Why is the thomson cross section constant over cosmological time?

Question

In all astrophysical calculations I'm aware of, the thomson cross-section (for electron scattering) is taken as a constant in time, why is this the case? I have only weak experience in cosmology and GR, but naively I would have guessed that if the wavelength of photons is red-shifted from expansion, then the debroglie wavelength of an electron should increase* and thus the thomson cross-section.

• I guess you could include, 'why isn't matter-wavelength similarly redshifted' in my question.

Answer 1

I'm not sure exactly how to understand your question, so I'm going to take a crack at re-stating it before I answer my version.I understand you to ask

If the photons distant sources are strongly red-shifted shouldn't we see the same effect in other particles coming from a very long way away?

The answer to that question is yes, we should. But you have to understand that the photons we observe from so far away have traveled the whole distance without undergoing any interaction except that with gravity. They have existing as a single quantum state for long enough to experience a significant change in the scale parameter of the universe.

Few other objects can say the same. Among them are

• The cosmic neutrino background. Which is actually purely theoretical at this point because we haven't a clue how to observe it as it is much colder than the microwave background. But it must be there and is exactly an example of red shifter massive radiation.

• Ultra-high energy cosmic rays must come from other galaxies (or indeed, other galactic clusters), which they ought to be red-shifted, but because we don't know the source spectrum we can't measure the extent of that red-shift.

• Possibly the dark matter (because it is so weakly interacting), but again we've haven't any observations to hold up for scrutiny.

Stuff that undergoes significant reactions with other matter or radiation between it's source and our detection will have the characteristics resulting from those interactions leaving us to deduce---but not measure---any cosmological effects it may have experienced.

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The other interpretation of your question that occurred to me comes down to "How do we know that the laws of physics have been consistent on cosmological time scales", which I belive has been addressed to some degree in other questions.

Answer 2

The Thomson cross section is independant of wavelength as long as $h\nu$ is much less than the rest energy of the electron. Red shifting the radiation just makes this approximation better.

According to Wikipedia, the cross section is given by:

$$ \sigma_t = \frac{8\pi}{3} \left( \frac{q^2}{4\pi\epsilon_0mc^2} \right)^2 $$