Global and Local Gauge Symmetries: Part II (Gravitation)
Table of Contents:
The Origin of Gravitation as a Conservation Force
Gravity is a conservation force which arises in response to losses or deficits in two intertwined "gauge" (regulatory) functions of light's symmetric energy state - losses consequent upon the conversion of light to matter, or free to bound energy forms, as in the "Big Bang", or simply in the capture of a photon by the electron shell of an atom. According to Noether's Theorem, reductions in light's symmetric energy state must be compensated by some conservation force, usually seen in the form of a conserved charge or inertial force. Light's symmetry losses specifically addressed by gravitation include: 1) the spatial entropy drive of light (light's intrinsic motion, regulating the creation, expansion, and cooling of spacetime); 2) the "non-local" energy state of light (regulating the symmetric distribution of free energy in spacetime). Both functions are consequences of light's intrinsic motion, as gauged by the electromagnetic constant "velocity c" (light's intrinsic motion creates space and the spatial metric, the conservation domain of free energy).
The universal gravitational constant "G" is the entropy conversion gauge, regulating how much space must be annihilated and converted to time (per unit mass) to provide matter with its requisite historical entropy drive, locally gauged by "velocity T". Time is produced by the gravitational annihilation of space and the extraction of a metrically equivalent temporal residue. The intrinsic motion of time is the primordial entropy drive of bound energy, creating the historic conservation domain of information and matter's "causal matrix" (historic spacetime). (Time is also ultimately gauged by c, since "velocity T" is defined as the duration (measured by a clock) required for light to travel a given distance (measured by a meter stick). "G" is therefore related to "c" through their common factor time, and as entropy is related to energy.) Time is a local and flexible dimensional gauge produced by the gravitational annihilation of space. Both G and c are globally invariant gauge constants. "c" gauges the spacetime metric of free energy (including spacetime's entropic expansion). "G" gauges the same spacetime metric, but as it is modified by the presence of bound energy (including spacetime's negentropic contraction).
The magnitude of G measures the small energetic difference between the symmetric spatial entropy drive (S) of free energy (the intrinsic motion of light as gauged by "velocity c"), and the asymmetric historical entropy drive (T) of bound energy (the intrinsic motion of matter's time dimension as gauged by "velocity T"):
S - T = -G
Equivalently, -G is the energetic difference between implicit and explicit time. It takes energy to create one-way temporal entropy from "all-way" spatial entropy, because an asymmetric, one-way temporal order must be imposed upon a symmetric, random spatial expansion. This entropy-energy cost of time is the origin of the "negative energy" characteristic of gravity and the negative sign of "-G". (See: "Gravity Diagram No. 2" and "The Conversion of Space to Time").
The intrinsic motion of light produces space and the expansion and cooling of space; hence the intrinsic motion of light is the primordial entropy drive of free energy. (See: "Spatial vs Temporal Entropy".) It is the function of entropy (in its primordial mode) to create a dimensional conservation domain in which its energy source, whether free or bound (light or matter), can exist and be transformed, used, and conserved: this is the relationship between the 1st and 2nd laws of thermodynamics. Because both the spatial entropy drive and spatially symmetric ("non-local") energy state of light are gauged by c (both are consequences of light's intrinsic motion), Noether's Theorem will automatically require the conservation of light's entropy drive in any transformation in which light's non-local symmetry must be conserved - as in the conversion of free to bound energy, and/or the creation of matter. Conserving either the entropy drive or the symmetry gauge of light conserves the other by default. (See: "The Double Conservation Role of Gravitation".)
One of gravity's several conservation roles concerns the spatial entropy drive of free energy (the intrinsic motion of light), which gravity conserves by transforming light's intrinsic motion to the historical entropy drive of bound energy (the intrinsic motion of time). Time is created by gravity via the annihilation of space and the extraction of a metrically equivalent temporal residue, resulting in the deceleration of the spatial expansion of the Cosmos. Because the spatial expansion is driven by the intrinsic motion of light, it is light's spatial entropy drive (S), which ultimately funds matter's historical entropy drive (T). We can represent this transformation by a non-quantitative "concept equation" as:
-Gm(S) = (T)m
This "concept equation" represents an entropic conservation loop between space (created by light), and time (created by gravity). The loop continues through the gravitational conversion of mass to light in stars (which essentially reverses this equation), reducing the stars' gravitational energy and resulting in the "acceleration" of the spatial expansion of the Cosmos. The equation also suggests that time, as Einstein observed, is a local characteristic of gravitating mass: (T)m is different for Earth, Mars, Jupiter, the Sun, etc., not only in quantity and intensity, but also in its metric effect (on clock rate, for example). The only global constant in the equation is G.
