designed based on the [[Theory of Relativity]] needs to prove the claim. Note that the claim is implausible because it is cheaper, easier, and more precise to synchronize GPS based on observations rather than theoretical speculation. Also note that no [[Nobel Prize]] has been given for verification of the [[Theory of Relativity]] with GPS.--[[User:Aschlafly|Andy Schlafly]] 19:55, 12 April 2012 (EDT)

===A Separate Question for Mr. Schlafly About References===

::Aschlafly, as a separate issue, in view of of your apparent attitude to references, could I ask you to have a look at the articles I have been working on over the last two months: [[Pi]], [[Programming language]], [[Compiler]], and the work-in-progress [[Chomsky hierarchy]]. Obviously I'm only asking you to consider the changes I have made. In particular, can you check if the references are acceptable to you, and can you also check that the general style and level of writing is in accordance with Conservapedia's aims? The next article I intend to turn my intention to is [[Context-Free Grammar]], since it seems to me that this fails to satisfy [[Conservapedia:Guidelines#Style]] "Articles on complex topics need an introduction which assumes little or no previous knowledge". [[User:RolandPlankton|RolandPlankton]] 11:03, 9 April 2012 (EDT)

:::Roland, your good edits are appreciated and I've seen no complaints about them. I agree that the [[Context-Free Grammar]] would benefit from a better introduction and look forward to reading what you add there.--[[User:Aschlafly|Andy Schlafly]] 17:39, 9 April 2012 (EDT)

== Why are adjustments needed to GPS? ==

A good question was raised above: if synchronization to GPS is not due to the [[Theory of Relativity]], then what is it due to?

And the answer is simply this: [[quantum mechanics]]. There are fundamental uncertainties, and those uncertainties will lead to clock differences. Otherwise a [[perpetual motion machine]] would be possible. It isn't.--[[User:Aschlafly|Andy Schlafly]] 22:50, 11 April 2012 (EDT)

:Well, this is progress indeed. Could you please provide references to support the contention that the synchronization is required as a result of quantum mechanical effects?

:Also, as an aside, how do you say that fundamental uncertainties described by quantum mechanics relate to the impossibility of a perpetual motion machine? Not sure I follow you there. --[[User:JeromeKJ|JeromeKJ]] 23:36, 11 April 2012 (EDT)

::It's basic logic. Unless someone denies [[quantum mechanics]] and the fundamental uncertainties it describes -- and many [[Relativists]] do deny it -- then synchronization will be required as a logical result.--[[User:Aschlafly|Andy Schlafly]] 23:58, 11 April 2012 (EDT)

:::Do you have any references? --[[User:JeromeKJ|JeromeKJ]] 00:04, 12 April 2012 (EDT)

::::I haven't looked ... nor is it necessary to. I wouldn't look for references to confirm any logical statement.--[[User:Aschlafly|Andy Schlafly]] 00:14, 12 April 2012 (EDT)

:::::Really? Is it fair to say then that this contention that the synchronization is required as a result of quantum mechanical effects is not something that you have read about but rather something that you yourself concluded from your own knowledge of quantum mechanics and GPS systems? --[[User:JeromeKJ|JeromeKJ]] 00:21, 12 April 2012 (EDT)
:::::P.S. As a result of this discussion I found a couple of articles which appear to confirm that GPS satellites have their clocks adjusted by about 38,000 nanoseconds per day before launch in compliance with relitavistic predictions (both Special and General Relativity are taken into account). The articles are [http://metaresearch.org/cosmology/gps-relativity.asp here] and [http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html here]. Is there really any question that this is what is happening? I would think that if these sources are to be questioned that some sort of reference should be provided. A mere assertion that the adjustments are as a result of quantum mechanical effects and that it is a matter of logic would not usually be enough for any serious encyclopedia. --[[User:JeromeKJ|JeromeKJ]] 00:53, 12 April 2012 (EDT)

::::::The references are [[hearsay]]. Logic is far more compelling, more efficient, and more likely to lead to the correct result.

::::::To take the analogy mentioned above, if you agree that [[perpetual motion machines]] are impossible, what is the reason?--[[User:Aschlafly|Andy Schlafly]] 01:45, 12 April 2012 (EDT)

:Quantum mechanics gives a probabilistic model of phenomena. Indeed, the page you linked for quantum mechanics states:
::"If we measure such an observable, generally the wave function does not predict exactly which value we will obtain. Instead, the wave function gives us the probability that a certain value will be obtained."
:If this is the case, that means that Quantum mechanical phenomena are ''unpredictable''. How is it that clock adjustments can be made based on unpredictable events, ie, probabilities?
:I'd also like to know how the GPS system is affected by these phenomena.
:--[[User:Cahnkj|Cahnkj]] 01:51, 12 April 2012 (EDT)

Logic is a nice thing. But engineers like to calculate. So could you give us a Ballpark estimate for the quantum mechanic effects which come into play here? [[User:AugustO|AugustO]] 01:59, 12 April 2012 (EDT)

:(Edit conflict x2) Andy, as a lawyer I can assure you that hearsay is a [[legal]] concept which is of little use in this sort of scientific discussion. Whilst I understand that non-legally trained people sometimes confuse the nature and applicability of the concept, I can confirm that it has no relevance here.

:The difficulty here arises from your wanting to assert the truth of a matter without providing either references or even the basis for you own logic. Just saying "quantum mechanics" is hardly enlightening. Do you deny that GPS satellite clocks are adjusted by approximately 38,000 nanoseconds as referred to in the references that I provided? If not, do you say that there is a quantum calculation that accounts for that adjustment? What is that quantum calculation and what is it based on? I am really having difficulty in understanding the basis for all of this. --[[User:JeromeKJ|JeromeKJ]] 02:03, 12 April 2012 (EDT)

:Aschlafly, this reference [http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf GPS and Relativity: An Engineering Overview] has been pointed out to you several times already. Since it is published by folks actually working on the GPS system, I hardly think that it qualifies as 'hearsay'. It contains all the relevant relativistic equations, which are not really that complicated, and derives the 38 nanosecond figure quoted above. An assertion on scientific matters without any evidence can't really be taken seriously. Can we please see the quantum mechanical equations and calculations which come up with the same or similar result? [[User:RolandPlankton|RolandPlankton]] 09:49, 12 April 2012 (EDT)

:Aschlafly, I'm inclined to suspect that your disbelief in relativity is so strong that you are unwilling to consider any evidence which might indicate that relativity could be correct, and are hence flailing around looking for some other explanation as to what actually happens (GPS clock adjustment by 38 ns). Would you care to comment on my suspicion? [[User:RolandPlankton|RolandPlankton]] 09:49, 12 April 2012 (EDT)

Quote: "A logical statement is a declarative sentence that is either true or false." [http://www.ontotext.com/factforge/logical-statement].

So Aschlafly, why don't you need a reference to confirm a logical statement? Just because a statement is logical doesn't mean that it is true. [[User:RolandPlankton|RolandPlankton]] 16:53, 12 April 2012 (EDT)

: It would be helpful to have a more modern reference. GPS switched to a system of daily updates to the satellites. Maybe those relativistic formulas cause errors that require daily clock synchronizations to correct. Not likely. But to prove the point we ought to find a reference that says that the satellites still use the 38 ns/day relativistic adjustments, and that the daily corrections are much smaller than that. [[User:RSchlafly|RSchlafly]] 17:18, 12 April 2012 (EDT)
::The best I've found so far is [http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/GPS/Neil_Ashby_Relativity_GPS.pdf] from Physics Today, May 2002. This confirms the initial adjustment and mentions further on page 7: "Additional small frequency offsets arise from clock drift, environmental changes, and other unavoidable effects such as the inability to launch the satellite into an orbit with precisely the desired semimajor axis. The satellite clock frequencies are adjusted so that they remain as close as possible to the frequency of the Naval Observatory's clock ensemble." Unfortunately it doesn't give the actual size of the adjustments, thought the word 'small' does indicate it as being much less than the initial adjustment. I rather like the last sentence of this paper: "Ordinary users of the GPS, though they may not need to be aware of it, have thus become dependent on Einstein's conception of space and time." [[User:RolandPlankton|RolandPlankton]] 18:26, 12 April 2012 (EDT)

:::The lack of evidence, amid so much political pressure to prove it, is indicative that no proof can be found. Notice how no [[Nobel Prize]]s have been given for GPS confirming the [[Theory of Relativity]]?--[[User:Aschlafly|Andy Schlafly]] 21:01, 12 April 2012 (EDT)
:::If you want to use the [[Nobel Prize]] as evidence against relativity, might I direct you to:
:::http://www.nobelprize.org/educational/physics/relativity/
:::Where the official Nobel Prize website discusses various experiments related to relativity, and the relevant [[Nobel Prize]]s awarded for them.

== Logic and the GPS ==

*Atomic watches work on the Earth quite fine
*[[Quantum mechanics]] describe the physics of ''very small length and energy scales''
*Satellites are macroscopic objects.
*Even a precision of 1cm on the surface of the Earth isn't a very small length.

So which kind of logic tells us that quantum mechanical effects influence the synchronization of the clocks? Why are not only the scientists involved lying, but also their calculations?

For me it seems to be a logical conclusion that you, Aschlafly, are even more knowledgeable of Greek than of Science! [[User:AugustO|AugustO]] 08:21, 12 April 2012 (EDT)
:He's trying to apply the Heisenburg Uncertainty principle to satellites? Are you kidding me? That principle is used for things at the ATOMIC LEVEL! Using ANYTHING with regards to quantum mechanics in an argument about satellites is absurdism and/or ignorance of the subject matter! Seriously Andy, I know you hate the Theory of Relativity, but you should really leave science to those who understand it. [[User:JanSmuts|JanSmuts]] 16:04, 12 April 2012 (EDT)

Talk:Theory of relativity

2012-04-12T05:51:46Z

Cahnkj: /* Why are adjustments needed to GPS? */

Talk:Theory of relativity

2012-04-11T04:44:39Z

Cahnkj: added signature

Talk:Theory of relativity

2012-04-11T04:43:18Z

Cahnkj: wait, so what are those adjustments for then?

Theory of relativity

2012-04-11T04:14:24Z

Cahnkj: /* Variable Speed of Light */ more clarification, resolution of a spelling error

''See also [[Counterexamples to Relativity]].''

The '''theory of relativity''' has been repeatedly contradicted by experiments, such as precise measurements of the advance of the perihelion of Mercury that show a shift greater than predicted by Relativity, well beyond the margin of error. Criticism of the theory, however, caused physicist [[Robert Dicke]] to be denied the [[Nobel Prize]], and it is unlikely tenure or a Ph.D would be awarded to any critic of the theory.

'''Relativity''' refers to two closely-related mathematical theories in [[physics]]:

*'''[[Special theory of relativity|Special relativity]]''' (SR) is a theory which describes the laws of motion for non-accelerating bodies traveling at a significant fraction of the [[speed of light]]. As speeds approach zero, Special Relativity tends towards equivalence with [[Newton's Laws of Motion]]. Special Relativity was developed by [[Hendrik Lorentz]], [[Henri Poincaré]], and Hermann Minkowski,<ref>"German mathematician who developed the geometrical theory of numbers and who made numerous contributions to number theory, mathematical physics, and the theory of relativity." [http://www.britannica.com/eb/article-9052860/Hermann-Minkowski Hermann Minkowski -- Britannica Online Encyclopedia]</ref><ref>[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Minkowski.html Hermann Minkowski, Biography]</ref> and [[Albert Einstein]].

*'''[[General theory of relativity|General Relativity]]''' (GR) is a theory which explains the laws of motion as viewed from accelerating reference frames and includes a geometric explanation for gravity. This theory was developed by [[David Hilbert]] and [[Albert Einstein]] as an extension of the postulates of Special Relativity.<ref>"[T]he German mathematician David Hilbert submitted an article containing the correct field equations for general relativity five days before Einstein."[http://nobelprize.org/educational_games/physics/relativity/history-1.html Nobel Prize historical account]</ref> A dramatic but later discredited claim by Sir [[Arthur Eddington]] of experimental proof of General Relativity in 1919 made Einstein a household name.

These theories have augmented earlier approaches, such as [[Galilean Relativity]].

