Wikipedia lists the graviton as a hypothetical particle. I wonder whether graviton is indeed hypothetical or does its existence directly follow from modern physics? Does observation of gravitational waves amount to the discovery of graviton or could there be gravitational waves not composed of gravitons?
Answer
Gravitons are hypothetical, but they're far less hypothetical than most of the other particles which theorists speculate about (such as axions, magnetic monopoles, strings, sterile neutrinos, and the like).
That probably sounds a little strange. Let me explain.
We don't have a complete theory of quantum gravity. But we do actually have an extremely good incomplete theory of quantum gravity. This theory is an "effective quantum field theory". It doesn't work for physics at distances smaller than the Planck scale, but it works just fine above that scale. In other words, it's good enough for all practical purposes. You get this theory -- maybe we should call it 'effective quantum general relativity' to distinguish it from classical GR -- by introducing a Planck scale cutoff into general relativity and then doing the path integral or canonical quantization or whatever your favorite procedure is.
Such effective theories are widely used in physics. One of the more famous ones was Fermi's theory of the weak interaction. It was broken in ways that drive theorists crazy -- non-renormalizable and non-unitary -- and it eventually had to be replaced with the Glashow-Weinberg-Salam theory. But it worked great. You can do essentially all of nuclear physics with just Fermi's theory. Hans Bethe even used it to explain how the sun produces energy.
So we have this theory, and it's ugly, but it works just fine at energies below the Planck scale. It gives correct answers; for example, it predicts that quantum gravity phenomena are practically impossible to detect in normal terrestrial physics. Moreover, this theory is mathematically pretty much unique: any theory of quantum gravity which reduces to classical general relativity at low energies must reduce to this effective QFT along the way. You really can't avoid it.
So we should take this theory pretty seriously, since it works well and doesn't require a lot of extra assumptions. And since this theory describes all gravitational phenomena we know about in terms of gravitons, it's probably fair to say that the existence of gravitons is a fairly good bet. (You might have to wait a long time to collect on that bet though.)
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