Non-geometric approach to gravity impossible?

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SUMMARY

The discussion centers on the feasibility of modeling gravity without relying on geometric frameworks, as highlighted in Steven Weinberg's paper on gravity. Participants debate the implications of flat spacetime on gravitational theories, questioning whether gravity can exist as a force without geometric properties. Key points include the unobservability of Minkowski spacetime's inertial structure, the bending of light rays in the presence of mass, and the potential for alternative models such as string theory and Geroch's "Einstein Algebras" that do not depend on curved spacetime. The consensus suggests that while geometric models are prevalent, non-geometric approaches are not inherently impossible.

PREREQUISITES
  • Understanding of General Relativity and its implications on gravity.
  • Familiarity with Minkowski spacetime and its inertial properties.
  • Knowledge of field theories and their role in modern physics.
  • Awareness of alternative theories such as string theory and Einstein Algebras.
NEXT STEPS
  • Research the implications of flat spacetime in gravitational theories.
  • Explore the concept of gravitational shielding and its experimental limitations.
  • Study string theory as a potential non-geometric model of gravity.
  • Investigate Geroch's "Einstein Algebras" and their significance in gravity modeling.
USEFUL FOR

Physicists, researchers in gravitational theory, and students of theoretical physics seeking to understand the complexities of gravity beyond geometric interpretations.

  • #31
yuiop said:
if you were at a midpoint between Jupiter and the Earth (and not falling) then the rate that Jupiter falls towards the Earth would be the same as the rate that a canonball falls towards the Earth.
In order to keep that midpoint one would have to accelerate and the acceleration would not be constant.

So in that case what do you think your measurements would actually prove?
 
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  • #32
waterfall said:
1. What is the reason for the Equivalence Principle in this Spin-2 field in Flat Spacetime Field Theory of Gravitation?

http://arxiv.org/abs/1105.3735
"Asking for consistent self interactions leads essentially uniquely to GR and full general coordinate invariance [4, 5, 6, 7, 8, 9, 10] (see also chapter 13 of [2], which shows how helicity 2 implies the equivalence principle)."

http://arxiv.org/abs/1007.0435
"As argued by Weinberg [38], the equivalence principle can be recovered as the spin-two case of his low energy theorem. ... In other words, massless particles of spin-two must couple in the same way to all particles at low energies."
 
  • #33
Thanks. I need to understand 2 basic things:

1. Say in the future gravitons were finally detected. Does it mean spin-2 fields actually existed and they occur in the backdrop of flat spacetime. Or do gravitons imply spacetime curvature is a priori? But in what sense is there spacetime curvature and at the same time gravitons existing when the two are more of a dual much like photons and electromagnetic wave (these are dual descriptions)? Unless you mean detection of gravitons don't tell us whether spacetime is really curved or dynamics just occurring in flat spacetime by spin-2 fields?

2. Can Loop Quantum Gravity be formulated as spin-2 field in flat spacetime? Or does LQG stay valid only if spacetime is actually curved?
 
  • #34
waterfall said:
But in what sense is there spacetime curvature and at the same time gravitons existing when the two are more of a dual much like photons and electromagnetic wave (these are dual descriptions)?

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.

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.
 
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  • #35
PAllen said:
Midpoint is also incorrect - you mean center of mass.

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

PAllen said:
That's true, but doesn't get at the issue of sloppy wording. Someone standing on the ground would see a Jupiter mass black hole dropped from a tower fall faster than cananball dropped earlier. That is a fact, period. The principle intended is that rate of fall is independent of composition, and is essentially independent of mass over many orders of magnitude (atom to mountain), but not exactly independent of mass.

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.
 
  • #36
yuiop said:
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.
 
  • #37
atyy said:
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?
 
  • #38
waterfall said:
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.
 
  • #39
atyy said:
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.
 
  • #40
waterfall said:
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.
 
  • #41
atyy said:
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.
 
  • #42
waterfall said:
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?
 
  • #43
btw.. how do you model Big Bang Expansion using spin-2 field on flat spacetime? Anyone got an idea?
 
  • #44
Weinberg exhibits harmonic coordinates for the FRW universe in his textbook.

I'm not sure whether the positive cosmological constant changes things.
 
  • #45
atyy said:
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.
 
  • #46
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.
 
  • #47
atyy said:
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.
 
  • #48
waterfall said:
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".
 
  • #49
atyy said:
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.
 
  • #50
waterfall said:
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.
 
  • #51
atyy said:
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.
 
  • #52
waterfall said:
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.
 
  • #53
atyy said:
I don't know what FTG is.

Field Theory of Gravitation is the formalism of Spin 2-Field on Flat Spacetime.
 
  • #54
waterfall said:
Field Theory of Gravitation is the formalism of Spin 2-Field on Flat Spacetime.

See post #44
 
  • #55
atyy said:
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.
 
  • #56
waterfall said:
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?
 
  • #57
atyy said:
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."
 
  • #58
waterfall said:
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.
 
  • #59
atyy said:
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.
 
  • #60
waterfall said:
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.
 

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