Unlike most of physics, the theories of relativity have discontinuities whereby the limit of a physical quantity as a variable (such as mass or velocity) approaches a fixed value is not the same as the physical quantity at the fixed value. For example, the limit of momentum as mass approaches 0 and velocity approaches the speed of light is not equal to the momentum of (massless) light.<ref>Discontinuities in General Relativity are also well-recognized. See, e.g., [http://www.springerlink.com/content/u47l341u2q555455/]</ref>

More generally, and also unlike most of physics, the theories of relativity consist of complex mathematical equations relying on several hypotheses. For example, at Hofstra University general relativity is taught as part of an upperclass math course on differential geometry, based on three stated assumptions.<ref>http://people.hofstra.edu/Stefan_Waner/diff_geom/tc.html</ref> The equations for special relativity assume that it is forever impossible to attain a velocity faster than the speed of light and that all inertial frames of reference are equivalent, hypotheses that can never be fully tested. Relativity rejects Newton's [[action at a distance]], which is basic to Newtonian gravity and [[quantum mechanics]]. The mathematics of relativity assume no exceptions, yet in the time period immediately following the origin of the universe the relativity equations could not possibly have been valid.

Relativity has been met with much resistance in the scientific world. To date, a Nobel Prize has never been awarded for Relativity.<ref>Increasingly the Nobel Prize Committee has attempted to relate its physics awards to Relativity in some way, including perhaps 20 of the more recent prizes.</ref> Louis Essen, the man credited with determining the speed of light, wrote many fiery papers against it such as ''The Special Theory of Relativity: A Critical Analysis''.<ref>http://ephysics.fileave.com/physics/Essen/oxford5-essen.pdf</ref> Relativity is in conflict with [[quantum mechanics]],<ref>For example, Relativity claims that space and time are smooth and continuous, while [[quantum mechanics]] suggests otherwise. [http://www.csmonitor.com/Science/Cool-Astronomy/2010/1025/Is-the-universe-a-big-hologram-This-device-could-find-out.] Relativity also denies [[action-at-a-distance]], while quantum mechanics suggests otherwise. Relativity denies any role for chance, while quantum mechanics is heavily dependent on it.</ref> and although theories like [[string theory]] and [[quantum field theory]] have attempted to unify relativity and quantum mechanics, neither has been entirely successful or proven.

Unlike [[Classical mechanics|Newtonian physics]], in which space and time intervals are each invariant as seen by all observers, in SR the only invariant quantity is a quadratic combination of space and time intervals (x2 - c2 t2). The (assumed) instantaneous transmission of Newtonian gravitational effects also contradicts special relativity.

In quantum mechanics, the [[uncertainty principle]] suggests that virtual particles can sometimes travel faster than the speed of light which would violate causality, but "[t]he only known way to resolve this tension involves introducing the idea of antiparticles."<ref>http://nobelprize.org/nobel_prizes/physics/laureates/2004/wilczek-lecture.pdf (p. 102)</ref> Consequently, in 1928 Paul Dirac derived the Dirac equation, one of the first quantum mechanical equations compatible with special relativity, by which Dirac predicted the existence of antimatter. Four years later, antimatter (the positron) was discovered by Carl Anderson, as successfully predicted by relativistic quantum mechanics. [[Quantum field theory]], a generalization of quantum mechanics, is fully compatible with special relativity but not with general relativity, and still lacks a vital piece: evidence of the [[graviton]].

== Special Relativity ==
Lorentz and Poincare developed Special Relativity as way of understanding how Maxwell's equations for electromagnetism could be valid in different frames of reference. Einstein famously published an explanation of Poincare's theory in terms of two assumptions (postulates):

# ''The [[speed of light]] is constant for all (inertial) observers, regardless of their velocities relative to each other.''
# ''The laws of physics are identical in all inertial reference frames.''

In layman's terms, these two assumptions can be restated as:
# It is impossible ever to transmit information faster than the speed of light.<ref>This assumption is commonly restated in this manner. For example, a discussion of hypothetical [[tachyons]] talks "about using tachyons to transmit information faster than the speed of light, '''in violation of Special Relativity'''."[http://www.math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html] However, there is some question whether the Theory of Special Relativity really restricts faster-than-light communication of information.</ref>
# The laws of physics are identical, without any variation, in every location throughout the universe.
# The laws of physics are identical, without any variation, no matter how fast something is traveling (in the absence of acceleration).

Or, in more concise, clearer terms, these assumptions are this:

#there is no [[action at a distance]] (because that would make observations dependent on the frame of reference)
#space and time are completely symmetric throughout the universe (because otherwise frames of reference would not be interchangeable)

When the assumptions are stated clearly as above, the weaknesses in the theory are more apparent. There ''is'' action at a distance in [[quantum entanglement]] and apparently also in gravity, as no gravitons can be found. However, no information has yet been transmitted via quantum entanglement, so while non-locality violates the spirit of relativity it is consistent with it if relativity is limited to the transmission of information. [[Quantum field theory]], an attempt to partially reconcile [[quantum mechanics]] with relativity, is incomplete at best. As to the second assumption, it is contrary to the [[arrow of time]], which illustrates the lack of symmetry in time. Logical defects include the incoherence of relativistic mass (see discussion below) and the lack of relativistic constraints near the beginning the universe (see above).

Special Relativity (SR) was initially developed by [[Henri Poincaré]] and [[Hendrik Lorentz]], working on problems in electrodynamics and the [[Michelson-Morley experiment]], which had not found any sign of [[aether (science)|luminiferous aether]], which was believed to be the substance which carried electromagnetic waves. Special relativity alters [[Isaac Newton]]'s laws of motion by assuming that the speed of light will be the same for all observers, despite their relative velocities and the source of the light. (Therefore, if A sends a beam of light to B, and both measure the speed, it will be the same for both, no matter what the relative velocity of A and B. In Newtonian/Galilean mechanics, If A sends a physical object at a particular velocity towards B, and nothing slows it, the velocity of the object relative to B depends on the velocities of the object and of B relative to A.)

At low speeds (relative to light-speed), the Lorentz-Poincare relativity equations are equivalent to Newton's equations. The famous equation ''[[E=mc²]]'', describes the relationship between energy and the rest mass of a body.

Under relativity, particles at low mass and low speed can be accurately approximated by [[classical mechanics]] (such as [[Isaac Newton]]'s laws of motion). At the two extremes, modeling the behavior of electrons requires that relativistic effects be taken into account (the chemically significant phenomenon of electron spin arises from relativity), and the course light passing through a region containing many massive bodies such as galaxies will be distorted ([[classical mechanics]], in which light travels in straight lines, does not predict this). These are both experimentally confirmed (electron spin was known before relativity arose, and telescopic observations confirm that galactic clusters distort the paths of the light passing through them).

Many scientists have indicated problems with the postulates of special relativity. Paul Davies, formerly of Macquarie University and now at the University of Arizona believes that the speed of light has changed over time. Since the speed of light is a constant speed 'c' this indicates problems with the theory [http://news.bbc.co.uk/2/hi/science/nature/2181455.stm light speed]. Other engineers and scientist have written about problems in the basic set of special relativity equations. Based on the ideas of not Einstein but of the scientist Fitzgerald as well as others, a length contraction effect was predicted as an explanation of the failure of the Michelson Morley experiment. This idea was taken up by Hendrik Lorentz and shown by others to be a useful mechanism by which theory could be forced into conformance with experimental results. However, in 2005, Michael Strauss a computer engineer invalidated much of Special Relativity theory by showing clear contradictions in the theory. [http://www.relativitycollapse.com relativity]

== General Relativity ==

General Relativity is a theory of gravity that is compatible with Special Relativity. Einstein explains a thought experiment involving two elevators. The first elevator is stationary on the Earth, while the other is being pulled through space at a constant acceleration of g. Einstein realized that any physical experiment carried out in the elevators would give the same result. This realization is known as the equivalence principle and it states that accelerating frames of reference and gravitational fields are indistinguishable. General Relativity is the theory of gravity that incorporates Special Relativity and the equivalence principle.

General Relativity is a mathematical extension of Special Relativity. GR views space-time as a 4-dimensional [[manifold]], which looks locally like [[Minkowski space]], and which acquires [[curvature]] due to the presence of massive bodies. Thus, near massive bodies, the geometry of space-time differs to a large degree from [[Euclidean geometry]]: for example, the sum of the angles in a triangle is not exactly 180 degrees. Just as in classical physics, objects travel along [[geodesic]]s in the absence of external forces. Importantly though, near a massive body, geodesics are no longer straight lines. It is this phenomenon of objects traveling along geodesics in a curved spacetime that accounts for gravity.

At one time the anomalous precession of Mercury's [[perihelion]] seemed to support the Theory of General Relativity, but increasingly accurate measurements show a divergence of the data from the theory.<ref>[[Counterexamples to Relativity]].</ref> There are other explanations based in Newtonian gravity, such as factoring in the pull of the other planets on Mercury's orbit. One Newtonian explanation requires a slight alternation to the precise inverse-square relation of Newtonian gravity to distance, which is disfavored by mathematicians due to its inelegance in integrating.

British Historian Paul Johnson declares the turning point in 20th century to have been when fellow Briton Sir [[Arthur Eddington]], an esteemed English astronomer, ventured out on a boat off Africa in 1919 with a local Army unit to observe the bending of starlight around the sun during a total eclipse. Upon his return to England declared that his observations proven the theory of relativity. In fact recent analysis of Eddington's work revealed that he was biased in selecting his data, and that overall his data were inconclusive about the theory of relativity. The prediction was later confirmed by more rigorous experiments, such as those performed by the [[Hubble Space Telescope]] <ref>[http://www.spaceimages.com/gravlen.html Hubble Gravitational Lens Photo]</ref><ref> [http://csep10.phys.utk.edu/astr162/lect/galaxies/lensing.html Gravitational Lensing] </ref><ref>[http://www.iam.ubc.ca/~newbury/lenses/glgallery.html]</ref>. Lorentz has this to say on the discrepancies between the empirical eclipse data and Einstein's predictions.

::''It indeed seems that the discrepancies may be ascribed to faults in observations, which supposition is supported by the fact that the observations at Prince's Island, which, it is true, did not turn out quite as well as those mentioned above, gave the result, of 1.64, somewhat lower than Einstein's figure.''<ref>Lorentz, H.A. [http://ia331314.us.archive.org/2/items/theeinsteintheor11335gut/11335-h/11335-h.htm The Einstein Theory of Relativity]</ref>

The prediction that light is bent by gravity is predicted both by Newtonian physics and relativity, but relativity predicts a larger deflection.

Special relativity is the limiting case of general relativity where all gravitational fields are weak. Alternatively, special relativity is the limiting case of general relativity when all reference frames are inertial (non-accelerating and without gravity).

==Lack of evidence for Relativity==
The Theory of relativity assumes that time is symmetric just as space is, but the biggest early promoter of relativity, Arthur Eddington, coined the term "[[arrow of time]]" admitting how time is ''not'' symmetric but is directional. The passage of time is tied to an increase in disorder, or [[entropy]]. The Theory of relativity cannot explain this, and implicitly denies it, specifically allowing for theoretical time travel (e.g., [[wormholes]]) and different rates of passage of time based on velocity and acceleration.

Claims that relativity was used to develop the [[Global Positioning System]] ([[GPS]]) are false. A 1996 article explains:

:"The Operational Control System (OCS) of the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein's general theory of relativity would seem to require - transformations to and from the individual space vehicles (SVs), the Monitor Stations (MSs), and the users on the surface of the rotating earth, and the geocentric Earth Centered Inertial System (ECI) in which the SV orbits are calculated. There is a very good reason for the omission: the effects of relativity, where they are different from the effects predicted by classical mechanics and electromagnetic theory, are too small to matter - less than one centimeter, for users on or near the earth."<ref>http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf</ref><ref>Some do claim that relativity is "vital" to GPS even though GPS developed independently of theoretical predictions and theoreticians disagree about how the relativistic effects for GPS should be calculated. ''See id. See also'' [http://www.rand.org/pubs/monograph_reports/MR614/MR614.appb.pdf]</ref>

This article, which was published in 1996, goes on to propose relativistic corrections that might be used to design more accurate GPS systems. Clocks on board GPS satellites require adjustments to their clock frequencies if they are to be synchronized with those on the surface of the Earth.

Tom Van Flandern, an astronomer hired to work on GPS in the late 1990s, concluded that "[t]he GPS programmers don't need relativity." He was quoted as saying that the GPS programmers "have basically blown off Einstein."<ref>http://archive.salon.com/people/feature/2000/07/06/einstein/index.html See also [http://www.metaresearch.org/solar%20system/gps/absolute-gps-1meter-3.ASP], where Van Flandern discusses how relativistic corrections might improve GPS accuracy.</ref> Asynchronization can be easily addressed through communications between the satellites and ground stations, so it is unclear why any theory would be needed for GPS. But other obscure physicists having no connection with GPS design claim that Van Flandern is wrong about GPS, and insist that relativity provides the best explanation for its timing adjustments.<ref>''Ibid.''</ref>

Some internet articles claim that GPS timing differences ''confirm'' the Theory of Relativity or its Lorentzian counterpart (which uses a preferred frame of reference). GPS clocks run slower in the weaker gravitation field of the satellites than on ground stations on Earth, with the effects predicted by general relativity far outweighing the effects predicted by special relativity. However, the articles claiming that the slower GPS satellite clocks confirm relativity do not address the effect, if any, of the weaker gravitational force under Newton's theory on the GPS satellite clocks, likely because in Newtonian Mechanics every clock in the universe keeps time at the same rate regardless of velocity, acceleration, or the presence or absence of force.