(See: "Currents of Entropy and Symmetry".)
Non-Local Light and "c" vs Local Matter and "G"
"Velocity c" is the gauge of both the primordial, spatial entropy drive of light, and the spatially symmetric "non-local" energy state of light (free electromagnetic energy). "Non-locality" is due to the fact, discovered by Einstein, that light has no time dimension and no spatial dimension in the direction of its motion. In Einstein's mathematical formulation of this symmetry, the "Interval" of light = zero. Within its own reference frame, the energy of any individual photon (quantum of light) is distributed uniformly, everywhere, simultaneously. This symmetry in the spatial distribution of light's energy is a consequence of light's "non-locality", and according to Noether's Theorem, "non-locality" is a symmetry of light which must be conserved.
Einstein's "Interval" is an invariant quantity of spacetime (in any reference frame) whose function is to rescue causality from the shifting dimensional perspectives of Einstein's relativity - the relative and variable motions of matter, rather than the absolute and invariant motion of light. Massless light is non-local, atemporal, and acausal; massive matter is local, temporal, and causal.
Light is a 2-dimensional transverse wave whose intrinsic motion sweeps out a third spatial dimension. Lacking both a time dimension and one spatial dimension (in its direction of propagation), light's position in 3-dimensional space or 4-dimensional spacetime cannot be specified. Since both time and distance are meaningless to light, light has in effect an infinite amount of time to go nowhere. Hence in its own reference frame (moving freely in spacetime (vacuum) at velocity c), light must be considered to be everywhere simultaneously. From this results the "non-local" character of light and light's zero "Interval".
The charges of matter are the symmetry debts of light, and light's "non-local" distributional and metric symmetry is conserved through the "location" charge of gravitation, of which time is the active principle. The time "charge" and the gravitational field it induces identify energetically the specifiable (and hence asymmetric) location of immobile, undistributed, mass-energy in 4-D spacetime, including the quantity and density of the distributional symmetry violation - the local concentration of matter. Einstein's "Interval" of mass is always greater than zero, due to the presence of time and a third spatial dimension. The time charge breaks the metric symmetry condition of light's "zero Interval", establishing the gravitational metric symmetry debt of bound energy (the warpage of space due to the intrinsic motion of time). Because time is an "entropic" charge (a charge - unlike any other - with intrinsic dimensional motion), the spatial "location" symmetry debt is combined with the asymmetric (one-way) temporal entropy debt. Both debts are dimensional or metric in character. The one-way character of time is necessary not only for reasons of causality and energy conservation, but also to break the otherwise symmetric metric of space, specifying an actual 4-D location amidst the isomorphic and entropic spatial expansion.
Gravity (eventually) restores (conserves) the non-local spatial symmetry of light by the conversion of bound to free energy in stars, quasars, supernovas, and other astrophysical processes, culminating in the complete gravitational conversion of matter to light via Hawking's "quantum radiance" of black holes, in full satisfaction of the symmetry conservation requirements of Noether's Theorem. The conversion of bound to free energy pays the entropy debt simultaneously with the symmetry debt, since light is both atemporal and non-local. The gravitational field "evaporates" along with the mass of the black hole, signifying the final and full payment of gravity's symmetry and entropy debt.
For a more complete discussion of gravitation the reader is referred to: "A Description of Gravitation"; and "Entropy, Gravitation, and Thermodynamics".
