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Isotopes are not 100% chemically equivalent and they form chemical bonds with different vibrational resonances because the vibrating masses are different. You c

Isotopes are not 100% chemically equivalent and they form chemical bonds with different vibrational resonances because the vibrating masses are different. You can see those differences in spectroscopic line shapes including in refraction (which is related to absorption by the Kramers-Kronig relation). My guess is that those effects would swamp out any relativistic ones by a lot, and because you can't tune the isotopic mass you wouldn't be able to isolate a gravitational effect. In fact it appears that the isotopic dependence for silicon isotopes is known, https://arxiv.org/abs/1105.0822 https://arxiv.org/abs/1105.0822 and the refractive index of Si 30 is lower than Si 28 in the IR, because of the different absorption lines.

javajosh 3y ago
Perfectly applicable paper, thanks! I skimmed it, but I didn't see an explanation for the lower refraction index for the heavier isotope. It had the lower RI at all wavelengths they looked at. I think it's useful to ignore the "phonon resonance" wiggle in the middle of their tested range on page 4, around 600nm, if looking for some other effect. (it's crazy that an electron that weighs like 10^-31 kg could actually jiggle a crystalline lattice to the point you can see it at all, but I suppose there's a lot of electrons, and Tacoma Narrows bridge reminds me of how powerful resonance effects can be).
- xmcqdpt2 3y ago
  The off-resonance curves look exactly like what you expect from the Kramers-Kronig relations https://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relations https://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relatio... which have very far reaching effects in term of refraction (the real part of the permittivity decays as 1/w). In term of resonances, it's important to note that the nuclei themselves are not neutral either. In the IR, the time dependence of the field is slow enough that the nuclei can follow it resonantly. Those fields are much below electronic resonances so the electrons aren't even contributing much beyond making the crystal stable!

javajosh 3y ago

Perfectly applicable paper, thanks! I skimmed it, but I didn't see an explanation for the lower refraction index for the heavier isotope. It had the lower RI at all wavelengths they looked at. I think it's useful to ignore the "phonon resonance" wiggle in the middle of their tested range on page 4, around 600nm, if looking for some other effect. (it's crazy that an electron that weighs like 10^-31 kg could actually jiggle a crystalline lattice to the point you can see it at all, but I suppose there's a lot of electrons, and Tacoma Narrows bridge reminds me of how powerful resonance effects can be).

xmcqdpt2 3y ago
The off-resonance curves look exactly like what you expect from the Kramers-Kronig relations https://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relations https://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relatio... which have very far reaching effects in term of refraction (the real part of the permittivity decays as 1/w). In term of resonances, it's important to note that the nuclei themselves are not neutral either. In the IR, the time dependence of the field is slow enough that the nuclei can follow it resonantly. Those fields are much below electronic resonances so the electrons aren't even contributing much beyond making the crystal stable!