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I read that a spin 0 graviton can't couple to traceless energy, such as a photon, in the introduction in the book The Feynman Lectures On Gravitation. Why is this true? What does it mean for a particle's energy to be "traceless"?

This has been my reference all along.

A spin 0 graviton can only couple to the trace of energy, and not to traceless energy.

New guy
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    can you give a link for your assertions about trace and traceless? and quantizing Newton's gravity? – anna v Apr 23 '18 at 19:10
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    This doesn't make sense. Newtonian gravity isn't a field theory, so there is no wave equation to quantize. –  Apr 23 '18 at 19:55
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    Newtonian gravity has all the book-keeping of a field theory within it. It is a field theory, and if you retard the speed of gravity to the speed of light, then you do get gravity waves predicted. All that is needed to predict waves is speed retardation. – New guy Apr 25 '18 at 17:40
  • I can't give a specific link. However, any number of books say that a spin O graviton is the simplest type of graviton, and you get it if you quantize Newton's theory. For example, Paul Davies's "Superforce" and "Forces " popular books. – New guy Apr 25 '18 at 17:47
  • Apparently, traceless energy simply means massless, and so trace of energy means mass. – New guy Apr 25 '18 at 18:25
  • Why has my second and expansively clear statement of my question -- although posed as an answer -- and people's comments on it been deleted? This is stupid, rude and unnecessary. The question is extremely clear -- although some people seem to be incapable of understanding it as a clear question. Moreover, the question does have a known answer -- I just don't know what is is. All that is needed is for a quantum gravity theorist to answer it. Classical scalar theories of gravity, such as Newton's and Nordstrom's don't deflect light -- look up Nordstrom's theory on stackexchange. – New guy Apr 26 '18 at 16:03
  • Also, there was no need to put my question on hold. Moreover, there was no need to edit my question AccidentalFourierTransform , as it was already clear what I was asking. – New guy Apr 26 '18 at 16:22
  • Also, Mr Ben Crowell why are you even commenting on my question when you don't even know that Newton's theory of gravity can very easily be regarded as a field theory. – New guy Apr 26 '18 at 16:26
  • AccidentalFourierTransform will you be so good as to undelete what you deleted. – New guy Apr 26 '18 at 16:27
  • Will those of you who did not understand my question explain how other people were able to? – New guy Apr 26 '18 at 16:30
  • Also, there is another problem with a spin O graviton -- it would predict that a gas of massive particles would interact less gravitationally when it is hot than it would when it is cold, which contradicts observation. This is because a spin O graviton would not couple to the kinetic energy of the rest mass particles because kinetic energy is also traceless. A spin O graviton only couples to rest mass, which is trace energy. Hence my question: why can't a spin O graviton couple to traceless energy, such as a photon? – New guy Apr 26 '18 at 16:44
  • I edited your question to make it easier to understand. Of course you have the right to change it back, but I think how it is now will make it most likely to be reopened! – knzhou Apr 27 '18 at 17:30
  • I have changed it back a bit. – New guy Apr 27 '18 at 17:44
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    Why do you keep writing the letter Oh instead of the number zero for spin? – Qmechanic Apr 27 '18 at 17:46
  • It doesn't really matter does it. I prefer it. – New guy Apr 27 '18 at 17:52
  • It makes no sense to close my question. It does have an answer. All that is needed is for a quantum gravity theorist to provide it. – New guy May 01 '18 at 18:52

2 Answers2

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You manifestly have a metric tnesor in the equation of motion for photons, and a spacetime containing photons manifestly has a nonzero stress-energy tensor, so you don't have to do any spin gynmastics to couple photons to gravitons, it's already there in the classical theory before you even quantize.

Zo the Relativist
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  • I don't understand your answer. It seems to me to apply to General Relativity, and not answer my question. - I would have edited my original question, but it had already received two responses. – New guy Apr 24 '18 at 16:01
  • @Newguy: you can't have Newtonian gravity coexisting with electromagnetism. Newtonian gravity is inconsistent with special relativity, but Maxwell theory requires special relativity. – Zo the Relativist Apr 24 '18 at 16:45
  • I'm not talking about classical Newtonian gravity. I'm asking about a zero-rest mass, traceless, moving at light-speed -- therefore consistent with special relativity -- spin O graviton. Why can't it couple to the traceless energy of a photon? – New guy Apr 24 '18 at 17:41
  • @Newguy: isn't the only renormalizable coupling between a scalar field and a vector field the one you get from the $D_{\mu}\phi^{*}D^{\mu}\phi$ term in the scalar QED Lagrangian, which would require your spin 0 graviton to have charge? – Zo the Relativist Apr 24 '18 at 19:54
  • I do not know. It is nothing to do with my question. – New guy Apr 25 '18 at 17:18
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The answer of Bob Bee here discusses zero spin gravitons.

Going into quantum field theories, one has to define the number of forces one is going to unite, and the couplings and gauge bosons , i.e. the force carriers. Whether there is a coupling between a photon, the gauge boson for the electromagnetic interaction, and the graviton ( whatever spin, limited up to 2 as said in the link above) is a decision for the model, and if the data validate the model .

For example there exists the possible triple vertex W+W-Z which is not allowed in the standard model of particle physics , so if measured will show a need for extending the model. Above the symmetry breaking energies all these particles have zero mass.

One can hypothesize a model where a zero spin graviton has a coupling with these zero mass gauge bosons,which include the photon, and then check if there is any evidence in data and observations. ( a bit hard with the coupling of the gravitational forces being so small). It is the smallness of the gravitational coupling that is the problem.

The main stream physics research models go in the direction of quantizing gravity (a goal not yet reached) in the framework of General relativity, which has to have a spin two graviton, and of course it couples to the gauge bosons, even with zero mass which happens above the symmetry breaking energies, as the massive W and Z are massless there.

Thus a photon and a graviton do have an interaction, as expected , in an appropriate quantized gravitational theory.

anna v
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