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I understand that normally when two waves combine destructively this happens only in certain places; the energy doesn't disappear but is redistributed to other places where the interference is constructive instead. In a sense, unless a noise cancelling speaker has the exact same origin as a noise creating speaker, there will always be an interference pattern with darker/quieter balanced by brighter/louder areas.

But what if instead of trying to have two speakers or a 0º phase laser and a 180º phase laser exist in the same place, we instead combined their two beams somewhere else:

signal A -+|+-+|+- ==>  \/  <== |+-+|+-+| signal B, 180º out of phase
                        ||
                        ||
                     combined

Where would the energy go, if one could perfectly focus and combine two sound or RF/light sources in an interfering fashion?

I am curious about this for both the acoustic and electromagnetic cases, but if there is no analogy then it's the photons I'm most interested in! I found some discussion of the latter in https://physics.stackexchange.com/a/601337/103805 (and perhaps as well in https://en.wikipedia.org/w/index.php?title=Beam_splitter&oldid=1076656730#Phase_shift) but I don't understand either well enough to answer my own question. One answer said:

If you really want to consider two waves with identical wave vectors, then you cannot emit a second photon that is 180∘ out of phase with the first. Generating an electric field with that phase is actually absorbing the first photon, not emitting another one.

An ideal "beam combiner" would seem to get around this idea of emitting two photons of opposite phase right at the same place; is it simply physically impossible to make such a thing?

But if perhaps one can only come close — perhaps the incoming "beams" aren't perfectly collimated or the combiner isn't perfectly balanced or whatnot — so the interference isn't 100% destructive in practice. But of course even if only 80% of the energy, or for that matter 1e-8% of the energy simply "disappeared" that would still be amazing, no?! So what prevents an arrangement like the beam combiner above from ever working even partially?

natevw
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2 Answers2

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The beam combiner you drew is effectively a knife-edge mirror. It will combine the beams but they won't overlap, think each half of the resulting beam comes from only one laser.

I understand what you're saying but I don't believe it's possible to make such a device. It would violate conservation of energy :)

rogerkoulitt
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Unfortunately the term "interference" for light, started with Young's DSE (1801) and also used Huygen's theory (1600s), is a very misleading word. Everyone in high school for the DSE is told that photons are cancelling each other (which is impossible as it violates energy conservation) in the dark areas ... or worse that energy is moving from the dark areas to the bright areas. The issue is worse when mathematicians show us how waves can cancel by addition ... it's not physics. Dirac and Feynman and many other scientists stated that each photon determines its own path .... based on the EM field which is very dynamic. Dirac, Feynman spent little time on the DSE as the nuclear age was dawning, a much more important topic.

In your experiment if 2 opposite photons are created they will propagate independently, if we could observe the EM field directly (which is impossible) we would see the waves superimpose .... when the photons strike your eye exactly out of phase they will be scattered apart and both photons will eventually be absorbed.

2 photons travelling exactly out of phase would appear as null in the EM field .... but the energy is always stored in the medium .... i.e. the EM field is very capable of storing the energy even though there's net zero E And M fields. If we try and observe these photons we just end up scattering them and absorbing them.

For sound, 2 traveling sounds of opposite phase will cancel at the midpoint ... but the sounds will reemerge ... the energy is stored in the elasticity of the air. Similar situation for water.

PhysicsDave
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