The Connection between Entropy and Symmetry (as Illustrated in
(revised May, 2011)
John A. Gowan
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This paper is part of a set of five, listed below, examining various relationships between the four conservation principles of the Tetrahedron Model of Natural Law (these short papers are not intended to stand alone):
The Connection Between Entropy and Symmetry
The line connecting Entropy and Symmetry (see diagram) includes gravity and the spacetime metric. This line also indicates there is at least functionally a connection between charge conservation and the dimensional conservation domains of spacetime. The most fundamental expression of the connection between Entropy and Symmetry is "velocity c", the electromagnetic constant, which gauges both the spatial entropy drive (the intrinsic motion of light) and the "non-local" metric and distributional symmetry of light. This connection is also demonstrated in that "velocity c" gauges the flight of the photon, the field vector of electric charge; the Dirac-Heisenberg domain of virtual particles; and the energetic equivalency between free and bound forms of electromagnetic energy: E = mcc. On the one hand, the intrinsic motion of light suppresses asymmetric time and maintains the symmetric status of the spatial metric and its energy content (inertial, non-local, and distributional symmetry), suppressing also "rogue" or sourceless gravitational fields and the capricious manifestation of virtual particles. On the other hand, the intrinsic motion of light causes the expansion and cooling of the Cosmos, reducing its capacity to perform "work". A related connection is that entropy and charge conservation play analogous roles in the unfolding of the manifest, "real" world from "virtual" reality. Entropy allows the transformation of free energy to work, and charge conservation allows the transformation of free energy to information. Together with weak force symmetry-breaking and the conservation of light's raw energy as mass and momentum, this "trinity" of conservation effects brings the virtual world of matter-antimatter particle pairs into the "real" (temporal) world of matter-only atoms. Finally, it is the existence of the time dimension which makes charge conservation a practical, functional option - producing a past, present, and future in which symmetry debts (charges) can be contracted, maintained, and eventually paid. Negentropic gravitational energy is the "interest" paid by the Cosmos on bound energy's symmetry debt, energy deducted from light's expansive entropy drive, creating instead the time dimension, entropy drive, and expanding (aging) historic conservation domain of matter's causal information network or "matrix" (historic spacetime).
All forms of energy must have an entropy drive: Entropy (the 2nd law of thermodynamics) is required to protect the 1st law of thermodynamics, the Conservation of Energy. Primordial or "pure" entropy is an embedded characteristic of energy which creates a dimensional conservation domain for its energy type: space for free energy (via the intrinsic motion of light), history for bound energy (matter's "causal matrix" - via the intrinsic motion of time), and historic spacetime for the mixture of free and bound energy (via the gravitational conversion of space to time). The function of the pure entropy forms is produced by an entropy "drive", or intrinsic motion: intrinsic motion "c" for light, creating space; intrinsic motion "T" for time, creating history; and intrinsic motion "G" (gravitation) as the conversion force between the two primordial entropy drives and domains, creating spacetime, the joint dimensional conservation domain of free and bound energy. The magnitude of G is determined by the small energy difference between the symmetric spatial entropy drive of light (S) (the intrinsic motion of light as gauged by "velocity c"), and the asymmetric historical entropy drive of matter (T) (the intrinsic motion of time as gauged by "velocity T"):
S - T = -G.
(See: "Spatial vs Temporal Entropy".)
When free energy (light) is converted to bound energy (matter, mass, momentum), the positive entropy drive of free energy (intrinsic motion c, the "velocity of light") is transferred to the positive entropy drive of bound energy (intrinsic motion T, the "velocity of time"). ("T" is also gauged by "velocity c" as the duration required by light to traverse a given distance.) Entropy is conserved and does not simply disappear when light or free energy is converted to matter or bound energy. The entropy of an isolated system always increases, whether in its temporal or spatial form and domain, or the mixture of both. When light is transformed to bound energy, light's symmetric energy state is conserved as the charges and spin of matter, and as the gravitational forces of the spatial metric; light's raw energy is conserved as the mass and momentum of matter; light's entropy drive is conserved as the intrinsic motion of matter's time dimension and the gravitational field of matter (gravity is both a symmetry and an entropy debt of light). Light's positive spatial entropy drive (light's intrinsic motion) - causing the expansion and cooling of space - reappears as matter's positive historical entropy drive (time's intrinsic motion) - causing the aging and decay of history (historic spacetime). The conversion is effected by the gravitational annihilation of space, revealing a metrically equivalent temporal residue. (See: "The Conversion of Space to Time".)
The intrinsic motion of light, which is light's primordial entropy drive (creating light's conservation domain, space, and causing the expansion and cooling of space), is conserved and transferred to matter as the intrinsic motion of time, which is bound energy's primordial entropy drive (creating the conservation domain of information and matter's "causal matrix" - history - and causing the aging and decay of historic spacetime as well as the aging and decay of matter). Gravitation is the force which converts either form of entropy drive and domain to the other, converting some of light's dimensional conservation domain, space, into historic spacetime, the dimensional conservation domain of information and matter's causal matrix. Spacetime is a combined conservation/entropy domain where both light and matter can coexist, interact, and find conservation. Thus the function of entropy (in its primordial forms), whether positive or negative, spatial, temporal, or gravitational, is to create a dimensional conservation domain for energy, whether free or bound. This is the connection between the first and second laws of thermodynamics. (See: "Entropy, Gravitation, and Thermodynamics").
Gravity creates time by annihilating space. By gravitationally linking to space (via time), matter retains an entropic connection to space, which light lost when it converted to bound energy and ceased its intrinsic motion. Hence gravity is the conserved entropic connection between bound energy and spatial dimensionality. "Velocity T" and history substitute for "velocity c" and space as matter's entropic connection to dimensionality. The intrinsic motion of matter's time dimension becomes the entropy drive for bound energy, and is the metric and functional equivalent of light's intrinsic motion in space ("time flies"). Matter requires a time dimension for many reasons, among them to serve as an entropy drive, to conserve causality, and to balance its raw energy accounts, since matter's energy content varies with its velocity and relative motion (momentum, kinetic energy). Light does not similarly require time, since unlike matter, light has but a single, invariant, and absolute (non-relative) velocity; light's energy varies instead with its frequency. (See: "The Time Train".)
Symmetry-breaking (via the weak force during the "Big Bang") changes light into the charge, mass, and momentum of matter, space into historic spacetime, and the drive of spatial entropy (gauged as "velocity c") into the drive of temporal entropy (gauged as "velocity T"). Matter is an asymmetric form of light, 1/2 of light's particle form (being derived from the broken symmetry of particle-antiparticle pairs), and one-way time is similarly an asymmetric form of space, 1/2 of a spatial dimension (see quote below from the book "Trance, Art, Creativity").
"Analysis of this equation [Einstein's Interval] provides us with the proportion that time is to space as "i" (the square root of -1) is to 1. Now "i" multiplied by itself is negative 1, so that in a metaphoric sense we can say that the time dimension is "half" a space dimension. Curiously one finds this out intuitively. We have full intuition of the three spatial dimensions, but we cannot intuit the fourth dimension, so we experience it as "time." Furthermore this experience is not full; it is partial, for we are on a one way street indicated by "time's arrow" which allows us always to experience duration as getting later and later, but never the opposite." (Prof. John Curtis Gowan Sr. in "Trance, Art, Creativity" page 253-4)
(For more on this topic, see: "Entropy, Gravitation, and Thermodynamics" and "A Description of Gravitation".)