Currently, GPS satellites are synchronized to Coordinated Universal Time by radio signals from the ground; therefore, they cannot currently be used to test general relativity.<ref>[http://www.phys.lsu.edu/mog/mog9/node9.html "General Relativity in the Global Positioning System."] Neil Ashby, U. of Colorado</ref>

There are claims that the effects of relativity have been observed with the frequency shift of the signal being sent back to [[Earth]] several times as various spacecraft have dipped into the gravity wells around massive objects such as the [[sun]] (see image at right)<ref>[http://saturn.jpl.nasa.gov/news/press-releases-03/20031002-pr-a.cfm Saturn-Bound Spacecraft Tests Einstein's Theory]</ref> or Saturn<ref>[http://www.newscientist.com/article/mg12517102.600-science-encounter-with-saturn-confirms-relativity-theory.html Encounter with Saturn confirms relativity theory]</ref>. A satellite called [[Gravity Probe B]] was put in orbit about the Earth to examine the effects of frame dragging and geodetic warping of space<ref>[http://www.nasa.gov/mission_pages/gpb/index.html NASA Gravity Probe B mission page]</ref><ref>[http://einstein.stanford.edu/ Gravity Probe B project page]</ref>, but the results were inconclusive. Note, however, that Newtonian mechanics also predicts deflection of light by gravity, and in the initial theory of relativity it predicted the same amount of deflection, but only if we treat light as capable of being accelerated and decelerated like ordinary matter, which is contrary to all measurements and observations to date.<ref>http://www.mathpages.com/rr/s6-03/6-03.htm</ref> Adjustments to the theory of relativity resulted in a prediction of a greater deflection of light than that predicated by Newtonian mechanics, though it is debatable how much deflection Newtonian mechanics should predict.

None of the NASA spacecraft incorporates predictions of relativity into their own timing mechanisms, as Newtonian mechanics is adequate even for probes sent deep into space so long as they do not undergo accelerations near the speed of light or enter any massive gravity wells.<ref>There is no reported reliance on relativity by any space probe.</ref>

A decade of observation of the [[pulsar]] pair [[PSR 1913 16|PSR B1913+16]] detected a decline in its orbital period, which was attributed to a loss in energy by the system. It is impossible to measure the masses of the pulsars, their accelerations relative to the observers, or other fundamental parameters. Professors Joseph Taylor and Russell Hulse, who discovered the binary pulsar, found that physical values could be assigned to the pulsars to make the observed decline in orbital period consistent with the Theory of General Relativity, and for this they were awarded the 1993 [[Nobel Prize]] for Physics, which is the only award ever given by the Nobel committee for the Theory of Relativity.<ref>http://nobelprize.org/nobel_prizes/physics/laureates/1993/press.html</ref> In 2004, Professor Taylor utilized a correction to the derivative of the orbital period to fit subsequent data better to the theory. At most, assumptions can be made and altered to fit the data to the theory, rather than the data confirming the theory. This is the typical scientific method, wherein a hypothesis is created, tested, adjusted, and further tested.

The [[perihelion]] of Mercury's [[orbit]] [[precession|precesses]] at a measurable rate, but even after accounting for gravitational perturbations caused all other planets in the [[solar system]], Newton's theory (assuming a precise inverse-square relationship for distance) predicts a rate of precession that differs from the measured rate by approximately 43 [[arcsecond]]s per century. General relativity was developed in part to provide an estimate for this rate of precession that better matches observations.<ref>http://physics.ucr.edu/~wudka/Physics7/Notes_www/node98.html#SECTION032121000000000000000</ref> <ref> http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200.pdf</ref> <ref> http://farside.ph.utexas.edu/teaching/336k/lectures/node117.html</ref> Newton's theory can also explain this perihelion by factoring in the gravitational pull due to other planets or making tiny adjustments to parameters in the gravitational equation.

General relativity predicts twice as much bending in light as it passes near massive objects than Newton's theory might predict.<ref>http://www.mathpages.com/rr/s6-03/6-03.htm</ref> This phenomenon is known as [[gravitational lens|gravitational lensing]]. A large number of instances of gravitational lensing have been observed, and it is now a standard astronomical tool.<ref> http://imagine.gsfc.nasa.gov/docs/features/news/grav_lens.html</ref> <ref> http://astro.berkeley.edu/~jcohn/lens.html</ref> <ref> http://www.iam.ubc.ca/~newbury/lenses/glgallery.html</ref> Note, however, that the extent of bending of light predicted by Newton's theory is open to debate, and depends on assumptions about the nature of light for gravitational purposes.<ref>http://cosmictimes.gsfc.nasa.gov/1919/guide/gravity_bends_starlight.html</ref>

In 1972, scientists flew extremely accurate clocks ("atomic clocks") around the world in both directions on commercial airlines, and claimed to observe relativistic time dilation; the eastbound clock gained 273 ns and the westbound clock lost 59 ns, matching the predictions of general relativity to within experimental accuracy.<ref>[http://www.answers.com/topic/hafele-keating-experiment Hafele-Keating Experiment]</ref> However, the inventor of the atomic clock, Louis Essen, declared that the experiment was inaccurate.<ref>Louis Essen, Electron. Wireless World 94 (1988) 238.</ref> Dr A. G. Kelly examined the raw data from the experiment and declared it inconclusive.<ref>A. G. Kelly,Reliability of Relativistic Effect Tests on Airborne Clocks, Monograph No.3 Feb.1996, The Institution of Engineers of Ireland, ISBN 1-898012-22-9</ref> The Nobel Committee chose not to honor this experiment for the significance that was claimed.

Despite [[censorship]] of dissent about relativity, evidence contrary to the theory is discussed outside of [[liberal]] universities.<ref>http://scitizen.com/screens/blogPage/viewBlog/sw_viewBlog.php?idTheme=8&idContribution=922</ref>

==Fallacious Claims of Experimental Verification of Relativity==

The different effects predicted by special relativity, compared to classical formulations, are extremely tiny. Most relativistic effects are negligible at the speeds of ordinary phenomena observed by humans. The effects only become significant when the speeds involved are a significant fraction of the speed of light, which is <math>3 \times 10^8</math> meters per second—such speeds are called ''relativistic''. (However, it's worth noting that ordinary magnetism can be considered an effect of relativity, dictated by the need for electrostatic theory to be correct under relativity. The speed of light in fact appears in the formulas ([[Maxwell's Equations]]) governing electricity and magnetism, though these equations were developed long before relativity was proposed.)

Because the effects of relativity are so tiny, scientists have been devising sophisticated and sensitive tests ever since the theory was formulated in 1905.

*At the end of Einstein's original 1905 paper [http://www.fourmilab.ch/etexts/einstein/E_mc2/www/ "Does the Inertia of a Body Depend its Energy Content?"], he speculates on the possibility that the equation <math>E = m c^2</math>, which would normally be very hard to verify, could be verified with the extremely high energies of the newly-discovered phenomenon of radioactivity.<ref>This equation is not related to [[quantum mechanics]].</ref> In the 1910's, with the invention of the mass spectrometer, it became possible to measure masses of nuclei accurately. This led to the clearing up of the mystery of atomic masses not being exact integers,and strongly suggested the existence of a "mass defect" (or "packing fraction") consistent with the mass-energy equivalence. In the 1930's, experiments with known nuclear reactions showed a very accurate correlation between the masses of the nuclei involved and the energy released.

*Another prediction of special relativity was time dilation in rapidly moving objects. This effect was most famously verified in the anomalously slow decay of relativistic cosmic muons<ref>Some have suggested that other explanations are possible for this effect. We are trying to track this down.</ref>. Time dilation has since been verified many times, and is routinely taken into account in all high-energy nuclear physics experiments, as in Hadron collision experiments<ref>Experiments specifically designed to check dilation are rarely conducted any more.</ref>.

Predictions of general relativity turned out to be more obscure and difficult to test. The two most famous predictions were the bending of light in a gravitational field and the precession of the perihelia of orbiting planets.

*The first of these was famously tested during a total eclipse in 1919. That test was somewhat muddled by an incorrect initial calculation, by several people including Einstein himself, of what the effect would be, and some "cherry picking" of the data to be used <ref>''Einstein's Luck'', John Waller, Oxford University Press, ISBN 0-19-860719-9</ref>. The data selection could be considered "manipulation" or "fudging", by a person (Arthur Eddington) who had a personal stake in the outcome. His analysis techniques would not pass muster today.

:It should be noted that pre-relativistic (Newtonian) physics may also predict a bending, of half the observed value, depending on whether one uses the 17th century "corpuscular" formulation or the 19th century "wave" formulation.

:Nevertheless, it has been verified with ever-increasing precision in subsequent eclipses, and in the observations of quasar 3C273.

*The second "classical" test of general relativity was the advance of the perihelion of the orbit of Mercury. There are many complex effects contributing to this, including gravitational perturbations from other planets and the effect of the oblateness of the Sun. These are hard to calculate accurately, but, by 1900 it was known quite accurately that there was an "anomalous" precession, that is, a precession beyond all other known effects, of 43 arc seconds per century. This is a very tiny effect, but astronomical measurements were sufficiently accurate by that time to show it clearly.

:This created quite a problem—physicists by then were accustomed to having their theories check out very accurately. One proposal that was made, by Simon Newcomb and Asaph Hall, was that the exponent of the radius in the gravitational formula wasn't exactly 2. He showed that, by choosing an exponent of <math>2+\delta</math>, the precession, as a fraction of a full orbit per planet's year, is <math>\delta/2</math>. By setting <math>\delta</math> to .000000157, that is, an exponent of 2.000000157, Newcomb was able to get a precession of .000000078 revolutions per Mercury year, or 43 arcseconds per Earth year. The primary resistance to this approach came from mathematicians unable to do the integration without an exponent of precisely 2, and they insisted, incorrectly, that was impossible for the exponent to be slightly different from 2. Due to this desire for mathematical elegance rather than objective observation-based science, Newcomb's approach was not pursued.

:While Newcomb's theory, and general relativity, don't lead to closed-form solutions, both theories can be solved numerically to as much precision as one desires.

:Increasingly precise measurements of the precession demonstrate that it conflicts with General Relativity, despite claims of relativists for decades that it predicted the precession accurately in the amount of <math>3{}v^2/c^2</math> revolutions per planet's "year", where <math>v</math> is the planet's average orbital speed.<ref>That is a simple approximation, designed to relate the precession to the planet's speed relative to the speed of light. A more accurate approximation is <math>\frac{3GM}{c^2 a(1-e^2)}</math>, where a is the semi-major axis and e is the eccentricity.</ref> The conflict is greater than the margin of error, and many relativists avoid the discrepancy rather than address it.

:The following table show some approximate parameters for the planets. Note that Mercury has the smallest orbit, the fastest speed, and the highest gravitational pull. Precession of planets other than Mercury is extremely hard to measure, but measurements of the actual anomalous precessions are in good agreement with the last column of the table.<ref>http://www.mathpages.com/rr/s6-02/6-02.htm</ref>

{| class="wikitable"
|-
!Planet
!Period, seconds x 106
!Semimajor axis, meters x 109
!Speed, meters/second x 103
!Gravitational force, Newtons per kilogram
!Anomalous precession, arcseconds per (Earth) century, pure Newtonian mechanics
!Anomalous precession, Newtonian with exponent of 2.000000157
!Anomalous precession, general relativity
|-
|Mercury
|7.57
|58.9
|48
|.039
|0
|43
|43
|-
|Venus
|19.6
|108
|35
|.011
|0
|16.6
|9
|-
|Earth
|31.6
|150
|30
|.006
|0
|10.3
|4
|-
|Mars
|59.3
|227.9
|24
|.0025
|0
|5.5
|1.4
|-
|Jupiter
|374
|778.4
|13
|.0002
|0
|0.87
|0.07
|-
|Saturn
|929
|1426
|9.7
|.00006
|0
|0.35
|0.014
|-
|Uranus
|2651
|2870
|6.8
|.000016
|0
|0.12
|0.002
|-
|Neptune
|5200
|4498
|5.5
|.000007
|0
|0.063
|0.0008
|}

[[Image:Cassini-science-289.jpg|right|thumb|The Shapiro effect: A spacecraft signal dipping into a gravity well around the [[Sun]] is delayed slightly.]]
As the 20th century progressed, more tests of general relativity were proposed.

