Non-geometric approach to gravity impossible?

[PAllen]

Yes, that is what I meant, more precisely I should of said for an observer at rest in the centre of mass frame.



I agree that it is true that in the rest frame of the the Earth that more massive objects fall faster than less massive objects (as long as they are not dropped at the same time) but the point that I was making (and I am sure you understood what I was getting at) in the rest frame of centre of mass of the Earth and falling object, the acceleration of the falling object is independent of its mass in Newtonian physics. Agree?

Put it another way. In the rest frame of the Earth the acceleration of a falling object is proportional to G(M+m) where M is the mass of the Earth and m is the mass of the falling object. It is easy to see that if m goes to zero, that the acceleration does not go to zero.

Yes, this is fine now for Newtonian gravity.

 

[waterfall]

The classical electromagnetic wave is a coherent state of photons on flat spacetime. Similarly, classical curved spacetime (that can be covered by harmonic coordinates) is a coherent state of gravitons on flat spacetime.

So since everybody believe there must be a quantum theory of gravity, then it's almost definite and categorical that "classical curved spacetime (that can be covered by harmonic coordinates) is a coherent state of gravitons on flat spacetime" then why don't we hearing from say sci.am or other news items reporting that "Universe is really flat spacetime a priori!". Hmm.. maybe I should write an article in sci am and make it a cover subject or someone else with credentials write it because sci am doesn't seem to accept contributions by unknown people. But in the book "Philosophy Meets Physics at the Planck Scale". It seems they are saying there that there is a quantum gravity programme where spacetime is really curved and gravitons just quanta of it without any flat spacetime underneath.

Within string theory, gravitons are only approximate degrees of freedom, and strings are more primary. So in the string theory picture, curved spacetime is a coherent state of strings on flat spacetime. In the AdS/CFT picture, strings and space are both emergent, and neither are primary.

This proves that in string theory, spacetime is really flat with the curved spacetime as only coherent state of strings.. although I'm still trying to imagine how these two can co-exist together.

Why didn't you answer this question "2. Can Loop Quantum Gravity be formulated as spin-2field in flat spacetime? Or does LQG stay valid only if spacetime is actually curved?" anyone else knows the answer?

 

[atyy]

But in the book "Philosophy Meets Physics at the Planck Scale". It seems they are saying there that there is a quantum gravity programme where spacetime is really curved and gravitons just quanta of it without any flat spacetime underneath

The gravitons on flat spacetime is a quantum theory of gravity, but it only works below the Planck scale. The question is how do we get a quantum theory near and above the Planck scale? LQG says maybe quantum spacetime is really curved, and there is no flat spacetime underneath it. AdS/CFT indicates that even curved spacetime is not radical enough, and completely different degrees of freedom than what are indicated classically are required.

 

[waterfall]

The gravitons on flat spacetime is a quantum theory of gravity, but it only works below the Planck scale. The question is how do we get a quantum theory near and above the Planck scale? LQG says maybe quantum spacetime is really curved, and there is no flat spacetime underneath it. AdS/CFT indicates that even curved spacetime is not radical enough, and completely different degrees of freedom than what are indicated classically are required.

In other words. LQG is about spacetime that is really curved, with no flat spacetime underneath it even far below the Planck scale. But this is the confusing part, in LQG, there are also gravitons. But these gravitons can't be modeled as occurring on flat spacetime even far below the Planck scale? If you say they can. But LQG is about spacetime that is really curved, with no flat spacetime underneath it even far below the Planck scale. Please resolve this confusing part. Thanks.

 

[atyy]

In other words. LQG is about spacetime that is really curved, with no flat spacetime underneath it even far below the Planck scale. But this is the confusing part, in LQG, there are also gravitons. But these gravitons can't be modeled as occurring on flat spacetime even far below the Planck scale? If you say they can. But LQG is about spacetime that is really curved, with no flat spacetime underneath it even far below the Planck scale. Please resolve this confusing part. Thanks.

LQG hopes that its predictions for experiments occurring far below the Planck scale will be almost identical to that of gravitons on flat spacetime.

 

[waterfall]

LQG hopes that its predictions for experiments occurring far below the Planck scale will be almost identical to that of gravitons on flat spacetime.

Yeah and I think this describes how it is done http://arxiv.org/pdf/gr-qc/0604044v2.pdf
"Graviton propagator in loop quantum gravity"

If you have read it already before, please comment on it on the important issues related to our discussions. Thanks.

 

[atyy]

Yeah and I think this describes how it is done http://arxiv.org/pdf/gr-qc/0604044v2.pdf
"Graviton propagator in loop quantum gravity"

If you have read it already before, please comment on it on the important issues related to our discussions. Thanks.

