re: Notes on Gennady Shipov's latest work on torsion field physics extension of Einstein's geometrodynamics
See also James Woodward's "Radiation Reaction" at
Lecture 9 "The Feynman Lectures on Gravitation":
"The Principle of Equivalence postulates that an acceleration shall be indistinguishable from gravity by any experiment whatsoever." p.123
This last condition "by any experiment whatsoever" is what concerns Paul Zielinski. But leave that on the back burner.
"There is evidently some trouble here, since we have inherited a prejudice that an accelerating charge should radiate, whereas we do not expect a charge lying in a gravitational field to radiate."
Indeed James Woodward writes:
"It is known as a matter of fact that electric charges subject to constant accelerations radiate electromagnetic waves ..."
Back to Feynman: "This is, however, not due to a mistake in our statement of equivalence but to the fact that the rule of the power radiated by an accelerating charge
dW/dt =(2e^2/3c^3)a^2 9.1.1
has led us astray. This is usually derived from calculating the flow from Poynting's theorem far away, and it is only valid for cyclic motions, or at least motions which do not grow forever in time (as a constant acceleration does)."
Thus, there appears to be a conflict between Feynman's and Woodward's statements?
Feynman: "It does not suffice to tell us 'when' the energy is radiated. This can only be determined by finding the force of radiation resistance, which is (2e^2/c^3)(da/dt). For it is the work against this force which represents energy loss. FOR CONSTANT ACCELERATION THIS FORCE IS ZERO." CAPS not in original. Note, Woodward also mentions this. He is aware of it.
Feynman: "Generally the work done against it is
dW/dt = -(2e^2/c^3)v.(da/dt) = +(2e^2/c^3)[a^2 - (d/dt)v.a] 9.1.2
For cyclic or limited motions the average contribution of the last term over the long run is small or zero ... and the simpler 9.1.1 suffices."
F(radiation resistance) = (2e^2/c^3)(da/dt)
Note that e^2 has dimensions of hc so that [(h/c^2)(da/dt)] = (ML^2/T)(T^2/L^2)(L/T^3) = ML/T^2
Dirac's treatment of the radiation resistance force:
Define the difference between EM signals arriving here-now at location of the electron from past and future light cones to be
S*^uv = (1/2)[F*^uv(retarded) - F*^uv(advanced)]
where, in general, Fuv is the Maxwell field tensor, i.e. the 4D curl of the 4-vector potential Au that is a connection field for parallel transport in a curled up internal space of one complex dimension.
Compute each F*^uv for a spatially extended electron with a given electric self-charge distribution. That is, only consider how different pieces of the spatially extended charge distribution act on the other pieces of the same distribution using both delays and presponses! That is, F*^uv only refers to internal self-signals connecting different pieces of the extended charge distribution! Think of say a thin shell of electric charge to make a definite visualizable model. Do not worry how that self-charge is stabilized. That comes later with quantum zero point energy and vacuum coherence not known to Dirac. Each F^uv, i.e. advanced and retarded for any definite classical electron model will individually explode to infinity as the radius rc of the electron shrinks to zero, but their difference will not. It has a finite value in the limit given by
f^u(rr) = Lim rc -> 0 eS^uvdx^u/dt = (2e^2/c^3)(da^u/dt)
p. 14 "Cosmology and Action at a Distance Electrodynamics" Hoyle and Narlikar.
The Lorentz force on a "point" charged particle now has a jerk term, i.e. a third order time derivative
F^u = md^2x^u/dt^2 = e[F^uv(external) +Lim rc -> 0S^uv(self)](dx^v/dt)
This leads to the problem of a run-away solution unless would violated retarded causality a wee bit with a tiny presponse that is not, however, big enough to explain what Dick Bierman sees in living conscious matter. That requires a new effect of post-quantum signal nonlocality violating micro-quantum theory and completely upsetting the Apple Cart of Quantum Computers, Quantum Cryptography, Quantum Teleportation, and No Cloning a Quantum to recover or erase information loss down a black hole event horizon. That is, unitarity has its limits. Our conscious minds cannot exist in a strictly unitary multiverse the way David Deutsch and Lenny Susskind conceive it in which the statistical laws of micro-quantum theory are absolute not to be broken. Indeed, all living matter breaks those orthodox quantum rules which only correspond to "sub-quantal heat death" in the sense defined by Antony Valentini. He has not, however, realized that all life is the evasion of sub-quantal heat death!