Parameters of Entropy and Gravity
(revised April, 2008)
John A. Gowan
The magnitude of G (the universal gravitational constant) is determined by the small energy difference between the symmetric spatial entropy drive (S) of light (the intrinsic motion of light, as gauged by "velocity c"), and the asymmetric historical entropy drive (T) of matter (the intrinsic motion of matter's time dimension, as gauged by "velocity T"):
S - T = -G
This is equivalent to the small energy difference between implicit (S) and explicit (T) time. (See: "Gravity Diagram No. 2"; see also: "The Conversion of Space to Time".)
The notion of the gravitational conversion of space and the spatial entropy drive of free energy (S), to time and the historical entropy drive of bound energy (T), can be symbolically represented by a non-quantitative "concept equation":
-Gm(S) = (T)m
-Gm(S) - (T)m = 0
A more complete mathematical representation (for the metric interpretation of the "concept equation") might be obtained by substituting for (S) an appropriate expression for space, and similarly for (T). The effect of the multiplier (-Gm) must be to collapse (or transform) the spatial component (S) and replace it with a metrically equivalent temporal component (T). But Einstein has already done this with the metric tensors of General Relativity. Einstein's complex metric tensor of the gravitational field is capable of quantitatively representing the dimensional transformation of space to time, whereas our simplistic "concept equation" of course cannot. Einstein's gravitational field equations are the exact, quantitative solutions of our "concept equation" in its metric version; conversely, the concept equation expresses in very general but simple terms the qualitative effect of Einstein's field equations - the transformation of space to time. The intrinsic, entropic motion of the time dimension so produced provides the accelerating gravitational force which collapses more space in an endless self-feeding cycle. The entropic motion of the time dimension is in turn derived from the antecedent and active entropic principle inherent in the gravitationally annihilated space - the intrinsic motion of the light which creates, expands, and cools the space. (see: "A Description of Gravitation").
We realize that time has intrinsic motion (the entropy drive of matter and history - see: "The Time Train"), but we don't usually think of space in the same way. But space also has intrinsic motion - supplied by the intrinsic motion of light (the expansive entropy drive of free energy). Space is created by the intrinsic motion of light, and does not exist without light: no energy form exists without an associated entropy drive and conservation domain. Einstein discovered this expansive (entropic) characteristic of space in his gravitational equations, which would not allow a static solution; he suppressed this natural, entropic, intrinsic motion with his infamous "cosmological constant". The reason we are not aware of the expansive motion of ordinary space is due to the size of the Cosmos and the "non-local" character of light. The expansion of space proceeds over the scale of the entire Cosmos (where it is actually visible as the "cosmological redshift" observed by our giant telescopes), but is locally so small that it is both insensible and overcome by the gravity of local astronomical masses. Conversely, it is only due to the intensely "local" character of matter that we are aware of the intrinsic motions of both time and gravitation. Regarding the universal expansion of spacetime, we are natively aware only of the temporal component (aging). Nevertheless, this historical expansion is inextricably linked with a metrically equivalent spatial counterpart. For example, distant galaxies must see us just as red-shifted as we see them. (See: "A Spacetime Map of the Universe".)
There should be nothing new in all this, other than our interpretation of the effects of Einstein's gravitational equations as actually converting space into time (whereas this effect is usually interpreted as the "warpage" or "curvature" of spacetime). (I obviously assume Einstein's equations are essentially correct, and allow either the "curvature" or the "conversion" interpretation). Black holes provide observational and theoretical evidence (the latter due to Hawking and Bekenstein) that this gravitational conversion of space to time actually happens; and our dynamic perspective with respect to the gravitational collapse of spacetime is allowed by Einstein's own "Equivalence Principle". Our only quarrel with Einstein's theory (at least as it is currently interpreted by the physics "establishment") is whether or not light moving freely in spacetime produces a gravitational field: I believe it does not, the "establishment" believes it does. The recently observed "acceleration" of the cosmic expansion constitutes observational evidence favoring my view. (See: "Does Light Produce a Gravitational Field?")
