I will try to fix it.
On Feb 18, 2012, at 2:52 PM,
Subject: Re: Misner Thorne Wheeler p. 53 no centrifuge redshift & speed of ligh t in accelerating frames
Date: Sat, 18 Feb 2012 12:13:58 -0800
Jack: I think Z means kinematical vs dynamical
Kinematical means in Minkowski space where Tuv = 0
Of course that split is real and can be measured in sense of EEP locally by the tetrad map connecting locally coincident LIF with LNIF.
But the only non zero tensors in the connection are torsion and nonmetricity both zero in 1916 GR they would be real forces on test particle not fictitious.
Indeed locally gauging the dS conformal group gives the old LC connection for inertial fictitious forces on test particle = real forces on coincident detector + real forces on both!
Jim: Yes, but Paul's and my point is that the "fictitiousness" of the inertial force on the test particle that registers as a real force in the detector is not a consequence of the the force actually being unreal.
Jack: What do you mean by "real"? Remember I took philosophy of physics with Max Black at Cornell. It's real on the detector. It's not real on the test particle. Also I was brainwashed by the Cornell Wittgensteinians - fortunately.
Definition of "real force" - a force on an material object is "real" IFF an accelerometer CLAMPED to the object registers a not-null value. In other words, only if the object is literally pushed off a timelike geodesic of the LOCAL GEOMETRODYNAMICAL FIELD (i.e. the GCT INVARIANT tetrad e^I and spin connection S^I^J Cartan 1-forms.
Jim: It is a consequence of the fact that like gravity, it can be removed with geometry (suitable choice of connection).
Jack: That's EEP (formally the tetrad mapping LNIF <---> LIF), but I fail to see your logic here. What is your point? In the LIF there is no g-force on the detector. The test particle does not give a wit about what the detector is or is not feeling (measured by pointer readings of the CLAMPED accelerometer).
Jim: Paul, I think, would like to see this force arise from the action of the quantum vacuum, whereas I am convinced that it is just the force of gravity due chiefly to cosmic matter.
Jack: You lost me completely. You are not making any sense to me. I don't know what you mean in terms of P.W. Bridgman's operational definitions. What is being measured on what? We have two objects here. The test particle and the detector of the the test particle's motion. Your sentences are not precise and detailed enough for my mind to get their meaning. As a question of style I always understand John Archibald Wheeler's writing on these topics. Please try to emulate him.
Operationalization - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Operationalization
P.W. Bridgman, Einstein's Theories and the Operational Point of View, in: P.A. Schilpp, ed., Albert Einstein: Philosopher-Scientist, Open Court, La Salle, Ill., ...
Operational definition - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Operational_definition
This is in contrast to Operationalization that uses theoretical definitions. ... The idea originally arises in the operationalist philosophy of P. W. Bridgman and ...
Overview - Limitations - Application - Examples
Operationalism (Stanford Encyclopedia of Philosophy)
plato.stanford.edu/entries/operationalism/
Jul 16, 2009 – Section 1 introduces Bridgman's key ideas on operational analysis, ......“P. W. Bridgman's Operational Perspective on Physics”, Studies in ...
Percy Williams Bridgman: Biography from Answers.com
www.answers.com › Library › Science
Percy Williams Bridgman American physicist (1882–1961) Bridgman, the son of a ...advocated operationalism, and he coined the term operational definition.
Jim: In the connection of universality arising from local masses m dropping out of equations of motion, let me respond to Paul's criticism of my comments on inertial forces. The proper way to show that is:
Egrav = - grad phi - (1/c)dA/dt (Sciama)
Jack: I do not understand this equation at all in terms of Einstein's gravity theory.
if phi = c^2, then you have grad c^2 =/= 0? What does that mean?
phi is pure timelike polarization
A 3-vector is transverse + longitudinal polarization
gauge invariance is
wphi* + k.A*longitudinal = 0 for zero mass spin 1 vector boson
no spin 2 here.
w = frequency, k = wave vector
* is 4D Fourier transform
"Lorenz gauge
See also: Covariant formulation of classical electromagnetism
The Lorenz gauge is given, in SI units, by:
and in Gaussian units by:
It may be rewritten in terms of the electromagnetic four-potential :
It is unique among the constraint gauges in retaining manifest Lorentz invariance. Note, however, that this gauge was originally named after the Danish physicist Ludvig Lorenz and not after Hendrik Lorentz; it is often misspelled "Lorentz gauge". (Neither was the first to use it in calculations; it was introduced in 1888 by George F. FitzGerald.)
The Lorenz gauge leads to the following inhomogeneous wave equations for the potentials:
It can be seen from these equations that, in the absence of current and charge, the solutions are potentials which propagate at the speed of light.
The Lorenz gauge is incomplete in the sense that there remains a subspace of gauge transformations which preserve the constraint. These remaining degrees of freedom correspond to gauge functions which satisfy the wave equation
These remaining gauge degrees of freedom propagate at the speed of light. To obtain a fully fixed gauge, one must add boundary conditions along the light cone of the experimental region.
Maxwell's equations in the Lorenz gauge simplify to , where jν is the four-current. Two solutions of these equations for the same current configuration differ by a solution of the vacuum wave equation . In this form it is clear that the components of the potential separately satisfy the Klein-Gordon equation, and hence that the Lorenz gauge condition allows transversely, longitudinally, and "time-like" polarized waves in the four-potential. The transverse polarizations correspond to classical radiation, i. e., transversely polarized waves in the field strength. To suppress the "unphysical" longitudinal and time-like polarization states, which are not observed in experiments at classical distance scales, one must also employ auxiliary constraints known as Ward identities. Classically, these identities are equivalent to the continuity equation .
Many of the differences between classical and quantum electrodynamics can be accounted for by the role that the longitudinal and time-like polarizations play in interactions between charged particles at microscopic distances."
http://en.wikipedia.org/wiki/Gauge_fixing
Jack: However, the above is not quite correct since near fields exist over macroscopic distance. Indeed most of electrical power engineering is primarily concerned with near fields. The above is really only for S-Matrix theory.
[edit]
I understand it for Maxwell's electromagnetic field theory.
http://en.wikipedia.org/wiki/Gauge_theory
It is a part of
F = dA
F = electromagnetic field 2-form
A = electromagnetic field 1-form aka potential, connection etc.
U1 gauge transformation is
A --> A + df
f is a 0-form
df is an exact 1-form
d^2 = 0
therefore
F ---> F' = dA' = dA = F
this fails in Yang-Mills theory and GR is like Yang-Mills theory in this regard.
Jim; - grad phi is zero for the case of cosmic matter, but dA/dt is not as A is the integral of matter currents which are not zero if your test object is moving (as the universe appears to move in the opposite direction with velocity v). This leads to:
Egrav = - (1/c^2)phi dv/dt
so the force on a test particle is
m Egrav = - (phi/c^2) m dv/dt = ma
where setting m Egrav equal to ma is just the equation of motion.
Jack: This still does not make sense to me.
Jim: When dv/dt =/= 0, there is a force on m. But note that m on the LHS of this equation is the passive gravitational mass, whereas on the RHS it is the inertial mass. By the EEP they are equal and cancel, just as in the case of Newtonian gravity, establishing the universality of real inertial forces that makes them "fictitious" in the conventional sense of the term, notwithstanding that they are real forces.
Satisfied Paul?
Jack: I'm not. I gave a physical definition of real vs fictitious forces in terms of pointer readings of accelerometers clamped to the several material objects in the measurement algorithms. I don't understand Jim's metaphysics above, e.g. "By the EEP they are equal and cancel, just as in the case of Newtonian gravity, establishing the universality of real inertial forces that makes them "fictitious" in the conventional sense of the term, notwithstanding that they are real forces." First of all the notion of global rigid motions is not physically meaningful in Einstein's theory.