Gravity and Symmetry
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 short papers are not intended to stand alone):
The charges of matter are the symmetry debts of light
According to Noether's Theorem, in a multi-component field such as the electromagnetic field (or the metric field of spacetime), wherever one finds a symmetry one will also find an associated conservation law, and vice versa. This great theorem, the basis of Group Theory (in mathematics) and much unification work in physics, leads us directly to the hypothesis that the charges of matter are the symmetry debts of light, debts incurred when symmetric light was converted to asymmetric matter in the "Big Bang". In other words, charge conservation is a manifestation of symmetry conservation in the particle metric, just as inertial and gravitational forces are the evidence of symmetry conservation in the spacetime metric. ("Spin" is a symmetry debt that has characteristics of both a quantized charge and an inertial force.)
If, like the other charges, gravity represents a particular kind of symmetry debt resulting from the conversion of symmetric light to asymmetric matter (or from any process that converts free to bound energy, such as the capture of a photon by the electron shell of an atom), then we have only to identify the nature of this broken symmetry of light to initiate the process of unification. In the case of gravity, the symmetry debt apparently results from the breaking of light's "non-local" dimensional symmetry, and the associated symmetric distribution of light's energy, simultaneously everywhere throughout spacetime. Light can be everywhere at once because light lacks a time dimension and one spatial dimension ("x") in the direction of its motion. In its own frame of reference, light "knows" neither distance nor time, and hence is everywhere simultaneously. This is the meaning of the zero "Interval" Einstein assigned to light - the essential mathematical statement of light's dimensional energetic symmetry state, light's hallmark "non-locality".
Since gravitation is a dimensionally active force, "warping" and "curving" spacetime, quite unlike the other charges and forces, there is clearly another possibility - that the gravitational charge represents a broken metric symmetry of spacetime. A third possibility is that both of the above apply simultaneously - the gravitational debt or charge is a consequence of both a broken distributional symmetry of light's energy, and a broken metric symmetry of spacetime. Precisely because velocity c, the intrinsic motion of light, is both the gauge of metric symmetry (preventing the explicit appearance of asymmetric time), and consequently is also the gauge of free energy's non-local distributional symmetry (light's Interval = zero), we shall see that this is so. Finally, we shall see how entropy is a unifying concept which simplifies and makes sense of it all. (See: "The Double Conservation Role of Gravitation".)
Identifying the various symmetry debts of light associated with the charges and forces of matter is the work of unification theory. (See: "Symmetry Principles of the Unified Field Theory" ).
The Gravitational Symmetry Debt
From the perspective of symmetry conservation, the "location" charge of gravitation is in response to free energy's loss of (dimensional) distributional symmetry when non-local light is converted to local, immobile matter. The "location" charge of gravitation is the symmetry debt of light's lost "non-locality", the symmetric dimensional distribution of light's energy, everywhere, simultaneously. The energy of matter has a specific location in spacetime and hence an asymmetric distribution of its energy, since matter lacks intrinsic motion c. The "Interval" of matter is always positive, never zero.
The temporal and spatial dimensions are intimately related to the nature of light. "Velocity c", the electromagnetic constant, the gauge of the intrinsic motion of light, is characterized as the product of the frequency of light and its wavelength - frequency multiplied by wavelength = c = the natural constant of metric symmetry: 300,000 kilometers of linear space are metrically equivalent to one second of temporal duration. When this metric symmetry condition is satisfied, light's "Interval" = zero, and the asymmetric temporal dimension is suppressed ("light's clock is stopped"). With the frequency of light we associate the temporal dimension, with the wavelength of light we associate the spatial dimension, two related dimensions whose union produces the 4-dimensional conservation domain of the two forms of light, particle and wave, bound and free electromagnetic energy. In the freely moving wave, the temporal dimension of light is suppressed or remains implicit, and the spatial dimension is dominant; when light is in its particle form, as matter, the spatial dimension is suppressed, and the temporal dimension becomes dominant. But it is no mystery where these dimensions come from: the dimensions of spacetime come directly from the natural characteristic of light, its frequency and wavelength. (See: "The Conversion of Space to Time".)