*One was the ''Shapiro effect'', involving time delay in radio signals passing through the gravity well of the Sun or a planet. Various spacecraft have confirmed this.

*Another is ''gravitational time dilation''. This is an effect separate from the time dilation of special relativity. It was tested by the Pound-Rebka experiment in 1959.

*Later in the 20th century, even more subtle phenomena were tested. One was the phenomenon of ''gravitational radiation'', or "gravity waves". These waves are incredibly difficult to observe, and have never been observed. But extremely dense binary pulsars radiate gravitational waves with sufficient energy loss that, even though we can't detect the waves from Earth, we can see the effect of the energy loss from the radiation. The extreme precision of the timing of pulses from pulsars makes it possible to observe their energy loss with great accuracy. Observations by Hulse and Taylor of the pulsar pair known as B1913+16 confirmed the energy loss consistent with the predicted radiation.

*Two other effects, ''geodetic precession'' (also known as "de Sitter precession"), and ''frame dragging'' (also known as the "Lense-Thirring effect") were tested by the "Gravity Probe B" satellite early in the 21st century<ref>http://prl.aps.org/accepted/L/ea070Y8dQ491d22a28828c95f660a57ac82e7d8c0</ref><ref>http://www.digitaljournal.com/article/306430</ref><ref>http://www.nap.edu/html/gpb/summary.html</ref><ref>http://www.sciencenews.org/view/generic/id/73870/title/Gravity_Probe_B_finally_pays_off_</ref><ref>http://www.nasa.gov/mission_pages/gpb/</ref><ref>http://einstein.stanford.edu/</ref><ref>http://spectrum.ieee.org/aerospace/space-flight/the-gravity-probe-b-bailout</ref><ref>http://www.engadget.com/2011/05/06/nasa-concludes-gravity-probe-b-space-time-experiment-proves-e/</ref>. The precision required to observe this was phenomenal. The results were announced on May 4, 2011.

{{clear}}

==Predicted consequences of the Theories==
===Time dilation===

[[Image:Light cone.png|right|thumb|Light-cone diagram]]
One important consequence of SR's postulates is that an observer in one reference frame will observe a clock in another frame to be "ticking" more slowly than in the observer's own frame. This can be proven mathematically using basic geometry, if the postulates are physically true without exception.

The length of an event <math>t</math>, as seen by a (relative) stationary observer observing an event is given by:

<math> t = \frac{t_{0}} {\sqrt{1 - \frac{v^{2}}{c^{2}}}}</math>

Where
:<math>t_0</math> is the "proper time" or the length of the event in the observed frame of reference.
:<math>v</math> is the relative velocity between the reference frames.
:<math>c</math> is the speed of light (3x108 ms-1).

Evidence for time dilation was discovered by studying [[muon decay]]. [[Muons]] are [[subatomic]] [[particles]] with a very short [[halflife]] (1.53 microseconds at rest) and a very fast speed (0.994c). By putting muon detectors at the top (D1) and bottom (D2) of a mountain with a separation of 1900m, scientists could measure accurately the proportion of muons reaching the second detector in comparison to the first. The proportion found was different to the proportion that was calculated without taking into account relativistic effects.

Using the equation for [[exponential decay]], they could use this proportion to calculate the time taken for the muons to decay, relative to the muon. Then, using the time dilation equation they could then work out the dilated time. The dilated time showed a good correlation with the time it took the muons to reach the second sensor, thereby supporting the existence of time dilation.

The time taken for a muon to travel from D1 to D2 as measured by a stationary observer is:

<math> t = \frac{s}{v} = \frac{1900}{0.994\times(3\times10^{8})} = 6.37\mu\textrm{s} </math>

The fraction of muons arriving at D2 in comparison to D1 was 0.732. (Given by <math> \frac{N}{N_0} = 0.732 </math>)

Since (from the equation for exponential decay) <math> \frac{N}{N_{0}} = e^{-\lambda t_{0}} </math> then

<math> t_{0} = \frac {ln(0.732)}{ln (0.2)} \times 1.53\times 10^{-6} = 0.689\mu\textrm{s}</math>

This gives the time for the proportion of decay to occur for an observer who is stationary, relative to the muon.

Putting this into the time dilation equation gives:

<math> t = \frac{t_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = \frac{0.689 \times{10^{-6}}}{\sqrt{1 - \frac{0.994^{2}}{1^{2}}}} = 6.3\times 10^{-6}\textrm{s}</math>

This is in good agreement with the value calculated above, thereby providing evidence to support time dilation.

====Time Dilation and Creation Science====

{{main|Starlight problem#Humphreys.27_model}}

Creation scientists such as physicists Dr. [[Russell Humphreys]] and Dr. [[John Hartnett]] have used relativistic time dilation to explain how the earth can be only 6,000 years old even though cosmological data (background radiation, supernovae, etc.) set a much older age for the universe.

===Length contraction===
When two inertial reference frames move past each other in a straight line with constant relative velocity, an observer in one reference frame would observe a metre rule in the other frame to be shorter.

The length, <math>l</math>, of an object as seen by a (relative) stationary observer is given by:

<math> l = l_{0} \sqrt{1- \frac{v^{2}}{c^{2}}}</math>

Where
:<math>l_0</math> is the "proper length" or the length of the object in the observed frame of reference.
:<math>v</math> is the relative velocity between the reference frames.
:<math>c</math> is the speed of light (3x108 ms-1).

===Mass increase===

For decades the theory of relativity taught that as a body moves with increasing velocity its [[mass]] also increases.<ref>For example, this was taught as recently as in the 1991 edition of the Encyclopedia Britannica.</ref>

Under this view, the mass, <math>m</math>, of an object as detected by a (relative) stationary observer is given by:

:<math> m = \frac{m_{0}} {\sqrt{1 - \frac{v^{2}}{c^{2}}}}</math>

Where
:<math>m_0</math> is the "rest mass" or the mass of the object when it is at rest.
:<math>v</math> is the relative velocity of the object.
:<math>c</math> is the speed of light (3x108 ms-1).

Since speed is relative, it follows that two observers in different inertial reference frames may disagree on the mass and kinetic energy of a body. Since all inertial reference frames are treated on an equal footing, it follows that mass and energy are interchangeable.

In recent years most physicists have shifted away from Einstein's original reliance on relativistic mass and his suggestion that mass increases{{Citation needed|date=January 2012}}. Instead, most physicists today teach that

:<math>F=\frac{d}{d\tau} p</math>

where <math>p</math> is the momentum defined by <math>\gamma m v</math>, <math>\gamma</math> is the standard Lorentz factor, and <math>\tau</math> is the proper time. Force F defined this way is a vector and thus can handle the directional aspect of the relativistic effects better than the concept of relativistic mass can.

The abandonment by physicists of the concept of relativistic mass, however, has the consequence of undermining the traditional claim under relativity that

:<math>m - m_0 = \frac{E}{c^2}</math>

also popularly known as

:<math>E = m c^2</math>

Now a concept of the 4-momentum <math>p</math> of a particle is taught, such that the square of the magnitude of <math>p</math> satisfies:

<math>||p||^2 = -p_x^2-p_y^2-p_z^2+E^2 = m_0^2c^4</math>

in any inertial reference frame. The magnitude of the 4-momentum, in any inertial frame, equals the rest mass <math>m_0</math> of the particle (in units where <math>c=1</math>).

== Paradoxes ==

The predictions of the theory of relativity throw up a number of apparent paradoxes and anomalies relating to the effects of time dilatation and length contraction. Whilst these paradoxes are consistent with the theory, they are contrary to everyday human experience and therefore can seem like impossibilities.

=== The Twin Paradox ===

The twin paradox is usually stated as a thought experiment involving two twins, one of whom is sent on a long journey in a spacecraft travelling at close to the speed of light, whilst the other remains on Earth. Time dilatation means that the travelling twin, on his return to Earth, is younger that the twin who has remained at home. However because neither twin is in a special position - each being in an inertial frame of reference - the reverse must also be true, and so the twin remaining on Earth must be younger. Hence each twin is younger than the other - a paradox.

The problem can be resolved in two ways. One is to examine the effects of General Relativity: to come back to Earth, the travelling twin must undergo acceleration in order to reverse his course, causing temporal effects which make him permanently the younger. Alternatively, it can be explained entirely using Special Relativity and noting that the twins are not in symmetrical situations: the one on earth has remained in a single inertial frame of reference, whilst the travelling twin has travelled in two<ref>http://mentock.home.mindspring.com/twins.htm</ref>.

=== The Ehrenfest Paradox ===

The Ehrenfest Paradox considers a rigid wheel or disc rotating a bout its axis at high speed (somewhat like a bicycle wheel spinning freely on its axle). The rim of the wheel travels at close to the speed of light and therefore undergoes length contraction, whereas the radius (the spokes, for the bicycle wheel) does not. Hence the circumference is no longer equal to 2<big><math>\pi</math></big>r, which is paradoxical.

The apparent paradox was finally resolved in 1975 by the Norwegian scientist [[Øyvind Grøn]]<ref>http://www.physicsforums.com/showthread.php?t=224955</ref>.

== Variable Speed of Light ==

The Theory of Relativity implies that physical constants like c, the speed of light in a vacuum, have remained constant. But at least one study suggests that physical constants, and possibly even the speed of light, have changed as the universe has aged.<ref>James Glanz and Dennis Overbye, "Cosmic Laws Like Speed of Light Might Be Changing, a Study Finds," August 15, 2001.[http://www.nytimes.com/2001/08/15/science/15PHYS.html?ex=1185076800&en=d6467b6e3e346796&ei=5070]</ref>

"For the first time, scientists have experimentally demonstrated that sound pulses can travel at velocities faster than the speed of light, c. William Robertson's team from Middle Tennessee State University also showed that the group velocity of sound waves can become infinite, and even negative. ... Although such results may at first appear to violate special relativity (Einstein's law that no material object can exceed the speed of light), the actual significance of these experiments is a little different. These types of superluminal phenomena, Robertson et al. explain, violate neither causality nor special relativity, nor do they enable information to travel faster than c. In fact, theoretical work had predicted that the superluminal speed of the group velocity of sound waves should exist. 'The key to understanding this seeming paradox is that no wave energy exceeded the speed of light,' said Robertson."<ref>http://www.physorg.com/news88249076.html</ref>

"A team of researchers from the Ecole Polytechnique Fédérale de Lausanne (EPFL) has successfully demonstrated, for the first time, that it is possible to control the speed of light – both slowing it down and speeding it up – in an optical fiber, using off-the-shelf instrumentation in normal environmental conditions. Their results, to be published in the August 22 issue of Applied Physics Letters, could have implications that range from optical [[computing]] to the fiber-optic telecommunications industry."<ref>http://www.scienceblog.com/light.html</ref> Both slowing down and speeding up of light within a substance other than a vacuum is made possible, because the light travels through the material, and that material affects the speed of light, i.e. a photon hits an electron, which then exits and emits a slightly lower energy photon out in the direction that the original photon was traveling, thus maintaining conservation of momentum. No matter how transparent an object may appear, it radically impacts the speed of the light traveling through it, as demonstrated by the refractive production of a rainbow by a crystal, which Newton himself discovered.

This apparent change in speed can be explained, however, by noting that the constant c refers to the speed of light in a vacuum, ie, when it is unimpeded. The speed of light when traveling through physical media is, in fact, variable.

