On Sep 7, 2011, at 12:43 AM, JACK

SARFATTI wrote:

*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/

dTdt/

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:*"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."