It should be no surprise, of course, that electromagnetic energy, in both its forms, is prepared to accommodate the conservation needs of these forms out of its own nature. Indeed, only those forms of energy which are so enabled could manifest at all. We need take only one further but crucial step in understanding: "velocity c" and "velocity T" are the entropy drives of free and bound energy. Each form of energy is furnished with an entropy drive (intrinsic motion) that creates its specialized dimensional conservation domain, be it space, time, or in the case of gravitation and "intrinsic motion G", the joint dimensional conservation domain of spacetime (for the mixture of free and bound energy). It is the conservation role of gravity to convert the entropy drive of free energy into the entropy drive of bound energy and vice versa, creating time by the annihilation of space, or converting mass to light, as in the stars. (See: "Entropy, Gravitation, and Thermodynamics".)
The mechanism of gravitation is straightforwardly simple - as one might expect; it is unusual only in that it is wholly a dimensional interaction (its unusual weakness is due to the fact that gravitational energy is equivalent to the energy of matter's temporal entropy drive - the energy required to produce the intrinsic motion of time). Gravity creates time by the annihilation of space, but conversely, the spatial flow of gravitation is a consequence of time's intrinsic motion - gravity and time induce each other. The active principle of gravity's "location" charge is time, an entropic charge (a charge with intrinsic dimensional motion) which appears at the center of mass due to the gravitational annihilation of space, or (initially) due to the quantum mechanical collapse of an electromagnetic wave. In the gravitational case, the time "charge" is the metrically equivalent residue of the annihilated space. The intrinsic motion of time is the primordial entropy drive of matter.
In the quantum mechanical case, the time charge is the explicit temporal character of the wave itself (the "frequency" aspect), revealed by the wave's collapse and loss of intrinsic spatial motion. When an electromagnetic wave collapses to a bound state, its implicit temporal component ("frequency") becomes explicit and its explicit spatial component ("wavelength") becomes implicit. The entropy parameter of the electromagnetic "coin" simply "flips" from a free to bound energy state. The magnitude of G 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 temporal entropy drive (T) of matter (the intrinsic motion of matter's time dimension as gauged by "velocity T"): S - T = -G. (See: "Gravity Diagram No. 2".)
Time is linked (connected) to space; the intrinsic motion of an explicit time charge drags space after it, causing the collapsing symmetric flow of space which we recognize as a gravitational field. Time is one-dimensional, one-way, moving at "right angles" to space. "Yesterday" is inaccessible to us because intrinsic velocity T is metrically equivalent to intrinsic velocity c; that is, time moves away from us at an effectively "infinite" velocity. Distant observers in the galaxy can briefly see our "yesterday" as it sweeps past them, just as we can catch a fleeting glimpse of theirs. The one-way motion of time is necessary to protect causality, and to provide a continuous updating of matter's variable energy accounts - because unlike the constant and absolute motion of light, the variable and relative motion of matter is completely unpredictable. (See: "The Time Paradox of the Traveling Twin".)
The spherically symmetric inrush of space ("gravity") self-annihilates all opposing spatial dimensions (+x, -x; +y, -y; +z, -z) when they reach the central dimensionless point of the beginning of the time line; time exits space at "right angles" to all three spatial dimensions. The +T time component of the metric does not self-annihilate because there is no -T, time being strictly one-way (to protect causality). The destruction of the spatial dimensions leaves behind a new time residue (the metric equivalent of the annihilated space), which replaces the old time charge - and so the cycle continues forever, one-way time and one-way gravity engendering each other, much as the electric and magnetic fields of light induce each other. (See: "A Description of Gravitation".)
The surface ("event horizon") of a black hole is a demonstration of the dimensional reality of time, and of the fact that space is converted to time by gravitation. The Bekenstein-Hawking theorem states that the surface area of a black hole is proportional to its entropy: the event horizon of a black hole is evidently a time surface. However, it is the intrinsic motion of time which initiates gravitational motion, and the intrinsic motion of light which is the first link in this chain. Light is the primal source of temporal motion, as light's intrinsic motion (the entropy drive of free energy) is converted to time's intrinsic motion (the entropy drive of bound energy) via the gravitational annihilation of space (or the quantum mechanical collapse of an electromagnetic wave). Time is implicit in light as "frequency". (See: "The Conversion of Space to Time".)
