Theory of relativity

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Relativity refers to two closely-related theories in physics, and to a principle which led to the first theory. 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. At speeds approaching zero, Special Relativity is identical to Newton's Laws of Motion. Special Relativity was developed by Hendrik Lorentz, Henri Poincaré, and Albert Einstein.

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.[1] A dramatic but later discredited claim by Sir Arthur Eddington of experimental proof of General Relativity in 1919 made Einstein a household name.

Special Relativity

Special Relativity is usually explained in terms of two assumptions (postulates):

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

In layman's terms, these two assumptions can be restated as:

  1. It is impossible ever to transmit information faster than the speed of light.Cite error: Closing </ref> missing for <ref> tag

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).

Time dilation

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.

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 proving the theory.

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.

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

We also see that as a body moves with increasing velocity its mass also increases.

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.

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. But mass is not a vector, and the notion of the mass of an object having different values depending on the direction of an applied force is unacceptable. Accordingly, relativistic mass and the suggestion that mass increases is avoided by leading physicists today. Instead, they prefer to speak in terms of F=<math>\gamma</math>ma where <math>\gamma</math> varies with velocity as mass m remains constant. Force F is a vector.

Evidence for Relativity

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.[2]

In 1972, scientists flew extremely accurate clocks around the world in both directions on commercial airlines, and were directly able to observe the relativistic "twin paradox" the eastbound clock gained 273 ns and the westbound clock lost 59 ns, matching the predictions of general relativity to within experimental accuracy [3] [4] [5]

Predictions of relativity have not historically been used to make the Global Positioning System (GPS) function properly, which are synchronized simply by communicating with stations on earth. [6].

A decade of observation of the pulsar pair 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 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.[7] In 2004, Professor Taylor utilized a correction to the derivative of the orbital period to fit the data better to the theory.

Ostensible Paradoxes

"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."[8]

"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."[9]

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 been complete failures. 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.[10].

Government Support for Relativistic research

The Theory of Relativity enjoys a disproportionate share of federal funding of physics research today,[11]. 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.[12]

Philosophical Impact of Relativity

There is a correlation between enthusiasm for the theory of relativity and political views, and there is an unmistakable effort to censor or ostracize criticism of relativity.[13] Physicist Robert Dicke of Princeton University was a prominent critic[14] of the theory of relativity and that may have hurt him professionally, even though his theory "has enjoyed a renaissance in connection with theories of higher dimensional space-time."[15] Despite being one of the most accomplished physicists in the 20th century, Dicke was never awarded a Nobel Prize just as other outspoken critics of scientific theories were passed over in granting the Nobel Prize to less-accompished colleagues.[16]

References

  1. ↑ "[T]he German mathematician David Hilbert submitted an article containing the correct field equations for general relativity five days before Einstein."Nobel Prize historical account
  2. ↑ http://nobelprize.org/
  3. ↑ Hafele-Keating Experiment [1]
  4. ↑ as described in What is the experimental basis of Special Relativity?, a personal web page, which cites Haefele and Keating (1972), Science Vol. 177 pp 166-170 as its source
  5. ↑ Sullivan, Walter (1972), "Relativity Theory Awaits Affirmation", September 23, 1972, p. 61. Note: Article refers to a different experiment, which Sullivan discusses, saying that if successful it would be "the second time within a year" that relativity had been confirmed, then proceeds to discuss Hafele[sic] and Keating's experiment as the first.
  6. ↑ Some do claim that relativity is "vital" to GPS even though GPS developed independently of theoretical preductions. See [2]
  7. ↑ http://nobelprize.org/nobel_prizes/physics/laureates/1993/press.html
  8. ↑ http://www.physorg.com/news88249076.html
  9. ↑ http://www.scienceblog.com/light.html
  10. ↑ See, for example, Not Even Wrong, by Peter Woit
  11. ↑ 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.
  12. ↑ http://www.npr.org/programs/atc/features/2002/sept/gravitywaves/index.html
  13. ↑ Although the 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 Theory of Relativity omits one word of criticism.
  14. ↑ http://www.time.com/time/magazine/article/0,9171,943324,00.html
  15. ↑ "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."[3]
  16. ↑ Other examples of scientists denied Nobel Prizes due to their criticisms of scientific theories are Sir Fred Hoyle and Dr. Raymond Damadian

External Links

The Einstein Theory of Relativity, by H.A. Lorentz.
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