"A pair of German physicists claim to have broken the speed of light - an achievement that would undermine our entire understanding of space and time. ... Dr Nimtz told New Scientist magazine: 'For the time being, this is the only violation of special relativity that I know of.'"<ref>http://www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2007/08/16/scispeed116.xml</ref>

==Pending research==

Today some physicists are working on hypothesizing how general relativity might have related to the other three forces of nature during the first fraction of a second of the [[Big Bang]]. Two of the more commonly studied attempts are [[string theory]] and [[loop quantum gravity]], but they have failed to produce any evidence that science mandates a science must have, and both typically take large amounts of work to even conform to what scientists believe. Critics increasingly point out that string theory and loop quantum gravity are largely untestable and unfalsifiable, and thus potentially unscientific under the principles of science advanced by [[Karl Popper]].<ref>See, for example, ''Not Even Wrong'', by Peter Woit</ref>

Relativity continues to be tested and some physics professors remain skeptical of the theory, such as University of Maryland physics professor Carroll Alley, who served as the principle physicist on the Apollo lunar project.<ref>http://science.nasa.gov/headlines/y2004/21jul_llr.htm</ref>

== Political aspects of relativity ==

Some [[liberal]] politicians have extrapolated the theory of relativity to metaphorically justify their own political agendas. For example, [[Democratic]] [[President of the United States of America|President]] [[Barack Obama]] helped publish an article by liberal law professor [[Laurence Tribe]] to apply the relativistic concept of "curvature of space" to promote a broad legal right to [[abortion]].<ref>Tribe, acknowledging help by Obama, argued that the [[Constitution]] should be interpreted to establish a right to federally funded [[abortion]] and that, more generally, ''[[Roe v. Wade]]'' does not go far enough. They insisted that a relativistic "curvature of space" could achieve this result by expanding application of the [[Constitution]] based on its impact on personal choice. "The ''[[Roe v. Wade]]'' opinion ignored the way in which laws regulating pregnant women may shape the entire pattern of relationships among men, women, and children. It conceptualized abortion not in terms of the intensely public question of the subordination of women to men through the exploitation of pregnancy, but in terms of the purportedly private question of how women might make intimately personal decisions about their bodies and their lives. That vision described a part of the truth, but only what might be called the Newtonian part. ... [A] change in the surrounding legal setting can constitute state action that most threatens the sphere of personal choice. And it is a 'curved space' perspective on how law operates that leads one to focus less on the visible lines of legal force and more on how those lines are bent and directed by the law's geometry." Laurence H. Tribe, The Curvature of Constitutional Space: What Lawyers Can Learn from Modern Physics, 103 Harv. L. Rev. 1, 16-17 (1989).</ref> As of June 2008, over 170 law review articles have cited this [[liberal]] application of the theory of relativity to legal arguments.<ref>Search conducted by [[User:Aschlafly]] in the LEXIS database "US Law Reviews and Journals, Combined," conducted June 1, 2008.</ref> Applications of the theory of relativity to change morality have also been common.<ref>"Mistakenly, in the minds of many, the theory of relativity became relativism."[http://www.worldnetdaily.com/news/article.asp?ARTICLE_ID=38081]</ref> Moreover, there is an unmistakable effort to censor or ostracize criticism of relativity.<ref>Although the [[Examples of Bias in Wikipedia|liberally biased Wikipedia]] contains lengthy criticisms of the subjects of many entries, and even though publications like ''The Economist'' recognize the lack of scientific satisfaction in the theory (see, e.g., "Weighing the Universe," The Economist (Jan. 25, 2007)), Wikipedia's entry on [http://en.wikipedia.org/wiki/Theory_of_Relativity Theory of Relativity] omits one word of criticism.</ref>

Physicist [[Robert Dicke]] of Princeton University was a prominent critic<ref>http://www.time.com/time/magazine/article/0,9171,943324,00.html</ref> of general relativity, and Dicke's alternative "has enjoyed a renaissance in connection with theories of higher dimensional space-time."<ref>"Initially a popular alternative to General Relativity, the Brans-Dicke theory lost favor as it became clear that omega must be very large-an artificial requirement in some views. Nevertheless, the theory has remained a paradigm for the introduction of scalar fields into gravitational theory, and as such has enjoyed a renaissance in connection with theories of higher dimensional space-time."[http://nedwww.ipac.caltech.edu/level5/Glossary/Essay_bekenstein.html] </ref> Despite being one of the most accomplished physicists in the 20th century, Dicke was repeatedly passed over for a [[Nobel Prize]], and in at least one case Dicke was insulted by the award being granted to others for contributions more properly credited to Dicke.

There has been little recognition by the Nobel Prize committee of either theory of relativity, and particularly scant recognition of the Theory of General Relativity.

===Government Support for Relativistic research===
The Theory of Relativity enjoys a disproportionate share of [[federal funding]] of physics research today.<ref>The Democratic Congress insisted on the $250 million LIGO project despite substantial criticism by scientists that it was wasting scarce research dollars. John Travis, "LIGO: a $ 250 million gamble; Laser Interferometer Gravitational-Wave Observatory; includes related article," ''Science'' p. 612 (Apr. 30, 1993). "Adding to the acrimony is LIGO's $ 250 million price tag, which some hold responsible for NSF's recent funding woes." ''Id.''</ref> In at least one case that research has been unsuccessful. The $365 million dollar [[LIGO]] project has failed to detect the gravity waves predicted by relativity.<ref>http://www.npr.org/programs/atc/features/2002/sept/gravitywaves/index.html</ref>

{{Relativity}}

== References ==
{{reflist|2}}

[[Category:Physics]]
[[Category:Science]]

==External Links ==
*[http://ia331314.us.archive.org/2/items/theeinsteintheor11335gut/11335-h/11335-h.htm The Einstein Theory of Relativity, by H.A. Lorentz.]
*[http://www.relativitycalculator.com Relativity Calculator - Learn Special Relativity Mathematics ] The mathematics of special relativity presented in as simple and comprehensive manner possible within philosophical and historical contexts.

Theory of relativity

2012-04-11T04:12:25Z

Cahnkj: improved credibility

''See also [[Counterexamples to Relativity]].''

The '''theory of relativity''' has been repeatedly contradicted by experiments, such as precise measurements of the advance of the perihelion of Mercury that show a shift greater than predicted by Relativity, well beyond the margin of error. Criticism of the theory, however, caused physicist [[Robert Dicke]] to be denied the [[Nobel Prize]], and it is unlikely tenure or a Ph.D would be awarded to any critic of the theory.

'''Relativity''' refers to two closely-related mathematical theories in [[physics]]:

*'''[[Special theory of relativity|Special relativity]]''' (SR) is a theory which describes the laws of motion for non-accelerating bodies traveling at a significant fraction of the [[speed of light]]. As speeds approach zero, Special Relativity tends towards equivalence with [[Newton's Laws of Motion]]. Special Relativity was developed by [[Hendrik Lorentz]], [[Henri Poincaré]], and Hermann Minkowski,<ref>"German mathematician who developed the geometrical theory of numbers and who made numerous contributions to number theory, mathematical physics, and the theory of relativity." [http://www.britannica.com/eb/article-9052860/Hermann-Minkowski Hermann Minkowski -- Britannica Online Encyclopedia]</ref><ref>[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Minkowski.html Hermann Minkowski, Biography]</ref> and [[Albert Einstein]].

*'''[[General theory of relativity|General Relativity]]''' (GR) is a theory which explains the laws of motion as viewed from accelerating reference frames and includes a geometric explanation for gravity. This theory was developed by [[David Hilbert]] and [[Albert Einstein]] as an extension of the postulates of Special Relativity.<ref>"[T]he German mathematician David Hilbert submitted an article containing the correct field equations for general relativity five days before Einstein."[http://nobelprize.org/educational_games/physics/relativity/history-1.html Nobel Prize historical account]</ref> A dramatic but later discredited claim by Sir [[Arthur Eddington]] of experimental proof of General Relativity in 1919 made Einstein a household name.

These theories have augmented earlier approaches, such as [[Galilean Relativity]].

Unlike most of physics, the theories of relativity have discontinuities whereby the limit of a physical quantity as a variable (such as mass or velocity) approaches a fixed value is not the same as the physical quantity at the fixed value. For example, the limit of momentum as mass approaches 0 and velocity approaches the speed of light is not equal to the momentum of (massless) light.<ref>Discontinuities in General Relativity are also well-recognized. See, e.g., [http://www.springerlink.com/content/u47l341u2q555455/]</ref>

More generally, and also unlike most of physics, the theories of relativity consist of complex mathematical equations relying on several hypotheses. For example, at Hofstra University general relativity is taught as part of an upperclass math course on differential geometry, based on three stated assumptions.<ref>http://people.hofstra.edu/Stefan_Waner/diff_geom/tc.html</ref> The equations for special relativity assume that it is forever impossible to attain a velocity faster than the speed of light and that all inertial frames of reference are equivalent, hypotheses that can never be fully tested. Relativity rejects Newton's [[action at a distance]], which is basic to Newtonian gravity and [[quantum mechanics]]. The mathematics of relativity assume no exceptions, yet in the time period immediately following the origin of the universe the relativity equations could not possibly have been valid.

Relativity has been met with much resistance in the scientific world. To date, a Nobel Prize has never been awarded for Relativity.<ref>Increasingly the Nobel Prize Committee has attempted to relate its physics awards to Relativity in some way, including perhaps 20 of the more recent prizes.</ref> Louis Essen, the man credited with determining the speed of light, wrote many fiery papers against it such as ''The Special Theory of Relativity: A Critical Analysis''.<ref>http://ephysics.fileave.com/physics/Essen/oxford5-essen.pdf</ref> Relativity is in conflict with [[quantum mechanics]],<ref>For example, Relativity claims that space and time are smooth and continuous, while [[quantum mechanics]] suggests otherwise. [http://www.csmonitor.com/Science/Cool-Astronomy/2010/1025/Is-the-universe-a-big-hologram-This-device-could-find-out.] Relativity also denies [[action-at-a-distance]], while quantum mechanics suggests otherwise. Relativity denies any role for chance, while quantum mechanics is heavily dependent on it.</ref> and although theories like [[string theory]] and [[quantum field theory]] have attempted to unify relativity and quantum mechanics, neither has been entirely successful or proven.

Unlike [[Classical mechanics|Newtonian physics]], in which space and time intervals are each invariant as seen by all observers, in SR the only invariant quantity is a quadratic combination of space and time intervals (x2 - c2 t2). The (assumed) instantaneous transmission of Newtonian gravitational effects also contradicts special relativity.

In quantum mechanics, the [[uncertainty principle]] suggests that virtual particles can sometimes travel faster than the speed of light which would violate causality, but "[t]he only known way to resolve this tension involves introducing the idea of antiparticles."<ref>http://nobelprize.org/nobel_prizes/physics/laureates/2004/wilczek-lecture.pdf (p. 102)</ref> Consequently, in 1928 Paul Dirac derived the Dirac equation, one of the first quantum mechanical equations compatible with special relativity, by which Dirac predicted the existence of antimatter. Four years later, antimatter (the positron) was discovered by Carl Anderson, as successfully predicted by relativistic quantum mechanics. [[Quantum field theory]], a generalization of quantum mechanics, is fully compatible with special relativity but not with general relativity, and still lacks a vital piece: evidence of the [[graviton]].

== Special Relativity ==
Lorentz and Poincare developed Special Relativity as way of understanding how Maxwell's equations for electromagnetism could be valid in different frames of reference. Einstein famously published an explanation of Poincare's theory in terms of two assumptions (postulates):

# ''The [[speed of light]] is constant for all (inertial) observers, regardless of their velocities relative to each other.''
# ''The laws of physics are identical in all inertial reference frames.''

In layman's terms, these two assumptions can be restated as:
# It is impossible ever to transmit information faster than the speed of light.<ref>This assumption is commonly restated in this manner. For example, a discussion of hypothetical [[tachyons]] talks "about using tachyons to transmit information faster than the speed of light, '''in violation of Special Relativity'''."[http://www.math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html] However, there is some question whether the Theory of Special Relativity really restricts faster-than-light communication of information.</ref>
# The laws of physics are identical, without any variation, in every location throughout the universe.
# The laws of physics are identical, without any variation, no matter how fast something is traveling (in the absence of acceleration).

Or, in more concise, clearer terms, these assumptions are this:

#there is no [[action at a distance]] (because that would make observations dependent on the frame of reference)
#space and time are completely symmetric throughout the universe (because otherwise frames of reference would not be interchangeable)

When the assumptions are stated clearly as above, the weaknesses in the theory are more apparent. There ''is'' action at a distance in [[quantum entanglement]] and apparently also in gravity, as no gravitons can be found. However, no information has yet been transmitted via quantum entanglement, so while non-locality violates the spirit of relativity it is consistent with it if relativity is limited to the transmission of information. [[Quantum field theory]], an attempt to partially reconcile [[quantum mechanics]] with relativity, is incomplete at best. As to the second assumption, it is contrary to the [[arrow of time]], which illustrates the lack of symmetry in time. Logical defects include the incoherence of relativistic mass (see discussion below) and the lack of relativistic constraints near the beginning the universe (see above).

