Question

Suppose we perform a double-slit experiment with a detector placed at a position of minimum intensity (maximum destructive interference), off-center where the path lengths differ by half a wavelength. The light source is alternately turned on and off (or blocked and unblocked near the source) and the intensity over time is recorded. I interpret the uncertainty principle to mean that there will be a peak in intensity at the times when the switch is flipped (whether on-to-off or off-to-on). i.e., it will look something like this (in ASCII art):

Is this correct? I have had trouble convincingly explaining my reasons for thinking so. What will be the measured intensity over time and why?

Answer 1

first of all, you shouldn't use the term "uncertainty principle" if you're talking about "light sources" and light may be explained by ordinary - classical (non-quantum) - electrodynamics where no uncertainty principle applies.

This is just an exercise in the propagation of waves.

Second, when you flip the switch, there may be temporary variations of the intensity, but they're not necessary, either. For example, you may find a minimum such that the number of wave peaks on the two trajectories (coming from the two slits) differs by 13.5 - one arm is 13.5 wavelengths longer than the other one. It will mean that the destructive interference only occurs when the beams from both slits are synchronized, and there will always be a period lasting about 13 periods after each flip of the switch when only one beam is coming to the detector. That will indeed eliminate the destructive interference, and give you the "apostrophes" in your ASCII art.

The precise shape of the graph depends on the character of the switches, geometry of the experiment, and other things.