On Aug 5, 2011, at 1:55 PM, Paul Zielinski wrote:
Einstein's theory of gravity aside, we can always choose a curved geometry to formulate physics.
This is false. You can choose curvilinear coordinates, but the tensor curvature Ruvwl will still be zero if it was initially.
There is no mathematical or empirical reason to prevent us from doing so as a matter of convention (as argued in detail by Poincare and others). Then free test objects will *not* move along geodesics.The actual physics, however, will be the same regardless. The law of inertia will still hold.
Another false statement. The geodesic equation is a tensor equation.
D^2x^u/ds^2 = 0
the covariant derivative of a tensor is still a tensor.
One way of looking at Einstein's theory is that the geodesics are simply deformed to agree with the inertial effects of a gravitational field produced by matter.
If you mean by that vague sentence
Guv + kTuv = 0
then I agree.
Again if you use equations instead of words when possible, you are less likely to be misunderstood.
From that POV, Einstein's curved spacetime is simply an abstract geometric model for gravity, with no more explanatory
content than Ptolemy's epicycles.
Epicycles were good for its time. However, I disagree with your opinion. Depends what you mean by explanation.
Then the real physical content of the Einstein-Hilbert field equations is simply that the presence of gravitating matter THERE alters the local conditions of inertial motion HERE
Wait a minute
Guv + kTuv = 0
means matter here bends spacetime here - it's a local equation.
Of course the solutions involve Green's function propagators (with boundary conditions) so indeed matter here will bend spacetime there, but that requires more information than only the local dynamical field equations.
This is true in all local field theories not just Einstein's.
-- and that this is simply modeled mathematically in terms of a curved spacetime geometry, treated as a pseudo-Riemannian manifold, where it is stipulated that the local Ricci curvature (and the coupled Weyl curvature outside the sources of the field) is determined by the matter distribution.
Now it is true, that if you use the graviphoton spin 1 vector gravity tetrad fields instead of the spin 2 metric tensor fields (the latter's graviton is composite from the former of course) that the four Cartan tetrad 1-forms e^I (LIF basis) describe the Sciama "origin of inertial motion" as geometrodynamic fields on a formally globally flat Minkowski background.
That Minkowski background cannot not be detected globally only locally (EEP). Background independence is obeyed because the tetrad components couple universally and minimally to all non-gravity matter source and force fields. Therefore, all the usual gravity time distortions of the classic GR tests and beyond are obeyed.
But, for example, you can make a globally flat Fourier decomposition of e^I(x) into plane waves like in ordinary classical/quantum field theory, but the universal minimal coupling of EEP will give complicated convolution integrals.
For example, given the EM vector potential A^I in a LIF, it transforms to a locally coincident LNIF as
A^u(x) = e^uI(x)A^I(x)
Formally then, the Fourier transform of A^u(x) in the fictitious non-dynamical Minkowski background (with trivial global topology for now) is the convolution integral of AI(k,f) with e^uI(k,f).
http://www-structmed.cimr.cam.ac.uk/Course/Convolution/convolution.html
At least it's another way of looking at this. And who now believes that the gravitational field is literally reducible to curved Riemannian geometry?
Depends what you mean by "literal" - your meta-theoretical concerns are usually too vague for me.
spin 2 tensor gravitons may be composite entangled pairs of spin 1 gravi-photons (not same as Maxwell's photons).
In addition spin 1 vector particles are entangled pairs of Weyl 2-component spinors ---> twistors (Penrose) indeed the Bell states of IT FROM BIT quantum information theory pop up here - quantum teleportation and all that.
But if all that is true there should be spin 0 (Dicke) as well as spin 1 gravity fields in addition to the spin 2 gravity fields. Perhaps the spin 0 and spin 1 gravitons get rest mass from a Higgs mechanism and are confined to short distances?
See the Penrose & Rindler book.
On 8/5/2011 11:18 AM, JACK SARFATTI wrote:
First of all this word "inertia" is bandied about too loosely causing much of the confusion. It has at least different meanings in relativity.
Meaning # 1 Origin of inertia in one of Sciama's senses is trying to explain why test particles move on geodesics.
i.e. zero g-force free-float "weightless" "inertial motion" universal independent of the rest masses m of the test particles.
This is essentially trying to explain Newton's first law of mechanical motion generalized to curved space-time. Einstein with Infeld actually proved the geodesic rule from his nonlinear field equations
Ruv + 8piGTuv/c^4 = 0
modeling the test particle as a singularity in the 4th rank curvature tensor Ruvwl field if I remember correctly off the top of my head.
