John A. Gowan
http://www.people.cornell.edu/pages/jag8/index.html
Contents:
Abstract
Noether's Theorem states that in a multicomponent field (such as the electromagnetic field of light, or the metric field of spacetime), where we find a symmetry we will find an associated conservation law, and vice versa: conservation laws are associated with symmetries. Time and gravitation follow the rule of Noether's theorem and all other charges of matter: charges produce forces that act to return the material system to the symmetric state of free energy from which it came. In the case of the entropic charge "time", that force is gravitation. By Noether's theorem, the symmetry of light must be conserved, typically through charge conservation (including spin) and the inertial and gravitational forces of the metric. The charges of matter are the symmetry debts of light: time and gravitation are entropic, dimensional examples of Noether's theorem enforced, conserving:
1) The intrinsic motion of light, as transformed to the intrinsic motion of matter's time dimension (or the entropy drive of free energy as transformed to the entropy drive of bound energy) - via the gravitational annihilation of space and the extraction of a temporal residue (see: "The Conversion of Space to Time");
2) The non-local or spatially symmetric state of light by converting bound energy to free energy - as in the stars and Hawking's "quantum radiance" of black holes. Through "quantum radiance", even the symmetry of entropy is conserved.
The intrinsic motion of time is matter's temporal entropy drive. Time is the conserved form of the spatial entropy drive of the free energy which created matter - the intrinsic motion of light. Because both asymmetric matter and its asymmetric temporal entropy drive are derived from the symmetric spatial energy state of light, by Noether's theorem we expect to find forces associated with matter which will act to return matter's asymmetric energy state to light's symmetric energy state. One such force is gravitation, converting bound to free energy (as in the stars and the quantum radiance of black holes). The magnitude of G is determined by the small energy difference between the entropy drive of symmetric spatial entropy (S) (the intrinsic motion of light causing the spatial expansion of the Cosmos), and the entropy drive of asymmetric temporal entropy (T) (the intrinsic motion of time causing the historic expansion of the Cosmos); or equivalently, between the implicit (S) state of time and the explicit (T) state of time: S - T = -G (see: "Gravity Diagram No. 2").
The active principle of the gravitational "location" charge is time itself. Gravitation is the spatial consequence of, and the evidence for, time's intrinsic motion. (See: "A Description of Gravitation".)
Light (free electromagnetic energy) is a 2-dimensional transverse wave whose intrinsic motion sweeps out a 3rd spatial dimension. Light's intrinsic motion creates a dimensional conservation domain, space, for itself. Light and space are primary and fully symmetric; light carries no charges of any kind. Light completely inhabits the conservation domain it creates: light is everywhere simultaneously in space. Light's energy is distributed symmetrically throughout its domain because light is "non-local", due to the effectively "infinite" velocity of light.
Light's "non-local" character is due to two remarkable attributes of light discovered by Einstein:
1) light has no time dimension - light's "clock" is stopped;
2) light has no spatial dimension in the direction of its motion - distance in the "x" dimension shrinks to nothing at velocity c.
Having no distance to travel and eternity to get there, in its own reference frame (traveling freely in vacuum at velocity c), light is everywhere in its conservation domain (space) simultaneously. Considerations of distance and time which mean everything to us, mean nothing to light. Hence light enjoys a singular unity, connectivity, and symmetry within its conservation domain. Einstein formalized this unique symmetry of light in his equations of the spacetime "Interval", an invariant unit of spacetime which separates any two events, protecting causality: the "Interval" of light, in either special or general relativity, is zero. Hence light is not only "atemporal", but of necessity "acausal" as well (causal linkages are not applicable to a non-local, atemporal energy form).
