# Work required to move photons?

## Main Question or Discussion Point

Classic double slit experiment.
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!

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Dale
Mentor
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.
In general you are correct that different states can correspond to different energies. However:

1) The conservation of energy states that the expectation value of the energy is conserved for the whole system including emitter, photon, slit detector, and screen, which is not the same as what you said.

2) The state of the photons in a double-split experiment is not usually an eigenstate for the energy, so variations can occur as long as the expectation value for the energy is conserved.

3) The changed spatial distribution of the energy expectation does not necessarily imply a difference in energy expectation.

I imagine it would require work to move photons . like deflecting them in a graviational field .
on second thought , like a magnetic field cannot do work on a particle , maybe the same is true for out photon case or maybe not , i am confusing myself .

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