Could gravitons be dimensionless?

In summary, the metric is just the flat metric ##\eta_{\mu\nu}=\hbox{diag}(-1,1,1,1)## with the dimensions in the co-ordinates ##x^\mu##. Photons can be detected - so does that imply that they can't be dimensionless? Gravitons are quantum excitations of the metric, so it seems that they must themselves have zero size. But this is unlike other fields and their associated particles that have dimensions of mass/energy ##[M]##.
  • #1
jcap
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If the metric ##g_{\mu\nu}## is dimensionless and gravitons are quantum excitations of the metric does that mean that gravitons themselves are dimensionless?

I say this as locally the metric is just the flat metric ##\eta_{\mu\nu}=\hbox{diag}(-1,1,1,1)## with the dimensions in the co-ordinates ##x^\mu##.

To put it another way:

Is graviton energy included in the stress-energy tensor ##T_{\mu\nu}##?

Actually classical gravitational waves can be detected so does that imply that gravitons can't be dimensionless?
 
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  • #2
jcap said:
Actually classical gravitational waves can be detected so does that imply that gravitons can't be dimensionless?
Photons can be detected - so does that imply that they can't be dimensionless?
 
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  • #3
jcap said:
If the metric ##g_{\mu\nu}## is dimensionless and gravitons are quantum excitations of the metric does that mean that gravitons themselves are dimensionless?

Are you asking if they are point particles, or something deeper than that?
 
  • #4
ohwilleke said:
Are you asking if they are point particles, or something deeper than that?
Ah, you beat me to it! :cool:

I was about to ask whether there might possibly be some confusion between two meanings of "dimensionless":

1. Not having associated dimensional units (e.g. in SI a.k.a. MKS units). The fine structure constant is dimensionless in this sense.

2. Having zero size, in some sense (e.g. an electron versus a proton)
 
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  • #5
I mean (1) : not having dimensional units.

In terms of Newtonian gravitation we have the gravitational potential given by:

$$\Phi \sim -\frac{G M}{R}$$

In natural units, ##\hbar=c=1## (dimensionless), Newton's gravitational constant is ##G=1/M_{pl}^2## where ##M_{pl}## is the Planck mass. Therefore the dimensions of the gravitational field ##\Phi## is

$$[\Phi] = \frac{[M]^{-2}[M]}{[M]^{-1}}=1$$

If gravitons are excitations of ##\Phi## then they must themselves be dimensionless.

This is unlike other fields and their associated particles that have dimensions of mass/energy ##[M]##.
 
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  • #6
OK. It is now much more clear what you mean.
 

1. What are gravitons?

Gravitons are hypothetical particles that are thought to carry the force of gravity in the framework of quantum mechanics. They are predicted by the theory of quantum gravity, but have not yet been observed or proven to exist.

2. Why is the dimensionlessness of gravitons important?

The dimensionlessness of gravitons is important because it is a key characteristic that distinguishes them from other particles. Dimensionlessness means that gravitons have no mass, charge, or other measurable properties, and therefore behave differently from other particles in the universe.

3. How do scientists study the dimensionlessness of gravitons?

Scientists study the dimensionlessness of gravitons through theoretical models and mathematical equations. They also use experiments and observations of the behavior of gravity and other particles to test the predictions of quantum gravity theories.

4. What are the implications if gravitons are found to be dimensionless?

If gravitons are found to be dimensionless, it would provide strong evidence for the existence of a theory of quantum gravity. It would also challenge our current understanding of the fundamental forces and particles in the universe, and could potentially lead to new discoveries and advancements in physics.

5. Are there any experiments currently being conducted to test the dimensionlessness of gravitons?

Yes, there are several experiments and observations being conducted to test the dimensionlessness of gravitons, including studies of gravitational waves, high-energy particle collisions, and the behavior of gravity in extreme environments. However, more research and advancements in technology are needed to definitively prove the dimensionlessness of gravitons.

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