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I have read this question:

What is the difference between gravitons and gravitational waves?

where annav says:

So photons are the building blocks of light, and gravitons are (hopefully) the building blocks of gravitational waves.

What is the difference between gravitational waves and gravitational distortions in spacetime?

where lemon says:

Gravitational waves are a type of space-time distortion and have nothing to do with gravitons

I thought that GWs are real. They have been confirmed and observed. We must have at least a theoretical description of what they are made of.

In the framework of quantum field theory, the graviton is the name given to a hypothetical elementary particle speculated to be the force carrier that mediates gravity. However the graviton is not yet proven to exist, and no scientific model yet exists that successfully reconciles general relativity, which describes gravity, and the Standard Model, which describes all other fundamental forces. Attempts, such as quantum gravity, have been made, but are not yet accepted. If such a particle exists, it is expected to be massless (because the gravitational force appears to have unlimited range) and must be a spin-2 boson. It can be shown that any massless spin-2 field would give rise to a force indistinguishable from gravitation, because a massless spin-2 field must couple to (interact with) the stress–energy tensor in the same way that the gravitational field does; therefore if a massless spin-2 particle were ever discovered, it would be likely to be the graviton without further distinction from other massless spin-2 particles.[55] Such a discovery would unite quantum theory with gravity.

https://en.wikipedia.org/wiki/Gravitational_wave

Gravitational waves are disturbances in the curvature of spacetime, generated by accelerated masses, that propagate as waves outward from their source at the speed of light.

In theories of quantum gravity, the graviton is the hypothetical quantum of gravity, an elementary particle that mediates the force of gravity. Alternatively, if gravitons are massive at all, the analysis of gravitational waves yielded a new upper bound on the mass of gravitons. The graviton's Compton wavelength is at least 1.6×1016 m, or about 1.6 light-years, corresponding to a graviton mass of no more than 7.7×10−23 eV/c2.[16] This relation between wavelength and mass-energy is calculated with the Planck–Einstein relation, the same formula that relates electromagnetic wavelength to photon energy. However, if gravitons are the quanta of gravitational waves, then the relation between wavelength and corresponding particle energy is fundamentally different for gravitons than for photons, since the Compton wavelength of the graviton is not equal to the gravitational-wave wavelength. Instead, the lower-bound graviton Compton wavelength is about 9×109 times greater than the gravitational wavelength for the GW170104 event, which was ~ 1,700 km. The report[16] did not elaborate on the source of this ratio. It is possible that gravitons are not the quanta of gravitational waves, or that the two phenomena are related in a different way.

https://en.wikipedia.org/wiki/Graviton

So one of them says gravitons theoretically are GWs' quanta, like photons are EM waves' quanta. The other one says gravitons have nothing to do with GWs.

Question:

  1. Which one is right, are GWs made of gravitons (theoretically) or not?
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no scientific model yet exists that successfully reconciles general relativity, which describes gravity, and the Standard Model, which describes all other fundamental forces.

In other words, we don't have an accepted theory that allows us to talk about quantum stuff in relation to gravity. Some clever tricks can be done in special circumstances, which is what led Hawking to propose Hawking radiation. But such tricks do not have a solid theoretical foundation.

So at this stage, we do not have a theory that tells us whether gravitons exist. We expect that they do, from the fact that there's one or more exchange bosons associated with each of the other 3 fundamental interactions. But without some sort of quantum gravity theory, we simply cannot say that gravitons exist.

But even if we did have a working quantum gravity theory, and it said that gravitons are real detectable particles, we may still never have the technology to detect a single graviton directly. It's hard enough just detecting powerful gravitational waves.

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Any statements on gravitons are speculation at this point in time. As there is no quantum theory of gravity, gravitons cannot yet be said to exist or not. If ever a quantum theory emerges then it is more than likely that its quanta will be called gravitons.

Since gravity is a weak force it is expected to be extremely difficult to observe gravitons, if they exist. Thus the absence of such observations is not a convincing argument aga instvtheir existence.

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    $\begingroup$ "As there is no quantum theory of gravity, gravitons cannot yet be said to exist or not". I do not think this is the reason why gravitons are up to now speculations (or why gravitons "cannot yet be said to exist or not"). Evidence of some sort of quantization of various observables was experimentally clear before the construction of QM. What is true is that, up to now, there is no such an experimental evidence of quantum behaviour of observables related to gravitation... Furthermore, there are some theoretical candidates of a quantum gravity theory.... $\endgroup$ Jul 7, 2019 at 12:50

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