Extending Einstein's Equivalence Principle: Symmetry Conservation
(revised April, 2008)
John A. Gowan
http://www.people.cornell.edu/pages/jag8/index.html
Extending Einstein's "Equivalence Principle" depends upon recognizing the dual conservation role of gravitation: entropy plus symmetry. Gravity's "primary" conservation role is entropy conservation, accomplished by the gravitational conversion of space to time. This is the role reflected in Einstein's gravitational field equations as the "warpage", "curvature", or "acceleration" of the spacetime metric. The "curvature" of the otherwise symmetric spatial metric is due to the presence of bound energy (mass), gravity, and asymmetric time, specifically time's intrinsic, one-way motion. Time is created by the gravitational annihilation of space, exposing a metrically equivalent temporal residue. (See: "The Conversion of Space to Time".) The primordial, spatial entropy drive of free energy (the intrinsic motion of light), is gravitationally converted (conserved) to the primordial, historical entropy drive of bound energy (the intrinsic motion of time). This primary or entropic conservation role of gravity is accomplished on every scale of bound energy, from electrons to quasars. (See: "Gravity, Entropy, and Thermodynamics".)
The extended equivalence principle includes gravity's "secondary" conservation role, the conservation of light's "non-local" symmetric energy state, accomplished by the gravitational conversion of bound to free energy, in obedience to "Noether's Theorem". This role is played out only on sufficiently large and energetic scales, such as stars, supernovas, quasars, and goes to completion through Hawking's "quantum radiance" of black holes. Gravity's symmetry conservation role essentially reverses the effect of its entropy conservation role. The two roles act upon matter simultaneously in stars, producing a "steady state" of tension between gravitational collapse and radiative expansion. This secondary, symmetry conserving role of gravitation was not emphasized (or recognized?) by Einstein, but results from a famous theorem formulated by his contemporary, Emmy Noether, in 1918. (See: "The Double Conservation role of Gravitation".)
The two conservation roles of gravity are consequences of the two gauge roles of the electromagnetic constant, "c" (the "velocity of light"). "Velocity c" gauges the primordial entropy drive of free energy (the intrinsic motion of light), which causes the creation, expansion, and cooling of space. "Velocity c" also gauges the "non-local" distributional symmetry of light's energy, including the symmetry of the metric of spacetime, in which light has no time dimension and lacks one spatial dimension (in the direction of propagation). Because both effects depend upon light's "intrinsic motion", as gauged by "velocity c", both are conserved together by gravity as it acts to conserve light's "non-local" distributional symmetry (in obedience to Noether's Theorem). (See: "A Description of Gravitation".)
"Noether's Theorem" implies that "the charges of matter are the symmetry debts of light", and requires that the symmetries of light must be conserved in any transformation of light's symmetric energy state, especially such a drastic transformation as the conversion of light's free energy state to a bound energy state (such as matter - or even the capture of a photon by the electron shell of an atom). Gravity is the force which conserves both light's spatial entropy drive (intrinsic motion) and "non-local" symmetric energy state, the former by converting light's intrinsic motion to time's intrinsic motion, and the latter by converting bound to free energy, as in the stars, supernovas, quasars, and (ultimately and completely) Hawking's "quantum radiance" of black holes. The importance of extending Einstein's "Equivalence Principle" into the symmetry conservation domain of "Noether's Theorem" is that it allows us to view gravitation as a symmetry debt of light, like the other charges of matter, and proceed with a plan of force unification upon this fundamental basis. (See: "Symmetry Principles of the Unified Field Theory".)
Einstein's original "Equivalence Principle" unified gravitation, spacetime, and the inertial symmetry-keeping and energy-conserving forces of the metric (the "g" forces of accelerated motion). Noether's Theorem shows us the way to extend this unification to all the charges of matter, that is, to particles, charges, and their symmetry-keeping forces - all under the mantel of Noether's Theorem of symmetry and charge conservation. Like the other charges and their forces, gravity results from a charge which carries a symmetry debt of light. This charge is "location", whose active principle is time, and which represents the symmetry debt of the non-local distribution of light's energy, a symmetry broken by immobile, massive, bound energy (matter).
Einstein's "Equivalence Principle"
"Big G" is the universal gravitational constant, familiar to us through Newton's famous formula for the gravitational force acting between two bodies: F = GMm/rr, where Mm is the mass of the respective bodies, and r is the distance between their centers. G is the invariant constant or "gauge" of gravitational force.
"Little g" is the local intensity of the gravitational field; it measures the force or "weight" we feel standing on Earth's surface. "Little g" (for example) is much less on the surface of the Moon, but "big G" is the same everywhere. Little g is also equivalent to the inertial "g" forces of acceleration experienced in sudden starts, stops, and sharp turns (Einstein's "Principle of Equivalence" of gravitational and accelerated reference frames). The equivalence holds because as we stand on the surface of the Earth, space accelerates through us toward Earth's center, while in the reciprocal situation (through the appropriate application of energy), we accelerate through space (in a "rocket ship", for example). "g" forces vanish in "free fall" (or orbit) because we become co-movers with the field. Similarly, acceleration forces vanish when we "turn off the engines" and drift freely in space with the metric's inertial field. An earlier version of the equivalence principle, attributed to Newton, noted only the unexplained correspondence between inertial mass and gravitational weight (see below). It is readily seen that Einstein's equivalence principle (the acceleration or "curvature" of spacetime) includes and explains its predecessor.
The Three Levels of the Equivalence Principle:
A) (Newton) Mechanical - The equivalence of inertial mass and gravitational weight
1) Inertial mass and gravitational weight are equivalent, so inertial mass can be measured by weighing objects against a standard in a gravitational field. The cause of this equivalence is unknown. The equivalence is invoked to explain why all things fall with the same acceleration in a gravitational field. (The inertial resistance to motion offered by any object's "mass" exactly counterbalances the attractive force of gravitation due to that object's "weight" - rendering all differences in weight irrelevant to the action of gravity.)
B) (Einstein) Geometric - The equivalence of the forces of gravitation and acceleration
1) The forces of gravitation and acceleration are equivalent, and "free fall", orbital motion, and "coasting" cause both to vanish: we deduce from this:
2) the force of gravity is actually the convergent, accelerated motion of spacetime, explaining the equivalence of gravitational weight and inertial mass;
3) Free fall, orbit, (or "coasting") is the condition of co-moving with the metric field, whether accelerated or not;
4) Since all falling, orbiting, (or "coasting") objects are co-movers with the metric field of spacetime, they are also co-movers with each other (or at rest relative to each other), explaining the fact that all objects fall with the same acceleration in a gravitational field. However, the reason why gravity accelerates spacetime (what is the conservation role of this force? - or equivalently: what natural law requires the existence of gravity?) remains unknown.
C) (Noether) Symmetric - The equivalence of gravity and charge (gravity is produced by one of matter's several conserved charges). The conservation of the non-local symmetric energy state of free energy (light): in any transformation of free to bound energy, the symmetry as well as the raw energy of light must be conserved (Noether's Theorem). Charge conservation, gravitation, and inertial force = symmetry conservation (in particles and the spacetime metric). Time is the active principle of gravity's "location" charge. Time is an entropic charge, a charge with intrinsic dimensional motion - a notion connecting gravity, relativity, and quantum mechanics.
1) Free and bound energy are energetically equivalent (E = mcc): matter is created from light in the Big Bang; conversely, light is created from matter in stars and via Hawking's "quantum radiance" in black holes. Matter is an (asymmetric) form of light's energy.
2) The charges of matter are the symmetry/entropy debts of the light (free energy) which created matter. Converting matter back to light pays all symmetry/entropy debts.
3) Noether's theorem - the conservation of light's symmetry - is exampled by the forces of charge conservation, inertia, and the primordial form of light's spatial entropy drive (the intrinsic dimensional motion of light as gauged by "velocity c"). The charges of matter are the symmetry debts of light. The entropy drive (intrinsic dimensional motion) and symmetry gauge of light are linked, both attributes of "velocity c", and therefore both are conserved together by Noether's symmetry conservation theorem. Charges produce forces which pay the symmetry/entropy debts they hold by returning the asymmetric bound energy system to its original symmetric free energy state (light). Time is an entropy and symmetry debt (charge) of light's (broken) non-local symmetric energy state which produces gravitation as a restorative or conservation force. A gravitational field is the spatial consequence of the intrinsic motion of time. All forms of energy originate as, and eventually return to, light. (See: "The Tetrahedron Model of Energy and Conservation Law".)
Entropy vs Symmetry Debts of Light and Matter
Since both the spatial entropy drive and the "non-local" symmetric energy state of light are regulated, scaled, or "gauged" by velocity c (the "intrinsic motion" of light), when one is conserved, the other is also. Entropy is a corollary of energy conservation, and when energy is transformed and conserved, some form of entropy must be transformed and conserved as well. When light transforms to matter, that new bound state will require a new entropy drive appropriate to that state - as provided by the quantum mechanical and gravitational transformation of space and free energy's (light's) spatial entropy drive to time and bound energy's (matter's) historical entropy drive. Time's intrinsic motion creates a new conservation domain for matter's causal information matrix - history (historic spacetime). Because velocity c is also the gauge of metric symmetry, we can bring the gravitational conversion of space to time under the symmetry conservation umbrella of Noether's theorem. (See: "Spatial vs Temporal Entropy".)
The universal character of all symmetry debts is seen in the fact that all charges produce forces which act to return the material system to its original symmetric state by converting bound to free energy - not only through chemical reactions, matter-antimatter annihilations, particle and proton decay, but also through gravitational processes exampled by our Sun and the stars, supernovas, quasars, and the ultimate, complete conversion of bound to free energy in Hawking's "quantum radiance" of black holes.
The enlarged framework of the extended equivalence principle allows gravity to join the other forces as a symmetry/entropy debt of free energy (by Noether's theorem, all charges of matter are the symmetry debts of light). The "entropic charge" of time, the active principle of gravity's "location" charge, contains in itself the essential joining of the dimensional aspects of General Relativity with the charge aspects of quantum mechanics: 1) the intrinsic dimensional motion of time, acting as matter's entropy drive, producing by its own motion the collapsing, accelerated spatial flow we commonly recognize as a gravitational field; 2) time as the "locating" charge of the four dimensions, the symmetry debt of light's "non-local" character, providing mass with a specifiable location in spacetime, a nonzero "Interval" resulting (eventually) in the gravitational conversion of mass to light in stars. Charges produce forces whose conservation purpose is to pay the symmetry debts they hold; payment of the temporal symmetry and entropy debt drives the gravitational conversion of bound to free energy - in stars, supernovas, quasars, and finally in Hawking's "quantum radiance" of black holes. (See: "The Conversion of Space to Time".)
The Bekenstein-Hawking theorem relates the surface area of the "event horizon" of a black hole to the entropy content of the hole. Black holes are the physical demonstration of the gravitational conversion of space and spatial entropy to time and historical entropy. The "surface" of a black hole (the area of its "event horizon") is a time "surface" where time effectively stands still because time is being replaced by the intense local gravitational field (g = c) as fast as time moves away into the historic domain. Hence while we can think of the ordinary rock as an asymmetric form of light's energy transformed to matter and brought to rest, we can likewise think of the event horizon or surface area of a black hole as an asymmetric form of light's entropy - transformed to time and brought to rest. (See: "The 'Tetrahedron Model' vs the 'Standard Model' of Physics: A Comparison".)
Hawking's "Quantum Radiance" of Black Holes
When we extend the "Equivalence Principle" to include gravity's symmetry conservation role, it is through the "location" charge of gravity, whose active principle is time. The "location" charge allows us to treat gravity like any other charge of matter, as a symmetry debt of light. Because time is an entropic "charge" of matter and gravitation (a charge with intrinsic dimensional motion), the extension of the Equivalence Principle from inertia to charge is natural. Time is the bridge between the charges of matter and the intrinsic dimensional motions of entropy's primordial forms (the intrinsic motions of light, time, and gravity). Time is the entropic charge of gravity and bound energy. Time's intrinsic motion produces both the primordial entropy drive of matter and eventually, in sufficiently large bound energy concentrations (such as stars), a gravitational force strong enough to begin the symmetry conservation role of gravity, converting bound energy back to light.
Do we ever see this charge aspect of time, "location charge", or gravity explicitly expressed in particle form, as the union of gravity with the other charges and forces suggests we might?
This is indeed the case in Hawking's "quantum radiance" of black holes, where extreme gravitational tidal warpage (or differential acceleration) of spacetime produces particle-antiparticle pairs directly out of the spacetime metric or "vacuum". This purely gravitationally produced source of antimatter and negative energy is used to completely transform the bound energy of the black hole to free radiation. This is the ultimate expression of the symmetry conservation role of gravity and the extended equivalence principle through particle charge, in which we see gravity acting like any other charge of matter - the equivalence of gravity and charge. The extended equivalence principle (we might call it "Noether's Equivalence Principle") thus leads us to the union of gravity and quantum mechanics, the unity of forces, and the unity of particles and spacetime, via Hawking's "quantum radiance" - as Einstein's original Equivalence Principle led us to the union of gravity with spacetime via Newton's inertial forces of acceleration.
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