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When an electron emits a photon from changing energy levels, the frequency of the photon depends on the difference between the energy levels.

But if someone is moving with respect to the atom, the frequency will be apparently red shifted or blue shifted.

Does this mean that the energy levels of the orbits of the atom look to have different values if you are moving with respect to them? But, the apparent energy difference can be different depending on whether the photon is emitted towards you or away from you.

What's going on? Aren't energy levels of orbits supposed to be a fixed value given the kind of atom?

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Good question, but is the photon really emitted in a given direction? I'm sure a hydrogen transition doesn't emit a plane wave photon (but I'm not sure what it does emit...maybe s-wave, at least for some transitions?) – twistor59 Jan 18 '13 at 14:02
Broadening of spectral lines occurs due to the Doppler effect (as well as a number of other effects) even in non-relativistic regimes. Otherwise emission and absorption spectra would be infinitely sharp. As a side note, you may be interested to know that relativistic mass increase becomes significant for bound electrons around about the second row of transition metals and quantum chemical calculations need to take it into account for accurate energy calculations. – Richard Terrett Jan 18 '13 at 15:08
Broadening of spectral lines happens due to chaotic motion, e.g. in a gas, in which many atoms are emitting at the same frequency. Also, there is broadening due to Heisenberg indetermination. Relative motion between the source and the observer, on the other hand, will results in a shift of energy. – zakk Feb 17 '13 at 20:16
up vote 2 down vote accepted

To answer briefly, I'm not very confident in this answer and invite editing or downvoting as appropriate!.

The energy levels of the electrons are determined via calculations of the electric potential/field around the nucleus. The electric field is a vector field that transforms under special relativity and hence we account for any relativistic effects through moderation of this field.

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Zakk said below that "there is no reason for the energy levels to be the same in every frame of reference". I was thinking along the lines that each atom is identical to each other atom and so should have the same energy levels (although obviously they don't), but this explains the mechanism - that the energy levels are about the electric field. I'm guessing, also, that polarisation is very much a relativistic thing. Once you account for everything, energy and momentum are conserved and the universe spins on its merry way unaltered. – PaulMurrayCbr May 11 '14 at 2:51

The answer is yes, the energy levels transform according to the Lorentz transformations and are blue/red-shifted if the source is moving towards/away from the observer.

Replying to your last question, there is no reason for the energy levels to be the same in every frame of reference. This phenomenon is well known, two examples being:

  • The emission spectra from stars, which are red-shifted as galaxies are moving away from each other. Actually the red-shift allows cosmologists to gain a lot of knowledge about the Universe.
  • Some applications of the Mössbauer effect, in which the shift in frequencies is actually exploited, by tuning the relative speed of the source and of the absorber, to modify the emission frequency making sure it matches the absorption frequency. See for instance:
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