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

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 <This email address is being protected from spambots. You need JavaScript enabled to view it.> 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:

A "paradoxical" property

Note that Rindler observers with smaller constant x coordinate are accelerating harder to keep up! This may seem surprising because in Newtonian physics, observers who maintain constant relative distance must share thesame acceleration. But in relativistic physics, we see that the trailing endpoint of a rod which is accelerated by some external force (parallel to its symmetry axis) must accelerate a bit harder than the leading endpoint, or else it must ultimately break. This is a manifestation of Lorentz contraction. As the rod accelerates its velocity increases and its length decreases. Since it is getting shorter, the back end must accelerate harder than the front. This leads to a differential equation showing, that at some distance, the acceleration of the trailing end diverges, resulting in the #The Rindler horizon.

This phenomenon is the basis of a well known "paradox". However, it is a simple consequence of relativistic kinematics. One way to see this is to observe that the magnitude of the acceleration vector is just the path curvature of the corresponding world line. But the world lines of our Rindler observers are the analogs of a family of concentric circles in the Euclidean plane, so we are simply dealing with the Lorentzian analog of a fact familiar to speed skaters: in a family of concentric circles, inner circles must bend faster (per unit arc length) than the outer ones.

http://en.wikipedia.org/wiki/Rindler_coordinates

Paul:

Okay. I just want to make sure we are on the same sheet of music...

Ufoguy...