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I have read these questions:

Gravitational mass defect

https://physics.stackexchange.com/a/60806/132371

And it made me curious. None of these answer my question.

The mass of an object is the same as the energy the object possesses at rest. Mass and rest energy are the same convertible thing, E=mc^2. The mass of an atomic nucleus is less then the mass of its constituents, and this missing mass is the mass defect, which is equivalent to the energy needed to separate the protons and neutrons from a nucleus. This is because of the strong force and the residual strong force, the nuclear force.

In the case of the strong force, the carrier, the gluon is massless. In the case of the residual strong force, nuclear force, the carrier, the pion does have rest mass.

Now in the case of gravity, there could be the same mass defect, but the mass of the graviton is not decided yet, it should be massless because of the long range of the gravitational force.

I do not know if there has been any experiment about the mass defect of the gravitational force, but could it decide whether gravitons should have mass?

Question:

  1. Has there been any experiment to prove or disprove the mass defect effect of gravity?

  2. If there is a mass defect, could that decide whether the graviton should be massless?

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Now in the case of gravity, there could be the same mass defect, but the mass of the graviton is not decided yet, it should be massless because of the long range of the gravitational force.

You are confusing the binding energy due to the electromagnetic and strong interactions with the possible binding energy due to the gravitational potential of the nucleons in the nucleus and the electrons with the nucleons to form atoms. Certainly the nucleons are not bound by the gravitational force, and if it is quantized, it will be only an infinitesimally small perturbation on the main potentials binding the nuclei and atoms. Look at the orders of magnitude difference in the coupling constants, not something measurable, not even for bounds.

The answer of my2cts gives a good example of the mass defect in classical general relativity.

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  • $\begingroup$ Thank you. I have one more question about the classical mass defect where the black hole's mass is smaller then the two constituent black hole's masses separately. Will that kind of mass defect tell us anything about the mass of the graviton, whether it has to be massless? $\endgroup$ – Árpád Szendrei Jun 20 '18 at 16:28
  • $\begingroup$ If quantization of gravity will follow on the steps of the quantization of the electromagnetic field, it is assumed that the graviton is massless and the classical gravitational wave observed by LIGO will be built up of zillions of gravitons, the way the classical electromagnetic wave is built up by zillions of photons. There are many ifs until we reach a point where the whole thing is tied mathematically and the assumption of zero mass can be tested by the observations. First we need a rigorous quantization of gravity. $\endgroup$ – anna v Jun 20 '18 at 18:37
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The first LIGO observation is interpreted as the gravitational wave of a black hole merger of 29 and 36 solar masses, resulting in a single black hole of 62 solar masses. This constitutes an example of gravitational mass defect.

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  • $\begingroup$ Thank you. Does that tell anything about the mass of the graviton? $\endgroup$ – Árpád Szendrei Jun 20 '18 at 16:29

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