Global and Local Gauge Symmetries: Gravitation
All these "global" phenomena are related to the action and character of the gravitational field vector, the "graviton", which produces a one-way local gauge symmetry "current" we recognize as "time". A graviton is a quantum unit of time or temporal entropy. The universal gravitational constant G determines, regulates, or "gauges" how much time or temporal entropy must be created per unit mass; time is created by the gravitational annihilation of space and the extraction of a metrically equivalent temporal residue. Hence G controls how much space must be collapsed to provide a given mass with its requisite time dimension or temporal entropy drive: -Gm(S) = (T)m. Time is the active principle of gravity's "location" charge.
The global gravitational symmetries are a result of the invariance of the universal gravitational constant G, and of the uniform character of time and spacetime. All mass of whatever type is interchangeable with respect to the production of a gravitational field because all mass produces an equivalent time dimension (Gm) or temporal entropy flow. The invariance of the time parameter, no matter when, where, or how it is produced, is essentially the same as for any other charge, except in the case of time, energy conservation is at stake as well as symmetry conservation. A gravitational field is the spatial consequence of the intrinsic motion of time.
All massive objects fall with an equivalent acceleration in a given gravitation field because they are all co-movers with the accelerated flow of spacetime. The acceleration of a gravitational field is due to the constant application of a force - the constant intrinsic, entropic motion of time. Einstein's equivalence principle of gravitational and inertial forces of acceleration is due to the fact that we cannot distinguish between the reciprocal effects of spacetime accelerating through us (as in our gravitational "weight" on Earth's surface) or we accelerating through spacetime (as in a rocket ship).
A third gravitational symmetry, the spherical spatial collapse of a gravitational field, is due to the equivalent coupling between time and each of the 3 spatial dimensions. As time marches off into history, it pulls the spatial dimensions along with it, until they self-annihilate at the point-like entrance to the time line at the gravitational center of mass. Time and space are connected through a tangent point at right angles to all three spatial dimensions.
A fourth global gravitational symmetry involves energy conservation within the whole spacetime metric. We expect the spacetime metric to be the same in New York City or Tokyo, yesterday, today, and tomorrow, and regardless of orientation - provided we remain at rest (and about the same distance from the center of the Earth). This is the "global" condition of metric symmetry - we could trade places with anyone on the surface of the earth and not notice any difference in the parameters of the spacetime metric - clock rate and length of meter sticks. Absent matter and its gravitational fields, we could exchange places with anyone (at rest) in the Cosmos and not notice any difference in the parameters of the spacetime metric. This global symmetry of the metric is obviously necessary for energy conservation.
Of course, Einstein discovered that gravitational fields slow clocks and shrink meter sticks, as does relative motion of any kind, breaking the global metric symmetry of spacetime. These local effects are caused by relative motions - either our motion through spacetime, or spacetime's motion through us (gravitation). These relative motions of matter require (or cause) compensatory adjustments in the local spacetime metric ("local gauge symmetry currents") which are necessary to protect and conserve the invariant values of various conserved material charges, including "velocity c", the electromagnetic constant, the fundamental gauge of the global metric and electromagnetic energy generally. Hence we find the "Lorentz invariance" of Special Relatively, in which "moving clocks run slow" and meter sticks shrink in the direction of motion, and similar effects due to gravitation in General Relativity. Time and space can vary, as Einstein realized, but only if both vary together in such a way as to maintain the value of the electromagnetic energy gauge "c", and the ability of the metric as as a whole to conserve energy.
Thus in spite of the fact that the metrics of gravitational spacetime vary continuously with distance from the center of the field's source, "velocity c" remains constant wherever it is measured. The same is true for relative motions of any kind: clocks may slow and meter sticks may shrink, but the measured value of velocity c remains invariant.
The purpose of a dimensional metric is energy conservation, and gravitation acts to convert the energy-conserving symmetric global metric of space and light to the energy-conserving asymmetric local metric of spacetime, light, and matter. This is essentially the conversion of a global Newtonian metric consisting of an invariant space and time, to an Einsteinian local metric consisting of an invariant electromagnetic constant "c", with co-varying space and time (Minkowski spacetime). The key interaction is the Lorentz transformation or "Lorentz invariance", in which space and time co-vary in such a way ("moving clocks run slow and meter sticks shrink in the direction of motion") that regardless of relative motions or gravitational fields, velocity c remains an invariant universal constant, conserving causality, the Interval, and the value of the various charges and symmetry debts of matter. This is the basic energy and entropy conservation role of gravity. The gravitational force will eventually fulfill and complete its symmetry conservation role via the conversion of bound to free energy in stars and through Hawking's "quantum radiance" of black holes.
