Re: New Paper: General Relativity, Maxwell's Electrodynamics, and the Foundations of the Quantum Theory of Gravitation and Matter (gr-qc/0511050)

Jay R. Yablon wrote:
> Igor Khavkine wrote:

> You do not need to check the derivation to (2.5). I did not "find" this
> identity. This identity can be found in John Archibald Wheeler's
> Geometrodynamics, page 251, note 22. It is a central identity to any
> consideration of electric magentic duality.

I see even less relevance of possible electric-magnetic duality to the
question at hand.

> > Let me say this again, your work does not include quantum mechanics.
> > So, regardless of what tensor identities you might have derived, it
> > cannot in principle be an approach to quantum gravity.
>
> I am going to respectfully request that you carefully read through Dr.
> Einstein's 1919 paper "Do Gravitational Fields Play and Essential Part in
> the Structure of the Elementary Particles of Matter?," so that we might
> perhaps discuss this paper and how it might (or might not) apply and be
> built upon in light of all that we know today. I know I would enjoy such a
> discussion; perhaps others would too.

After a brief glance at this paper (which is, BTW, included in the
collection of paper "The Principle of Relativity" published by dover),
I see that it is a symptom of the "when you only have a hammer,
everything looks like a nail" syndrome. In 1919 quantum theory was
still in its infancy. Today we have a much better model of elementary
particles than back then, and it does not require the introduction of
gravitational effects to "hold them together". Elementary particles are
simply not elastic solids, as turn of the century models have assumed.
Again, this paper has nothing to do with an approach to quantum
gravity.

> But, let me note a few things about this paper to begin with. First, Dr.
> Einstein is attempting to set the Maxwell energy tensor (his equation (3))
> to equal some field equation which, of course, is a second differential
> order differential equation for the spacetime metric. (His field equations
> are either (1) or (1a), which later end up with a pressure term involving
> the cosmological constant.)
>
> Second, he establishes a constant, non-zero curvature scalar, which is
> exactly what sqrt(-g) E dot B becomes in my paper when kappa^v=0. (I also
> point out that in my paper, the covariant derivatives of the energy tensor
> divergence turn into ordinary derivatives, which may ultimately address
> DRL's bottom line objection -- communicated privately to me -- about, e.g.,
> being able to convert a volume integral into a surface integral in curved
> spacetime; I am still reviewing that.)

In curved space-time, the result of an integration over a finite region
may not have any free indices. That is so for the simple reason that we
have no caonical way of adding tensors attached to different points of
space-time.

> Now, there are many people who have deeper expertise than I do in the
> intricacies of quantum theory and especially calculating discrete energy
> levels . . . but, it seems to me that one cannot assert that F^uv is
> strictly a classical object and that we do not know how to relate F^uv to
> quantum mechanics.

And this is precisely where the flaw in your reasoning lies. You say
"cannot assert that F^uv is stricly a classical object", but provide no
precise reason for this assertion. You are letting this vague statement
cloud your judgement. The only specific interpretation that I can
assign to your statement is that F^uv is the expectation value of the
appropriate observable with respect to some given quantum state (note
that not even this simplistic introduction of quantum theory can be
found in your work). In this case the idea is a very old one, where all
matter is treated quantum mechanically, except for gravity, which is
treated classically coupled to the expectation value of the
stress-energy tensor. This idea has even been discussed here in s.p.r a
while ago. If you are interested, you may search for a thread titled
"Quantum-classical dynamics". AFAIK, the gravity community finds this
approach unsatisfactory.

But, as I said, your paper does not introduce quantum mechanics into
the picture, neither in this way nor in any other way. So as you wrote
them down, the F^uv's and the T^uv's, associated to whatever fields you
choose to couple to gravity, are in deed "strictly classical objects".

> Look at AE's paper noted above, then let's discuss what we can learn from it
> in the context of today's knowledge. This paper is worth a 21st century
> brainstorming revival.

Yes, we can learn somthig from it. We learn that at the turn of the
century, the scientific minds, including great ones like Einstein, knew
very little about elementary particles.

Igor

.

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