Special Relativity (SR) was initially developed by [[Henri Poincaré]] and [[Hendrik Lorentz]], working on problems in electrodynamics and the [[Michelson-Morley experiment]], which had not found any sign of [[aether (science)|luminiferous aether]], which was believed to be the substance which carried electromagnetic waves. Special relativity alters [[Isaac Newton]]'s laws of motion by assuming that the speed of light will be the same for all observers, despite their relative velocities and the source of the light. (Therefore, if A sends a beam of light to B, and both measure the speed, it will be the same for both, no matter what the relative velocity of A and B. In Newtonian/Galilean mechanics, If A sends a physical object at a particular velocity towards B, and nothing slows it, the velocity of the object relative to B depends on the velocities of the object and of B relative to A.)

At low speeds (relative to light-speed), the Lorentz-Poincare relativity equations are equivalent to Newton's equations. The famous equation ''[[E=mc²]]'', describes the relationship between energy and the rest mass of a body.

Under relativity, particles at low mass and low speed can be accurately approximated by [[classical mechanics]] (such as [[Isaac Newton]]'s laws of motion). At the two extremes, modeling the behavior of electrons requires that relativistic effects be taken into account (the chemically significant phenomenon of electron spin arises from relativity), and the course light passing through a region containing many massive bodies such as galaxies will be distorted ([[classical mechanics]], in which light travels in straight lines, does not predict this). These are both experimentally confirmed (electron spin was known before relativity arose, and telescopic observations confirm that galactic clusters distort the paths of the light passing through them).

Many scientists have indicated problems with the postulates of special relativity. Paul Davies, formerly of Macquarie University and now at the University of Arizona believes that the speed of light has changed over time. Since the speed of light is a constant speed 'c' this indicates problems with the theory [http://news.bbc.co.uk/2/hi/science/nature/2181455.stm light speed]. Other engineers and scientist have written about problems in the basic set of special relativity equations. Based on the ideas of not Einstein but of the scientist Fitzgerald as well as others, a length contraction effect was predicted as an explanation of the failure of the Michelson Morley experiment. This idea was taken up by Hendrik Lorentz and shown by others to be a useful mechanism by which theory could be forced into conformance with experimental results. However, in 2005, Michael Strauss a computer engineer invalidated much of Special Relativity theory by showing clear contradictions in the theory. [http://www.relativitycollapse.com relativity]

== General Relativity ==

General Relativity is a theory of gravity that is compatible with Special Relativity. Einstein explains a thought experiment involving two elevators. The first elevator is stationary on the Earth, while the other is being pulled through space at a constant acceleration of g. Einstein realized that any physical experiment carried out in the elevators would give the same result. This realization is known as the equivalence principle and it states that accelerating frames of reference and gravitational fields are indistinguishable. General Relativity is the theory of gravity that incorporates Special Relativity and the equivalence principle.

General Relativity is a mathematical extension of Special Relativity. GR views space-time as a 4-dimensional [[manifold]], which looks locally like [[Minkowski space]], and which acquires [[curvature]] due to the presence of massive bodies. Thus, near massive bodies, the geometry of space-time differs to a large degree from [[Euclidean geometry]]: for example, the sum of the angles in a triangle is not exactly 180 degrees. Just as in classical physics, objects travel along [[geodesic]]s in the absence of external forces. Importantly though, near a massive body, geodesics are no longer straight lines. It is this phenomenon of objects traveling along geodesics in a curved spacetime that accounts for gravity.

At one time the anomalous precession of Mercury's [[perihelion]] seemed to support the Theory of General Relativity, but increasingly accurate measurements show a divergence of the data from the theory.<ref>[[Counterexamples to Relativity]].</ref> There are other explanations based in Newtonian gravity, such as factoring in the pull of the other planets on Mercury's orbit. One Newtonian explanation requires a slight alternation to the precise inverse-square relation of Newtonian gravity to distance, which is disfavored by mathematicians due to its inelegance in integrating.

British Historian Paul Johnson declares the turning point in 20th century to have been when fellow Briton Sir [[Arthur Eddington]], an esteemed English astronomer, ventured out on a boat off Africa in 1919 with a local Army unit to observe the bending of starlight around the sun during a total eclipse. Upon his return to England declared that his observations proven the theory of relativity. In fact recent analysis of Eddington's work revealed that he was biased in selecting his data, and that overall his data were inconclusive about the theory of relativity. The prediction was later confirmed by more rigorous experiments, such as those performed by the [[Hubble Space Telescope]] <ref>[http://www.spaceimages.com/gravlen.html Hubble Gravitational Lens Photo]</ref><ref> [http://csep10.phys.utk.edu/astr162/lect/galaxies/lensing.html Gravitational Lensing] </ref><ref>[http://www.iam.ubc.ca/~newbury/lenses/glgallery.html]</ref>. Lorentz has this to say on the discrepancies between the empirical eclipse data and Einstein's predictions.

::''It indeed seems that the discrepancies may be ascribed to faults in observations, which supposition is supported by the fact that the observations at Prince's Island, which, it is true, did not turn out quite as well as those mentioned above, gave the result, of 1.64, somewhat lower than Einstein's figure.''<ref>Lorentz, H.A. [http://ia331314.us.archive.org/2/items/theeinsteintheor11335gut/11335-h/11335-h.htm The Einstein Theory of Relativity]</ref>

The prediction that light is bent by gravity is predicted both by Newtonian physics and relativity, but relativity predicts a larger deflection.

Special relativity is the limiting case of general relativity where all gravitational fields are weak. Alternatively, special relativity is the limiting case of general relativity when all reference frames are inertial (non-accelerating and without gravity).

==Lack of evidence for Relativity==
The Theory of relativity assumes that time is symmetric just as space is, but the biggest early promoter of relativity, Arthur Eddington, coined the term "[[arrow of time]]" admitting how time is ''not'' symmetric but is directional. The passage of time is tied to an increase in disorder, or [[entropy]]. The Theory of relativity cannot explain this, and implicitly denies it, specifically allowing for theoretical time travel (e.g., [[wormholes]]) and different rates of passage of time based on velocity and acceleration.

Claims that relativity was used to develop the [[Global Positioning System]] ([[GPS]]) are false. A 1996 article explains:

:"The Operational Control System (OCS) of the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein's general theory of relativity would seem to require - transformations to and from the individual space vehicles (SVs), the Monitor Stations (MSs), and the users on the surface of the rotating earth, and the geocentric Earth Centered Inertial System (ECI) in which the SV orbits are calculated. There is a very good reason for the omission: the effects of relativity, where they are different from the effects predicted by classical mechanics and electromagnetic theory, are too small to matter - less than one centimeter, for users on or near the earth."<ref>http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf</ref><ref>Some do claim that relativity is "vital" to GPS even though GPS developed independently of theoretical predictions and theoreticians disagree about how the relativistic effects for GPS should be calculated. ''See id. See also'' [http://www.rand.org/pubs/monograph_reports/MR614/MR614.appb.pdf]</ref>

This article, which was published in 1996, goes on to propose relativistic corrections that might be used to design more accurate GPS systems. Clocks on board GPS satellites require adjustments to their clock frequencies if they are to be synchronized with those on the surface of the Earth.

Tom Van Flandern, an astronomer hired to work on GPS in the late 1990s, concluded that "[t]he GPS programmers don't need relativity." He was quoted as saying that the GPS programmers "have basically blown off Einstein."<ref>http://archive.salon.com/people/feature/2000/07/06/einstein/index.html See also [http://www.metaresearch.org/solar%20system/gps/absolute-gps-1meter-3.ASP], where Van Flandern discusses how relativistic corrections might improve GPS accuracy.</ref> Asynchronization can be easily addressed through communications between the satellites and ground stations, so it is unclear why any theory would be needed for GPS. But other obscure physicists having no connection with GPS design claim that Van Flandern is wrong about GPS, and insist that relativity provides the best explanation for its timing adjustments.<ref>''Ibid.''</ref>

Some internet articles claim that GPS timing differences ''confirm'' the Theory of Relativity or its Lorentzian counterpart (which uses a preferred frame of reference). GPS clocks run slower in the weaker gravitation field of the satellites than on ground stations on Earth, with the effects predicted by general relativity far outweighing the effects predicted by special relativity. However, the articles claiming that the slower GPS satellite clocks confirm relativity do not address the effect, if any, of the weaker gravitational force under Newton's theory on the GPS satellite clocks, likely because in Newtonian Mechanics every clock in the universe keeps time at the same rate regardless of velocity, acceleration, or the presence or absence of force.

Currently, GPS satellites are synchronized to Coordinated Universal Time by radio signals from the ground; therefore, they cannot currently be used to test general relativity.<ref>[http://www.phys.lsu.edu/mog/mog9/node9.html "General Relativity in the Global Positioning System."] Neil Ashby, U. of Colorado</ref>

There are claims that the effects of relativity have been observed with the frequency shift of the signal being sent back to [[Earth]] several times as various spacecraft have dipped into the gravity wells around massive objects such as the [[sun]] (see image at right)<ref>[http://saturn.jpl.nasa.gov/news/press-releases-03/20031002-pr-a.cfm Saturn-Bound Spacecraft Tests Einstein's Theory]</ref> or Saturn<ref>[http://www.newscientist.com/article/mg12517102.600-science-encounter-with-saturn-confirms-relativity-theory.html Encounter with Saturn confirms relativity theory]</ref>. A satellite called [[Gravity Probe B]] was put in orbit about the Earth to examine the effects of frame dragging and geodetic warping of space<ref>[http://www.nasa.gov/mission_pages/gpb/index.html NASA Gravity Probe B mission page]</ref><ref>[http://einstein.stanford.edu/ Gravity Probe B project page]</ref>, but the results were inconclusive. Note, however, that Newtonian mechanics also predicts deflection of light by gravity, and in the initial theory of relativity it predicted the same amount of deflection, but only if we treat light as capable of being accelerated and decelerated like ordinary matter, which is contrary to all measurements and observations to date.<ref>http://www.mathpages.com/rr/s6-03/6-03.htm</ref> Adjustments to the theory of relativity resulted in a prediction of a greater deflection of light than that predicated by Newtonian mechanics, though it is debatable how much deflection Newtonian mechanics should predict.

None of the NASA spacecraft incorporates predictions of relativity into their own timing mechanisms, as Newtonian mechanics is adequate even for probes sent deep into space so long as they do not undergo accelerations near the speed of light or enter any massive gravity wells.<ref>There is no reported reliance on relativity by any space probe.</ref>

A decade of observation of the [[pulsar]] pair [[PSR 1913 16|PSR B1913+16]] detected a decline in its orbital period, which was attributed to a loss in energy by the system. It is impossible to measure the masses of the pulsars, their accelerations relative to the observers, or other fundamental parameters. Professors Joseph Taylor and Russell Hulse, who discovered the binary pulsar, found that physical values could be assigned to the pulsars to make the observed decline in orbital period consistent with the Theory of General Relativity, and for this they were awarded the 1993 [[Nobel Prize]] for Physics, which is the only award ever given by the Nobel committee for the Theory of Relativity.<ref>http://nobelprize.org/nobel_prizes/physics/laureates/1993/press.html</ref> In 2004, Professor Taylor utilized a correction to the derivative of the orbital period to fit subsequent data better to the theory. At most, assumptions can be made and altered to fit the data to the theory, rather than the data confirming the theory. This is the typical scientific method, wherein a hypothesis is created, tested, adjusted, and further tested.

The [[perihelion]] of Mercury's [[orbit]] [[precession|precesses]] at a measurable rate, but even after accounting for gravitational perturbations caused all other planets in the [[solar system]], Newton's theory (assuming a precise inverse-square relationship for distance) predicts a rate of precession that differs from the measured rate by approximately 43 [[arcsecond]]s per century. General relativity was developed in part to provide an estimate for this rate of precession that better matches observations.<ref>http://physics.ucr.edu/~wudka/Physics7/Notes_www/node98.html#SECTION032121000000000000000</ref> <ref> http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200.pdf</ref> <ref> http://farside.ph.utexas.edu/teaching/336k/lectures/node117.html</ref> Newton's theory can also explain this perihelion by factoring in the gravitational pull due to other planets or making tiny adjustments to parameters in the gravitational equation.

