What happens to the energy in destructive interference?

[rocknrollkieran]

TL;DR Summary

energy destructive interference

I asked Chat GPT this but could'nt get a satisfactory answer. I felt he was making it up as he went along.

In principle it should be possible to set up two lasers emitting the same frequency and synchronize them so they are perfectly out of phase so that both beams destructively interfere.

I can understand all the waves cancel each other out but where does the energy go and how can you get it back?

 

[PeroK]

TL;DR Summary: energy destructive interference

I asked Chat GPT this but could'nt get a satisfactory answer. I felt he was making it up as he went along.

In principle it should be possible to set up two lasers emitting the same frequency and synchronize them so they are perfectly out of phase so that both beams destructively interfere.

I can understand all the waves cancel each other out but where does the energy go and how can you get it back?

They can only destructively interfere at certain points in space - and will constructively interfere elsewhere.

In the QM picture, that means that the probability of an interaction of the light with a detector has a higher probability in some places than in others - and at some points in space it the probability of a detection may effectively be zero.

 

[Ibix]

In principle it should be possible to set up two lasers emitting the same frequency and synchronize them so they are perfectly out of phase so that both beams destructively interfere.

The two beams would have to be going in exactly the same direction through the same space with zero beam divergence. That means two infinitely wide lasers, one behind the other and somehow firing through the one infront without disrupting its operation at all. If you imagine that the waves are "just there" without any source then they always cancel everywhere and there never was a wave with any energy to worry about - it's the wave physics version of having no apples and trying to understand it as having +1 apple and -1 apple.

Essentially, you are imagining an idealised picture of perfect plane waves. That kind of picture can be useful because the maths is often simpler than a more realistic case and the errors can be small under some circumstances. But here you are asking about one of the errors that arises from that simplification, which is where the energy goes. It goes into the parts of the waves that don't cancel - i.e., where they reinforce each other and produce a brighter region.

 

[Dale]

As others have said, it is not possible to get destructive interference everywhere with two distinct coherent sources. When there is destructive interference somewhere there will be constructive interference elsewhere

 

[Baluncore]

That means two infinitely wide lasers, one behind the other and somehow firing through the one infront without disrupting its operation at all.

Two identical amplitude waves, would need to be emitted by the same source, but with a 180° phase difference. There are no waves, no energy is involved.

 

[Nugatory]

I asked Chat GPT this but could'nt get a satisfactory answer. I felt he was making it up as he went along.

Not surprising that you couldn't get a satisfactory answer - chatgpt is designed in such a way that it doesn't work well with factual questions that you couldn't have answered with your own Google search. And yes, of course it was "making it as it goes along", it's a computer program that arranges words in patterns until it comes up with one that you like.

 

[rocknrollkieran]

Many thanks all for the considered replies, and clarifying that for me