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I've heard that it is incredibly difficult to detect a graviton, but I don't quite understand why. With all of the knowledge I have at the present time it seems like it should be possible to create a graviton in a particle accelerator. This is how I figure: a graviton is massless, so the collision shouldn't need to have too high of an energy. Since gravity acts upon anything with energy, a graviton field should couple with all of the other fields, so it seems like gravitons could be created in collisions. A graviton created this way would probably not show up on traditional detectors, but the two units of spin associated with the particle would be missing from the observed decay products. What is wrong with this picture?It may come from a naive understanding of scattering, as I am no physicist (yet.)

p.s. I have the same misunderstanding regarding axions. They are predicted to be light particles, so why aren't they created in collisions?

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You need to distinguish between the virtual gravitons that appear in a quantum field theory calculation of a gravitational interaction and real gravitons that form a gravitational wave. The sort of experiment you're describing requires the emission of real graviton i.e. the emission of a gravitational wave.

The trouble is that the coupling constant for the gravitational field is very very small. From dimensional arguments the order of magnitude of the (dimensionless) gravitational coupling constant is given by:

$$ \alpha_g = O\left( \frac{G}{\hbar c} \frac{E^2}{c^4} \right) $$

where $G$ is the Newton's gravitational constant and $E$ is the energy of the system. Let's take the LHC, where the energy is around 14 TeV. This gives a value for $\alpha_g$ of around $10^{-31}$. For comparison the electromagnetic coupling constant is about $0.007$. So graviton emission at the LHC is about 29 orders of magnitude less likely than photon emission.

That's why we would have to wait an exceedingly long time to see graviton emission at the LHC.

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Why can't gravitons be created in traditional particle accelerators?

Because gravitons are hypothetical virtual particles, proposed by particle phyicists advocating an "exchange mechanism" for gravity. This exchange mechanism is modelled using virtual particles, and it's perfectly valid for electromagnetism: when the electron and the proton attract each other they "exchange field", such that the hydrogen atom has very little in the way of a field left. Note though that there aren't any actual photons flying back and forth - hydrogen atoms don't twinkle. Also note that when hydrogen atoms attract each other gravitationally, they don't exchange field - the combination of fields is additive. So the exchange mechanism doesn't work, and gravitons remain hypothetical. There is a way to get past the problem, but that's one for another day.

By the by, I'm confident that gravitational waves do exist. If you called gravitons virtual gravitons and called gravitational waves gravitons, then IMHO we could in theory create gravitons. But maybe not in a particle accelerator.

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