General relativity predicts twice as much bending in light as it passes near massive objects than Newton's theory might predict.<ref>http://www.mathpages.com/rr/s6-03/6-03.htm</ref> This phenomenon is known as [[gravitational lens|gravitational lensing]]. A large number of instances of gravitational lensing have been observed, and it is now a standard astronomical tool.<ref> http://imagine.gsfc.nasa.gov/docs/features/news/grav_lens.html</ref> <ref> http://astro.berkeley.edu/~jcohn/lens.html</ref> <ref> http://www.iam.ubc.ca/~newbury/lenses/glgallery.html</ref> Note, however, that the extent of bending of light predicted by Newton's theory is open to debate, and depends on assumptions about the nature of light for gravitational purposes.<ref>http://cosmictimes.gsfc.nasa.gov/1919/guide/gravity_bends_starlight.html</ref>

In 1972, scientists flew extremely accurate clocks ("atomic clocks") around the world in both directions on commercial airlines, and claimed to observe relativistic time dilation; the eastbound clock gained 273 ns and the westbound clock lost 59 ns, matching the predictions of general relativity to within experimental accuracy.<ref>[http://www.answers.com/topic/hafele-keating-experiment Hafele-Keating Experiment]</ref> However, the inventor of the atomic clock, Louis Essen, declared that the experiment was inaccurate.<ref>Louis Essen, Electron. Wireless World 94 (1988) 238.</ref> Dr A. G. Kelly examined the raw data from the experiment and declared it inconclusive.<ref>A. G. Kelly,Reliability of Relativistic Effect Tests on Airborne Clocks, Monograph No.3 Feb.1996, The Institution of Engineers of Ireland, ISBN 1-898012-22-9</ref> The Nobel Committee chose not to honor this experiment for the significance that was claimed.

Despite [[censorship]] of dissent about relativity, evidence contrary to the theory is discussed outside of [[liberal]] universities.<ref>http://scitizen.com/screens/blogPage/viewBlog/sw_viewBlog.php?idTheme=8&idContribution=922</ref>

==Fallacious Claims of Experimental Verification of Relativity==

The different effects predicted by special relativity, compared to classical formulations, are extremely tiny. Most relativistic effects are negligible at the speeds of ordinary phenomena observed by humans. The effects only become significant when the speeds involved are a significant fraction of the speed of light, which is <math>3 \times 10^8</math> meters per second—such speeds are called ''relativistic''. (However, it's worth noting that ordinary magnetism can be considered an effect of relativity, dictated by the need for electrostatic theory to be correct under relativity. The speed of light in fact appears in the formulas ([[Maxwell's Equations]]) governing electricity and magnetism, though these equations were developed long before relativity was proposed.)

Because the effects of relativity are so tiny, scientists have been devising sophisticated and sensitive tests ever since the theory was formulated in 1905.

*At the end of Einstein's original 1905 paper [http://www.fourmilab.ch/etexts/einstein/E_mc2/www/ "Does the Inertia of a Body Depend its Energy Content?"], he speculates on the possibility that the equation <math>E = m c^2</math>, which would normally be very hard to verify, could be verified with the extremely high energies of the newly-discovered phenomenon of radioactivity.<ref>This equation is not related to [[quantum mechanics]].</ref> In the 1910's, with the invention of the mass spectrometer, it became possible to measure masses of nuclei accurately. This led to the clearing up of the mystery of atomic masses not being exact integers,and strongly suggested the existence of a "mass defect" (or "packing fraction") consistent with the mass-energy equivalence. In the 1930's, experiments with known nuclear reactions showed a very accurate correlation between the masses of the nuclei involved and the energy released.

*Another prediction of special relativity was time dilation in rapidly moving objects. This effect was most famously verified in the anomalously slow decay of relativistic cosmic muons<ref>Some have suggested that other explanations are possible for this effect. We are trying to track this down.</ref>. Time dilation has since been verified many times, and is routinely taken into account in all high-energy nuclear physics experiments, as in Hadron collision experiments<ref>Experiments specifically designed to check dilation are rarely conducted any more.</ref>.

Predictions of general relativity turned out to be more obscure and difficult to test. The two most famous predictions were the bending of light in a gravitational field and the precession of the perihelia of orbiting planets.

*The first of these was famously tested during a total eclipse in 1919. That test was somewhat muddled by an incorrect initial calculation, by several people including Einstein himself, of what the effect would be, and some "cherry picking" of the data to be used <ref>''Einstein's Luck'', John Waller, Oxford University Press, ISBN 0-19-860719-9</ref>. The data selection could be considered "manipulation" or "fudging", by a person (Arthur Eddington) who had a personal stake in the outcome. His analysis techniques would not pass muster today.

:It should be noted that pre-relativistic (Newtonian) physics may also predict a bending, of half the observed value, depending on whether one uses the 17th century "corpuscular" formulation or the 19th century "wave" formulation.

:Nevertheless, it has been verified with ever-increasing precision in subsequent eclipses, and in the observations of quasar 3C273.

*The second "classical" test of general relativity was the advance of the perihelion of the orbit of Mercury. There are many complex effects contributing to this, including gravitational perturbations from other planets and the effect of the oblateness of the Sun. These are hard to calculate accurately, but, by 1900 it was known quite accurately that there was an "anomalous" precession, that is, a precession beyond all other known effects, of 43 arc seconds per century. This is a very tiny effect, but astronomical measurements were sufficiently accurate by that time to show it clearly.

:This created quite a problem—physicists by then were accustomed to having their theories check out very accurately. One proposal that was made, by Simon Newcomb and Asaph Hall, was that the exponent of the radius in the gravitational formula wasn't exactly 2. He showed that, by choosing an exponent of <math>2+\delta</math>, the precession, as a fraction of a full orbit per planet's year, is <math>\delta/2</math>. By setting <math>\delta</math> to .000000157, that is, an exponent of 2.000000157, Newcomb was able to get a precession of .000000078 revolutions per Mercury year, or 43 arcseconds per Earth year. The primary resistance to this approach came from mathematicians unable to do the integration without an exponent of precisely 2, and they insisted, incorrectly, that was impossible for the exponent to be slightly different from 2. Due to this desire for mathematical elegance rather than objective observation-based science, Newcomb's approach was not pursued.

:While Newcomb's theory, and general relativity, don't lead to closed-form solutions, both theories can be solved numerically to as much precision as one desires.

:Increasingly precise measurements of the precession demonstrate that it conflicts with General Relativity, despite claims of relativists for decades that it predicted the precession accurately in the amount of <math>3{}v^2/c^2</math> revolutions per planet's "year", where <math>v</math> is the planet's average orbital speed.<ref>That is a simple approximation, designed to relate the precession to the planet's speed relative to the speed of light. A more accurate approximation is <math>\frac{3GM}{c^2 a(1-e^2)}</math>, where a is the semi-major axis and e is the eccentricity.</ref> The conflict is greater than the margin of error, and many relativists avoid the discrepancy rather than address it.

:The following table show some approximate parameters for the planets. Note that Mercury has the smallest orbit, the fastest speed, and the highest gravitational pull. Precession of planets other than Mercury is extremely hard to measure, but measurements of the actual anomalous precessions are in good agreement with the last column of the table.<ref>http://www.mathpages.com/rr/s6-02/6-02.htm</ref>

{| class="wikitable"
|-
!Planet
!Period, seconds x 106
!Semimajor axis, meters x 109
!Speed, meters/second x 103
!Gravitational force, Newtons per kilogram
!Anomalous precession, arcseconds per (Earth) century, pure Newtonian mechanics
!Anomalous precession, Newtonian with exponent of 2.000000157
!Anomalous precession, general relativity
|-
|Mercury
|7.57
|58.9
|48
|.039
|0
|43
|43
|-
|Venus
|19.6
|108
|35
|.011
|0
|16.6
|9
|-
|Earth
|31.6
|150
|30
|.006
|0
|10.3
|4
|-
|Mars
|59.3
|227.9
|24
|.0025
|0
|5.5
|1.4
|-
|Jupiter
|374
|778.4
|13
|.0002
|0
|0.87
|0.07
|-
|Saturn
|929
|1426
|9.7
|.00006
|0
|0.35
|0.014
|-
|Uranus
|2651
|2870
|6.8
|.000016
|0
|0.12
|0.002
|-
|Neptune
|5200
|4498
|5.5
|.000007
|0
|0.063
|0.0008
|}

[[Image:Cassini-science-289.jpg|right|thumb|The Shapiro effect: A spacecraft signal dipping into a gravity well around the [[Sun]] is delayed slightly.]]
As the 20th century progressed, more tests of general relativity were proposed.

*One was the ''Shapiro effect'', involving time delay in radio signals passing through the gravity well of the Sun or a planet. Various spacecraft have confirmed this.

*Another is ''gravitational time dilation''. This is an effect separate from the time dilation of special relativity. It was tested by the Pound-Rebka experiment in 1959.

*Later in the 20th century, even more subtle phenomena were tested. One was the phenomenon of ''gravitational radiation'', or "gravity waves". These waves are incredibly difficult to observe, and have never been observed. But extremely dense binary pulsars radiate gravitational waves with sufficient energy loss that, even though we can't detect the waves from Earth, we can see the effect of the energy loss from the radiation. The extreme precision of the timing of pulses from pulsars makes it possible to observe their energy loss with great accuracy. Observations by Hulse and Taylor of the pulsar pair known as B1913+16 confirmed the energy loss consistent with the predicted radiation.

*Two other effects, ''geodetic precession'' (also known as "de Sitter precession"), and ''frame dragging'' (also known as the "Lense-Thirring effect") were tested by the "Gravity Probe B" satellite early in the 21st century<ref>http://prl.aps.org/accepted/L/ea070Y8dQ491d22a28828c95f660a57ac82e7d8c0</ref><ref>http://www.digitaljournal.com/article/306430</ref><ref>http://www.nap.edu/html/gpb/summary.html</ref><ref>http://www.sciencenews.org/view/generic/id/73870/title/Gravity_Probe_B_finally_pays_off_</ref><ref>http://www.nasa.gov/mission_pages/gpb/</ref><ref>http://einstein.stanford.edu/</ref><ref>http://spectrum.ieee.org/aerospace/space-flight/the-gravity-probe-b-bailout</ref><ref>http://www.engadget.com/2011/05/06/nasa-concludes-gravity-probe-b-space-time-experiment-proves-e/</ref>. The precision required to observe this was phenomenal. The results were announced on May 4, 2011.

{{clear}}

==Predicted consequences of the Theories==
===Time dilation===

[[Image:Light cone.png|right|thumb|Light-cone diagram]]
One important consequence of SR's postulates is that an observer in one reference frame will observe a clock in another frame to be "ticking" more slowly than in the observer's own frame. This can be proven mathematically using basic geometry, if the postulates are physically true without exception.

The length of an event <math>t</math>, as seen by a (relative) stationary observer observing an event is given by:

<math> t = \frac{t_{0}} {\sqrt{1 - \frac{v^{2}}{c^{2}}}}</math>

Where
:<math>t_0</math> is the "proper time" or the length of the event in the observed frame of reference.
:<math>v</math> is the relative velocity between the reference frames.
:<math>c</math> is the speed of light (3x108 ms-1).

Evidence for time dilation was discovered by studying [[muon decay]]. [[Muons]] are [[subatomic]] [[particles]] with a very short [[halflife]] (1.53 microseconds at rest) and a very fast speed (0.994c). By putting muon detectors at the top (D1) and bottom (D2) of a mountain with a separation of 1900m, scientists could measure accurately the proportion of muons reaching the second detector in comparison to the first. The proportion found was different to the proportion that was calculated without taking into account relativistic effects.

Using the equation for [[exponential decay]], they could use this proportion to calculate the time taken for the muons to decay, relative to the muon. Then, using the time dilation equation they could then work out the dilated time. The dilated time showed a good correlation with the time it took the muons to reach the second sensor, thereby supporting the existence of time dilation.

The time taken for a muon to travel from D1 to D2 as measured by a stationary observer is:

<math> t = \frac{s}{v} = \frac{1900}{0.994\times(3\times10^{8})} = 6.37\mu\textrm{s} </math>

The fraction of muons arriving at D2 in comparison to D1 was 0.732. (Given by <math> \frac{N}{N_0} = 0.732 </math>)

Since (from the equation for exponential decay) <math> \frac{N}{N_{0}} = e^{-\lambda t_{0}} </math> then

<math> t_{0} = \frac {ln(0.732)}{ln (0.2)} \times 1.53\times 10^{-6} = 0.689\mu\textrm{s}</math>

This gives the time for the proportion of decay to occur for an observer who is stationary, relative to the muon.

Putting this into the time dilation equation gives:

<math> t = \frac{t_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = \frac{0.689 \times{10^{-6}}}{\sqrt{1 - \frac{0.994^{2}}{1^{2}}}} = 6.3\times 10^{-6}\textrm{s}</math>

This is in good agreement with the value calculated above, thereby providing evidence to support time dilation.

====Time Dilation and Creation Science====

{{main|Starlight problem#Humphreys.27_model}}

Creation scientists such as physicists Dr. [[Russell Humphreys]] and Dr. [[John Hartnett]] have used relativistic time dilation to explain how the earth can be only 6,000 years old even though cosmological data (background radiation, supernovae, etc.) set a much older age for the universe.

