Non-geometric approach to gravity impossible?

[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 Schwarzschild 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]

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 Schwarzschild 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.

No. It only makes things clearer now. Thanks.

 

[waterfall]

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.

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.

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.

 

[Mentz114]

See: http://www.scribd.com/doc/81449908/Flat-spacetime-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.

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]

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.

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]

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?

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]

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.

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]

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.

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]

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."

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]

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?

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

 

[waterfall]

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

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]

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.

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]

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.

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]

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.

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

 

[waterfall]

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

I wonder what is your nationality because your sentences are formulated in very difficult to understand terms. What you are saying above is like saying classical gravity is classical "graviton" theory. It is not standard usage. Please use more standard usage. Or write in complete description assuming the recipient is a non-physicist because it may literally make any laymen heard spin. Thanks.

 

[atyy]

I wonder what is your nationality because your sentences are formulated in very difficult to understand terms. What you are saying above is like saying classical gravity is classical "graviton" theory. It is not standard usage. Please use more standard usage. Or write in complete description assuming the recipient is a non-physicist because it may literally make any laymen heard spin. Thanks.

Classical electrodynamics is the classical limit (Planck's constant goes to zero) of quantum electrodynamics, which has a photon.

Analogously for gravity.

 

[waterfall]

Classical electrodynamics is the classical limit (Planck's constant goes to zero) of quantum electrodynamics, which has a photon.

Analogously for gravity.

I understand things you are saying which are basic. What I'd like to know is this. I know curved spacetime contained spin 2 fields. I'm not asking what is the best way to describe it. I'm interested in the meat of the details or how to breakdown it to component parts because I'd like to understand the foundations of quantum gravity and see where there may be weaknesses. In this formalism of spin-2 fields over flat spacetime. We know the curved spacetime is just an illusion. Therefore in my analysis. I want to use only spin-2 fields and flat spacetime. Now as the universe is expanding like it is now. What if there is no matter in between the depth of interstellar space, then there is no spin-2 fields but only flat minkowski spacetime and from this space expands? Please don't mention anything about milne model or curved spacetime. If others comprehend what I'm asking. Please reply too if atyy still can't get what I'm asking. Thanks.

 

[waterfall]

I understand things you are saying which are basic. What I'd like to know is this. I know curved spacetime contained spin 2 fields. I'm not asking what is the best way to describe it. I'm interested in the meat of the details or how to breakdown it to component parts because I'd like to understand the foundations of quantum gravity and see where there may be weaknesses. In this formalism of spin-2 fields over flat spacetime. We know the curved spacetime is just an illusion. Therefore in my analysis. I want to use only spin-2 fields and flat spacetime. Now as the universe is expanding like it is now. What if there is no matter in between the depth of interstellar space, then there is no spin-2 fields but only flat minkowski spacetime and from this space expands? Please don't mention anything about milne model or curved spacetime. If others comprehend what I'm asking. Please reply too if atyy still can't get what I'm asking. Thanks.

I think I misunderstood something that is why we are not communicating well. So the FRW Metric describes the entire universe so even in regions in space without matter, it is still curved as seen in the bigger view. Now Milne universe is about flat spacetime throughout the universe, therefore the following is the thing that I need to know.

Can one consider FRW spacetime = Milne Spacetime + Spin-2 fields?? Why not? It's analogous to curved spacetime = flat spacetime + spin-2 fields?

 

[waterfall]

I think I misunderstood something that is why we are not communicating well. So the FRW Metric describes the entire universe so even in regions in space without matter, it is still curved as seen in the bigger view. Now Milne universe is about flat spacetime throughout the universe, therefore the following is the thing that I need to know.

Can one consider FRW spacetime = Milne Spacetime + Spin-2 fields?? Why not? It's analogous to curved spacetime = flat spacetime + spin-2 fields?

atyy, Are you talking about some kind of Correspondence or duality thing like for example the AsD/CFT Correspondence which is defined as "the conjectured equivalence between a string theory and gravity defined on one space, and a quantum field theory without gravity defined on the conformal boundary of this space, whose dimension is lower by one or more.". They are dual in that one can use either for modelling purpose. This is in contrast to Replacement or Subtitution thing where one theory can be used as an actual replacement.

Now do you treat this "curved spacetime = flat spacetime + spin-2 field" thing as some kind of Correspondence or Duality like the Asd/CFT Correspondense? Here the FRW Universe is treated as curved spacetime and never as flat spacetime + spin-2 field because this is not actual but only a dual just like the AsD/CFT Correspondense where the boundary thing of some distance area is just dual and can't be taken as actual?

Please elaborate what is your thinking or let others assist here because over days I'm so frustrated already why my simple question of how the FRW Space can't be treated as an actual flat spacetime + spin-2 field is not answered. When I asked you this, you always replied continuously to use curved spacetime which was not what I was asking.. unless you treat this whole curved spacetime=flat spacetime + spin-2 field as just correspondense and the latter not an actual replacement for the former? Hope you can answer clearly now or please others assist here. Thanks.

 

[atyy]

The FRW solutions have matter everywhere. In the case where they don't have matter anywhere, we get the Milne universe.

 

[waterfall]

The FRW solutions have matter everywhere. In the case where they don't have matter anywhere, we get the Milne universe.

I know that. But you are not answering my questions for over 4 days already. Well. I'll re words them in the following context.

Curved Spacetime = Flat Spacetime + spin-2 Field
FRW Spacetime = Milne Spacetime + Spin-2 Field

In the first case, the spin-2 field stands for matter and attraction. Without matter. It's

Curved Spacetime = Flat Spacetime meaning there is no curved spacetime and all flat.

Hence without matter. It's FRW Spacetime = Milne Spacetime meaning there is no curvature hence the universe would be a Milne and all flat.

Can't you see the analogy. It's plain logic 101. Where is the flaw? Can't anyone see where I'm coming from or stating? Please address this directly and not discuss others. Maybe you reply will be "Curved spacetime is classical" or others totally irrelevant to my questions!

 

[Mentz114]

Curved Spacetime = Flat Spacetime + spin-2 Field

Not true.

FRW Spacetime = Milne Spacetime + Spin-2 Field

Not true.

The Milne spacetime is the Minkowski spacetime with a weird coordinate transformation which gives an expanding spatial coordinates so that a 'comoving' observer sees all other comoving observers moving away.

The FRW solution is that of non-interacting matter in an expanding or contracting spactime.

You can't add metrics (spacetimes) together.

 

[atyy]

Not true.

Why not? Isn't the only requirement to write the EFEs as a field on flat spacetime that the curved spacetime be coverable by harmonic cooridinates? Weinberg gives the FRW solution in harmonic coordinates in his textbook.

There's a similar viewpoint in http://relativity.livingreviews.org/Articles/lrr-2006-3/index.html Eq 62. "Equation (62) is exact, and depends only on the assumption that spacetime can be covered by harmonic coordinates."

 

[bcrowell]

Here are two other useful sources of information on this:

Feynman Lectures on Gravitation. This has a 1995 foreword by Preskill and Thorne, which describes in considerable detail the ideas behind the argument that the spin-2 theory is equivalent to GR. This suggests that if there are doubts about the validity of this claim of equivalence to GR, those doubts were either not known in 1995 or not taken seriously enough by Preskill and Thorne to be worthy of mention -- in a lengthy foreword to an entire book that is mainly concerned with this topic.

L.Butcher, M.Hobson and A.Lasenby, Phys. Rev D80 084014(2009),
http://arxiv.org/abs/0906.0926

Deser, Gravity from self-interaction redux, 2009, http://arxiv.org/abs/0910.2975

 

[Mentz114]

Ben, thanks for the Deser reference. Now to hear it from the man himself ...

