GR and the role of the graviton

[La Guinee]

If I understand things correctly, GR says that gravity isn't really a force at all, gravity is just particles moving in the geometry of spacetime. Given this, I don't understand the role of the graviton. I thought that gauge bosons were force mediators, that they somehow communicated and transmitted a force to other particles. So why the need for a graviton?

 

[HallsofIvy]

If I understand things correctly, GR says that gravity isn't really a force at all, gravity is just particles moving in the geometry of spacetime. Given this, I don't understand the role of the graviton. I thought that gauge bosons were force mediators, that they somehow communicated and transmitted a force to other particles. So why the need for a graviton?

The "graviton" doesn't have any role at all in GR. The "graviton", or any "bosons" for that matter, is an artifact of Quantum Physics, not GR. Reconcileing GR with Quantum Physics is the main problem of Physics at the present time.

 

[jtbell]

Similarly, photons have no role at all in classical electrodynamics. They are part of quantum electrodynamics. The difference with gravitions is that we do not yet have a successful theory of "quantum gravitodynamics."

 

[La Guinee]

Similarly, photons have no role at all in classical electrodynamics. They are part of quantum electrodynamics. The difference with gravitions is that we do not yet have a successful theory of "quantum gravitodynamics."

My whole point was that QED is completely different because the photon mediates the EM force between particles, but in the case of gravity, it seems like there's no need for a mediator because the geometry of spacetime is the force.

I know this gets into quantum gravity, but I think there's a better answer than, "We don't have a theory of quantum gravity so nobody knows."

 

[Fredrik]

My whole point was that QED is completely different because the photon mediates the EM force between particles, but in the case of gravity, it seems like there's no need for a mediator because the geometry of spacetime is the force.

I know this gets into quantum gravity, but I think there's a better answer than, "We don't have a theory of quantum gravity so nobody knows."

You were also told that gravitons are not a part of GR. Those are the two best answers to your questions. There isn't a whole lot more to be said. I can think of a couple of things though:

1. It's been well known for a long time that a quantum theory describing massless spin 2 particles (i.e. gravitons) must look more more or less like general relativity. So people tried to construct a quantum field theory of gravity (i.e. a theory of gravitons). I think they were able to use it to "derive" classical GR, but they couldn't really derive any new results because the theory isn't renormalizable, which means that the result of most calculations is "infinity".

2. Science can't really answer questions such as "Is this force mediated by particles?". A theory of physics is just a bunch of postulates that can be used to predict the probabilities of possible results of experiments. Science can actually only answer one question: "How well does this theory predict those probabilities?"

 

[jtbell]

My whole point was that QED is completely different because the photon mediates the EM force between particles, but in the case of gravity, it seems like there's no need for a mediator because the geometry of spacetime is the force.

In classical electrodynamics, the electric and magnetic fields "mediate" the electromagnetic interaction, and photons do not exist. In quantum electrodynamics, photons "mediate" the electromagnetic interaction, and classical electric and magnetic fields do not exist, except as an "effective theory" in the non-quantum limit (very large numbers of photons).

In "classical" (non-quantum) GR, the curvature of spacetime mediates the gravitational interaction, and gravitons do not exist. In a (so far hypothetical) fully quantum theory of gravitation, gravitons (or something similar) will mediate the gravitational interaction, and spacetime curvature will presumably appear only as an "effective theory" in non-quantum limit (very large numbers of gravitions).

 

[La Guinee]

In classical electrodynamics, the electric and magnetic fields "mediate" the electromagnetic interaction, and photons do not exist. In quantum electrodynamics, photons "mediate" the electromagnetic interaction, and classical electric and magnetic fields do not exist, except as an "effective theory" in the non-quantum limit (very large numbers of photons).

In "classical" (non-quantum) GR, the curvature of spacetime mediates the gravitational interaction, and gravitons do not exist. In a (so far hypothetical) fully quantum theory of gravitation, gravitons (or something similar) will mediate the gravitational interaction, and spacetime curvature will presumably appear only as an "effective theory" in non-quantum limit (very large numbers of gravitions).

I see. That makes sense. I suppose this is a little off topic, but does string theory provide an answer to how curvature arises from the graviton?

 

[HallsofIvy]

My whole point was that QED is completely different because the photon mediates the EM force between particles, but in the case of gravity, it seems like there's no need for a mediator because the geometry of spacetime is the force.

My point was that the statement " GR says that gravity isn't really a force at all, gravity is just particles moving in the geometry of spacetime." is wrong. General relativity represents gravity as the curvature of spacetime, not as particles.

 

[MeJennifer]

My point was that the statement " GR says that gravity isn't really a force at all, gravity is just particles moving in the geometry of spacetime." is wrong. General relativity represents gravity as the curvature of spacetime, not as particles.

Indeed and in addition GR represents EM forces and all other forces as waves not as particles.

 

[Naty1]

I suppose this is a little off topic, but does string theory provide an answer to how curvature arises from the graviton?

I'd be very reluctant to say the graviton curves space as curvature is a classical field concept while as noted above the graviton is a quantum concept...no one knows how to reconcile the viewpoints at this point...