Yes, that is a proposal for how it's done. I don't know if the proposal is correct. Why don't you start a thread in the BTSM forum about it?

 

[waterfall]

btw.. how do you model Big Bang Expansion using spin-2 field on flat spacetime? Anyone got an idea?

 

[atyy]

Weinberg exhibits harmonic coordinates for the FRW universe in his textbook.

I'm not sure whether the positive cosmological constant changes things.

 

[waterfall]

Weinberg exhibits harmonic coordinates for the FRW universe in his textbook.

I'm not sure whether the positive cosmological constant changes things.

Gee.. they have even addressed that.. maybe one can imagine say a flat paper size thing expanding to the size of the universe, so the minkowski metric can stretch too.. if anyone has objections.. please say so.

 

[atyy]

There's a famous rewrite of the Minkowski metric as expanding space called the Milne universe. It's not relevant to our universe, since it has no matter (in GR, flat spacetime has no matter).

The FRW universe is expanding space with matter, and corresponds to curved spacetime.

 

[waterfall]

There's a famous rewrite of the Minkowski metric as expanding space called the Milne universe. It's not relevant to our universe, since it has no matter (in GR, flat spacetime has no matter).

The FRW universe is expanding space with matter, and corresponds to curved spacetime.

if flat spacetime has no matter, then how does the spin-2 field in flat spacetime expand with matter? I can't find anything in the internet from goggling "expanding flat spacetime". Hope you have some references.

 

[atyy]

if flat spacetime has no matter, then how does the spin-2 field in flat spacetime expand with matter? I can't find anything in the internet from goggling "expanding flat spacetime". Hope you have some references.

It's a silly trick (nothing to do with spin 2 - since it's pure flat spacetime - spin 2 adds spacetime curvature). Try googling "Milne universe".

 

[waterfall]

It's a silly trick (nothing to do with spin 2 - since it's pure flat spacetime - spin 2 adds spacetime curvature). Try googling "Milne universe".

I know. I have read it. Milne Universe doesn't describe out universe so let us forget it. My question is simply how spin-2 field on flat spacetime expand in the Big Bang? Pls just describe how. Thanks.

 

[atyy]

I know. I have read it. Milne Universe doesn't describe out universe so let us forget it. My question is simply how spin-2 field on flat spacetime expand in the Big Bang? Pls just describe how. Thanks.

The basic idea is expanding space (not expanding spacetime) is just curved spacetime. Spin-2 on flat spacetime produces curved spacetime.

 

[waterfall]

The basic idea is expanding space (not expanding spacetime) is just curved spacetime. Spin-2 on flat spacetime produces curved spacetime.

atyy.. i think you missed my question here... that was why I had to start the FRW thread just to inquire about this confusion. Well. I'm referring to the Field Theory of Gravitation. I was asking how space expanded in Field Theory of Gravitation. Someone said space didn't expand in it. Knowing my question now. If you have answers to this correct question, pls let me know. Thanks.

 

[atyy]

atyy.. i think you missed my question here... that was why I had to start the FRW thread just to inquire about this confusion. Well. I'm referring to the Field Theory of Gravitation. I was asking how space expanded in Field Theory of Gravitation. Someone said space didn't expand in it. Knowing my question now. If you have answers to this correct question, pls let me know. Thanks.

I don't know what FTG is.

 

[waterfall]

I don't know what FTG is.

Field Theory of Gravitation is the formalism of Spin 2-Field on Flat Spacetime.

 

[atyy]

Field Theory of Gravitation is the formalism of Spin 2-Field on Flat Spacetime.

See post #44

 

[waterfall]

See post #44

You said there that "Weinberg exhibits harmonic coordinates for the FRW universe in his textbook. I'm not sure whether the positive cosmological constant changes things.".

I'm talking about the Field Theory of Gravitation. Which is about Fields. What you meant above was that the FRW universe is covered by harmonic coordinates and can be modeled as spin-2 fields on flat spacetime. Now Field Theory of Gravitation is the formulism for this. Here one must separately model how space expands. In the other thread, someone said Field Theory of Gravitation doesn't have space expansion because this belongs to the curved spacetime formalism. Note the distinctions there are two formalisms involved. We must not mix them.

 

[atyy]

You said there that "Weinberg exhibits harmonic coordinates for the FRW universe in his textbook. I'm not sure whether the positive cosmological constant changes things.".

I'm talking about the Field Theory of Gravitation. Which is about Fields. What you meant above was that the FRW universe is covered by harmonic coordinates and can be modeled as spin-2 fields on flat spacetime. Now Field Theory of Gravitation is the formulism for this. Here one must separately model how space expands.

