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May 23

## Zielinsky-Sarfatti Dialogue on Einstein's 1916 General Relativity 1

Posted by: JackSarfatti
Tagged in: Untagged

So what is the actual technical problem here?

"The Question is: What is The Question?" John A. Wheeler
All gravity fields are approximately uniform in a small region of 4D space-time from Taylor's theorem of calculus.
This is all that is needed in Einstein's 1916 GR.
We never need to invoke a global static uniform gravity field.
Is such a field even possible? --  one might ask.
For static LNIFs Newton's idea of a global static gravity field is deconstructed as a possible Einstein metric field with observer-dependent representation for the vacuum outside the source Tuv
guv(static LNIF) = (1 + VNewton/c^2)(cdt)^2 - (1 + VNewton/c^2)^-1dz^2 - dx^2 - dy^2
where (note no factor of 2 in above model - unlike central force problem 1/r potential)
VNewton =  gz
the g-force is then
- g = -dVNewton /dz
directed back toward z = 0
there is no event horizon in this "dark matter" model and, of course, the g-force is independent of the rest mass of the test particles.
If the g-force is repulsive away from z = 0 then there is an event horizon for a "dark energy" slab vacuum domain wall! (Rindler?)
The source must be something like an infinite uniform density mass plane at z = 0 in the x-y plane (analog to electrical capacitor problem)
The problem is whether the above intuitive guess at a solution is what one gets from Einstein's field equation
Guv + kTuv = 0
where Tuv corresponds to a Dirac delta function &(z) uniform density.
On Mar 31, 2010, at 11:20 PM, Paul Zielinski wrote:

Jack, I believe you've just scored yet another of your world famous "own goals" here.

When he refers to a "homogeneous" gravitational field, Einstein is not talking about a uniform frame acceleration field.
He is talking about an *actual* gravity field of uniform field strength.

There is no problem with defining such a field operationally, since test object acceleration can always be measured at
every point at *zero test object velocity*, eliminating any SR-related effects.

So what Einstein has in mind here when he uses the term "homogeneous to first order" is the non-vanishing curvature
associated with typical gravity fields produced by matter.

Now it is nevertheless true that a RIndler frame (relativistic accelerating frame of reference) does exhibit such SR-type
effects -- but this is just another argument against Einstein's proposed principle, since it ensures that the phenomena observed
in such a frame differ from those observed from a non-accelerating frame even in the presence of a perfectly homogeneous
gravity field (Einstein's best case).

So yes Einstein was later forced to retreat even from this version of the principle, even given his best case of a perfectly
homogeneous ("certain kind of") gravity field compared with a uniform acceleration field, eventually restricting the principle to what
we like to call "local" observations, irrespective of the question of spacetime curvature.

You don't seem to realize that this is an argument *against* Einstein's original concept of equivalence, not for it.

In any case, even if one is restricted to pure local observations, the principle as stated still does not work. Why? Because you
cannot
recover non-tidal gravitational acceleration -- a locally observable phenomenon -- from *any* kind of frame acceleration,
either
globally or locally!

You can always bring a test object as close as you like to a source boundary, and locally measure its acceleration with respect
to the source. Such locally observable gravitational acceleration will not be observed in *any* kind of frame acceleration field. Which
means that Einstein's proposed principle as stated is simply false: the laws observed even in a perfectly homogeneous gravity
field are not the same as those observed in a homogeneous gravitational field -- not even approximately.

Vilenkin's vacuum domain wall solutions, in which the vacuum geometry is completely Riemann flat,  show that this kind of situation
does exist in 1916 GR. A test object released near such a gravitational source will experience locally observable gravitational
acceleration with respect to the source, which will not be observed in *any* pure frame acceleration field with the gravitational source
switched off (by which I mean a Rindler frame in a Minkowski spacetime -- a pure frame acceleration field).

So the only way to get Einstein's principle as stated to work is to ignore the phenomenon of gravitational acceleration. But what kind of a
"theory of gravity" can be based on such a principle?

My answer here is simple: Einstein's version of the equivalence principle is simply not supported by his 1916 theory of gravity. It is
simply a figment of Einstein's fevered imagination.

Which is what I've been saying all along.

Z.

On Wed, Mar 31, 2010 at 6:41 PM, JACK SARFATTI  wrote:
As I have been trying to explain to Zielinski without success is that such a global uniform gravity field does not exist because of special relativity time dilation and length contraction - I mean it does not exist in same sense that it would in Newton's gravity theory using only the v/c ---> 0 Galilean group limit of the Lorentz subgroup of the Poincare group. Einstein was perfectly aware of this in the quote Zielinski cites - Zielinski simply does not understand Einstein's text in my opinion.
On Mar 31, 2010, at 6:23 PM, Paul Murad wrote: