# Photon mean free path (regarding CMB black body assumption)

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• bahamagreen

#### bahamagreen

Per Wikipedia (Outer Space) referencing Davies, P. C. W. (1977), "...the mean free path of a photon in intergalactic space is about 10E23 km, or 10 billion light years."
Per Lawrence Krauss (1999), it is longer than the size of the visible universe.

Per Wikipedia (Outer Space) referencing Davies, P. C. W. (1977), "...the mean free path of a photon in intergalactic space is about 10E23 km, or 10 billion light years."
Per Lawrence Krauss (1999), it is longer than the size of the visible universe.
Ten billion light years isn't longer than the size is the visible universe, so I think you've made a mistake there.

But the way this is measured is via the CMB, which in the 13 billion or so years since it was emitted, roughly 93% of the photos haven't scattered.

JMz
How am I making a mistake by asking about the discrepancy between to values of the photon MFP in space?

I looked up the MFP of a photon a while back and found the Wiki reference to Davies 1977 (over a decade before COBE) of 10 billion light years. Science topics on Wiki are pretty well managed by the university academics, so I thought perhaps the forty year old referenced figure was still in good standing.

Lately I'm reading Krauss 1999 about the logical steps of interpreting the CMB. He italicizes a caveat that assumes the photons have not been subject to having been scattered, absorbed, re-emitted, etc. to which he subsequently returns and asserts without reference that the MFP is greater than the visible universe (so he takes the assumption as being met).

"Consider the microwave background that has a black body spectrum with maximum energy at some frequency (f) associated with a temperature (T) of 2.7K (see figure 2.1). If this light has not been interacting with anything else that might have kept it at a fixed temperature, then earlier it must have had a spectrum with maximum energy at some higher frequency (f '), since each light wave has been "redshifting" during the expansion." (Krauss' italics)

If the MFP were an independent figure not dependent on CMB and figured to be greater than the observable universe, then the CMB black body assumption would be considered met. However, if the MFP were inferred via CMB and yet the CMB interpretation were based on MFP assumptions, how is this not problematic?

How am I making a mistake by asking about the discrepancy between to values of the photon MFP in space?
The mistake is that 10 billion light years is far too short. This is probably because the mean free path was not well-measured until WMAP in the early 2000's, so the 1977 estimate is naturally quite far off.

The way this is parameterized in modern experiments is via ##\tau##, which is the optical depth to the CMB. The portion of photons which do not scatter between the CMB and us are ##e^{-\tau}##.

Polarization is the critical component in measuring this parameter (which was first done on large scales through WMAP) because the scattered photons become polarized, which ends up creating a relationship between CMB temperature anisotropies and polarization. Now, with the Planck satellite, our current best estimate for the optical depth is ##\tau = 0.05##, indicating that around 95% of photons between us and the CMB never scattered (my earlier estimate was from memory based on earlier WMAP measurements).

The reason why the mean free path isn't used, by the way, is that it changes over time as the universe becomes less dense. You could interpret the ##\tau## as a mean free path, but you wouldn't get a meaningful answer because the universe will expand quite a bit in the time it takes a photon to cross that much distance.

...around 95% of photons between us and the CMB never scattered...

"...the CMB is linearly polarized at the 10% level due to Thomson scattering of photons off free electrons in the surface of last scattering. CMB polarization was first detected by DASI from the South Pole in 2002 and has since been observed by many other experiments."
https://www.cfa.harvard.edu/~cbischoff/cmb/

Does "polarized at the 10% level" mean only 10% of the photons are polarized or does it mean that all the photons are polarized 10%?

"...the CMB is linearly polarized at the 10% level due to Thomson scattering of photons off free electrons in the surface of last scattering. CMB polarization was first detected by DASI from the South Pole in 2002 and has since been observed by many other experiments."
https://www.cfa.harvard.edu/~cbischoff/cmb/

Does "polarized at the 10% level" mean only 10% of the photons are polarized or does it mean that all the photons are polarized 10%?
It means that roughly 10% of the signal we receive is polarized at any point on the sky.

Does "10% of the signal" mean 10% of the photons are polarized or all the photons are polarized 10% or the average polarization is 10%?

Does "10% of the signal" mean 10% of the photons are polarized or all the photons are polarized 10% or the average polarization is 10%?
The polarization is only measured in the aggregate. The total signal at each point on the sky is polarized by some amount.