Non-geometric approach to gravity impossible?

waterfall

See: http://www.scribd.com/doc/81449908/F...time-Gravitons

find this starting line:

"5. Einstein's geometrodynamics viewed as the standard field theory for a field of spin 2 in an "unobservable flat spacetime" background...".

Please share how it differs to your description of Baryshev's as when you described it in the other thread:

"FTG is a classical field theory that begins with the Lagrangian which has three terms, one each for the field, one for the matter and crucially one for the interaction between the field and the matter. The exchange boson, if the theory was quantized would be spin-2. All this is done in Minkowski spacetime."

atyy.. since you are familiar with the MTW approach, please share how it differs to the above FTG theme. Thanks.

PAllen

All of the authors atyy cites believe that spin-2 field theory is identical to GR in physical predictions at least up to the event horizon, and possibly beyond (except, of course, for Hawking radiation). Baryshev believes that spin 2 field theory predicts that the event horizon doesn't exist, and therefore that Bekenstein-Hawking thermodynamics of black holes is incorrect. You can see this more clearly from some of Baryshev's other papers.

See, for example: http://arxiv.org/abs/0809.2328

Almost all other authors on spin 2 field theory would disagree with every prediction of the above paper, believing that spin 2 field theory would agree with GR instead. As with atyy, I am not in a position to judge Baryshev on the merits.

One comment on the disagreement is noted in the following:

http://arxiv.org/abs/1106.2476 :

"Finally, let us mention that approaches exist that treat gravity as simply a spin-2
field on
flat space [114, 115]. It has been conjectured that one could reconstruct the
Einstein-Hilbert action in such an approach by considering consisitency conditions order
by order in perturbation theory. This will, of course, be an invalid treatment when
gravity is strong, and in cosmology."

Most authors disagree with this paragraph and argue that such recovery of the Einstein-Hilbert action is imperative, and that the comment on invalidity is itself invalid.

Haelfix

There is a sublety regarding scaling when you go from the linear to the full nonlinear theory around certain solutions. So when doing perturbation theory around say the Schwarschild solution you naively run into an inconsistency and that is what Baryshev is picking up on.

What he fails to mention is that this problem was dealt with long ago by Vanshtein.
"To the problem of nonvanishing gravitation mass”, Phys. Lett. B, 39, 393–394, (1972)

But anyway, this is way beyond the scope of this thread and is just arguably going to confuse things more than they already are.

waterfall

No. It only makes things clearer now. Thanks.

waterfall

What for me is the more important issue is whether space can expand or space already there. Baryshev says space already there, while MTW according to atyy says space can expand. Now what in the formalism in MTW versus Baryshev that can say whether space can expand or not?

Also in the MTW approach where space can expand (according to atyy). Take note of this logic:

Since expanding space is automatically curved spacetime, and since curved spacetime is just spin-2 field on flat spacetime. Then expanding space is composed of spin-2 field and flat spacetime. Therefore expanding space is related to expanding space&spin-2 field and expanding space&flat spacetime. How does one imagine or model expanding space&spin-2 field for example? Or expanding space&flat spacetime which is a Milne model that isn't valid. Can one say that when one adds spin-2 to Milne model. It becomes valid? Do you see if there is something wrong with my analysis. Thanks.

Mentz114

Thanks a lot for that, Waterfall. It makes very interesting reading. From your point of view the important thing is that GR emerges in its full form with the Einstein-Hilbert action. So it is equivalent to GR.

For me, the eye-opener is that the non-linearity of GR emerges from the coupling of the boson field to the whole Lagrangian, requiring the infinite series.

I think it also shows the deficiency in the FTG approach which has been highlighted in other posts.

PAllen

This was posted in another thread, but here is a recent defense by Deser of the derivation of GR from spin 2 field:

http://arxiv.org/abs/0910.2975

waterfall

Why in the FTG approach, the coupling of the boson field is not to the whole Lagrangian, but portion only? But it still doesn't answer my original question. What in the formalism in MTW versus Baryshev that can say whether space can expand or not? And how does a spin-2 field over flat spacetime expand? Atyy kept saying it is covered by harmonic coordinates. What I want to know is whether the space expansion is for the combined spin-2 field/flat spacetime as a unit (and why) or separately for the flat spacetime. Let me illustrate:

Spin-2 field over flat spacetime produces an illusion of curved spacetime.
Now when space expand. Why did it use the curved spacetime thing when it is just an illusion. Shouldn't it interact with the more primary flat spacetime as it's the more original?

atyy

The point is that classically it makes no difference - they are equivalent as long as we restrict to curved spacetimes that can be covered by harmonic coordinates. Since they are equivalent, we use whichever picture is most convenient for describing the phenomenon in question.

waterfall

I'm interested not classically, but quantumly like how the step by step process occurs from the big bang.. like at planck time, how does the flat spacetime and spin 2 interact and expand. The details are what I'm interested in. You just kept mentioning the classical limit which was not what I was asking.

atyy

The only quantum theory of gravity we have is spin 2 on flat spacetime. This doesn't work when the curvature is Planck scale, so it doesn't work near the big bang singularity. Consequently, there is no picture of space expanding from the big bang singularity.

http://www.einstein-online.info/spotlights/big_bangs
"The term "big bang" has two slightly different meanings, and the answer to questions like "Did the big bang really happen" depends crucially on which of the two big bangs you are talking about."

waterfall

Thanks for the article and knowing the distinctions. So let's not talk about the singularity (if there is) that gave rise to the Big Bang but just focus on what occurs afterwards, the expansions.. or better yet.. since the universe is still expanding right now.. then just focus on the details of the expanding space. Maybe what you are saying is that spin-2 is like h20 molecules and the water is the emergence or spacetime curvature. So when we are talking about space expansion.. it's like water being expanded into gas or contracted into ice?

Intermission: About milne expansion... In between supergalatic clusters are empty space devoid of any matter and spin-2 fields (let's say we can ignore the CMB and cosmic rays), then the region of the space can be considered flat. Then can't it be considered a milne expansion?

atyy

In this regime the quantum theory is essentially the classical theory. So it's just curved spacetime.

waterfall

Let's say in an exam in a physics class, the professor told one to model it without any attribution to curved spacetime and classical theory. This means even outside singularity we have to use the quantum theory. So in this sense we can say that space expands... and the present of spin-2 fields make it appear a certain manner. And in space like between supergalactic clusters without any spin-2 fields, space expand too? Let's analyze it this way. Don't mention anything about curved spacetime in your reply.

atyy

The classical spin 2 theory is derived from the quantum spin 2 theory. The classical spin 2 theory is equivalent to the curved spacetime theory, so when we use the curved spacetime theory we are using the spin 2 theory.

waterfall

How do you define:

classical spin 2 theory?
quantum spin 2 theory?

I thought all spin 2 theory are quantum. But then you can't have spin 2 particles in classical theory just like you can't have photons in classical electrodynamics.

atyy

Exactly the same way that classical electrodynamics is classical "photon theory".