# The influence of gravity on the energy levels of atoms

There´s an ongoing debate if gravitational waves (or gravity?) contains energy.

But what if a very strong gravitational wave hits an atom. Let´s for simplicity say a hydrogen atom. Not a wave that is supposed to have hit us recently (that´s too faint to bring about a modification in the hydrogen´s energy levels), but let´s say the same wave very close to the it´s origin (the two black holes), and put the hydrogen atom there.

I assume that the energy (the hydrogen is in the ground state) of the hydrogen during the passage of the wave is tilted a little bit because of the asymmetric space surrounding the atom (as in a very strong static field). Shall after the passage the electron emit a photon, to restore the minimum energy, or shall the energy disappear again in the curved spacetime of gravity? I find it hard to believe that afterwards the energy is again put back in the gravitational field. Of course is after the passage of the wave the situation again the same as before, but maybe in the short time the wave passes, the atom decays to a lower state and afterwards get´s a bit energy from the vacuum, to restore again the normal ground state.

Is this the same as saying that the gravitational waves (and the same can be said about gravity: just put a hydrogen atom in a very strong curved spacetime) possess energy? So not only energy passes through spacetime, but spacetime also possesses energy?

• Is there an ongoing debate about the energy in gravitational waves? It seems like the consensus that spiralling black holes collide because gravitational waves are the only way they can radiate energy (substantially). – Lacklub Mar 24 '16 at 17:46
• 1. We don't have a proper quantum theory of gravity, so asking what a gravitational wave does when hitting an atom is ill-described by current theories. 2. There is no ongoing debate over whether ravity waves contain energy; if you have reason to believe otherwise, please substantiate that claim. – ACuriousMind Mar 24 '16 at 18:02
• @ACuriousMind surely a QFT + curved space approximation is tractable (in principle at least) and would be an extremely good approximation as long as one is away from Planck-scale curvatures- right? After all, we don't need quantum gravity to predict the results of atom interferometer experiments like these: journals.aps.org/pra/abstract/10.1103/PhysRevA.91.033629 – Rococo Mar 24 '16 at 20:21
• @Rococo: Although I am admittedly not versed in this field, I would expect that the interaction of a gravitational wave is akin to the interaction of an electromagnetic wave with an atom, which is only well-described in some regimes by modelling the wave as an external classical field, and needs the description in terms of the quantized electromagnetic field to be fully valid in all cases. – ACuriousMind Mar 24 '16 at 20:46
• Please remember that electrons bound in atoms will be removed only if the transferred energy is quantized to the available energy levels, and that the potential is an electric potential, and only higher order diagrams with electromagnetic and gravitational vertices will be able to transfer energy to an individual electron, even if it is correct for the difference in quantization levels. It might be that electrons in the conduction band of a metal might have small enough energy differences that the energy of a gravitational wave might have a tiny probability to excite them . – anna v Mar 25 '16 at 16:14

Gravitational waves will have a characteristic wavelength $\lambda = c/\nu$, where $c$ is the velocity (equal to the speed of light for gravitational waves), and $\nu$ is the frequency. If $\lambda$ is much larger than the size of the atom, then the entire atom only sees a constant gravitational potential at any moment in time. In this case the potential may affect the center of mass dynamics, but not the internal dynamics (such as the energy levels). This is the same effect as an atom near the earth, gravity causes the entire atom to fall down together, but does nothing to affect the internal structure in any way.

In order for the gravitational waves to have an effect on the internal dynamics, you need $\lambda$ to be smaller than the size of the atom. This is of the order of an Angstrom or $0.1\,\text{nm}$. The frequency for $\lambda = 0.1\,\text{nm}$ is $\nu = c/\lambda \sim 10^{18}\,\text{Hz}$ which is extremely high energy (note LIGO only detects events 10–1,000Hz). This is so large that assuming there is a quantum theory of gravity, a single graviton would have an energy given by Planks law $E = h\nu \approx 12,\!000\,\text{eV}$, which is about 1,000 times larger than the binding energy of the atom ($\approx 13 eV$). Therefore a single graviton at this frequency would ionize the atom.

• I think it is actually around 12 keV- a "gravitational x-ray." Of course, this does not change your general conclusion. – Rococo Mar 24 '16 at 21:26
• @Rococo Computed using $\hbar c/(2\pi*0.1nm) \approx 300eV$ (google.com/search?btnG=1&pws=0&q=hbar*c%2F(2*pi*0.1nm)+in+eV&gws_rd=ssl) – Punk_Physicist Mar 25 '16 at 1:03
• Ah, yes. You want the 2 pi in the numerator, I believe. – Rococo Mar 25 '16 at 2:26
• @Rococo You are absolutely right. I've corrected the answer to reflect this. Thanks. – Punk_Physicist Mar 25 '16 at 16:03

Gravitational wave is nothing but a fluctuation in gravity itself. When the gravitational wave passes through (say the atom), the atom is, intermittently, as if it was in a higher, or lower gravitational field, or a in a little, more, or little less curved space. That little could be a lot depending upon the strength of the wave.

Space(time) must possess energy, otherwise, it could not cause mass/energy to move in the first place. Gravitational wave is fluctuation of energy level of space on top of what it is without the wave.

To answer your question about the atom - the atom will impacted in same way as is it would be impacted by equivalent change in gravity for the period of passing.

Gravity impacts the atoms. One way it is known to impact atoms is when it is too high and it merges electrons into protons to create neutron stars onward. How it impacts state of atom due to smaller changes, I can not say.