Is there a probability that an electron in an atom change its orbital by emitting a quantum of gravitational radiation instead of photon?


Yes. There is a nonzero probability for such a process, however it is extremely small in comparison with the probability of transition with emission of a photon.

To understand how small this probability is let us check two formulas (both are from Landau & Lifshitz' The Classical Theory of Fields).

First the intensity of quadrupole electromagnetic radiation: $$ I=\frac{1}{180 c^5} (\dddot{Q}_{\mu\nu})^2,\tag{1} $$ where $Q_{\mu\nu}$ is an electric quadrupole moment.

Analogous equation for an intensity of quadrupole radiation: $$ I=\frac{G}{45 c^5} (\dddot{D}_{\mu\nu})^2,\tag{2} $$ with $G$ the gravitational constant an $D_{\mu\nu}$ is an inertial quadrupole moment.

As we see, the formulas are quite similar, and if electric and inertial quadrupole moment change due to the motion of a single type of particle (electron in our case) with a constant charge to mass ratio then $\dddot{D}_{\mu\nu}$ would be proportional to $\dddot{ Q}_{\mu\nu}$.

In quantum mechanics both equations (1) and (2) could be used to write probability of transition. (1) gives us the probability for the emission of photon $P_\gamma$, (2) probability of emission of graviton $P_g$. Therefore the ratio of probabilities would be: $$ \frac{P_g}{P_\gamma}=\frac{4 \,G\, m_e^2}{e^2} = 9.6×10^{-43}. $$ This is incredibly small (but finite) number.

In actuality, since the quadrupole EM radiation is not the most dominant type of transitions, the actual ratio would be even smaller.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.