Question about quantum superposition in CMB photons

[Gerinski]

Hi,

CMB photons reaching our telescopes have traveled for over 13 billion years without interacting with anything.

If I understand correctly, from the event of the photon emission, its wavefunction gradually spreads, encompassing more and more possible states for the photon, coexisting in superposition, until the photon will interact with another quantum (the detector in our telescope). So for example, the longer the photon travels the bigger the chances that it will collapse in a more improbable state. If the photon has a certain momentum and it interacts very shortly after its emission, most chances are that it will collapse at a location in the precise direction of its momentum. But the longer it travels undisturbed, the possible states diverge and the more chances that it will collapse at a location a bit farther from the original momentum line.

If this is the case, after 13 billion years the wavefunction of the CMB photons should have spread enormously and contain many possible different states (i.e. locations where the photon may collapse) in the superposition, including many which would have seemed very improbable at much earlier epochs during the photon's travel.

So by the time they finally interact, there should be significant chances of an unlikely state to become the actual outcome of the collapse.

Following this reasoning it seems that we should expect the CMB to show significant "distortions", its photons collapsing at relatively unlikely locations and not in the line of the momentum they were originally emitted.

Is this reasoning more or less correct?

Thanks

 

[DEvens]

Word arguments are troublesome in such situations. You really need some math to throw around to get a more exact feel for what you are doing. Phrases like "should have spread enormously" are potentially misleading.

You need to write an equation for what really happens to a photon as it travels along in an expanding geometry background. And then, what happens to the probability of observing various possible momentum values. And once you have that, you need to think about what happens to a distribution of photons that start out at a cosmologically high temperature (round about the point the universe became transparent) and what that distribution would look like now.

What you should find is, the distribution now looks like a thermal distribution at about 3 K. If you can demonstrate something different then you have a remarkable result.

 

[atyy]

The reasoning is completely wrong or completely right depending on how what you mean by "distortion". Anyway, all the "distortions" that you expect from the time evolution from the time the photon is created to now when the collapse is measured are already included in the calculation that matches what we observe.