When free energy is transformed to bound energy, the implicit temporal component of an electromagnetic wave becomes explicit. The magnitude of G is determined by the energy difference between symmetric implicit time and asymmetric explicit time - or equivalently, between the symmetric spatial entropy drive of light (S) and asymmetric temporal entropy drive of matter (T): S - T = -G. In terms of single quantum units, this difference is equal to the energy of a graviton.
The graviton is the presumed field vector of the gravitational "location" charge, the dimensional force carrier of a dimensional charge, connecting the 4 dimensions to each other, causing the infall of space to the center of gravitational mass, just as the photon is the field vector of the electric charge. The graviton links space to time, connecting space to matter, whereas the photon links light to electric charge, connecting light to matter. A graviton is a negative quantum unit of spatial entropy, metrically and energetically equivalent to a positive quantum unit of time. (See: "The Time Train".)
Time is the active principle of gravity's "location" charge, unique among the charges in that it is a dimensionally active, entropic charge, that is, a charge with intrinsic dimensional motion - in the case of time, a one-way motion (protecting causality). The time charge encompasses the symmetry debt, both distributional and metric, of light's non-locality, as well as the entropy debt of light's lost intrinsic motion. Time's intrinsic motion is matter's entropy drive; time also specifies the 4-dimensional location of matter, producing the "location" charge of gravity. The gravitational conversion of matter to light (in stars and via Hawking's "quantum radiance" of black holes) repays both gravity's entropy and symmetry debt simultaneously - since non-local light has no time dimension and produces no gravitational field. (See also: "The Double Conservation Role of Gravitation".)
The Gravitational Entropy Debt
The electromagnetic constant c is the gauge of light's symmetric energy state and entropy drive. On the one hand, light's intrinsic motion creates, expands, and cools space, establishing the symmetry of the metric by banishing time, mass, charge, and gravitation, and establishing light's "non-local" dimensional symmetry, the "zero Interval" of light. On the other hand, the expansion cools the Universe, reducing its capacity to perform "work". When gravity conserves the "non-local" symmetry of light, it converts space and the entropy drive of free energy (the intrinsic motion of light), into time and the entropy drive of bound energy (the intrinsic motion of time), conserving both the symmetric energy state and the entropy drive of light simultaneously. The double nature of the gravitational symmetry/entropy debt is encapsulated in the gravitational "location" charge, of which time itself is the active principle. The time charge both identifies the location of the undistributed lump of immobile mass-energy in 4-dimensional spacetime, but also, because it is an entropic charge with intrinsic dimensional motion, initiates the flow of space which establishes the gravitational production of time. It is therefore often difficult or impossible to distinguish the separate contributions of symmetry or entropy conservation in gravitational processes. In general, however, we can say that the gravitational production of time is the entropy conserving process, while the gravitational conversion of bound to free energy (as in stars) is the symmetry conserving process.
It is the multiple nature of gravity's symmetry, entropy, and metric debts that creates such confusion regarding gravity's origin and role. Gravity's entropy debt explains its persistent, unquenchable nature, because entropy is a constant force (time's intrinsic motion persists so long as bound energy persists); gravity's metric debt is likewise due to the constant, asymmetric, one-way nature of time's motion (protecting causality), which causes the accelerated flow of space, and the "warpage" and "curvature" of the metric; gravity's symmetry debt (light's non-local energy distribution) causes the conversion of bound energy to free energy, in stars and by Hawking's quantum radiance of black holes. This complex picture, involving the linked conservation laws of entropy, causality, and symmetry, is greatly simplified, however, from the singular perspective of entropy. (See also: "The Energy Tetrahedron Diagram".)