In the gravitational force, time is the analog of light's magnetic field, the local gauge symmetry "current" or force (see Abstract, above). Time is implicitly resident in the spacetime metric, just as magnetism is implicitly resident in light's electromagnetic field.
The graviton is the presumed field vector of gravitation, the local symmetry current exchanged between all massive particles (via its effect upon the spacetime metric). The graviton is actually a form of time or spacetime. A graviton is a quantum unit of time or temporal entropy. All massive objects have a "location" charge, whose active principle is time, and as the time charge exits space (at right angles to all three spatial dimensions, marching off into history), time pulls the spatial dimensions along behind it, causing them to annihilate each other at the point-like entrance to the one-way time line, leaving a temporal residue which is the metric equivalent of the collapsed space. This new temporal residue likewise moves off down the time line into history, pulling more space behind it, repeating the endless, self-feeding entropic cycle. A gravitational field is the spatial consequence of the intrinsic motion of time.
(See: "A Description of Gravity".)
Gravitation has two principle conservation roles: 1) an entropy conservation role, creating matter's time dimension by the annihilation of space (in the process, transferring the spatial entropy drive of light (the intrinsic motion of light), to the historical entropy drive of matter (the intrinsic motion of time)); 2) a symmetry conservation role, converting bound to free energy in stars and via Hawking's "quantum radiance" of black holes - conserving light's non-local symmetric energy state, in complete fulfillment of the symmetry conservation requirements of Noether's Theorem. This connects the symmetry/entropy conservation function of gravity back to its origin in the symmetric energy state of light, completing the conservation loop from global metric to local metric, and back again to global metric (light - matter - light); (light - gravity - light); (space - time - space). (See: "The Double Conservation Role of Gravitation".)
The geometric symmetry of spherical gravitational contraction is exactly the inverse of the geometric symmetry of light's spherical expansion. This is just the difference between explicit vs implicit time, or the negative gravitational entropy drive of matter vs the positive spatial entropy drive of light. In one case, "wavelength" flees "frequency" to create space; in the other case, "wavelength" chases "frequency" to create history (wavelength x frequency = c). (See: "Gravity Diagram No. 2".) (See: "The Conversion of Space to Time".)
The eventual effect of the gravitational local gauge symmetry current with respect to mass (the time "current" or "graviton" flow produced by the gravitational "location" charge of mass), is to gather all massive objects in one place and return them to light (as in the stars). The effect of the spherical geometric symmetry of gravitation is therefore to reconnect the global and local metric gauge symmetries in a loop of conservation that circles from free energy, space, and the intrinsic motion of light, to mass, history, and the intrinsic motion of time, then finally back to light and space again - as in our Sun. These transformations are mediated in both directions by gravitation. The Sun's radiance represents a completed circuit of symmetry conservation. The loop also circles from the global metric of light, to the local metric of gravity, back to the global metric of light; and similarly, from the symmetric entropy drive of light (the intrinsic motion of light), to the asymmetric entropy drive of matter (the intrinsic motion of time), back to the symmetric entropy drive of light. (See: "Currents of Symmetry and Entropy".)
Energy Conservation within a Gravitational Metric
In the case of the electric, number, and color charges we recognize a quiescent state of local symmetry brought about by the field vectors of the forces as they transform globally invariant charges to locally invariant charges, evidenced as a condition of charge neutrality and balance (the ground state of cold atomic matter). This neutral state is achieved despite the relative (rather than absolute) motions, differing histories and species, and partial charges of the massive charge carriers (electrons vs protons, for example). In the case of gravitation, because gravity is an entropic charge, creating matter's time dimension, its activity is always apparent to us. Of course, the electrons are always active in their orbits as well (as the ordinary bar magnetic demonstrates), but we are just usually not aware of their ceaseless activity.
The gravitational analog of the cold, crystalline, locally charge-neutral ground state of atomic matter is realized only at the center of a massive object such as our planet Earth, where the gravitational forces neutralize, balance, and annihilate one another, summing to zero. On planet Earth, gravity only creates the time dimension, fulfilling its entropy, causality, and energy conservation role, but gravity does not yet have sufficient strength to begin fulfilling its symmetry conservation role, the conversion of matter to light, as in our Sun. On a more abstract level of analysis, the quiescent, local symmetry state of gravitation is seen as energy conservation achieved within the local, gravitationally defined temporal metric (spacetime). The spacetime metric exists to ensure, facilitate, and accomplish energy conservation; this goal and purpose must be achieved within the gravitationally defined local metric gauged by G (spacetime), no less than within the globally defined electromagnetic metric gauged by c (space). Because the gravitational forces (metric) of any object all sum to zero at the center of mass, no net motion is imparted to either spacetime or the gravitating mass, as energy conservation requires.
Energy conservation within the locally defined gravitational metric is accomplished in a relative (rather than absolute) environment ruled by the entropic march of time. Time is necessary to balance and conserve the energy accounts of matter because unlike light, the energy content of matter varies with matter's relative motion. Light's energy varies with its frequency, not with its motion, which is absolute and invariant. Time protects causality and accomplishes energy conservation in bound energy, while providing the entropic drive of matter, all the consequence of the gravitational conversion of space to time. The "Interval" of matter is always greater than zero, and the motion of matter is always relative (less than c), never absolute. Nevertheless, because of time, energy conservation is accomplished in a local, relative, and imperfect (variable) world. The (conceptual) expression of the conversion of global into local metric "symmetry":
-Gm(S) = (T)m
also represents the gravitational deceleration of cosmic spatial expansion, which transfers entropy-energy from space and the global entropy drive of light (S), to history and the local entropy drive of time (T). The intrinsic (entropic) motion of light and space funds the intrinsic (entropic) motion of time and history via the gravitational annihilation of space and the consequent deceleration of the cosmic expansion. This is the natural energetic linkage between our three intrinsic dimensional motions or entropy drives: light, gravity, time (spatial entropy drive, entropic conversion force, historical entropy drive). (See: "The Tetrahedron Model of Light and Conservation Law".)
Energy conservation is readily achieved in the global, symmetric, spatial metric defined by c, the invariant electromagnetic constant. Energy conservation must also be achieved in the local, asymmetric, spacetime or temporal metric defined by G. The new invariant global parameters in this gravitational metric are G, the "Interval", and causality. The new variable parameter that achieves energy conservation in the gravitational metric is time, protecting the invariance of causality and the Interval, accommodating the relative motion and variable energy content of matter, providing the entropy drive for bound energy, and creating historic spacetime, the conservation domain for matter's causal information field. Time is the active principle of gravity's "location" charge. Time in the gravitational metric is the functional analog of magnetism in the electromagnetic metric. Just as the magnetic field is part and parcel of the electromagnetic field vector (the photon), so too, time is part and parcel of the gravitational field vector (the "graviton").
The field vectors of all forces, which act as local gauge symmetry "currents", function (in the present moment) to conserve energy in the material, relative system, and (when possible) to return the asymmetric system of matter to its original symmetric energy state, light. They always contain a variable component which "copes" with local, relative conditions - time, magnetism, or the virtual particle-antiparticle components of the strong and weak forces (gluons, mesons, and alternative charge carriers). Time is created by the gravitational annihilation of space and the extraction of a metrically equivalent temporal residue. (The conversion of globally symmetric space and the spatial entropy drive of light, to locally asymmetric time and the historical entropy drive of matter, is necessary to conserve the invariance of matter's Interval and causality, and also to achieve energy conservation within a metric characterized by relative motion.) (See: "The Conversion of Space to Time".)
Because time is extracted directly from space, the dimensional parameters of spacetime are from the beginning metrically and entropicly equilibrated, and can function together seamlessly in their compound conservation domain for free and bound forms of electromagnetic energy.
Massless, 2-D light is non-local, atemporal, and acausal. Massive, 4-D matter is local, temporal, and causal. Energy conservation is observed in both the globally symmetric state (of light) and the locally asymmetric state (of matter). The spherical symmetry of a gravitational field (which vanishes or self-annihilates at the center) is an essential feature of its energy conserving role, by this means not only producing time, but also avoiding producing any net spatial motion in the gravitating mass. Gravitation accomplishes the transformation of the global metric into a local metric; the field vector is time (or spacetime), the active principle of the gravitational "location" charge. The entropy- energy to create matter's time dimension is taken from the intrinsic motion of light via the gravitational annihilation of space and the deceleration of the cosmic expansion. This entropy-energy debt is repaid by the (eventual) gravitational conversion of matter to light, as in the stars and via Hawking's "quantum radiance" of black holes, satisfying the symmetry conservation mandate of Noether's Theorem. The cosmic expansion "accelerates" (rebounds) in consequence of these symmetry payments, which reduce the Universe's total gravitational energy - as recently observed.
Gravitation and Charge Conservation
The weakness of gravity is due to the tangential connection (experienced as the ephemeral "present moment") between matter and its causal conservation domain (historic spacetime). (See: "The Half-Life of 'Proton Decay' and the 'Heat Death' of the Cosmos".) This tangential connection reflects the fact that it is matter's time dimension that has intrinsic, entropic motion, and not matter itself. Matter has no (net) intrinsic motion in either space or time, although matter's associated gravitational field (Gm) consumes space to produce matter's moving temporal dimension. Matter's gravitational field represents bound energy's primordial, intrinsic entropy drive, producing time via the annihilation of a metrically equivalent quantity of space.
The separation (or tenuous, tangential connection) between matter and its historical, causal conservation domain is the root cause of human anxiety regarding our fleeting experience of life, but is necessary to protect both the energy and charge of atoms from the vitiating action of temporal entropy (aging). In consequence of this protection, atoms retain the full value of their energy content and charge magnitudes until their energy and symmetry debts are paid in full - either gravitationally by Hawking's "quantum radiance" of black holes, or via the electromagnetic annihilation of matter-antimatter particle pairs, or by the strong and weak nuclear forces through particle and "proton decay".
Within our electromagnetic, 4-D universe, the electromagnetic constant c is the dominant global energy gauge, establishing spacetime and its perfectly symmetric metric, with massless, non-local light as the perfectly symmetric energy form. Next below light, c, and the symmetric (inertial) spacetime metric, is matter and gravity, both derived from light and light's metric. G is a global gauge but defines a local metric, which is characterized and "warped" by asymmetric time. The gravitational charge recognizes all particles only in terms of their mass equivalency, the broadest category among material particles, matter or antimatter. Next below the gravitational "location" charge (in terms of generality) is the electric charge, recognizing the equivalency of all electrically charged particles. The weak charge follows, recognizing four subcategories of number or "identity" charge (lepton and baryon "number" charges); finally at the bottom, we find the narrowest category, the strong force charge recognizing only the global category of color charge (all quarks are equivalent with respect to color charge, regardless of other charges they may bear).
This same hierarchy is like a set of nested Russian dolls with respect to the physical volumes of space within their domains. At the top, we have the multiverse of infinite potentiality and n-dimensional conservation domains; next, our 4-D unbounded universe of light, followed by our gravitationally bounded universe, and the gravitational boundaries of galaxies, stellar systems, stars, and planets; below planets is the electrical domain of crystals and organic molecular systems and forms, and atomic electron shells; below the atomic level is the realm of the two nuclear forces, the weak force at the level of elementary particles (creation, destruction, decay, and transformation), followed by a final (?) layer of the sub-elementary quarks, permanently confined by the color charges of the strong force. Biological (living) systems, depending upon how one defines them, fit somewhere below stellar systems (space-faring species) and above crystals (bacteria, virus).
At every level, from the "Big Crunch" to the Sun, stars, and Hawking's "quantum radiance" of black holes, to the matter-antimatter annihilations of particle-antiparticle pairs, or particle and proton decay, the system of interwoven and nested global and local symmetries drives toward a single goal: the return of bound to free energy, the transformation of matter to light, as required by the symmetry conservation mandate of Noether's Theorem.
A diagrammatic representation of the global-local gauge symmetry structure of natural law and the physical forces can be seen in: "The Tetrahedron Model of Light and Conservation Law". A comparison of the "Tetrahedron Model" vs the "Standard Model" of physics is also available.
Postscript
References:
http://www.people.cornell.edu/pages/jag8/gauge12.html
John A. Gowan
(Revised March, 2008)
http://www.people.cornell.edu/pages/jag8/index.html
(See also:
As magnetism is the invisible, "intrinsic" projective electrical force ("electro-motive" force) of the loadstone, so gravity is the invisible, "intrinsic" projective dimensional force ("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 the atoms in the loadstone; in the case of gravity, we trace the force back to the moving (and one-way) temporal charges of the 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. The relation is reciprocal as well: moving magnetic and spatial fields (gravity) create electric and temporal currents (time). This is the analogy between gravity and electromagnetism which so intrigued Einstein. A gravitational field is the spatial consequence of the intrinsic motion of time. See: "Gravity, Entropy, and Thermodynamics".
The charges of matter are the symmetry debts of light.
-Gm(S) - (T)m = 0
Massless light is non-local, atemporal, and acausal; massive matter is local, temporal, and causal.
"c" is a global constant gauging a global metric; "G" is a global constant gauging a local metric. The "global" symmetries of gravitation originate with the universal gravitational constant "G". These include (at least) 4 major physical phenomena: 1) the equivalence of mass, in whatever form, with respect to the production of a gravitational field; 2) all massive objects of whatever composition fall with an equivalent acceleration in a given gravitational field; 3) the universal equivalence of gravitational vs inertial forces of acceleration (Einstein's "Equivalence Principle"); 4) the global symmetry of a given spacetime metric (everywhere on the surface of planet Earth, for example). ("Mass" is any form of 4-D bound energy which does not have intrinsic motion c, has a time dimension, produces a gravitational field, and whose spacetime "Interval" is greater than zero.)
Since we are making the assumption that the field vectors of the forces are in effect "local gauge symmetry currents", converting global symmetries into local symmetries, we must allow the field vectors to inform us regarding the activity and conservation role of the force in question. In the case of gravitation, the field vector or "graviton" is time or spacetime, the activity is the conversion of space into time, and the conservation role is extremely broad, encompassing the conservation of energy, entropy, symmetry, and causality, among others. In the context of the "global vs local gauge symmetry" paradigm, the conservation role of gravitation is most generally characterized as the conversion of the symmetric global, spatial metric, whose only energy form is light, to an asymmetric, local spacetime metric which accommodates both light and matter (free and bound electromagnetic energy).The invariant, global magnitude of gravity's time or "location" charge - like all other charges - must be maintained, because of the intimate connection between time and energy conservation (entropy, causality, the Interval, relative motion, etc.). Hence both c and G (the latter gauges the entropic equivalence of T and extracts time from space), must be universal and invariant metric constants. Nevertheles, time can vary locally if space co-varies, a combination which maintains the constant value of c, which in turn gauges and protects the global value of T. T can vary locally only within the framework of a global metric structure which as a whole remains capable of conserving energy (Lorentz invariance). Charge invariance - including time invariance - is the key to understanding the local forces and the local action of the field vectors (local "gauge symmetry currents"). The local, relative motions of matter require local compensatory forces to maintain and protect the invariant, global parameters of charge, including time and the electromagnetic constant, "c".
We see a hierarchy of global-local gauge symmetries, with the "multiverse" at the top, existing purely in terms of creative potential, with all the various possible universes as the local gauge expressions of the next lower (derivative) level. Our universe is one such local choice among these (infinite?) global possibilities, whose physical laws and constants (by chance alone) favor the evolution of our life form (the "Anthropic Principle"). At the multiverse level, the energy type, dimensional parameters, and physical constants of our universe are but the local gauge parameters of a specific (electromagnetic) choice or realization, among an infinitude of possible universes. I would guess that the only restriction upon the physical parameters of any universe is that: 1) it requires no net energy (or charge) to create; 2) it must be capable of conserving such energy as it does contain.
A Hierarchy of Gravitational Conservation Roles and Domains
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