You might think of the quandary as analogous to the wave particle duality...which is an electron, a wave/field or a particle? So far it seems to depend on the measurement technique...

regarding the graviton in string theory: No it does not; a string pops out that has spin 2, and other gravity like characteristics. But string string is background dependent..that means you pick a fixed background for space time and compute from there...there is no dynamic curving/bending of space...loop quantum gravity, in contrast, provides a dynamic (flexible) spacetime more like general relativty...but that has not been reconciled with GR either.

 

[Fredrik]

I suppose this is a little off topic, but does string theory provide an answer to how curvature arises from the graviton?

I think it does. I don't know enough about string theory or quantum field theories of gravity to be certain about what I'm saying here, but I'll describe the connection between gravitons and curvature as I understand it (or possibly misunderstand it):

The field that's described by the (non-renormalizable) quantum field theory of gravity is the part of the metric that represents its deviation from the Minkowski metric. You write the metric as $g_{ab}=\eta_{ab}+h_{ab}$ and only quantize $h_{ab}$. This means that a graviton is a quanta of "non-Minkowskiness" for lack of a better word. A lot of that "non-Minkowskiness" is curvature.

String theory predicts the existence of massless spin 2 particles, which apparently is the same thing as describing the quantum theory of the field $h_{ab}$.

I read an interview with Edward Witten where he said (roughly) that it's obvious to those who understand string theory really well that it is background independent even though the language they're using is background dependent.

 

[La Guinee]

Thank you all for the replies!

 

[Naty1]

I read an interview with Edward Witten where he said (roughly) that it's obvious to those who understand string theory really well that it is background independent even though the language they're using is background dependent.

I'd love to see the quote if anyone can find it...

 

[MeJennifer]

You write the metric as $g_{ab}=\eta_{ab}+h_{ab}$ and only quantize $h_{ab}$. This means that a graviton is a quanta of "non-Minkowskiness" for lack of a better word. A lot of that "non-Minkowskiness" is curvature.

Do you think you can write this form for all non-stationary spacetimes?

 

[Fredrik]

I tried to find the interview, but didn't succeed. I thought I found it the first time by following DrGreg's link to a Scientific American article in this thread, and by clicking around on the site. But I wasn't able find an interview with him. (Yes, I tried the search feature too). Hm...maybe it wasn't a sciam article at all.

Weird...when I try to google for it, this thread comes up in the search results even though It's only been a few hours since I posted the words that matched the search.

 

[Fredrik]

Do you think you can write this form for all non-stationary spacetimes?

I have no idea. Is there any reason why we shouldn't? I mean, whatever g is, we should always be able to write $g=\eta+(g-\eta)$ and define $h=g-\eta$, right?

 

[Mentz114]

Hi Fredrik,
the form $g_{ab}=\eta_{ab}+h_{ab}$ is not suitable for general gravitational fields. It's not a tensor. All attempts to start from this point lead to inferior theories, as far as I can tell.

M

 

[Fredrik]

Why is it not a tensor? To me it looks like all three quantities are defined as tensors.

 

[Mentz114]

I'm not so sure now but I do know that for g_mn to be a covariant tensor, then under transformation from $x^\mu$ to $x^\bar{\mu}$
$$g_{\bar{m}\bar{n}}=g_{mn}A^n_{\bar{n}}A^m_{\bar{m}}$$
where
$$A^n_{\bar{n}}=\frac{\partial x^n}{\partial x^\bar{n}}$$

I don't think $\eta_{mn}+h_{mn}$ satisfies this rule.

I could be wrong, maybe someone can clarify ?

 

[jnorman]

in my view, quantum gravity (ie, gravitational force as a result of the interaction of graviton particles with other particles) is a non-starter. there is no conceivable mechanism by which particle interaction could result in the perfectly smooth "bending" of light as it passes a massive star.

 

[Fredrik]

I'm not so sure now but I do know that for g_mn to be a covariant tensor, then under transformation from $x^\mu$ to $x^\bar{\mu}$
$$g_{\bar{m}\bar{n}}=g_{mn}A^n_{\bar{n}}A^m_{\bar{m}}$$
where
$$A^n_{\bar{n}}=\frac{\partial x^n}{\partial x^\bar{n}}$$

I don't think $\eta_{mn}+h_{mn}$ satisfies this rule.

I could be wrong, maybe someone can clarify ?

I just assumed that the separation of g into two pieces is done like this: You start with a quantity g, which is assumed to be a tensor. Then you just express it as $g=\eta+g-\eta$ where $\eta$ is defined as the tensor that has components $\eta_{\mu\nu}$ in some coordinate system. That makes sure that both $\eta$ and $h$ are tensors.

It's a bit strange that we have to mention a coordinate system. There will be issues to deal with, like "In what coordinate systems are the components of $\eta$ equal to $\eta_{\mu\nu}$?". I don't know anything about how those issues were dealt with. It's been about 10 years since that time when I took a quick look at an old article where they did these things. I never tried to really understand it.

 

[Naty1]

Fredrik:

when I try to google for it, this thread comes up in the search results even though It's only been a few hours since I posted the words that matched the search.

You are being watched!

jnorman :

there is no conceivable mechanism by which particle interaction could result in the perfectly smooth "bending" of light as it passes a massive star.

Harsh assessment..you just killed all of string theory...