Gravity is a negative spatial entropy drive (-G) producing the positive temporal entropy drive (+T) of matter from the positive spatial entropy drive (c) of light - gravity is the force converting space and its entropy drive (the intrinsic motion of light) to history and its entropy drive (the intrinsic motion of time). We say therefore that gravity conserves the spatial entropy drive of light (light's intrinsic motion) by converting it to the temporal entropy drive of matter (time's intrinsic motion) via the annihilation of space. The conversion pathway is via the annihilation of space because space contains a metrically equivalent component of time, whose implicit character is rendered explicit when the spatial dimensions annihilate each other at a gravitational center of mass. Since the time residue is the metric equivalent of the gravitationally annihilated space, the spatial and temporal dimensional conservation domains of free and bound electromagnetic energy are by this means joined in an exact equilibration, both metrically and entropically. (See also: "The Conversion of Space to Time".)
The collapse of space is the gravitational source for time, while the collapse of an electromagnetic wave is the quantum mechanical source for time. This double source illustrates the intimate connection between space and light, and suggests a connection between gravitation and quantum mechanics. However, the wave collapse simply reveals a single, asymmetric, initiating time charge which "gauges" the strength of the gravitational interaction (determines the magnitude of G) and begins the process, precipitating the gravitational spatial collapse which sustains the continuous flow of time.
The quantum mechanical collapse of an electromagnetic wave - as in the creation of matter or the absorption of light by an atomic electron shell - is the pathway by which the time charge of gravity is initiated, illustrating a quantum mechanical connection to gravitation. Because c, T, and G are all interconnected gauge constants and hence independent of mass or energy, the specific energy of the collapsing wave, after making its contribution to mass, is otherwise irrelevant. When the wave collapses (when free energy loses its intrinsic motion), the spatial or "wavelength" character of the electromagnetic energy packet becomes implicit and the temporal or "frequency" character of energy becomes explicit. This is just to say the entropy drive of the wave changes from spatial (intrinsic motion c) to temporal (intrinsic motion T), like a coin changing from head to tails. As soon as the time (or "location") charge is revealed, it begins its intrinsic motion, pulling space after it; the ensuing gravitational annihilation of space continuously replenishes the moving temporal charge. Hence time effectively renews itself via its own intrinsic motion. (See: Gravity Diagram 1 and Gravity Diagram 2).
Time and history are alternative entropy carriers to light and space, a role which is analogous to the lepton's role as alternative charge carriers to the quarks. The role of entropy itself is also analogous to the role of charge, in that the former makes possible the transformation of free energy to work, while the latter makes possible the transformation of free energy to information. Such analogies illustrate the fundamental nature of the intimate connection between spacetime and particles. (See: "The Flower Force Diagram"). When space cannot carry the entropy drive of matter (because matter lacks intrinsic motion c), the "location" charge and the gravitational force of matter converts space to time, and time takes over matter's entropy drive with intrinsic motion T. 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. (See: "The Time Train".)
In the gravitational interaction, space is pulled by time, just the opposite of the interaction producing the intrinsic motion of light, in which we see symmetric space forever fleeing asymmetric time, time being an internal, latent (implicit) potential of light's own nature. This flight of space prevents the manifestation of the asymmetric 4th dimension, preserving light's dimensional, non-local symmetry. Light is a 2-dimensional transverse wave whose intrinsic motion sweeps out a third spatial dimension. The difference between the intrinsic motion of light and gravity is therefore simply the difference between the implicit and explicit presence of time, spatial vs temporal entropy. (See: "The Conversion of Space to Time.") The gravitational deceleration of the Cosmos tells us that it is ultimately the intrinsic motion of light which funds the creation of matter's time dimension. (See also: "The Half-Life of Proton Decay and the 'Heat Death' of the Universe".)
Parameters of Entropy and Gravity
The magnitude of G is determined by the small energy difference between the symmetric drive of spatial entropy (S) (the intrinsic motion of light, as gauged by "velocity c"), and the asymmetric drive of temporal entropy (T) (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".)
The gravitational conversion of space and the spatial entropy drive (S) to history and the temporal entropy drive (T), can be represented in symbolic conceptual terms as:
-Gm(S) = (T)m
-Gm(S) - (T)m = 0
(See: "The Conversion of Space to Time".) Links:
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