If the IGM (inter-galactic medium) had a massive particle (proton) every cubic metre, or a carbon grain every cubic kilometre, what would be the MFP of a CMBR photon? The coherence length of the photon would be expected to be in the order millimetres. The time evolution of the wave front, in the plane at right angles to the direction of propagation would grow to the order of light years on its journey to our present observations. Considering the carbon particles alone would collapse the wave function within a few kilometres, a new wave function of slightly lower energy could be created along with two very much lower energy photons, one associated with the heat generated in the carbon particle, and the other associated with the momentum gained by the particle. This process of annihilation and creation would continue all the way to our observations. This is a reasonable attempt at a qualitative interpretation. This attempt is also consistent with several modern theories and observations of the affect of dust in the IGM.
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$\begingroup$ Wikipedia: “Shortly after recombination, the photon mean free path became larger than the Hubble length.” $\endgroup$– G. SmithCommented May 19, 2021 at 19:10
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$\begingroup$ @ G. Smith...What about re-ionization? How does that effect the MFP? Even carbon dust grains are ionized, how does that effect the interaction cross section of carbon dust and the subsequent interaction with CMBR photons? $\endgroup$– barryCommented May 29, 2021 at 8:43
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$\begingroup$ Read the second paragraph here. It doesn’t give the MFP but it says that the universe remained transparent after re-ionization, implying a huge MFP. For more detail, I think you would need to consult a graduate-level cosmology textbook since no experts have answered. $\endgroup$– G. SmithCommented May 29, 2021 at 16:44
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$\begingroup$ @G. Smith....This is an active area of research and as such textbooks may not help, this link may indicate the current level of research in this area. jumpshare.com/v/lCw7nbSN6P79vNU2zObh $\endgroup$– barryCommented May 30, 2021 at 3:18
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$\begingroup$ OK. This site may not a good place to get answers about current research. Unfortunately, we don’t have experts in every physics subfield who are up-to-date on the latest research. If we had an expert on the latest thinking about the MFP of the CMB, they probably would have provided an answer. $\endgroup$– G. SmithCommented Jun 1, 2021 at 0:39
1 Answer
The mean free path of a CMB Wave function (assuming Copenhagen interpretation) would be no more than a few metres on average over the 13.5 billion years of travel, if we assumed an ion or dust mote every metre or so. The wave function would collapse and a new slightly lower energy photon would be created because the ion or dust would gain some tiny amount of momentum from the collapsed wavefunction. this means after 13.5 billion years the CMB bears no relationship to the original source. The blackbody (BB) spectrum would develop over time as the many ion's and dust constantly exchange energy between one another over time, this is the mechanism non Doppler redshift and BB radiaton in this case, the BB component is just as in the old carbon cavity experiments. In summary the CMB is not a clear window into the past!
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$\begingroup$ How would you explain the persistence of the structure (anisotropies) in the observed CMB signal? $\endgroup$– TLDRCommented Aug 12, 2023 at 4:16
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$\begingroup$ Also, wouldn’t one sub micron sized particle per cubic meter be associated with a mean free path of order 10^3km for microwave photons? (And if the particles are roughly micron sized, wouldn’t they have a somewhat noticeable gravitational effect?) $\endgroup$– TLDRCommented Aug 12, 2023 at 4:32