Light is a wave whose electric and magnetic components induce each other transversely (at right angles), causing its "propagation" or motion, sweeping out and creating three symmetric spatial dimensions. It seems most convenient to think of light as a vibration of the spatial metric structure it creates. Velocity c is the entropy drive and symmetry gauge of free energy, not only creating space, but causing the expansion and cooling of space, thereby reducing the capacity of the spatial domain for work, while conserving its total energy as the product of a falling temperature but increasing volume. The "work done" by the system of space and light at the beginning of the Universe (the "Big Bang") was the creation of matter, an "uphill" process since symmetric light was transformed into asymmetric bound energy, producing a gravitational entropy and symmetry debt, -Gm, in consequence. (The spatial entropy drive of light (the intrinsic motion of light as gauged by "velocity c") was converted to the metrically equivalent temporal entropy drive of matter (the intrinsic motion of matter's time dimension, as gauged by "velocity T"), requiring in consequence a deceleration of the spatial expansion of the Cosmos.) The expansion of the Cosmos is produced by the intrinsic motion of light. The gravitational deceleration of the spatial expansion transfers energy from spatial to temporal entropy, funding the creation of matter's time dimension and the expansion of historic spacetime.
"Velocity c" gauges the entropy drive of free energy and of space, regulating the Cosmos' rate of cooling; but "velocity c" is also the symmetry gauge of free energy and space, banishing the asymmetries of time, charge, matter, and gravitation, establishing also the metric relationship between and within the spatial and temporal dimensions: meter sticks and clocks must be the same everywhere, and 1 second of (implicit) temporal duration must equal 300,000 kilometers of space everywhere. Failure of this metric gauge and symmetry would allow the spontaneous, random appearance of "rogue" or sourceless gravitational fields, violating energy conservation. Only a non-local gauge with an effectively infinite velocity such as c could maintain metric symmetry in a conservation domain expanding at c; the entropy and symmetry gauge of the metric must be one and the same, velocity c.
The fact that light has no temporal dimension is a consequence of velocity c; time is an asymmetric dimension, always in "bad company" with its asymmetric companions, mass, charge, and gravitation. It is precisely the function of velocity c to suppress the associated asymmetries of "the Gang of Four": time, charge, mass, and gravitation.
Velocity c is calculated as the constant product of light's wavelength and frequency - as wavelength increases, frequency decreases, and vice versa, the two characteristics locked together like the opposite ends of a teeter-totter, such that their product is always c. Now it is obvious that time is implicit in the "frequency" aspect of light, just as space is implicit in the "wavelength" aspect of light. As free energy, the waveform of electromagnetic energy is explicitly expressed as space, but its frequency or temporal aspect is suppressed and remains implicit. The suppression of the implicit temporal dimension is the chief symmetry function of the electromagnetic constant c.
Just as the electric and magnetic characteristics of light induce each other and cause the propagation or intrinsic motion of the wave, so we can also imagine the spatial and temporal (wavelength and frequency) components of the wave inducing, repelling, motivating and propelling each other. We can imagine symmetric space "fleeing" asymmetric time, and by moving at c, forever keeping time implicit, always keeping "one jump ahead of the sheriff", moving forward in space just fast enough to prevent the clock hand of time from also moving forward, thereby maintaining metric symmetry. Because time or frequency is an internal or embedded characteristic of light, the intrinsic motion of light is explained as the flight of symmetric space from an internal asymmetry of its own nature, time, whose implicit presence light can never escape (the original "bur under the saddle"): time's explicit expression is suppressed by light's absolute eternal motion, "velocity c". Hence it turns out that time, the explicit driver of the material realm of bound energy, is also the implicit driver of the immaterial realm of free energy. Time is the "metabolism of the Universe", whose implicit presence causes the intrinsic motion of light and the expansion of the Universe, and whose explicit presence causes gravitation and the deceleration of Cosmic expansion. The intrinsic motion of light is therefore explained as the entropy and symmetry conservation drive of metric spacetime, serving energy conservation. (See: "Entropy, Gravitation, and Thermodynamics".)
