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Consider an interstellar medium of one hydrogen atom/cm$^3$ with $500$ photons/cm$^3$ coming from CMB. This density of particles is very weak according to quantum decoherence. So, according to Schrödinger equation, the wave function of each atom could be quite flat/spread.

Is there an equilibrium coherence/decoherence due to Schrödinger equation and CMB?
In other words, is the wave function of each atom stable (on average)?

Can (the squared modulus of) this wave function be almost equidistributed in one cm$^3$?
Can then the interstellar matter be correlated?

If relevant, we can ask the same questions for an intergalactic medium of one hydrogen atom/m$^3$.

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    $\begingroup$ To corroborate the OP's statement that decoherence is very weak: Using $\lambda\sim 1$ mm for a typical CMB wavelength, and using $\sigma\sim d^6/\lambda^4$ for the Rayleigh cross section of an atom with diameter $d$, we can estimate the survival time for a superposition of locations $x,y$ with $|x-y|\gg\lambda$ as $1/(\Phi\sigma)$ where $\Phi$ is the flux of CMB photons. (See arxiv.org/abs/gr-qc/9310032 .) This estimate of the survival time comes out to be much longer than the age of the universe. $\endgroup$ – Chiral Anomaly Jul 13 at 1:22
  • $\begingroup$ @ChiralAnomaly maybe that is why we are measuring CMB as such perfect black body radiation? $\endgroup$ – anna v Jul 13 at 4:42
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CMB photons interact extremely weakly with interstellar matter (and with each other), so it is indeed the case that if the photons were coherent, it would take a long time for them to decohere. However, the CMB spectrum shows no coherence at all, the spectrum is a perfect black body (the most perfect black body ever observed). This is in agreement with our best theories of the evolution of the universe, which predict that CMB photons were emitted by an $ep\gamma$ plasma in thermal equilibrium (which recombined into $H\gamma$, with the photons falling out of equilibrium with matter, but retaining their thermal spectrum).

The interstellar medium in galaxies is very dilute, but it is interacting with the light produced by stars, and frequently re-ionized. It varies in temperature quite a bit, sometimes reaching thousands of K. Even at temperatures of a few K the thermal de Broglie wave length is very short (much shorter than the inter-particle spacing), so this is a classical gas.

P.S.: If you are interested in coherent matter waves in cosmology, the place to look is (speculative) ultra-light dark matter candidates (like axions).

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  • $\begingroup$ Then (as suggested at the end of the post), what about the intergalactic medium (the farthest from any star)? $\endgroup$ – Sebastien Palcoux Jul 18 at 14:43
  • $\begingroup$ I think in practive even the inter-galactic medium is believed to be ionized (but even it were not, it would be a classical gas left over from recombination, with a temperature close to the CMB), $\endgroup$ – Thomas Jul 18 at 15:21
  • $\begingroup$ What (approximately) is the thermal de Broglie wave length for a temperature close to the CMB? Then, what about an hypothetical gas somewhere in the universe, whose inter-particle spacing is "just" less than this wave length? $\endgroup$ – Sebastien Palcoux Jul 18 at 15:24
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    $\begingroup$ I added a P.S. that mentions an example $\endgroup$ – Thomas Jul 18 at 15:31

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