Why?

 

[waterfall]

Why?

Mentz in message #31 in https://www.physicsforums.com/showthread.php?t=582440&page=2 stated:

"I think your logic is wrong in that not all curved spacetime is expanding. The expanding spacetimes of GR are a special class where spatial parts of the metric depend on t.

Also field gravity is not the same as GR. They are two different theories, both claim to explain the observed cosmological phenomena but in different ways. In fact I don't think FTG needs expanding space but supposes a fractal distribution of mass.

So you can't talk about splicing them together in the way you suggest."

 

[atyy]

Mentz in message #31 in https://www.physicsforums.com/showthread.php?t=582440&page=2 stated:

"I think your logic is wrong in that not all curved spacetime is expanding. The expanding spacetimes of GR are a special class where spatial parts of the metric depend on t.

Also field gravity is not the same as GR. They are two different theories, both claim to explain the observed cosmological phenomena but in different ways. In fact I don't think FTG needs expanding space but supposes a fractal distribution of mass.

So you can't talk about splicing them together in the way you suggest."

I don't know what he means by FTG.

 

[waterfall]

I don't know what he means by FTG.

Of course he means Field Theory of Gravitation (FTG). What else. Anyway. I'll ask him more thoroughly and references.

 

[Mentz114]

Of course he means Field Theory of Gravitation (FTG). What else. Anyway. I'll ask him more thoroughly and references.

There seems to be one worker in this field, Yurij V. Baryshev, and I gave reference to a review kind of paper (arXiv:gr-qc/9912003 v1) in an earlier post. There are about six papers in the arXiv on FTG, which makes it a rather insignicant subject.

But this theory is not as good as GR in explaining observations, and some authorities say it always leads to GR in any case.

 

[waterfall]

There seems to be one worker in this field, Yurij V. Baryshev, and I gave reference to a review kind of paper (arXiv:gr-qc/9912003 v1) in an earlier post. There are about six papers in the arXiv on FTG, which makes it a rather insignicant subject.

But this theory is not as good as GR in explaining observations, and some authorities say it always leads to GR in any case.

to Atyy, here's the reference (in the above paper) which says that in Field Theory of Gravitation, one must not use the same concept as space expansion in General Relativity.
Instead one must use the FTG version which is in the following terms:

Cosmology is another field of application of gravitation theory. Present data about large scale galaxies distribution contradict to the main point of Friedmann cosmology — its homogeneity. It turned out that galaxies form a fractal structure with dimension close to 2 at least up to the distance scales bout 200 Mpc. This leads to a new possibilities in cosmology (see an analysis of FTG cosmological applications in the review of Baryshev et al., 1994). One of the main difference between FTG and GR is that the field approach allows the existence of the infinite stationary matter distribution (Baryshev, Kovalevskij, 1990). In a stationary fractal distribution the observed redshift has gravitational and Doppler nature and is not connected with space expansion as in Friedmann model.

Now if cosmological observations prove beyond the shadow of a doubt that space indeed expand. Then spin-2 field over flat spacetime as a priori is falsified. If so. Then all quantum gravity theories that use gravitons in this terms like string theories are falsified. Think of the implications if space indeed expand. What do you think atyy?

 

[atyy]

to Atyy, here's the reference (in the above paper) which says that in Field Theory of Gravitation, one must not use the same concept as space expansion in General Relativity.
Instead one must use the FTG version which is in the following terms:Now if cosmological observations prove beyond the shadow of a doubt that space indeed expand. Then spin-2 field over flat spacetime as a priori is falsified. If so. Then all quantum gravity theories that use gravitons in this terms like string theories are falsified. Think of the implications if space indeed expand. What do you think atyy?

You can evaluate Baryshev and his FTG for yourself.

See post #44.

 

[waterfall]

You can evaluate Baryshev and his FTG for yourself.

See post #44.

I don't know what you were trying to say with your one line sentence written in riddles. I've tried reading his paper again. Maybe you were thinking FTG (Field Theory of Gravitation) is different from Weinberg Spin-2 over flat spacetime valid in spacetime covered by harmonic coordinates. What you didn't seem to get is it is identical to FTG as the following paragraph shows:

"The field theory of gravitation is based on the principle of universality of gravitational interaction and has some forms of the principle of equivalence as its particular cases. In FTG there are Minkowski background space and usual concepts of gravity force, gravity field EMT and quanta of gravity field - gravitons. Within FTG there is no infinite force at gravitational radius and compact massive stars could have masses much more than OV-limit. FTG is actually a scalar-tensor theory and predicts existence of tensor (spin 2) and scalar (spin 0) gravitational waves. Astrophysical tests of FTG will be available in near future. It is quite natural that fundamental description of gravity will be found on quantum level and geometrical description of gravity may be considered as the classical limit of quantum relativistic gravity theory."

