Time and Entropy
(revised April 2006)
John A. Gowan
http://www.people.cornell.edu/pages/jag8/index.html
This paper is part of a set of four, listed below, examining various relationships between the four conservation principles of the Tetrahedron Model of Natural Law (these small papers are not intended to stand alone):
The intrinsic motions of light and time are metric equivalents; they are the primordial entropy drives of free and bound energy (See: "The Time Train"; see also: "The Paradox of the Traveling Twin".)
Entropy
History is an alternative conservation/entropy domain which allows the Universe to retain "working energy" by storing it in matter, and get old rather than large. Temporal aging and deterioration replaces spatial expansion and cooling - the expansion and cooling of space and the expansion, aging, decay, and dilution of history are analogous entropy drives (as gauged by "velocity c" and "velocity T"). As a surrogate dimension, the role of time is analogous to that of the alternative charge carriers of the "particle metric", the leptons. (Leptons replace the antiparticle partners of the quarks as substitute charge carriers, and thereby allow matter to manifest rather than simply annihilate with its usual antimatter charge carriers.) Furthermore, the role of entropy is analogous to the role of charge, in that entropy conservation allows the conversion of free energy to work, and charge conservation allows the conversion of free energy to information. Finally, just as matter is one-half of light's particle form (one-half of a particle-antiparticle pair), so one-way time is one-half of light's dimensional form (one-half of a two-way spatial dimension).
Gravitation converts positive spatial entropy into positive temporal entropy, and vice versa. The magnitude of G is determined by the energetic difference between the drive of symmetric spatial entropy (S) (the intrinsic motion of light as gauged by "velocity c"), and the drive of asymmetric temporal entropy (T) (the intrinsic motion of time as gauged by "velocity T"): S - T = -G. Gravitational energy, creating time, is siphoned from the expansion of space, which slows in consequence. Thus it is the cosmic expansion of space, driven by the intrinsic motion of light, which ultimately funds the creation of matter's time dimension. Since entropy (the 2nd law of thermodynamics), creates dimensional conservation domains and prevents the "misuse and abuse" of energy, it is an essential adjunct to the 1st law of thermodynamics (the conservation of energy), and therefore must also be conserved (in transformations between free and bound energy), which is one of the several conservation roles of gravitation. The gravitational conversion of space and the spatial entropy drive (S) to time and matter's temporal entropy drive (T), can be represented symbolically by a "concept equation" as:
-Gm(S) = (T)m
-Gm(S) - (T)m = 0
Matter requires a time dimension to establish its "causal matrix", provide an entropy drive, and to balance its energy accounts, since matter's energy depends upon its relative velocity, which can vary from zero to (nearly) c. Light does not similarly need a time dimension because light is "non-local", acausal, and moves only with absolute (non-relative) velocity c. The energy of light varies with its frequency, not with its constant velocity. Entropy is the "interest" paid to energy conservation for the use of energy; energy conservation allows the use of energy only through the entropy pathway.
Entropy allows energy to be used even while it is conserved. The accommodation is that energy may be used provided entropy increases while total energy remains constant. It is this increase in entropy which allows energy to be used at all, without violating the 1st law (energy conservation). Without actually using up or destroying energy in the process, energy is degraded (its capacity for work is reduced) but never destroyed; rather its entropy increases. The increase in entropy insures that the same energy cannot be used twice to produce the same net work, avoiding the perpetual motion machine and any violation of energy conservation (no machine can create net energy). Thermal entropy is typically expressed as the production and loss of heat during work; "heat" (randomized molecular motion) is a universal entropic stage in energy transformations. (See: "Heat as the Currency of "Work" Transformations".) By the necessity for entropy, in principle no work can ever be accomplished with 100% efficiency; thermal entropy is often defined as the energy in an isolated system which in principle cannot be transformed to work. (See: "Spatial vs Temporal Entropy".)