This brings us to a consideration of light's dual nature and its secondary, asymmetric form, massive particles and matter. The particle expression of light is found in the vacuum formation of virtual particle-antiparticle pairs. We don't know how (or why) light produces this secondary form, but all of matter is testimony that it does. Evidently, particles are produced as entanglements of a free electromagnetic wave with the metric web of spacetime; particles get their energy content from light and their structural content from the spatial metric. (The hypothetical "Higgs" boson is also presumed to be somehow involved in the transformation of light's free energy to the bound energy or mass of the elementary particles of matter. I think of the "Higgs" as the sticky component of the metric web which entangles light (see: "The Higgs Boson vs the Spacetime Metric"). The higher dimensional character of these "knots" or entanglements of light in the metric prevent them from being transmitted as vibrations of spacetime (the culprit is certainly the asymmetric 4th dimension of time). Particles therefore have intrinsic rest with respect to space, rather than light's intrinsic motion. In the case of massive particles, the dimension (time) moves rather than the energy form (matter); time's intrinsic motion in historic spacetime is the metric equivalent of light's intrinsic motion in space. This equivalency (also gauged by c) is required by energy conservation so that the two forms of electromagnetic energy (free and bound - light and matter) can interact within their joint dimensional conservation domain of spacetime. (See: "The Time Train".)
When light is converted to particles, or simply to bound energy, it loses its intrinsic motion, and the frequency or temporal aspect of the wave becomes explicit while the spatial or wavelength aspect of the wave becomes implicit - the electromagnetic "entropy coin" simply flips, showing time rather than space. (See the Gravity Figures "One" and "Two".) It should be no surprise that light can produce the dimensional conservation domains required by and appropriate for its two energy forms: space for its free energy or wave form; time and spacetime for its bound energy or particle form. (See: "The Conversion of Space to Time".)
The great entropic or dimensional/inertial difference between these massless and massive forms of electromagnetic energy is that in the case of free energy it is the energy form (light) which moves, creating space; in the case of bound energy, it is the dimension (time) which moves, creating history. Matter itself remains at rest in the "Eternal Now", the "Universal Present Moment". Hence elementary particles simply do not "age" in terms of a dilution of their energy content, since they do not participate in the entropic expansion of either the spatial or the historical dimensions. It is this difference which is the root cause of the weakness of gravity, the creator of time, matter's temporal entropy drive. (See: "The Half-Life of Proton Decay and the 'Heat Death' of the Cosmos".)
Conservation, Connection, Causality
We have seen that light is completely connected to (unified with) its conservation domain by virtue of its "non-local" character, an attribute due to the symmetry and entropy gauge c, producing the "non-ordinary", "infinite velocity" of the intrinsic motion of light. When light is converted to matter in the "Big Bang", (or, less spectacularly, absorbed by the electron shell of an atom), light loses its intrinsic motion: matter is inherently "at rest" with respect to space, and so has no connection to light's spatial conservation domain. An energy form without a dimensional entropy/conservation domain is unthinkable from the point of view of energy conservation - such a state cannot exist. Matter must be given a conservation domain; it cannot be space but it must be compatible with space if the two forms of electromagnetic energy are to coexist and interact.
One of the problems to be overcome (in the creation of a conservation domain for matter) is that matter cannot travel at velocity c, because its mass would become infinite and it would likewise require an infinite amount of energy input to accelerate matter to such an "infinite" velocity. Matter would have to become 2-dimensional, massless, and non-local to travel at velocity c. There is a good reason why velocity c is an "infinite" velocity with respect to its conservation domain; since nothing massive can travel at c, the spatial domain is both sealed in the sense that nothing can escape (since nothing can outrun light), and for the same reason, causality within the spatial domain is protected. Both conditions, closure and the protection of causality, are required by energy conservation of any dimensional conservation domain. The effectively infinite velocity of light also establishes the basic mechanism by which entropy protects energy from abuse, allowing energy to be transformed, used, and still conserved. The dimensions of spacetime are entropy domains.
