Speed of photons through dual slit.

[yuiop]

Let us say we have source that can emit a single photon. We can in principle detect when the photon leaves the source due to the momentum kick. Now let us say this single photon passes through both slits and forms a dot on the far right of the screen. Now if we draw paths through the two slits, the path going through the left slit to the dot on the screen is longer than the path through the right slit due to simple geometry. If the path through the right slit is consistent with the speed of light, then anything traversing the path from the left slit must be traveling faster than the speed of light to arrive at the same time as the photon that passed through the right slit and constructively interfere with it. Alternatively, if the longer path through the left slit is consistent with the speed of light, then the photon going through the right slit must have been delayed somewhat to arrive at the back screen at the same time as the part that followed the left path. What is though to happen here? Is the answer neither, because quantum particles are not precisely located in space at any given time?

 

[Cthugha]

Let us say we have source that can emit a single photon. We can in principle detect when the photon leaves the source due to the momentum kick.

For most real light sources you cannot do that. The momentum kick is pretty tiny and might be (depending on the source) so small that it is even unmeasurable in principle due to uncertainty. However, if you manage to realize such a situation, the light emitted is pretty incoherent. As you need light with a coherence volume large enough such that both slits are within it, incoherent light will not show any interference in a double slit setup. This is also the reason, why Young used a single slit in front of the double slit. Sunlight is too incoherent to show interference unless you use slits placed really close to each other. Placing a single slit in front of the double slit increases (spatial) coherence significantly.

 

[DrChinese]

You may enjoy this analysis:

Quantum interference with slits, Thomas V Marcella (2007)

"In the experiments considered here, we measure the y-component of momentum for a particle passing through a system of slits. The source-slit system is the preparation apparatus that determines the state vector. Recognizing that a system of slits is a position-measuring device allows us to ascertain that the state vector is a position state. Then, writing the state vector in momentum space provides a straightforward calculation for the probability amplitude and its corresponding probability function. Interference effects, if any, are inherent in the probability function We determine the statistical distribution of scattered particles for four different slit systems. The results are in agreement with the well-known interference patterns obtained in classical wave optics."

In essence, this is an analysis of how the HUP applies.