Does Energy Redistribution in Wave Interference Happen Superluminally?

[peter.ell]

Because energy cannot be destroyed, when waves interfere destructively the energy doesn't really disappear, it's simply redistributed to areas of constructive interference, right? But isn't this energy redistribution instantaneous?

 

[The_Duck]

No, the energy flows continuously and always at speeds less than or equal to c.

 

[questionpost]

No, the energy flows continuously and always at speeds less than or equal to c.

What about when a photon is measured? When you have a radio wave, it expands over many many meters, but then when a device picks it up it becomes measured and the entire photon localizes to that interaction point instantaneously.

 

[eaglelake]

Because energy cannot be destroyed, when waves interfere destructively the energy doesn't really disappear, it's simply redistributed to areas of constructive interference, right? But isn't this energy redistribution instantaneous?

There is no redistribution of energy going on here!

Here, we are discussing classical waves that carry energy and momentum as they propagate through a vibrating medium. The wavefunction $$\psi (\vec r,t)$$ represents the displacement of the vibrating medium from its equilibrium position. In an interference experiment, some parts of the vibrating medium have a greater displacement than normal (constructive interference) and other regions have no displacement at all (destructive interference).

Where destructive interference occurs, the medium is not vibrating. That region never was vibrating. There is no such thing as “interference of displacements”. The medium can only vibrate in one direction at a time. It is impossible to get a medium to vibrate in opposite directions at the same time so that the total displacement “cancels out”. We need not worry about energy not being conserved.

If we set up the experiment so that interference occurs, then there are regions in the medium of enhanced displacement and regions of no displacement. Those regions are always there. There is no sudden destruction of the displacement going on and, likewise, there is no sudden transfer of energy from the “destructive” region to the “constructive” region in order to save conservation of energy.

Best wishes