Photon Wavefunction Evolution

[Flamel]

Suppose that the position of a photon is measured such that the position Wavefunction collapses to minimum uncertainty without the photon being destroyed. At approximately what rate would the wavefunction spread out and approximately what size would the collapsed wavefunction be?

[swansont]

6 hours ago, Flamel said:

Suppose that the position of a photon is measured such that the position Wavefunction collapses to minimum uncertainty without the photon being destroyed.  

How would one do this?

[Flamel]

2 hours ago, swansont said:

How would one do this?

For this scenario, we can imagine a very small, sensitive mirror that can tell when a photon reflects off of it due to the momentum it imparts.

[swansont]

3 hours ago, Flamel said:

For this scenario, we can imagine a very small, sensitive mirror that can tell when a photon reflects off of it due to the momentum it imparts.

I don’t see how that could work, and it’s not clear it’s the same photon.

[Flamel]

42 minutes ago, swansont said:

I don’t see how that could work, and it’s not clear it’s the same photon.

Perhaps I haven't been clear enough. There would be a series of nanoscopic mirrors each linked to pressure sensors sensitive enough to detect the impact of a photon. Upon reflection, the position is determined and the wavefunction collapses. At what rate then would the wavefunction spread out, and how small would the wavefunction be at minimum uncertainty?

[swansont]

3 hours ago, Flamel said:

Perhaps I haven't been clear enough. There would be a series of nanoscopic mirrors each linked to pressure sensors sensitive enough to detect the impact of a photon.

Do these exist? In the real world, that is. ( both the nanoscopic mirrors and the sensors) 

 

[Flamel]

1 hour ago, swansont said:

Do these exist? In the real world, that is. ( both the nanoscopic mirrors and the sensors) 

Not yet that I'm aware of. I'm pulling the concept from a thought experiment where bombs are triggered to detonate via a similar mirror mechanism and half-silvered mirrors and the nature of light waves and observation can be used to determine if the bomb is a dud without triggering it.

Is the exact scenario needed? Would the wavefunction spread rate and the size of the minimum uncertainty collapsed wavefunction be able to be determined in the hypothetical scenario where a CCD magically detected the photon without destroying it?

[swansont]

12 minutes ago, Flamel said:

Not yet that I'm aware of. I'm pulling the concept from a thought experiment where bombs are triggered to detonate via a similar mirror mechanism and half-silvered mirrors and the nature of light waves and observation can be used to determine if the bomb is a dud without triggering it.

Is the exact scenario needed? Would the wavefunction spread rate and the size of the minimum uncertainty collapsed wavefunction be able to be determined in the hypothetical scenario where a CCD magically detected the photon without destroying it?

Yes. The same physics you are investigating might make the detection you want impossible.

[Enthalpy]

This can be fluorescence or diffusion for instance. It can work as well when the pumping photon has the energy of the emitted one. Whether one wants to call it the "same" photon, I don't care.

If the incoming photon has a decently known direction and the diffused one a direction different enough, we know diffusion has take place. If only one atom is present, for instance one dopant in a crystal (this is done for quantum cryptography) then we know the diffused photon comes from that atom. At the beginning, the photon is very well localized, to the size of an atom, which is much smaller than a photon wavelength.

How fast the wavefunction spread results from its equations. An atom is very little directional for being small, so it emits light very broadly. As for time, at least a few quarterwaves away from the small source, the speed of light in the medium applies. In local field, I don't know - looks like EM waves are faster in local field.