If matter cannot travel at c, how then can matter's conservation domain be constructed to effect closure of the domain and to protect causality, entropy, and energy conservation within it, and at the same time be compatible with light's spatial domain? An apparently impossibly difficult task, but one which Nature performs effortlessly by the creation of spacetime, a joint dimensional conservation domain in which the intrinsic motion of time is the metric equivalent of light's spatial motion. The compatibility constraint is surmounted by extracting time directly from space (either gravitationally or quantum mechanically) - the flip of the electromagnetic coin from wavelength to frequency - and the closure, entropy, and causality constraints are met by providing the dimension itself, rather than the massive energy form, with an "infinite" one-way velocity which is the metric equivalent of c (see: "The Conversion of Space to Time"). Time moves, but we do not, which is why we look backward in time as we look outward in space. (See: "The Time Train".)
The protection of causality is the reason for time's one-way character; we cannot outrun time anymore than we can outrun light; and the seamless connection between today and yesterday - right back to the beginning of time itself in the "Big Bang" - connects material objects with the Universe as a whole in a manner analogous to light's habitation of space. Free energy (light) is connected by space; bound energy (matter) is connected by time. All material objects exist in a universal "now" and a historical domain which is coextensive with space (historic spacetime). This continuum of spacetime is actually visible through our telescopes: as we look outward in space, we look backward in time, all the way to the Big Bang itself. See: "A Spacetime Map of the Universe".
The intrinsic motion of time is the entropy drive of matter, decaying and aging matter and information, and expanding and diluting history in a manner analogous to the expansion and cooling of space. Space and time are gravitationally welded into historic spacetime. The historic temporal domain is the analog of space. Macroscopic structures age and decay, even though they do not move in time, since the motion of the time dimension carries them along. (See: "The Time Train".) The function of entropy (intrinsic dimensional motion as in c, T, G) in all cases, whether positive or negative, spatial or temporal, is the creation of a dimensional conservation domain in which energy can be both used and conserved simultaneously. This is the connection between the 1st and 2nd laws of thermodynamics. Thus light creates space, time creates history, gravity creates spacetime. Without the second law (entropy), the first law (energy conservation) would prevent any use of energy at all. Entropy allows energy to be used by preventing its abuse: the same energy cannot be used twice for the same net work, preventing the perpetual motion machine, or any machine that creates net energy. Conservation laws prevent some actions so that others may occur.
In addition and related to its need for an entropy gauge, matter requires a time dimension for reasons of causality, and to keep its energy accounts; this is because matter's energy varies according to its relative velocity, and velocity is accounted by distance/time. Because matter can have any velocity less than c, matter's energy accounts must be continuously updated, while causality requires the linear and one-way motion of the time dimension. Light does not similarly require time, because light's absolute (non-relative) velocity is a universal constant; light's energy varies not with velocity but with frequency. Without time, matter could not move in space, and a 2-way time dimension would imply we could move into the future, violating causality. (See: "The Time Train".)
Light is spatial: non-local, atemporal, and acausal. Matter is historic: local, temporal, and causal. The protection of causality is the fundamental energy conservation reason for the creation of the one-way time dimension of bound energy, and hence also for the existence of gravitation, which creates matter's time dimension. Causality and entropy in bound energy are both gauged by time's intrinsic motion (as gauged by "velocity T"), just as symmetry and entropy in free energy and are both gauged by light's intrinsic motion (as gauged by "velocity c").
In some regards, the time charge is a typical symmetry debt of light: time identifies the 4th spacetime coordinate of matter's stationary position, as matter's huge immobile rest energy (E = mcc) represents a large asymmetry with respect to the former equitable distribution in space of its free energy content. However, time is not an ordinary symmetry debt of light, such as electric charge. Time also has intrinsic dimensional motion; time is an entropic charge, an entropy debt as well as a symmetry debt. -Gm measures the temporal entropy-energy debt of matter. (See: Entropy, Gravitation, and Thermodynamics".)
Gravitation represents both a symmetry debt and an entropy debt, unique among the charges and their forces. This double nature is reflected in two different mechanisms, both of which convert space to time, one at the quantum level of charge - the entropy debt, involving time, causality (local relative motion), and energy conservation, and one at the macroscopic level of gravitational force - the symmetry debt, involving time, the distributional symmetry of energy (non-local absolute motion), and symmetry conservation.
