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). Interestingly, the etymological meaning of the word "Devil" is synonymous with disorder.

Focusing on order and disorder as the defining principles for nature has this additional benefit: action at a distance is no problem. Field theories typically deny action at a distance (and predict never-found particles like gravitons). Miracles in the Bible that entail action at a distance, such as Jesus curing the centurion's son, are no problem under this approach.

Another advantage of this approach is that it casts new light on other miracles described in the Bible, such as walking on water or curing medical ailments. Those deeds might be understood simply as restoring greater order. Cancer cells are typically highly disordered and chaotic in replication; curing cancer might be understood as restoring order.

Most of the objections to Noah's Ark are based on modern notions of disorder; perfect order would facilitate that monumental task and overcome most, if not all, objections.

Teaching students about the fundamental roles of order and disorder has benefits. It would cause increased awareness about the need to affirmatively avoid accidents. It would illustrate the importance of mental "order" or clarity, and the need to recognize and defend against mental disorders.

No one has ever quantified order, and it is a difficult challenge. It helps to make some initial observations:

• precise locations are more ordered than imprecise ones; spatial proximity to other objects is more ordered than distant proximity
• fast, predictable motion is more ordered than slow or unpredictable motion
• sharp delineation is more ordered than diffusion
• transmission of information is more ordered if there is less error
• the human eye is more ordered than other human organs
• in thinking, faith is more ordered than mental instability or disease

Query: is it a mistake to quantify order based on position or motion? Are spatial considerations even relevant to relative amounts of ordering?

The challenge is to devise a metric for quantifying order, which can apply across all forms of ordering.

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
• transmission of highly complex information without error or loss

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 42.98 (±0.04) arc-seconds per century. At the time, that provided a fit to the observed data of a precession of 5600.0. 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 the margin of error. Professor Clifford Will, a leading advocate for General Relativity, omits this test entirely from his paper summarizing experimental evidence for relativity.

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.

Proximity of Objects

A close proximity of objects is more ordered than distant scattering.

Specifically, order could be quantified as roughly proportional to the inverse of the surface area of the smallest sphere that encloses the objects. A precise correlation to the inverse-square of distance would not be expected, particularly as distances vastly increase. State another way, order may not diminish as quickly as the surface area expands for large distances.

The theories of General Relativity and Newtonian gravity are contradicted by the "Pioneer anomaly." That anomaly or effect consists of the Pioneer slowing down more than expected as it left the solar system. "Dubbed the Pioneer Anomaly, the unexplained force appears to be acting against NASA’s identical Pioneer 10 and 11 probes, holding them back as they head away from the Sun." Of course, it begs the question to describe the cause as an "unknown force," as the relativity and Newtonian models may be fundamentally incorrect views of nature.

Relativity and Newtonian gravity have also failed to explain anomalies in spacecraft that have flown by Earth ("flybys").

The disorder (entropy) of 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.

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:

where S is entropy, Q is heat or energy, and T is temperature.