The total negative gravitational energy of matter is equal to its positive rest mass energy - as demonstrated by black hole theory (through the total conversion of the gravitational field energy to light, via Hawking's "quantum radiance"). This concept (apparently originally due to Pascual Jordan) helps us understand the creation of matter (or bound energy generally) as a zero-sum enterprise requiring no net energy. This argument is used (in "inflationary" theories) to explain how the universe could possibly have originated as a quantum-mechanical fluctuation of the primordial vacuum.
The inertial mass of a particle is wholly due to its gravitational field. The inertial resistance to acceleration by a massive particle is a result of the interaction between the particle's gravitational field and the metric field of spacetime. The reciprocal relation between accelerated motion and the gravitational flow of spacetime is the ultimate reason for the exact equivalence between a particle's inertial and gravitational mass; obviously, the gravitational field of the particle is likewise reciprocally involved. The interaction/feedback between these two metric fields is also the reason for the increase in mass of a moving/accelerating particle, and for the effect of motion upon its "proper" length and clock rate. (See also: "The Higgs Field vs the Metric Field of Spacetime".)
Compare the above description of matter's inertial status with the energy state of light, which has no mass and hence no gravitational field, no "x" or "t" dimension, and consequently exhibits the "inertial" condition of "non-local" intrinsic motion c, in satisfaction of the symmetry/entropy demands of Noether's Theorem and the 2nd law of thermodynamics. Conversely, the time dimension of matter (not matter itself) moves with a metrically equivalent intrinsic motion "velocity T", in satisfaction of the energy/entropy demands of the 1st and 2nd laws of thermodynamics. (See: "Gravity, Entropy, and Thermodynamics".)
The charges of matter are the symmetry debts of light. Gravitation "pays the interest" on the symmetry debts of matter, creating matter's time dimension from space, and slowing the light-driven expansion of the Cosmos in consequence. Gravity is the entropy conversion force, converting the spatial entropy drive of light or free energy (the intrinsic motion of light as gauged by "velocity c") to the historical entropy drive of matter or bound energy (the intrinsic motion of time, as gauged by "velocity T") - and vice versa, as in the gravitational conversion of mass to light in stars and quasars, in the "quantum radiance" of black holes, or in gravitationally induced "proton decay". (See: "The Half-Life of Proton Decay and the 'Heat Death' of the Cosmos".)
The 1st law of thermodynamics, energy conservation, can be regarded as the primary role of gravitation, with entropy, causality, and symmetry conservation as corollaries, since the role of the spacetime metric is first and foremost to conserve energy. The action of gravitation converts a global metric of space, light, and absolute motion gauged by c, to a local metric of time, matter, and relative motion gauged by G. Time or historical entropy can be regarded as a "local" form of entropy drive, distilled from the "global", spatial entropy drive of light (by the gravitational annihilation of space and the extraction of a metrically equivalent temporal residue). Time is the local compensating component of the gravitational field vector (spacetime) - the local gauge symmetry "current" - protecting the invariance of the "Interval" and causality, accomplishing energy conservation despite the variable and relative motions of matter, and the variable gravitational metric. To this end, time itself must be flexible and co-vary with space (as per Special and General Relativity). In this regard, time is the functional analog of the magnetic component of the electromagnetic field. ("Lorentz invariance" produces a magnetic field when associated with electrically charged particles in relative motion, and both time and magnetism function as "local gauge symmetry currents" protecting the Interval, causality, and the invariance of charge and velocity c.) (See: Robert Resnick: Introduction to Special Relativity. John Wiley and Sons, Inc. 1968 pp. 175 - 177.) (See: "Global vs Local Gauge Symmetry and Gravitation".)
As magnetism is the invisible, projective, electrically active ("electro-motive") force of the loadstone, so gravity is the invisible, projective, dimensionally active ("inertio-motive") force of the ordinary rock. In the case of magnetism, we trace the force back to the moving (and aligned) electric charges of atoms in the loadstone; in the case of gravity, we trace the force back to the moving (and one-way) temporal charges of bound energy in the rock. A moving electric charge creates a magnetic field; a moving temporal charge creates a gravitational field. In both cases the field is produced at right angles to the current. Both relations are reciprocal: moving magnetic and spatial fields (gravity) create electric and temporal currents (time). This is the analogy between electromagnetism and gravitation which so intrigued Einstein. Finally, time and gravity induce each other endlessly, as do the electric and magnetic components of an electromagnetic field.
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