Essay:Quantifying Order
| “ | In the beginning was perfect order, and this perfection was with God, and this perfection was God. | ” |
This is a tantalizing translation of John 1:1,[1] and it suggests that insight into the universe may be best understood by examining order, and its converse of disorder (entropy). A starting point is this: quantifying order.
No one has ever quantified order, and it is difficult challenge. It helps to make some initial observations:
- precise locations are more ordered than imprecise ones.
- fast, predictable motion is more ordered than slow or unpredictable motion
- sharp delineation is more ordered than diffusion
There are several examples of highly ordered systems from diverse corners of physics:
- a wave function collapsed by observation
- a high concentration of mass
- a tightly wound orbit, such as Mercury's
- the transmission of light
- the transmission of electromagnetic waves
A perpetual ordered system, or a perpetual motion machine, is thought to be impossible by virtue of the Second Law of Thermodynamics.
Contents
Tightly Wound Orbit
The orbit of Mercury provides nature's closest example, both conceptually and spatially, of a highly ordered, nearly perpetual motion machine. The orbit will not last forever, and it is enlightening to observe and understand signs of degradation in the orbit.
The advance (or precession[2]) of the perihelion of Mercury is observed but not predicted by an elementary application of Newtonian mechanics to Mercury and the sun alone. This provided one of the great mysteries of physics around the turn of the century. A planet's "perihelion" is the point in its path of orbit that comes closest to the sun. For Mercury, that point of closest proximity is shifting with each revolution.
The theory of relativity developed to explain the then-observed shift in Mercury's perihelion of 42.98 (±0.04) arc-seconds per century. At the time, that provided a fit to the observed data. Subsequently, however, more accurate measurements with more sophisticated technology have determined a precise value of this precession (5599.7 arc-seconds per century), and the number provided by relativity no longer fits the data within a margin of error. Professor Clifford Will, a leading advocate for General Relativity, omits this test entirely from his paper summarizing experimental evidence for relativity.[3]
Wave Functions
The Heisenberg Uncertainty Principle describes an inherent disorder in subatomic particles such as electrons. Their position is uncertain until observed, for example. The act of observing brings a type of order to the system which does not otherwise exist.
This disorder may be what underlies an interpretation of the Second Law of Thermodynamics, or the impossibility perpetual motion machines. The disorder is not well-quantified.
High Concentration of Mass
The disorder (entropy) of a hypothetical high-density black hole is controversial.[4]
Transmission of Light
The transmission of light is extremely fast with predictable motion, and thus is highly ordered. But even light has diffusion (except in a vacuum[5]), so it typically is not perfectly ordered.[6]
Transmission of Electromagnetic Waves
Entropy and Thermodynamics
The Second Law of Thermodynamics holds that entropy never decreases. If it remains constant during a process, then the process can be reversed without a loss in energy. More typically, such as the popping of a balloon, entropy increases and the process is not reversible.
Physicists provide a rudimentary equation for infinitesimal entropy as follows:
