Feynman Diagrams and "Time's Arrow"
John A. Gowan
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(revised Nov., 2010)
On page 118-119 of his biography of Richard Feynman "Genius" (Pantheon books, New York, 1992), James Gleick recounts a meeting between Feynman, J. A. Wheeler, and Albert Einstein in which the three of them agree that the fundamental equations describing the absorption and emission of light waves by atoms are symmetric with respect to the sign of the time parameter - that is, there is no directionality of "time's arrow" at the microscopic level of phenomena; it is only at the macroscopic level that the irreversible character of time begins to assert itself, and then for no other reason than probability.
From this meeting (1941), the general notion of time symmetry and the irrelevance of causality in microscopic "fundamental" or quantum-level interactions was born. However, what is true for light waves (which Einstein had shown earlier really are "non-local" and do not have a time dimension), is not true for material, "ponderable" particles with rest mass which do not travel with intrinsic motion c, such as the electron.
Nevertheless, DeBroglie had shown (1923) that subatomic particles do have a wave component, which is more strongly expressed the less massive the particle. Since electrons are very light indeed, their wave character is correspondingly magnified. The wave component of electrons has been convincingly demonstrated in the canonical two-slit experiments of quantum mechanics, in which electrons in fact show some of the wavelike or "non-local" interference effects usually associated with photons.
The photon is the field vector of electric charge, the force carrier of the electromagnetic field, and the notion of temporal symmetry in the equations of interaction between electrons and photons at the quantum level was simply assumed, including the famous Feynman diagrams in which anti-electrons (positrons) are diagrammed as moving backward in time. The acausal, atemporal, non-local character of light was extended in these diagrams and equations to massive objects (electrons) without justification, ignoring: 1) the principle of causality; 2) the time dimension; 3) the gravitational field of matter; 4) the principle of entropy - disregarding the causal, temporal, and local character of electrons and by implication, all massive particles.
It is not permissible to ignore the gravitational field of an electron, just because it is small. "Big G", the universal gravitational constant, has the same value with regard to the electron's mass as it does with regard to the Earth's mass. The electron's gravitational field produces its time dimension, which is the fundamental entropy drive of bound energy. There can be no temporal symmetry in the interactions of light with matter because matter has a time dimension, a causal and historical relation, an entropy drive, and a gravitational field which are all intimately related and are all one-way asymmetric physical phenomena. The temporal symmetry of the Feynman diagrams are useful for computational purposes, but it is not physically valid for massive particles.
In this we see also the beginning of the difficulty of constructing a unification theory incorporating gravitation, since gravitation, time, causality, and entropy are simply banished by fiat from the quantum interactions from the beginning. I am not complaining about other parts of Feynman's "sum over histories" ("path integrals") model, just the time-reversed aspects. It seems that in nature these paths are moot in any case, as particle-antiparticle interactions result in annihilations rather than causality violations. In the case of light itself, the notion of time reversal is harmless since light has no time dimension at all, either forward or backward. Considering light only, the notion of time reversal could actually be usefully applied to cancel out any inappropriately conceived "forward" temporal motion.
In my own theory of gravitational unification (See: "A Description of Gravitation"), gravity is the spatial consequence of the intrinsic motion of time, arising from the quantum mechanical "flip" or "switch" of the temporal component of a light wave from implicit to explicit (see: "The Conversion of Space to Time"). Thus the whole difference between the intrinsic motion of light and the intrinsic motion of either time or gravitation is the quantum mechanical difference between the implicit vs explicit presence of the time component ("frequency") in a moving vs stationary electromagnetic wave or energy form. The "up" ("heads") or "down" ("tails") of the electromagnetic entropy "coin" (a quantum unit of temporal entropy) determines the expansion and cooling of space vs the aging and decay of history. (See: "Gravity Diagram No. 2.")
Frequency multiplied by wavelength = c, the velocity or intrinsic motion of light. Thus both time ("frequency") and space ("wavelength") are at least implicitly present in the fundamental formulation of light's intrinsic motion, even though light itself has no time dimension and no spatial extension in its direction of propagation (light is a 2-dimensional transverse wave). The "intrinsic" (self-motivated) motion of light is caused by the symmetric spatial component ("wavelength") of the electromagnetic wave "fleeing" the asymmetric temporal component ("frequency"), which, however, is an embedded potential of the wave's own nature, the archetypal case of the "bur under the saddle". Only by constant motion at velocity c is the temporal component suppressed to an implicit condition, maintaining light's metric and distributional symmetry. Metric symmetry conservation in the service of both energy conservation and entropy is the ultimate cause of light's intrinsic motion. In matter, exactly the opposite reaction occurs: space "chases" (or is "pulled" by) the "fleeing" time dimension (matter's entropy drive) to produce the gravitational field. Here the entropy drive and causality relations of bound energy produce an asymmetric metric (historic spacetime), also for reasons of energy conservation. This is just the difference between the positive spatial entropy drive of light and the negative spatial entropy drive of gravitation - the expansion vs the contraction of spacetime. Hence time is the universal entropy driver of both free and bound energy, implicit in light and explicit in matter. (See also: "Entropy, Gravitation, and Thermodynamics".)
P. A. M. Dirac, the great British mathematical physicist, holder of Newton's chair at Cambridge, was Richard Feynman's scientific hero. Dirac was justly famous for, among other theoretical "heavy lifts", his discovery of the positron and the realm of antimatter, purely through his insistence upon the reality of a positive-negative symmetry in his mathematical representation of energy. It is highly probable that Feynman (and Wheeler) were following Dirac's lead in their mathematical modeling of a positive-negative symmetry between matter and antimatter concerning the temporal paths of electrons vs positrons. But this attempt fails for several reasons: 1) there is no positive-negative temporal symmetry for obvious reasons of causality; 2) time runs one-way and the same way for antimatter as for matter, just as there is no anti-causality, no anti-energy, no anti-light, no anti-spacetime, no anti-mass, and no anti-gravity; 3) while gravity is negative entropy, it is negative spatial entropy, not negative temporal entropy. Gravity slows clocks, it does not reverse them. Thus while Dirac "got lucky" with his symmetry relations because he ascribed them to the charges of antimatter, Feynman was not likewise lucky with his interpretation of a similar positive-negative sign symmetry, because he tried to apply it to one-way time, not to two-way space or charge. Time is one-way because of causality; gravity is one-way because it is the spatial consequence of the intrinsic motion of time. Energetically, gravity is one-way because it represents negative energy, due to the energy debt incurred when creating an asymmetric temporal entropy drive from a symmetric spatial entropy drive. It cost energy to "flip" the electromagnetic entropy "coin" from implicit (light's intrinsic motion) to explicit (time's intrinsic motion), energy in the amount -Gm. (See: "The Conversion of Space to Time".)
Apparently Feynman himself eventually became disenchanted with the notion of antiparticles moving backward in time, disavowing his work with Wheeler and "retarded waves", claiming (during his Nobel acceptance speech) that such ideas were not essential to his final formulation of quantum electrodynamics (see page 381 of Gleick's book).*
* Mr. Murray Lewis of Cornell has volunteered the following information (Aug. 17, 2011):
I believe this to be much less than Feynman's last word on the matter. In his book "QED" Princeton Univ. Press: Princeton, New Jersey), 7th Ed 1988 You can find on page 98 (beginning of third Paragraph) his much later statement: "Every particle in Nature has an amplitude to move backwards in time, and therefore has an anti-particle."