Re: Definition of LET and SR

Tom Van Flandern wrote:
> "Tom Roberts" <[EMAIL PROTECTED]> writes:
> > [Roberts]:  The closest thing to
> > "equations of motion" in GR are: (D/dx^i) T^ij = 0 [where] T^ij are the
> > components of the energy-momentum tensor .
>
>             "Equations of motion" are expressions for 3-space
> acceleration in coordinate time. These are essential for a comparison of
> GR with real world observations, which are of necessity made in 3-space
> at some proper time. The GR n-body equations of motion may be found in
> MTW, p. 1095.

Oh. You mean the equations of motion for an APPROXIMATION TO GR. That is 
something else entirely. In particular, if you bother to examine the 
nature of the approximation used, you will find that it has:
	1. Destroyed the inherent coordinate-independence of GR.
	2. Selected a set of Newtonian-like coordinates.
	3. Used equations in which small quantities are ignored.

Speed-of-light propagation delays are small quantities in this 
approximation, so in view of #3 it's not very surprising that you claim 
things which propagate at c in GR are "instantaneous".

        I strongly suspect this can be put on a much more rigorous
        footing....


>             When you leave the abstract mathematical world and convert
> to a 3-space, proper time context, GR does have classical forces and
> potentials in its field interpretation.

No, that is true for the APPROXIMATION TO GR you are using. <shrug>

        Yes, yes. PMB will chime in here and claim such forces
        and potentials are part of GR -- that's a PUN on both "forces"
        and "potentials"....


> While it is true that the
> geometric interpretation ("gravity is just geometry") tried to do away
> with those, it does so at the expense of the causality principle (no
> cause and effect to produce 3-space acceleration because curvature alone
> is incapable of initiating motion) 

That's nonsense. In GR spaceTIME curvature is certainly capable of 
"initiating motion": this is clearest for gravitation in a static 
manifold, where the timelike Killing vector is the natural time 
coordinate, massive objects' trajectories are proportional to the 
timelike Killing vector, and the 3-space in which they are at rest is 
orthogonal to it[#]. But timelike geodesics are NOT proportional to the 
timelike Killing vector -- thus a freefalling test particle initially at 
rest wrt the natural 3-space MUST start to move (wrt that 3-space)[%]. 
The idea holds for all particles in freefall, in all manifolds....

        [#] Example: Schwarzschild coordinates on Schw. spacetime, r>2M;
            the timelike Killing vector is d/dt, and {r,\theta,\phi}
            define the 3-space orthogonal to it.
        [%] Timelike geodesics "fall". If this weren't true, GR would
            have been a non-starter from the beginning -- you REALLY
            need to learn the basics of GR....


> and at the expense of the "no
> creation ex nihilo" principle (by requiring that the new momentum
> acquired by target bodies arise from nothing).

Again nonsense, IN GR. A test particle (of constant mass) following its 
geodesic has constant 4-momentum (i.e. there is no "new momentum") -- 
that's what the geodesic equation says, literally.

        You seem to be so wrapped up in your beloved approximation
        (which you think is GR) that you clearly don't understand
        the basics of the actual theory of General Relativity.


> But IMO, no one will ever acquire
> a sensible physical understanding of the math of GR without learning the
> field interpretation because of those two "impossible things" required
> by the geometric interpretation.

You delude yourself with your own mistakes. Neither one of your 
"impossible things" is present in GR. And _YOU_ quite clearly have no 
"sensible physical understanding of the math of GR" -- your statements 
above are simply false in GR.


There is a very real "power of understanding" in the geometric aspects 
of GR. It is more than a mere "interpretation" -- geometry is the very 
ESSENCE of GR. But you seem to be so entrenched in your approximation 
that you completely missed this important fact.


> > [Roberts]: Why not apply GR to those experiments? Somehow I doubt any
> > of them actually refute GR.
> We did of course apply GR, and none of the experiments
> refute GR. What they refute is the geometric interpretation of GR,

That is not possible. Either the experiments are consistent with GR or 
they refute it. It is not possible to refute an essential part of a 
theory but not the theory itself.

        Ask yourself how you "applied GR" -- you used some equations
        of GR, applied the specific values corresponding to the
        physical situation, and compared the computed results to the
        actual measurements. Nowhere in this procedure is there any
        use of "the geometric interpretation" of GR. So this procedure
        is powerless to "refute" it.


> See, for example, this statement to that effect
> from R.P. Feynman [Feynman Lectures on Gravitation, (Addison-Wesley, New
> York; 1995), p. 113]:
>
> "It is one of the peculiar aspects of the theory of gravitation, that it
> has both a field interpretation and a geometrical interpretation. ...
> the fact is that a spin-two field has this geometrical interpretation:
> this is not something readily explainable -- it is just marvelous. The
> geometrical interpretation is not really necessary or essential to
> physics."

Actually the "field interpretation" is NOT an interpretation of GR, it 
is an interpretation of an APPROXIMATION TO GR. Yes, many authors miss 
this rather important fact (e.g. Feynman above).

Fields on a flat spacetime mean the manifold can only have the topology 
consistent with a flat manifold; geometry in a curved manifold implies 
the manifold can only have a topology consistent with that curved 
manifold. So these two theories are not equivalent, and in principle the 
difference is subject to experimental observation of the topology of 
spacetime. But we have no likelihood of being able to do that anytime 
soon.... All your experiments are incapable of doing this.



The beauty and power of GR is its elegant set of postulates and their 
universal application. They are lost in the APPROXIMATION you keep 
discussing as if it was GR itself. Nobody would consider those equations 
on MTW p1095 to be an elegant "theory of physics", and justifying them 
is probably impossible EXCEPT as an approximation to GR....


Tom Roberts	[EMAIL PROTECTED]