The Einstein-Infeld calculation is purely local not needing Mach's Principle.
Mach's Principle is archaic and quaint referring to "distant matter" that makes no real sense at all in modern precision cosmology since the 1990's because the only kind of "matter" Mach knew about is only 4% of all the gravitating stuff in the universe!
Woodward refers to the distant matter in "causal contact" with his local flux capacitor space drive prototype device that he actually has running in his lab much to his engineering credit. On the other hand, the situation seems to be like cold fusion and high-frequency-gravity-wave propulsion & Podkletnov type allegations discussed at the JASON meeting I attended a few years ago at General Atomics in La Jolla - hard to replicate by independent parties.
Woodward is not clear what he means by "causal contact" at times he seems to mean only the past light cone out to the "particle horizon" of the flux capacitor, but this contradicts the key assumption in his eq (44) that the universe as a constant density of "distant matter" if by that he means what Mach meant the "distant stars" - there is great ambiguity here and his equations rest on very shaky ground.
Keep in mind Tamara Davis's diagram
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At other times Woodward alludes to Wheeler-Feynman and of course Sciama worked with Hoyle who developed the Wheeler-Feynman classical retrocausal ideas to quantum theory and cosmology. This brings in the future light cone of his device reaching to our future event horizon - hence John Cramer's "transactions" and Yakir Aharonov's "destiny" (post-selection final boundary condition) and even 't Hooft-Susskind's hologram conjecture.
Meaning #2 of "inertia" as resistance to non-gravity forces pushing the test particle of rest mass m off its timelike geodesic determined locally by source stress-energy density tensors Tuv(non-gravity fields). No need for Mach's Principle here.
So this is essentially F = ma Newton's 2nd law of mechanical motion of test particles generalized to curved spacetime.
The computation of the rest masses m of ordinary matter (real on mass shell in sense of quantum field theory's Feynman propagators) does not require gravity or Mach's principle, but is explained quantitatively for hadrons by Franck Wilczek's quantum chromodynamic supercomputer computations using the Higgs field couplings to the quarks in the input to the program.
What Sciama means by the "origin of inertia" is really the origin of the universal geodesic inertial motion of neutral test particles. He does not mean that Mach's principle is needed to explain why or how the rest mass of the electron is ~ 10^-27 grams or the rest mass of the proton is ~ 10^-24 grams - that is not a gravity physics problem needing the cosmological scale Mach's Principle.
Subject: What Sciama means by the "origin of inertia"
He does not at all mean the computation of the rest masses m of the elementary particles. He simply means the geodesic structure of the curved spacetime - the LIFs (Local Inertial Frames) with zero g force. By "inertial properties of matter" he means neutral point test particles moving along geodesics - the generalized Newton first law of motion in curved spacetime. His language is ambiguous, but in context it's clear he is not thinking of how much acceleration one gets when applying a non-gravity force to a test particle pushing it off its subluminal timelike geodesic in possibly curved spacetime. Sciama is not thinking of Newton's 2nd law of motion in this 1952 paper only the first law. In other words his problem here is "why do neutral test particles follow geodesics" - a metaphysical quest for sufficient reason for what most of us accept pragmatically because it works. Note that his Maxwell vector model here is only meant as a rough qualitative toy model. Sciama is doing what Zielinski tried to do. That is, here Sciama is using Newton's picture where gravity is a real force that is canceled out by the rest of the universe in the free float geodesic motion. It's Rube Goldberg and is not necessary as Einstein's curved spacetime picture is better, more elegant, in my opinion. Also what is "distant matter"? When is it as well as where is it. Remember 1952 was the Dark Age of primitive cosmology. Sciama's ideas are now quaint and obsolete in the light of the 1998 discovery of dark energy - not to mention dark matter as well. On the other hand the gravity effect of the universe as a whole sounds like Wheeler- Feynman's future universe quantum influence functional as developed by Hoyle and Narlikar. The analogy to Wheeler-Feynman is not perfect because the future total absorber was the emitter of Cramer's advanced waves needed to complete a "transaction" for the emission of a photon. This is a retrocausal explanation for the manifestly non-geodesic motion "jerk" of Dirac's radiation reaction. Hoyle and Narlikar (1995 Rev Mod Phys) show that our future de Sitter horizon is the Wheeler-Feynman total absorber explaining why there is an Arrow of Time at least on the cosmological scale i.e. why we age as the universe expands and indeed is now accelerating for several billion years since the turning point.