===Length contraction===
When two inertial reference frames move past each other in a straight line with constant relative velocity, an observer in one reference frame would observe a metre rule in the other frame to be shorter.

The length, <math>l</math>, of an object as seen by a (relative) stationary observer is given by:

<math> l = l_{0} \sqrt{1- \frac{v^{2}}{c^{2}}}</math>

Where
:<math>l_0</math> is the "proper length" or the length of the object in the observed frame of reference.
:<math>v</math> is the relative velocity between the reference frames.
:<math>c</math> is the speed of light (3x108 ms-1).

===Mass increase===

For decades the theory of relativity taught that as a body moves with increasing velocity its [[mass]] also increases.<ref>For example, this was taught as recently as in the 1991 edition of the Encyclopedia Britannica.</ref>

Under this view, the mass, <math>m</math>, of an object as detected by a (relative) stationary observer is given by:

:<math> m = \frac{m_{0}} {\sqrt{1 - \frac{v^{2}}{c^{2}}}}</math>

Where
:<math>m_0</math> is the "rest mass" or the mass of the object when it is at rest.
:<math>v</math> is the relative velocity of the object.
:<math>c</math> is the speed of light (3x108 ms-1).

Since speed is relative, it follows that two observers in different inertial reference frames may disagree on the mass and kinetic energy of a body. Since all inertial reference frames are treated on an equal footing, it follows that mass and energy are interchangeable.

In recent years most physicists have shifted away from Einstein's original reliance on relativistic mass and his suggestion that mass increases{{Citation needed|date=January 2012}}. Instead, most physicists today teach that

:<math>F=\frac{d}{d\tau} p</math>

where <math>p</math> is the momentum defined by <math>\gamma m v</math>, <math>\gamma</math> is the standard Lorentz factor, and <math>\tau</math> is the proper time. Force F defined this way is a vector and thus can handle the directional aspect of the relativistic effects better than the concept of relativistic mass can.

The abandonment by physicists of the concept of relativistic mass, however, has the consequence of undermining the traditional claim under relativity that

:<math>m - m_0 = \frac{E}{c^2}</math>

also popularly known as

:<math>E = m c^2</math>

Now a concept of the 4-momentum <math>p</math> of a particle is taught, such that the square of the magnitude of <math>p</math> satisfies:

<math>||p||^2 = -p_x^2-p_y^2-p_z^2+E^2 = m_0^2c^4</math>

in any inertial reference frame. The magnitude of the 4-momentum, in any inertial frame, equals the rest mass <math>m_0</math> of the particle (in units where <math>c=1</math>).

== Paradoxes ==

The predictions of the theory of relativity throw up a number of apparent paradoxes and anomalies relating to the effects of time dilatation and length contraction. Whilst these paradoxes are consistent with the theory, they are contrary to everyday human experience and therefore can seem like impossibilities.

=== The Twin Paradox ===

The twin paradox is usually stated as a thought experiment involving two twins, one of whom is sent on a long journey in a spacecraft travelling at close to the speed of light, whilst the other remains on Earth. Time dilatation means that the travelling twin, on his return to Earth, is younger that the twin who has remained at home. However because neither twin is in a special position - each being in an inertial frame of reference - the reverse must also be true, and so the twin remaining on Earth must be younger. Hence each twin is younger than the other - a paradox.

The problem can be resolved in two ways. One is to examine the effects of General Relativity: to come back to Earth, the travelling twin must undergo acceleration in order to reverse his course, causing temporal effects which make him permanently the younger. Alternatively, it can be explained entirely using Special Relativity and noting that the twins are not in symmetrical situations: the one on earth has remained in a single inertial frame of reference, whilst the travelling twin has travelled in two<ref>http://mentock.home.mindspring.com/twins.htm</ref>.

=== The Ehrenfest Paradox ===

The Ehrenfest Paradox considers a rigid wheel or disc rotating a bout its axis at high speed (somewhat like a bicycle wheel spinning freely on its axle). The rim of the wheel travels at close to the speed of light and therefore undergoes length contraction, whereas the radius (the spokes, for the bicycle wheel) does not. Hence the circumference is no longer equal to 2<big><math>\pi</math></big>r, which is paradoxical.

The apparent paradox was finally resolved in 1975 by the Norwegian scientist [[Øyvind Grøn]]<ref>http://www.physicsforums.com/showthread.php?t=224955</ref>.

== Variable Speed of Light ==

The Theory of Relativity implies that physical constants like the speed of light have remained constant. But at least one study suggests that physical constants, and possibly even the speed of light, have changed as the universe has aged.<ref>James Glanz and Dennis Overbye, "Cosmic Laws Like Speed of Light Might Be Changing, a Study Finds," August 15, 2001.[http://www.nytimes.com/2001/08/15/science/15PHYS.html?ex=1185076800&en=d6467b6e3e346796&ei=5070]</ref>

"For the first time, scientists have experimentally demonstrated that sound pulses can travel at velocities faster than the speed of light, c. William Robertson's team from Middle Tennessee State University also showed that the group velocity of sound waves can become infinite, and even negative. ... Although such results may at first appear to violate special relativity (Einstein's law that no material object can exceed the speed of light), the actual significance of these experiments is a little different. These types of superluminal phenomena, Robertson et al. explain, violate neither causality nor special relativity, nor do they enable information to travel faster than c. In fact, theoretical work had predicted that the superluminal speed of the group velocity of sound waves should exist. 'The key to understanding this seeming paradox is that no wave energy exceeded the speed of light,' said Robertson."<ref>http://www.physorg.com/news88249076.html</ref>

"A team of researchers from the Ecole Polytechnique Fédérale de Lausanne (EPFL) has successfully demonstrated, for the first time, that it is possible to control the speed of light – both slowing it down and speeding it up – in an optical fiber, using off-the-shelf instrumentation in normal environmental conditions. Their results, to be published in the August 22 issue of Applied Physics Letters, could have implications that range from optical [[computing]] to the fiber-optic telecommunications industry."<ref>http://www.scienceblog.com/light.html</ref> Both slowing down and speeding up of light within a substance other than a vacuum is made possible, because the light travels through the material, and that material affects the speed of light, i.e. a photon hits an electron, which then exits and emits a slightly lower energy photon out in the direction that the original photon was traveling, thus maintaining conservation of momentum. No matter how transparent an object may appear, it radically impacts the speed of the light traveling through it, as demonstrated by the refractive production of a rainbow by a crystal, which Newton himself discovered.

This apparent change in speed can be explained, however, by noting that the constant c refers to the speed of light in a vaccuum, ie, when it is unimpeded. The speed of light when traveling through physical media is, in fact, variable.

"A pair of German physicists claim to have broken the speed of light - an achievement that would undermine our entire understanding of space and time. ... Dr Nimtz told New Scientist magazine: 'For the time being, this is the only violation of special relativity that I know of.'"<ref>http://www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2007/08/16/scispeed116.xml</ref>

==Pending research==

Today some physicists are working on hypothesizing how general relativity might have related to the other three forces of nature during the first fraction of a second of the [[Big Bang]]. Two of the more commonly studied attempts are [[string theory]] and [[loop quantum gravity]], but they have failed to produce any evidence that science mandates a science must have, and both typically take large amounts of work to even conform to what scientists believe. Critics increasingly point out that string theory and loop quantum gravity are largely untestable and unfalsifiable, and thus potentially unscientific under the principles of science advanced by [[Karl Popper]].<ref>See, for example, ''Not Even Wrong'', by Peter Woit</ref>

Relativity continues to be tested and some physics professors remain skeptical of the theory, such as University of Maryland physics professor Carroll Alley, who served as the principle physicist on the Apollo lunar project.<ref>http://science.nasa.gov/headlines/y2004/21jul_llr.htm</ref>

== Political aspects of relativity ==

Some [[liberal]] politicians have extrapolated the theory of relativity to metaphorically justify their own political agendas. For example, [[Democratic]] [[President of the United States of America|President]] [[Barack Obama]] helped publish an article by liberal law professor [[Laurence Tribe]] to apply the relativistic concept of "curvature of space" to promote a broad legal right to [[abortion]].<ref>Tribe, acknowledging help by Obama, argued that the [[Constitution]] should be interpreted to establish a right to federally funded [[abortion]] and that, more generally, ''[[Roe v. Wade]]'' does not go far enough. They insisted that a relativistic "curvature of space" could achieve this result by expanding application of the [[Constitution]] based on its impact on personal choice. "The ''[[Roe v. Wade]]'' opinion ignored the way in which laws regulating pregnant women may shape the entire pattern of relationships among men, women, and children. It conceptualized abortion not in terms of the intensely public question of the subordination of women to men through the exploitation of pregnancy, but in terms of the purportedly private question of how women might make intimately personal decisions about their bodies and their lives. That vision described a part of the truth, but only what might be called the Newtonian part. ... [A] change in the surrounding legal setting can constitute state action that most threatens the sphere of personal choice. And it is a 'curved space' perspective on how law operates that leads one to focus less on the visible lines of legal force and more on how those lines are bent and directed by the law's geometry." Laurence H. Tribe, The Curvature of Constitutional Space: What Lawyers Can Learn from Modern Physics, 103 Harv. L. Rev. 1, 16-17 (1989).</ref> As of June 2008, over 170 law review articles have cited this [[liberal]] application of the theory of relativity to legal arguments.<ref>Search conducted by [[User:Aschlafly]] in the LEXIS database "US Law Reviews and Journals, Combined," conducted June 1, 2008.</ref> Applications of the theory of relativity to change morality have also been common.<ref>"Mistakenly, in the minds of many, the theory of relativity became relativism."[http://www.worldnetdaily.com/news/article.asp?ARTICLE_ID=38081]</ref> Moreover, there is an unmistakable effort to censor or ostracize criticism of relativity.<ref>Although the [[Examples of Bias in Wikipedia|liberally biased Wikipedia]] contains lengthy criticisms of the subjects of many entries, and even though publications like ''The Economist'' recognize the lack of scientific satisfaction in the theory (see, e.g., "Weighing the Universe," The Economist (Jan. 25, 2007)), Wikipedia's entry on [http://en.wikipedia.org/wiki/Theory_of_Relativity Theory of Relativity] omits one word of criticism.</ref>

Physicist [[Robert Dicke]] of Princeton University was a prominent critic<ref>http://www.time.com/time/magazine/article/0,9171,943324,00.html</ref> of general relativity, and Dicke's alternative "has enjoyed a renaissance in connection with theories of higher dimensional space-time."<ref>"Initially a popular alternative to General Relativity, the Brans-Dicke theory lost favor as it became clear that omega must be very large-an artificial requirement in some views. Nevertheless, the theory has remained a paradigm for the introduction of scalar fields into gravitational theory, and as such has enjoyed a renaissance in connection with theories of higher dimensional space-time."[http://nedwww.ipac.caltech.edu/level5/Glossary/Essay_bekenstein.html] </ref> Despite being one of the most accomplished physicists in the 20th century, Dicke was repeatedly passed over for a [[Nobel Prize]], and in at least one case Dicke was insulted by the award being granted to others for contributions more properly credited to Dicke.

There has been little recognition by the Nobel Prize committee of either theory of relativity, and particularly scant recognition of the Theory of General Relativity.

===Government Support for Relativistic research===
The Theory of Relativity enjoys a disproportionate share of [[federal funding]] of physics research today.<ref>The Democratic Congress insisted on the $250 million LIGO project despite substantial criticism by scientists that it was wasting scarce research dollars. John Travis, "LIGO: a $ 250 million gamble; Laser Interferometer Gravitational-Wave Observatory; includes related article," ''Science'' p. 612 (Apr. 30, 1993). "Adding to the acrimony is LIGO's $ 250 million price tag, which some hold responsible for NSF's recent funding woes." ''Id.''</ref> In at least one case that research has been unsuccessful. The $365 million dollar [[LIGO]] project has failed to detect the gravity waves predicted by relativity.<ref>http://www.npr.org/programs/atc/features/2002/sept/gravitywaves/index.html</ref>

{{Relativity}}

== References ==
{{reflist|2}}

[[Category:Physics]]
[[Category:Science]]

==External Links ==
*[http://ia331314.us.archive.org/2/items/theeinsteintheor11335gut/11335-h/11335-h.htm The Einstein Theory of Relativity, by H.A. Lorentz.]
*[http://www.relativitycalculator.com Relativity Calculator - Learn Special Relativity Mathematics ] The mathematics of special relativity presented in as simple and comprehensive manner possible within philosophical and historical contexts.