1

**Physics, Astronomy & Cosmology / Re: Does gravitational time dilation/GTD really cause gravity?**

« **on:**

**Today**at 02:03:27 »

Hi.

Feynman.JPG (27.32 kB . 742x228 - viewed 46 times)

The vertical swirls are virtual gravitons. The diagram on the left shows two electrons interacting, the one on the right shows a graviton interacting with another graviton by exchanging a virtual graviton.

There are some important features that would seem to be present in the scheme:

Electromagnetism is mediated by virtual photons which only couple to (electrically) charged particles and, as you (Colin2B) said earlier, photons do not couple to each other and exchange a virtual photon - so they don't experience an electromagnetic force. As far as the gravity is concerned, anything with energy-momentum is a charge. Since gravity couples to energy-momentum, gravitons should interact with every kind of particle, including other gravitons.

[reference: p.166-167, Spacetime and Geometry]

The interaction of gravitons with other gravitons is supported by the non-linear nature of the Einstein Field Equations. A solution involving two masses as a source of gravitation is not the sum or superposition of the solutions for each mass individually. This is completely different to anything in electrodynamics.

The discussion of gravitons in Chapter 4 is not based around gravitational waves, actually gravitational waves aren't even mentioned anywhere in that chapter. Carroll describes the virtual graviton quite directly as

You (Colin2B), Halc and most others (including myself) have generally referred to gravity as a geometric effect rather than any force. Gravitons do not naturally fall out from classical GR and you are correct that LIGO has not been detecting any forces towards or away from any sources but just a disturbance in the metric.

Section 4.7 on p. 177-181, Spacetime and Geometry seems most relevant here:

Which is enough to suggest that any quantum field theory for gravity would be unlike anything else you've seen.

Carroll goes on to state the following:

So that we are left with the possibility that curvature of the metric on spacetime may not ultimately be the cause of gravity and the "graviton" will not be a quantised perturbation of the metric field. GR is an effective field theory only.

It is just one of those interesting things that in this effective field theory, the metric field doesn't just describe a fundamental particle (or approximately describe it), the metric field also directly determines how we measure lengths and times. Most of the time, such as in the LIGO experiments, it is the distortion of lengths that we measure. A Gravitational wave may be indicative of a bundle of gravitons travelling through space but in most quantum theories of gravity, gravitons are still being exchanged even where the metric field appears to remain static (upto the limit of our ability to measure it or determine the absolute positions and lengths of separtion between any two objects).

It's late, I'm going to try and put the image in the right place and then sign off. I don't know if any of the above helped.

Best Wishes.

In any quantum gravity field theory the graviton would be an elementary particle that mediates the force of gravitational interaction. As @Halc says it's not often used in this way. probably because the theory has real problems at the moment.Agreed. When it is used it's used this way:

*Upon qunatization, Einsteins equation predicts spin-two particles called gravitons. We don't know how to carry out such a quantization consistently, but the existence of gravitons is sufficiently robust that it is expected to be a feature of any well-defined scheme*[Fig. 4.2 and text, p. 167, Introduction to Spacetime and Geometry, Sean Carroll]As you know QED treats photons as particles that carry or mediate the electromagnetic force. In this model charged particles interact by emitting and absorbing photons, but these photons don't experience the electromagnetic force themselves, and so they do not interact with each other, but the effects of electromagnetism are produced by the energy and momentum they carry. The photons that carry force are known as virtual particles in QED and are shown as internal interactions in the Feynman diagrams and basically are there to make the energy equations add upThe analagous Feynmann diagrams with gravitons look like this:

Feynman.JPG (27.32 kB . 742x228 - viewed 46 times)

The vertical swirls are virtual gravitons. The diagram on the left shows two electrons interacting, the one on the right shows a graviton interacting with another graviton by exchanging a virtual graviton.

Clearly, the graviton would have to fit a similar model, but I wonder what would take the place of charged particle interactions when, as @Halc says, the gravitational wave causes a disturbance in spacetime. We would certainly see that as a movement of test particles (as a distant observer)and in a Newtonian system would describe it as a force. Also, that movement (oscillation) of the test particles is not in the direction of the wave propagation, so nothing is being pulled towards the source, but it is similar to light exerting an effect on electrons in the photoelectric effect. Does GR give a clue? This isn’t an area I’ve looked into.See above. Note that there aren't any consistent quantum theories of gravity that I am aware of. The general properties are based on .... well, in my case, whatever Sean Caroll was basing it on.

There are some important features that would seem to be present in the scheme:

Electromagnetism is mediated by virtual photons which only couple to (electrically) charged particles and, as you (Colin2B) said earlier, photons do not couple to each other and exchange a virtual photon - so they don't experience an electromagnetic force. As far as the gravity is concerned, anything with energy-momentum is a charge. Since gravity couples to energy-momentum, gravitons should interact with every kind of particle, including other gravitons.

[reference: p.166-167, Spacetime and Geometry]

The interaction of gravitons with other gravitons is supported by the non-linear nature of the Einstein Field Equations. A solution involving two masses as a source of gravitation is not the sum or superposition of the solutions for each mass individually. This is completely different to anything in electrodynamics.

The discussion of gravitons in Chapter 4 is not based around gravitational waves, actually gravitational waves aren't even mentioned anywhere in that chapter. Carroll describes the virtual graviton quite directly as

*a quantised perturbation of the metric*and is discussing the ability for the exchange of a virtual graviton to deflect the path of two particles that approach each other.You (Colin2B), Halc and most others (including myself) have generally referred to gravity as a geometric effect rather than any force. Gravitons do not naturally fall out from classical GR and you are correct that LIGO has not been detecting any forces towards or away from any sources but just a disturbance in the metric.

Section 4.7 on p. 177-181, Spacetime and Geometry seems most relevant here:

*In practice, it is common to invoke the equivalence principle to justify any of the following four ideas:*

1. ... (usual stuff)...

2. There exists a metric on spacetime, the curvature of which we interpret as gravity.

3. There do not exist any other fields that resemble gravity.

4. The interactions of matter fields to curvature are minimal: they do not involve direct couplings to the Riemann tensor or its contractions.

.........1. ... (usual stuff)...

2. There exists a metric on spacetime, the curvature of which we interpret as gravity.

3. There do not exist any other fields that resemble gravity.

4. The interactions of matter fields to curvature are minimal: they do not involve direct couplings to the Riemann tensor or its contractions.

.........

Which is enough to suggest that any quantum field theory for gravity would be unlike anything else you've seen.

Carroll goes on to state the following:

*...the demands of eventually reconciling general relativity with quantum mechanics suggest to many that the metric will ultimately be revealed as a concept derived from a more fundamental collection of degrees of freedom....*So that we are left with the possibility that curvature of the metric on spacetime may not ultimately be the cause of gravity and the "graviton" will not be a quantised perturbation of the metric field. GR is an effective field theory only.

It is just one of those interesting things that in this effective field theory, the metric field doesn't just describe a fundamental particle (or approximately describe it), the metric field also directly determines how we measure lengths and times. Most of the time, such as in the LIGO experiments, it is the distortion of lengths that we measure. A Gravitational wave may be indicative of a bundle of gravitons travelling through space but in most quantum theories of gravity, gravitons are still being exchanged even where the metric field appears to remain static (upto the limit of our ability to measure it or determine the absolute positions and lengths of separtion between any two objects).

It's late, I'm going to try and put the image in the right place and then sign off. I don't know if any of the above helped.

Best Wishes.

The following users thanked this post: Furious Cat