Is Gravity a Force or a Deformation of Space?

[tonyxon22]

For what I understand from GR, gravity is a deformation of space due to the presence of mass. This deformation could be interpreted as a force of attraction between two bodies with mass for general uses and simplification of calculation, but in reality it is not a force. That is why it affects the path of a beam of light, which has no mass.

On the other hand, in some literature I have encountered the prediction of a particle called graviton which would be the carrier of the gravitational force, as the photon is for the electromagnetic force. (Among others, one article I read is the main Wikipedia article about gravitons http://en.wikipedia.org/wiki/Graviton. It is also mentioned in Stephen Hawking’s A brief history of time, and many other publications I have read.)

My questions:

- Isn’t the assumption of a gravitational force carrying particle another way of saying that gravity IS a force?

- How could this model be coherent with GR?

- Does this particle have anything to do with the Higgs boson or Higgs field?Thanks,

 

[craigi]

For what I understand from GR, gravity is a deformation of space due to the presence of mass. This deformation could be interpreted as a force of attraction between two bodies with mass for general uses and simplification of calculation, but in reality it is not a force. That is why it affects the path of a beam of light, which has no mass.

On the other hand, in some literature I have encountered the prediction of a particle called graviton which would be the carrier of the gravitational force, as the photon is for the electromagnetic force. (Among others, one article I read is the main Wikipedia article about gravitons http://en.wikipedia.org/wiki/Graviton. It is also mentioned in Stephen Hawking’s A brief history of time, and many other publications I have read.)

My questions:

- Isn’t the assumption of a gravitational force carrying particle another way of saying that gravity IS a force?

- How could this model be coherent with GR?

- Does this particle have anything to do with the Higgs boson or Higgs field?Thanks,

The graviton is a possible feature of a sucessful theory of quantum gravity, which combines quantum theory with general relativity.

String Theory is our best candidate for this which models gravity as force carried by the graviton.

 

[Demystifier]

Gravity is a pseudo-force, which means a phenomenon with many but not all properties of a proper force. Gravitons can be thought of as carriers of this pseudo-force.

 

[tonyxon22]

And where would that leave the General Theory of Relativity?

 

[jtbell]

It would leave general relativity as an approximate "effective theory" that emerges from a more fundamental theory of quantum gravity, similarly to classical mechanics emerging from quantum mechanics and classical electrodynamics emerging from quantum field theory.

 

[tonyxon22]

But there are still other predictions of the GR that can be measured with experiments and that are not explained by quantum gravity

 

[bhobba]

But there are still other predictions of the GR that can be measured with experiments and that are not explained by quantum gravity

At present quantum gravity explains everything:
http://arxiv.org/abs/1209.3511

Only beyond the plank scale is there issues. We haven't reached there yet in experiments. But physicists are working hard to lift that veil.

Thanks
Bill

 

[ShayanJ]

At present quantum gravity explains everything:
http://arxiv.org/abs/1209.3511

Only beyond the plank scale is there issues. We haven't reached there yet in experiments. But physicists are working hard to lift that veil.

Thanks
Bill

People seem happy but has anyone considered this paper?

 

[Demystifier]

People seem happy but has anyone considered this paper?

I always wanted to, but never found time to do it properly.

 

[ShayanJ]

I always wanted to, but never found time to do it properly.

I hope you find the time. I'll look forward for the interesting results.
But for now, it seems its been ignored which I don't like.

 

[atyy]

People seem happy but has anyone considered this paper?

Yes, the questions raised by that paper are not relevant to the idea that quantum gravity at present is adequate.

 

[ShayanJ]

Yes, the questions raised by that paper are not relevant to the idea that quantum gravity at present is adequate.

Could you clarify a bit?

 

[atyy]

Could you clarify a bit?

The paper is about whether it can be shown that a spin 2 particle can be uniquely "bootstrapped" to give Einstein's theory. However, all we need for quantum gravity is that Einstein's theory can be written as spin 2, which is uncontested.

 

[stevendaryl]

People seem happy but has anyone considered this paper?

I read it, and it's sort of interesting. The conclusion seems to be that if you write the metric in the form:

$g_{\mu \nu} = \eta_{\mu \nu} + \lambda h_{\mu \nu}$

and consider the Einstein field equations to be a kind of equations of motion for the spin-2 field $h_{\mu \nu}$, then the natural "source" for $h_{\mu \nu}$ is not the generally covariant quantity $T^{\mu \nu}$ (the full stress-energy tensor) but the non-covariant quantity $S^{\mu \nu}$ (you'll have to read the paper to see how it is defined). In retrospect, I'm not sure how surprising that should be, since writing $g_{\mu \nu}$ as a perturbation of $\eta_{\mu \nu}$ is itself not a generally covariant thing to do.

The paper actually brings up a mystery that I've wondered about before. Exactly why are we able to obtain the stress-energy tensor $T^{\mu \nu}$ by varying the Lagrangian with respect to $g_{\mu \nu}$?