The primordial or "pure" forms of entropy create dimensional conservation domains, space and history, via the intrinsic motions of light (gauged by "velocity c") and time (gauged by "velocity T"), while gravity's intrinsic motion (gauged by "velocity G") creates spacetime - a compound dimensional conservation domain in which both free and bound energy can interact, be used and transformed, and yet find conservation through the mechanism of entropy. Gravity joins these two conservation domains of electromagnetic energy into a metrically equilibrated joint domain, spacetime. For reasons of energy conservation, bound energy (matter) requires an entropy drive - an intrinsic dimensional motion (time) - to create its spacetime conservation domain, just as free energy (light) requires an entropy drive (intrinsic motion c), to create its spatial conservation domain. Unlike light, "local" matter requires time to establish its "causal matrix", which is an embedded requirement of energy conservation in the case of bound energy. "Non-local" light, however, is both atemporal and acausal. The creation of matter's entropy drive (intrinsic motion T) from light's entropy drive (intrinsic motion c) is the role of gravity and its "location" charge, whose active principle is time itself. Light is spatial: non-local, atemporal, and acausal. Matter is historic: local, temporal, and causal.
Gravity and Temporal Entropy
Gravity is the entropy debt of light as well as the symmetry debt of light, the only one of the 4 forces arising from 2 kinds of debts and hence involving a doubly complex charge ("location" charge). The active principle of the "location" charge is time, whose entropic character is its intrinsic dimensional motion, but whose asymmetric (one-way) character identifies the 4-dimensional locus of bound energy. Both debts are satisfied simultaneously by the gravitational conversion of matter to light (as in stars and Hawking's "quantum radiance" of black holes). (See: "The Double Conservation Role of Gravitation".)
Gravity is produced by every form of bound energy, but not by free energy. "Non-local" energy which moves freely through space with intrinsic motion c (light) does not produce a gravitational field; bound energy which can be localized in space around a center of mass and therefore has a time dimension, will produce a gravitational field. Electromagnetic energy moves either with intrinsic (entropic) motion c or T; if with T, then it will also have intrinsic motion G, because G creates T; in fact, they induce each other. (See: "Entropy, Gravitation, and Thermodynamics".)
"Non-local" energy forms (with intrinsic motion c) cannot produce gravitational fields because they cannot center them; an uncentered gravitational field violates energy conservation. Einstein's "zero Interval" statement for light is a symmetry condition of "non-locality" for free energy and the absence of both time and gravitational fields. If light did produce a gravitational field, the Universe would never have escaped a black hole at its birth; furthermore, if all forms of energy produce gravity, then there is nothing to distinguish a role for gravitation. So long as the scientific "establishment" continues to believe that free energy produces a gravitational field (for the insufficient reason that E = mcc), so long will it fail to achieve the unification of gravity with the other forces.
Only when a photon is absorbed by matter does it become bound energy with a positive "Interval", and only then does it begin to produce a gravitational field - converting its intrinsic spatial motion into intrinsic temporal motion, creating a temporal entropy and a time dimension to service the energy conservation requirements of its new (bound and massive) inertial status. Although Einstein held that "gravity gravitates" (the "self energy" of a gravitational field itself produces more gravity and contributes to the total gravitational force), light does not similarly produce a metric stress or warpage of the spacetime metric - instead, light creates the metric, and gauges and establishes its symmetry. (See: "Does Light Produce a Gravitational Field?")
From the perspective of entropy, we gain a simplified view of gravitation. All forms of energy require entropy for reasons of energy conservation, including causality in the case of bound energy, as noted above. The "infinite" velocities c and T are the actual "pure" or "primordial" mechanisms of entropy, insuring that radiant energy and opportunity escape in space and/or time with irretrievable velocity; these "infinite" velocities also seal and protect their domains against violations of causality and energy conservation via fast "space ships" or "time machines". Similarly, gravity seals the borders of its spacetime domain (against "wormholes") through the creation of the "event horizon" and "central singularity" of black holes. Spacetime is a wholly protected dimensional conservation domain for both free and bound forms of electromagnetic energy, created by the intrinsic motions of entropy, as gauged by c, T, and G. (See: "The Energy Tetrahedron Diagram".)
