Essay:Quantifying Order

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In the beginning was perfect order, and this perfection was with God, and this perfection was God.

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This is a tantalizing translation of John 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.

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) 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 43 arc-seconds per century. Subsequently, however, more accurate measurements with more sophisticated technology have determined this precession to be 55 arc-seconds per century, nearly 30% off the number provided by relativity. Other sources of the deviation have been suggested by physicists attempting to explain the gap.

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 entropy a hypothetical high-density black hole is controversial.

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), so it typically is not perfectly ordered.