 

[ShayanJ]

I read it, and it's sort of interesting. The conclusion seems to be that if you write the metric in the form:

$g_{\mu \nu} = \eta_{\mu \nu} + \lambda h_{\mu \nu}$

and consider the Einstein field equations to be a kind of equations of motion for the spin-2 field $h_{\mu \nu}$, then the natural "source" for $h_{\mu \nu}$ is not the generally covariant quantity $T^{\mu \nu}$ (the full stress-energy tensor) but the non-covariant quantity $S^{\mu \nu}$ (you'll have to read the paper to see how it is defined). In retrospect, I'm not sure how surprising that should be, since writing $g_{\mu \nu}$ as a perturbation of $\eta_{\mu \nu}$ is itself not a generally covariant thing to do.

The paper actually brings up a mystery that I've wondered about before. Exactly why are we able to obtain the stress-energy tensor $T^{\mu \nu}$ by varying the Lagrangian with respect to $g_{\mu \nu}$?

Yeah, I read the paper before. It says several other things too. One is that its impossible to obtain the EH action from the action of a spin-2 field on a Minkowski spacetime but it is possible at the level of equations of motion. He also states that people who start from spin-2 field on a Minkowski spacetime to reach GR, actually make choices that are coming from their knowledge of GR and so they're just reinterpreting GR in terms of spin-2 fields not building an equivalent theory!

 

[stevendaryl]

Yeah, I read the paper before. It says several other things too. One is that its impossible to obtain the EH action from the action of a spin-2 field on a Minkowski spacetime but it is possible at the level of equations of motion. He also states that people who start from spin-2 field on a Minkowski spacetime to reach GR, actually make choices that are coming from their knowledge of GR and so they're just reinterpreting GR in terms of spin-2 fields not building an equivalent theory!

Yes, but I think that's related to the question of general covariance, which in turn is related to the question of why varying $g_{\mu \nu}$ gives you the stress-energy tensor $T^{\mu \nu}$. I take the authors to be saying that if you honestly started with a spin-two field equation and introduced self-coupling, then self-consistency wouldn't lead to the EH action, but to some other Lagrangian that is not generally covariant. (But I'm confused: does this Lagrangian have the exact same equations of motion as the EH action, or just the same linearized equations?)

 

[ShayanJ]

Yes, but I think that's related to the question of general covariance, which in turn is related to the question of why varying $g_{\mu \nu}$ gives you the stress-energy tensor $T^{\mu \nu}$. I take the authors to be saying that if you honestly started with a spin-two field equation and introduced self-coupling, then self-consistency wouldn't lead to the EH action, but to some other Lagrangian that is not generally covariant. (But I'm confused: does this Lagrangian have the exact same equations of motion as the EH action, or just the same linearized equations?)

To be honest, I'm confused too. I'm not good enough to delve into it more deeply in a reasonable amount of time that I can afford now. So for now I just can be happy with knowing the results.

 

[atyy]

Does spin 2 impy GR? Apart from the old papers, here is a more recent one.

http://arxiv.org/abs/hep-th/0007220
Inconsistency of interacting, multi-graviton theories
Nicolas Boulanger, Thibault Damour, Leonardo Gualtieri, Marc Henneaux

samalkhaiat made an interesting comment on related issues in gauge theories: https://www.physicsforums.com/threads/stress-energy-tensors-in-gr.787233/page-5#post-4954681.

 

[bhobba]

Does spin 2 impy GR?

Feynman thought so and the detail of that claim can be found in his Lectures on Gravitation which I have read:
https://www.amazon.com/dp/0813340381/?tag=pfamazon01-20

But that's not the issue with an EFT of gravity exists valid up to the plank scale as per the link I gave.

The logic is this. That an EFT of gravity exists where its spin 2 particles, is independent of if spin 2 particles uniquely defines such as theory - as you correctly pointed out before.

Thanks
Bill

 

[ShayanJ]

Feynman thought so and the detail of that claim can be found in his Lectures on Gravitation which I have read:
https://www.amazon.com/dp/0813340381/?tag=pfamazon01-20

In the paper I linked to, the author states that the only one who actually did such a calculation is Deser. Others just claimed it to be true, including Feynman. But then he points out some problems with Deser's approach too.

 

[bhobba]

In the paper I linked to, the author states that the only one who actually did such a calculation is Deser.

Its been a number of years since I went through it - but can't remember that.

However its not germane to the issue at hand.

Thanks
Bill

 

[ShayanJ]

Its been a number of years since I went through it - but can't remember that.

Page 3 :

The by far cleverest mathematical procedure was the one employed by Deser, in which he exploits the fact that, with a suitable choice of variables, the gravitational action becomes a cubic polynomial allowing the iteration to stop at a finite order. To achieve this mathematical economy, he has to start with the Palatini variational form (see his equation 2) based on the Lagrangian $f_{ab} R_{ab}$where$f^{ab}=\sqrt{−g}g^{ab}$ is the preferred variable. It is no surprise that he obtains $\sqrt{−g}R$ as the final result. (This is the only previous work that actually attempts an iteration; we shall comment on Deser’s derivation in more detail in Section VI C.)

However its not germane to the issue at hand.

Sorry for the interruption! I hope I didn't distract the thread from answering the OP.

 

[bhobba]

Sorry for the interruption! I hope I didn't distract the thread from answering the OP.

That's OK.

Its been so long now since I was into it, someone else will have to help in sorting out if the papers criticisms are valid or not.

Thanks
Bill