The collapse of an electromagnetic wave confers a quantized time charge on a massive particle. This is the "primary" or quantum mechanical process of producing the entropy debt or time charge. We can visualize this as a switching or flipping of the "wavelength" or spatial aspect of the moving electromagnetic wave, to the "frequency" or temporal aspect of the particle or stationary wave (see: "Gravity Figure No. 2"). Once this time charge is gauged and "set", the "secondary" or symmetry aspect of gravitation comes into play, the cyclic, continuous flow of space as it is pulled into the historic domain by the intrinsic motion of time, producing the macroscopic gravitational field (see fig. "New Gravity Diagram"). The continuous secondary process simply copies or reproduces the time charge set and gauged by the one-time primary process. We can visualize this secondary process as the actual symmetric flow and annihilation of the spatial dimensions, leaving in their place an uncanceled time residue whose intrinsic motion - at right angles to all three spatial dimensions - pulls space after it, producing the continuous spatial collapse that is a gravitational field (see fig. "Gravity Diagram 1").
Finally, we can visualize the ephemeral nature of the time charge as a manifestation of its actual motion from the spatial dimensions, where it is "set" and begins, to the temporal (historic) dimension, where only information can follow. It is the intrinsic motion of the time charge which "pulls" space after it and produces the gravitational flow. Hence a gravitational field is the spatial consequence of the intrinsic motion of time. The collapse of space leaves a temporal residue whose intrinsic motion pulls more space after it, in an endlessly repeating cycle. The intrinsic motions of gravitation and time continuously induce each other, much as the oscillations of an electric and magnetic field induce each other. In both cases, the motion of a current, either moving space or moving electrically charged particles, produces a field at right angles to the current flow (time or a magnetic field). Conversely, a moving time or magnetic field produces a spatial (gravitational) or electric current.
The two mechanisms are distinct but both are part of the gravitational conversion of space to time, connecting the quantum-mechanical aspect of gravitational charge (the entropy debt) to the macroscopic aspect of gravitational flow (the symmetry debt). Both are linked by time, their common gauge c, and Noether's Theorem requiring the conservation of light's non-local symmetry. The gravitational charge, "location", is unique among charges in that its active principle is time. The gravitational charge is an "entropic" charge, a charge with intrinsic dimensional motion. It is the entropic nature of the gravitational charge which connects the quantum mechanical (charge-time-entropy) and macroscopic (location-space-symmetry) aspects of gravity. In turn, the double nature of the gravitational charge gives gravity a double conservation role, on the one hand conserving the entropy drive of free energy (the intrinsic motion of light) by converting it to the entropy drive of bound energy (the intrinsic motion of time), and on the other hand conserving the non-local symmetry of light by converting bound to free energy (as in the stars). This duality extends backward in a conservation chain to the dual role of velocity c, which is both the symmetry and the entropy gauge of free energy. Gravity must conserve both roles of light's intrinsic motion if it conserves either one (see: "The Double Conservation Role of Gravitation"). Because of their common linkage through the gauge c, gravity's entropy conservation role as well as gravity's symmetry conservation role are both covered by the mantle of Noether's Theorem.
The "graviton" or field vector of the gravitational charge is a quantum unit of temporal entropy, the gravitationally transformed entropy or intrinsic motion of the photon, equivalent to a quantum unit of time. The magnitude of G is determined by the small energy difference between the entropy drive of symmetric spatial entropy (S) (the intrinsic motion of light), and the entropy drive of asymmetric temporal entropy (T) (the intrinsic motion of time); or equivalently, the energy difference between implicit (S) and explicit (T) time: S - T = -G. At the level of quantum units, this difference also measures the energy of the "graviton", the presumed field vector of gravitation, effecting the link between space, time, and mass. (See: "Entropy, Gravitation, and Thermodynamics", and "A Description of Gravitation").
The Weakness of Gravity
(See: "The Half-Life of Proton Decay and the 'Heat Death' of the Universe".)
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