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Situation 1: No detectors at slits.

Result 1: Self-interference occurs. Diffraction pattern of photons landing on wall with well-defined spacings.

Situation 2: Detector(s) at slit(s).

Result 2: Probability wavefunction collapses, no self-interference. Diffuse pattern of photons landing on wall with intensity varying continuously away from maxima related to the slit positions.

Conservation of energy would require that the cumulative energy density of all photons striking the screen be the same in both situations (ie - summing the energy of all photons striking the screen should yield the same result in both cases).

However, the spatial distribution of photons striking the wall changes depending on whether or not self-interference can occur.

My questions:

(1) Does it take work to move a photon?

Assuming the answer to (1) is yes:

(2) How much work would be required to change the spatial distribution of photons striking the screen from case 1 to case 2?

and finally, as a follow-up to (2):

(3) Does the amount of work needed to change the photon pattern vary with experimental variables such as distance to screen and slit spacing, since these would affect the diffraction pattern spacings and intensity distributions at the wall.

Thanks!