With these principles in mind, we readily see that when free energy is converted into bound energy, an entropy drive will have to be created for that bound energy. This is (one of) the conservation roles of gravitation. When light or free energy is converted into matter or bound energy, three major attributes of light must be conserved: 1) light's raw energy, conserved as the mass and momentum of matter (1st law of thermodynamics); 2) light's entropy drive (intrinsic motion c), conserved as matter's entropy drive (intrinsic motion T), created by the gravitational field of matter converting space into time (2nd law of thermodynamics - establishing also matter's causal relations); 3) light's symmetry, conserved as the charges and spin of matter and the inertial and gravitational forces of the metric (Noether's Theorem).
Time is implicit in free energy as "frequency", and is the actual driver of light's intrinsic motion: symmetric space ("wavelength") flees asymmetric time ("frequency"), which is an embedded characteristic of light's own nature (frequency x wavelength = c). Time is the implicit, hidden, internal motivator of light's perpetual, self-motivated, "intrinsic" motion, velocity c. "Velocity c" is actually a symmetry condition of free energy, which, in obedience to Noether's Theorem, forever moves in such a way as to prevent the explicit appearance of time, with its inevitable companions, mass, charge, and gravitation, the asymmetric "Gang of Four". (See: "The Conversion of Space to Time".)
Gravity and Quantum Mechanics
The quantum-mechanical collapse of an electromagnetic wave, which initiates the conversion of free energy to bound energy, switches the position of the temporal component of the wave from an implicit to an explicit state, and conversely for the wave's spatial component - like flipping a coin (see the "Gravity Diagram 2"). This is the initial quantum-mechanical "setting" of the time component of gravity's "location" charge, and it positively identifies in four dimensions the spatial position of the center of mass of the immobile lump of matter, while gauging the magnitude (-Gm) of the gravitational response. Matter (mass) is asymmetrically (locally) distributed in space, having no intrinsic spatial motion and hence no spatial distribution; therefore, matter breaks the non-local spatial distributional symmetry of the energy of the light which created it. This is the distributional aspect of gravity's symmetry debt, a consequence of light's "non-local" character. Gravity's symmetry and entropy debts will be simultaneously repaid through the gravitational transformation of matter into light, as in the stars, and Hawking's "quantum radiance" of black holes. See: "The Double Conservation Role of Gravitation".
The temporal residue or time charge which identifies the local spatial position of matter is unusual in that it is an "entropic" charge, that is, a charge with intrinsic dimensional motion. In the case of time, this is also one-way motion (to protect causality), and at right angles to all three spatial dimensions. Time therefore immediately exits space as it is formed, but because time and space are linked, the intrinsic motion of time drags space after it, collapsing the 3 dimensions of space symmetrically (because time is linked symmetrically to all three) into the zero-dimensional beginning point of the one-dimensional time line, localized at the center of gravitational mass (See: "New Gravity Diagram") and "A Description of Gravitation".
The constant motion of the entropic time charge causes the accelerated, symmetric collapse of space into the center of any mass; this spatial flow we recognize as a gravitational field. This accelerated spatial motion is the metric "warpage" or "curvature" of the gravitational field. At the center of mass, the collapsing spatial dimensions annihilate each other, always leaving a new temporal residue (which being one-way, cannot self-annihilate). The new temporal residue, the metric equivalent of the annihilated mass, moves on down the time line, dragging more space after it, producing in its turn a new and metrically equivalent temporal residue, etc., forever. Gravity and time induce each other: gravity is the spatial consequence of (and evidence for) time's intrinsic motion, while the gravitational annihilation of space continuously produces a metrically equivalent temporal residue - the active principle of the gravitational "location" charge.
Hence while the quantum-mechanical "switch" or "flip" of the implicit temporal component of the electromagnetic wave to its explicit state initiates, "sets", and gauges the gravitational field, the field is maintained by the subsequent intrinsic motion of the time dimension so established, which drags space after it to destruction at the center of mass, where a new temporal residue, the metric equivalent of the annihilated space and an exact copy of the original, is extracted to repeat forever the self-feeding cycle. Two different processes are thus involved in the 1) initiation and 2) maintenance of a gravitational field, and they unite the quantum-mechanical and relativistic features of gravitation in a single charge, the entropic character of time. Time is the active principle of gravity's "location" charge.
