*On Sep 6, 2011, at 1:07 PM, Paul Zielinski wrote:*

*In 1905 SR, it is the coordinate speed that is an absolute invariant under the Einstein-Lorentz transformations and this is at the core of Einstein's 1905 version of relativity.*

I replied:

(ct)^2 - L^2 = (ct')^2 - L'^2 S and S' both GLOBAL inertial frames

L^2 = x^2 + y^2 + z^2

PZ:

*In modern GR, the coordinate speed is not invariant under general transformations; so it is deprecated as "coordinate speed" in favor of invariant measures, in the spirit of general covariance.*

I replied:

(cdt)^2 - dx^2 - dy^2 - dz^2 = guv(LNIF)dx^udx^v = gu'v'dx^u'dx^v'

first = is the tetrad map

2nd = is a GCT

You really can't define the speed of light very well when there is gravimagnetism g0i = Ai =/= 0

Define dL^2 = gijdx^idx^j

i,j = 1,2,3

for a light ray ds^2 = 0

dT = g00^1/2dt

c^2dT^2 - dL^2 + cAidtdx^i = 0

(dL/dT)^2 = c^2 + cAidx^i/dT

c(LNIF) = [c(LIF)^2 + cAi(dt/dT)dx^i/dT]^1/2

v^I = dx^i/dT

dt/dT = 1/g00^1/2

c(LNIF) = c(LIF)[1 + Aiv^i'/c(LIF)g00^1/2]^1/2

Only when Ai = 0

c(LNIF) = c(LIF) and in this case speed of light in a non-dispersive vacuum is an absolute invariant.

*PZ: Of course in Minkowski's version of SR, we already have the Lorentz-invariant interval s which gives us the time actually read by moving clocks. And of course this goes over to the generally covariant infinitesimal interval ds^2 = g_uv dx^udx^v in GR. I think this illustrates very clearly how GR supersedes 1905 SR, and how the definition of "light speed" is not the same in both theories. I think the most one can say is that in LIFs, the locally observed empirical predictions of the two theories agree, since the laws of SR "work" in such local frames.*

On 9/4/2011 10:05 PM, JACK SARFATTI wrote:

*On Sep 4, 2011, at 9:24 PM, Paul Zielinski wrote:*

Jim and Jack,

I think it's high time we got this straightened out. I can;t believe this is still in dispute.

Here's Baez:

Jim and Jack,

I think it's high time we got this straightened out. I can;t believe this is still in dispute.

Here's Baez:

*"The problem here comes from the fact that speed is a coordinate-dependent quantity, and is therefore somewhat ambiguous. To determine speed (distance moved/time taken) you must first choose some standards of distance and time, and different choices can give different answers."*

"This is already true in special relativity: if you measure the speed of light in an accelerating reference frame, the answer will, in general, differ from c."

"This is already true in special relativity: if you measure the speed of light in an accelerating reference frame, the answer will, in general, differ from c."