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Atomic transitions produce photons. You can create beams of photons with a laser. In lasers rays of light are produced. Will rays of gravitons (or small directed gravitational waves) be produced also?

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    $\begingroup$ I think this question will only get speculative answers since there is no complete working theory for quantum gravity. Because of this, I don't think you can get a definitive answer. $\endgroup$
    – Tachyon
    Jun 6 at 21:18
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    $\begingroup$ @Tachyon But what if you consider it as a general relativistic problem? It looks that waves are produced then. $\endgroup$
    – user303670
    Jun 6 at 21:21
  • $\begingroup$ I still have no idea even if electrons emit EM waves when transitioning from one atomic orbital to another. I have no clue as to this could be the same case for gravitons. Again, we could speculate, but not answer the question. Gravitons might or might not be produced. It is a complete unknown. $\endgroup$
    – Tachyon
    Jun 6 at 21:27
  • $\begingroup$ @Tachyon Why do you think that electrons don't emit an em wave? It's a quantized wave though. After the transition, the mass distribution has changed (in a non-spherically symmetric way). So you'd expect a gw. $\endgroup$
    – user303670
    Jun 6 at 21:29
  • $\begingroup$ I never said that electrons "don't emit an em wave". What I am saying is that you might be comparing the wrong things: that if electrons emit EM waves, then they could emit gravitons as well. They might be completely unrelated to each other, but I could be wrong. I don't know the answer and I won't pretend to know the answer, nor could I speculate about it. $\endgroup$
    – Tachyon
    Jun 6 at 21:34
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If you're transitioning between the two orbital states, the quadrupole moment of the atom definitely changes, and the gravitational potential energy of the system definitely changes. Unless the new complete quantum theory has some novel way of suppressing gravitational radiation, the system should definitely radiate some gravitational waves, and if the final theory's radiation profile is expressible in some sort of "graviton" basis, it will "radiate at least one graviton"

Of course, all of the caveats about how vanishingly undetectable all of this is would still apply, though, and note how speculative the above paragraph was.

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    $\begingroup$ What I was asking myself: if you have a huge collection of hydrogen atoms and you calculate the energy emission. What if you measure a value smaller than the calculated value? could the difference be attributable to graviton emission, that is if you can measure it? I'm not sure how much energy is contained in such an emission graviton. Notmuch I guess... $\endgroup$
    – user303670
    Jun 7 at 0:46
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    $\begingroup$ @Duepietri, consider the ground state energy of the electron, $ke^{2}/r_{0}$, the gravitational potential of that configuration is $Gm_{e}m_{p}/r$. Their ratio is of order: $(10^9){(10^-16)^2}/(10^{-11}10^{-27}10^{-31}) = 10^{46}$. Before you even factor in "quadrupole radiation is less than dipole radiation", you'd have to measure the energy of the transition out to something like 46 decimal places before you could even begin to expect knowing about gravitational effects. On the way to that, you'd also have to account for exotic effects from the electroweak force and higher order QED stuff $\endgroup$ Jun 7 at 0:56

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