We can relate the microscopic quantum-mechanical process to gravity's entropy debt (time), and the macroscopic annihilation of space to gravity's symmetry debt (location), but such a separation of function is academic, as it is impossible to disentangle the entropy and symmetry components of velocity c, or the gravitational response to the broken non-local symmetry of light when free energy is transformed to bound energy. Gravity must conserve both aspects of c if it conserves either one. Inertial force, gravitation, and entropy all fall under the sway of Noether's symmetry conservation theorem, due to the double role of c as the symmetry gauge and entropy drive of free energy and the metric of spacetime, which the intrinsic motion of light creates. Gravitation is the double conservation response to the loss of light's entropy drive, the intrinsic motion of light, and to the breaking of the non-local distributional symmetry of light's energy in space by local, immobile mass. The active principle of gravity's "location" charge is time: gravity is the spatial consequence of the intrinsic motion of time. Time is the implicit entropy drive of light, conserved explicitly in matter. Thermodynamic entropy, metric symmetry, and the principle of causality are all bound together in matter's time charge, and all provide a rationale for gravitation. All these debts are paid by the gravitational conversion of bound to free energy in stars, and via Hawking's "quantum radiance" of black holes.
Implicit vs Explicit Time
In its implicit form, time, like the proverbial "bur under the saddle", drives the intrinsic motion of light: the symmetric "wavelength" or spatial component of the electromagnetic wave "flees" the asymmetric "frequency" or temporal component which is an embedded potential of its own nature (frequency multiplied by wavelength = c). Entropy, in the service of energy and symmetry conservation, is the ultimate cause of light's intrinsic motion. In its explicit form, time creates gravitation, spacetime, and the historic conservation domain of information and matter's causal matrix (historic spacetime). Time is therefore the universal driver of the action and entropy of the Universe and its energy forms, in its implicit form causing the expansion of space, in its explicit form causing the contraction of space and the compensatory expansion of history. The difference between the positive entropy of spatial expansion and the negative entropy of gravitational contraction is thus the simple difference between the implicit or explicit state of time - the "heads" or "tails" of the electromagnetic entropy "coin". Similarly, the magnitude of G is gauged by the energy difference between the drive of symmetric spatial (S) entropy (the intrinsic motion of light, gauged by velocity c) and the drive of asymmetric temporal (T) entropy (the intrinsic motion of matter's time dimension, gauged by velocity T) - in other words, by the energetic difference between implicit and explicit time: S - T = -G.
The gravitational annihilation of space causes the deceleration of the cosmic expansion, since spatial entropy is being transferred to temporal entropy. Hence the deceleration of the spatial expansion of the cosmos supplies the gravitational energy to produce matter's time dimension. The conversion of spatial expansion to historic expansion, that is, the transformation of spatial to temporal entropy, occurs locally and immediately with the "flip" of the entropy "coin" from implicit to explicit time. The universal expansion decelerates because space is being annihilated rather than created (see: "The Conversion of Space to Time"). As we saw earlier, the concept of the gravitational conversion of space and the drive of spatial entropy (S) to time and the drive of temporal entropy (T), can be symbolically represented in a "concept equation" as:
-Gm(S) = (T)m
-Gm(S) - (T)m = 0
Finally, due to the operation of Noether's theorem, we note that gravity, like all other charges, seeks to release as much free energy from bound energy as possible, restoring light's non-local distributional symmetry. This is the symmetry debt aspect of gravity, which drives the gravitational conversion of mass to light in stars. In the case of black holes, Hawking's "quantum radiance" carries the process to completion, conserving not only the symmetry of light, but even the symmetry of light's entropy.
Black holes are the observational evidence of the gravitational conversion of space and spatial entropy to time and temporal entropy. The "event horizon" of a black hole is a temporal entropy surface (the Bekenstein-Hawking theorem). (See: "Entropy, Gravitation, and Thermodynamics".)
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