 

[waterfall]

Here are two other useful sources of information on this:

Feynman Lectures on Gravitation. This has a 1995 foreword by Preskill and Thorne, which describes in considerable detail the ideas behind the argument that the spin-2 theory is equivalent to GR. This suggests that if there are doubts about the validity of this claim of equivalence to GR, those doubts were either not known in 1995 or not taken seriously enough by Preskill and Thorne to be worthy of mention -- in a lengthy foreword to an entire book that is mainly concerned with this topic.

L.Butcher, M.Hobson and A.Lasenby, Phys. Rev D80 084014(2009),
http://arxiv.org/abs/0906.0926

Deser, Gravity from self-interaction redux, 2009, http://arxiv.org/abs/0910.2975

hi bcrowel.. I'd been asking something from atyy and for 5 days he isn't answering it directly so I'm so frustrated now and gave up asking him. Now let me ask it to you maybe you understand what I'm talking about. It's just very simple. It's like this.

FRW spacetime is curved, right? Now from the theory that spin-2 field in flat spacetime is equivalent to GR (curved spacetime). Then why can't the FRW spacetime be formulated as spin-2 field in flat spacetime? And how does one do it? Do you turn the FRW spacetime first into flat equivalent which may be the Milne Spacetime and then add spin-2 field? or if you haven't heard of Milne. Just reply using the simple statement how do you turn the FRW spacetime into flat spacetime + spin-2 fields. Thanks.

 

[Mentz114]

Why not? Isn't the only requirement to write the EFEs as a field on flat spacetime that the curved spacetime be coverable by harmonic cooridinates? Weinberg gives the FRW solution in harmonic coordinates in his textbook.

There's a similar viewpoint in http://relativity.livingreviews.org/Articles/lrr-2006-3/index.html Eq 62. "Equation (62) is exact, and depends only on the assumption that spacetime can be covered by harmonic coordinates."

I don't know what "curved spacetime be coverable by harmonic coordinates" means so I can't argue about this.

 

[atyy]

Then why can't the FRW spacetime be formulated as spin-2 field in flat spacetime?

But do we know it can't? I'm not sure, but my understanding is that it can.

 

[waterfall]

But do we know it can't? I'm not sure, but my understanding is that it can.

How? that's what I've asking your for the past 5 days.

 

[atyy]

How? that's what I've asking your for the past 5 days.

I don't know in detail. I can point you to Weinberg's text and you'll have to do some additional work yourself, but I believe it doable from general considerations.

 

[waterfall]

I don't know in detail. I can point you to Weinberg's text and you'll have to do some additional work yourself, but I believe it doable from general considerations.

I think this is how to do it. How does one decompose the FRW spacetime into flat and spin-2 fields. There is already a version of the flat in the Milne Spacetime. Therefore, perhaps one can imagine that our universe is really Flat or Milne Spacetime and spin-2 fields just turn it into FRW. You know that in Milne universe, there is zero energy density, no cosmic microwave background radiation, no matter of any kind. Now when you add the spin-2 fields. It would recreate FRW... hmm.. wait.. I think I see the problem. It seems adding spin-2 field is not enough to produce matter, one has to add matter. Therefore let me go to the original formulation of

Curved Spacetime = Flat Spacetime + Spin-2 Fields

How does one embed matter into the above? We forgot about matter. Is it like this?

Curved Spacetime = Flat Spacetime + Spin-2 Fields + Matter?

When one can do it. One can apply it to the FRW Spacetime.

 

[PAllen]

Ben, thanks for the Deser reference. Now to hear it from the man himself ...

I gave the same Deser link in #75.

 

[Mentz114]

I gave the same Deser link in #75.

Thanks, but I missed it. These threads have grown to unmanageable sizes ...

 

[bcrowell]

These threads have grown to unmanageable sizes ...

And none of us who have been posting have the combination of theory chops and several months of spare time that it's now clear would be needed to do more than skim through some of the literature and note what different experts seem to be claiming.