Uncertainty of a single photon in light scattering question

[invisigo]

I have a mental picture of photon scattering that goes like this:

An atom spontaneously emits a single photon (or particle). Since the photon hasn't been observed, its wavefunction and probability expands out like a sphere. If I take my photodetector and place it at some point on this expanding sphere, I will detect this photon with probability 1/(4*Pi*radius). If I detect the photon, this collapses the wavefunction and I say the photon momentum was in the direction of my photodetector. If I don't detect the photon, but I know it was emitted, the photon is still traveling in a outward sphere. Or is the wavefunction now affected by my photodetector?

Can anyone comment on this picture?

 

[meopemuk]

I think it is very dangerous to assume that "photon is propagating in the form of a spherical wave, which collapses when it reaches the photodetector". If you take this statement as the actual physical mechanism of what happens, then there are lots of unpleasant questions that you would be forced to answer. For example, what is the physical interaction responsible for the collapse? Will the photon's "wave" collapse if instead of the photodetector you put there a piece of wood?

I think it is better to use the following explanation: We cannot say for sure what happens with the photon while it is not observed. Whatever statement we make about the non-observed photon, this statement is empty, because it cannot be verified experimentally (simply due to the condition that the photon is not observed). Any statement that cannot be directly verified by experiment should not belong to physics. The best thing we can do is to suggest a mathematical model (photon's state described by a complex spherical wave function or by a vector in the Hilbert space). This abstract model (which does not attempt to provide a physical mechanism of the photon's propagation) is sufficient to predict the outcomes of measurements (the probability that the detector will click) with good accuracy. This agreement with experiment is all we can (and should) ask from a successful physical theory, such as quantum mechanics.

If you accept quantum mechanics (wave functions etc.) as an abstract mathematical model rather than a physical mechanism of non-observed events, then all paradoxes and inconsistencies will go away.

 

[physicssantha]

Hi invisigo,

Good, Shaking Fundamentals of QM, let's say, instead of a photo detector you have an electron the way to calculate Wave function is to apply Schrödinger equation indicating the presence of the electron(you will be adding Potential Energy due to the electron etc.),once you know the Hamiltonian you can get the dynamics of the wavefunction.But if you have a classical object like the photo detector I really don't know how to solve the issue(the collapse concept is very difficult for Humans to understand, this is my opinion but I don't know the current situation).