B Interference of Light in the Double-Slit Experiment

Ken Hughes

It is said that interference occurs when a peak (of the light wave) meets a trough and the wave cancels to zero, giving a dark band on the screen. However, if light waves are bands or "shells" of high densities of photons interspersed with bands of zero photons, then how can this be? When a peak meets a peak then yes, we get constructive interference (light bands). When a trough meets a trough there are zero photons (dark bands), but when a peak meets a trough then surely this is the mid point between light and dark with a "half" illumination. In other words, I do not see that destructive interference can occur with light since light is quantised. Can anyone confirm or refute?

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PeroK

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It is said that interference occurs when a peak (of the light wave) meets a trough and the wave cancels to zero, giving a dark band on the screen. However, if light waves are bands or "shells" of high densities of photons interspersed with bands of zero photons, then how can this be? When a peak meets a peak then yes, we get constructive interference (light bands). When a trough meets a trough there are zero photons (dark bands), but when a peak meets a trough then surely this is the mid point between light and dark with a "half" illumination. In other words, I do not see that destructive interference can occur with light since light is quantised. Can anyone confirm or refute?
You are mixing your metaphors here. Either you treat light as a classical electromagnetic wave, in which case interference can be explained by peaks and troughs - or, more accurately, by sinusoidal oscillations in the electromagnetic fields. Or, you treat light as a quantised phenomenon, in which case the interference is caused by the oscillating phase of the light.

In fact, all of quantum interference boils down to the concept of quantum (probability) amplitudes being complex and able to cancel each other out.

vanhees71

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I don't understand your problem. The only what's quantum here is that you assume to build up an interference pattern with single-photon states. What you get is the same interference as within classical electrodynamics. The only difference is the interpretation that what's the intensity (energy density) of the electric field in the classical theory is a probability distribution for the detection of a photon on a screen as function of position.

An interference pattern is not simply "dark" or "light" but it's a continuous distribution. That's true for the energ density in classical as much as for the probability distribution in quantum electrodynamics.

Ken Hughes

vanhees71,

"Interference of Light in the Double-Slit Experiment"

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