How does the above differ to Weinberg formulation. They are the same.

Hope you can read the paper yourself instead of writing in one line riddles that is so difficult to understand.

 

[atyy]

I don't know what you were trying to say with your one line sentence written in riddles. I've tried reading his paper again. Maybe you were thinking FTG (Field Theory of Gravitation) is different from Weinberg Spin-2 over flat spacetime valid in spacetime covered by harmonic coordinates. What you didn't seem to get is it is identical to FTG as the following paragraph shows:

"The field theory of gravitation is based on the principle of universality of gravitational interaction and has some forms of the principle of equivalence as its particular cases. In FTG there are Minkowski background space and usual concepts of gravity force, gravity field EMT and quanta of gravity field - gravitons. Within FTG there is no infinite force at gravitational radius and compact massive stars could have masses much more than OV-limit. FTG is actually a scalar-tensor theory and predicts existence of tensor (spin 2) and scalar (spin 0) gravitational waves. Astrophysical tests of FTG will be available in near future. It is quite natural that fundamental description of gravity will be found on quantum level and geometrical description of gravity may be considered as the classical limit of quantum relativistic gravity theory."

How does the above differ to Weinberg formulation. They are the same.

Hope you can read the paper yourself instead of writing in one line riddles that is so difficult to understand.

I'll pass on this.

Wald, p383, we may view the full Einstein equation (γ_ab not assumed to be "small") as the sum of this free piece, plus a nonlinear self-interacting term, ie. we may view Einstein's equation as an equation for a self-interacting spin-2 field ...

 

[waterfall]

I'll pass on this.

Wald, p383, we may view the full Einstein equation (γ_ab not assumed to be "small") as the sum of this free piece, plus a nonlinear self-interacting term, ie. we may view Einstein's equation as an equation for a self-interacting spin-2 field ...

But the Field Theory of Gravitation (FTG) also involves self-interacting spin-2 field on flat spacetime, it just summarizes the findings of others like Ward. It is not a new theory. In other words, Wald proposal also comprises the Field Theory of Gravitation (FTG). Please address this first by accepting or not accepting and why (in clearer terms because I'm always confused by your replies).

 

[atyy]

But the Field Theory of Gravitation (FTG) also involves self-interacting spin-2 field on flat spacetime, it just summarizes the findings of others like Ward. It is not a new theory. In other words, Wald proposal also comprises the Field Theory of Gravitation (FTG). Please address this first by accepting or not accepting and why (in clearer terms because I'm always confused by your replies).

Sorry to seem unhelpful. I'm just telling you what I learned from the textbooks. As Baryshev states, his view is not the textbook view - he says it is different from Misner, Thorne & Wheeler, as well as Zeldovich & Novikov. I merely added the cite from Wald to give a more modern citation, in case you think MTW and ZN are out of date. To that one can also add Straumann, Carlip, & Donoghue. Perhaps Baryshev is right, but since it takes more time, energy and interest than I have to evaluate Baryshev, I'm just saying I'm not interested in discussing Baryshev's work at this moment. But if you are interested in reading it for yourself, I'd certainly like to hear when you are done whether you think his view, or the textbook view is right.

 

[waterfall]

Sorry to seem unhelpful. I'm just telling you what I learned from the textbooks. As Baryshev states, his view is not the textbook view - he says it is different from Misner, Thorne & Wheeler, as well as Zeldovich & Novikov. I merely added the cite from Wald to give a more modern citation, in case you think MTW and ZN are out of date. To that one can also add Straumann, Carlip, & Donoghue. Perhaps Baryshev is right, but since it takes more time, energy and interest than I have to evaluate Baryshev, I'm just saying I'm not interested in discussing Baryshev's work at this moment. But if you are interested in reading it for yourself, I'd certainly like to hear when you are done whether you think his view, or the textbook view is right.

Thanks for being clear that there are two views. I thought they were the same. But then they are both about spin-2 fields on flat spacetime. The differences may be subtle. So you are saying that in the MTW views, it is compatible with expanding space. Ok. I have most of these references on ebooks. I'll go over them again noting the distinctions as well as read Bayshev for the third time.

 

[Mentz114]

Can you point me to some e-lit that shows the MTW treatment ?

 

[waterfall]

Can you point me to some e-lit that shows the MTW treatment ?

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.

 

[PAllen]

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.

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.