Where does energy go during destructive interference? | Hacker News Reader

Where does energy go during destructive interference?

van.physics.illinois.edu

32 pointsamelius17 comments

"You might think that you could devise an interferometer or other device which combines two beams in such a way as to cancel completely, without having observation points for which the wave crests align. In fact, I tried my best before writing this answer. I encourage you to try as well, but if you are careful to take everything into account, you will find it just isn't possible!"

Is there a video of someone attempting this? Is there a name for the experiment? It's been in the back of my mind for awhile and I'm still not sure what would happen.

Not sure what you mean, since it is clearly explained that such a device is mathematically impossible. A naive way to it would be with a Michelson interferometer where the two beams are displaced exactly by (2n+1)*pi radians and thus interfere so that the target detector sees nothing. Most physics undergraduates do this experiment at least once during their lab courses. But again, if you account for everything, you'll find that the "missing" energy at the detector just went back to the source via the mirror.

I'd like to see a video showing the experiment with some of the more complex interferometer setups so that it's easier to understand the coherent effect.

I've seen series like this before:

https://www.youtube.com/playlist?list=PL4E7FAAD67B171EBC

But they never seem to explain cases where the expected outputs are all destructive.

I can dig down the reddit hole with lots of interesting ideas and explanations:

https://www.reddit.com/r/askscience/comments/2fsol9/where_do...

But what I really want to see is a good experiment on video that show the effect.

You mean something like this? https://www.youtube.com/watch?v=RRi4dv9KgCg

Yes, I linked that video because I'd like something like that, but attempting to make all paths cancel completely and showing why it can't be done.

Huh. It didn't really answer the question for me, but, anyway, now I'm more wondering about how comes that this question never occured to me in my entire life. This seems like the most obvious thing to ask, but I don't remember ever wondering about it.

Short answer: It gets pushed out in other places.

Long answer: When you try to do destructive interference, you do it only in specific places, you have valleys and peaks somewhere else. Energy from valleys (detructive interference) just enlarges peaks and makes them brighter. As first commenter on that topic said, you can't make destructive interference without making constructive one in different place, so energy is not lost.

At uni professor was drawing inverse FFT of impulse response in a filter and he only used first few frequencies and then asked "can anybody see what's wrong with this chart?". We were all silent...

Turns out if you only use first few frequencies of FFT the filter output will look like it respond slightly before the signal arrives. It's a freaking time machine.

What are you talking about? Do you mean first few frequency bins, and setting the others to zero? That would be a simple linear-phase lowpass filter. And if you do the shifting properly then you will see that it has a positive group delay.

There are filters with negative group delay, however. But FFT is irrelevant for that and it's not a time machine either.

Non-causal filters can be quite useful, and can be realized when the entire input sequence is available. And if one puts in a delay line, then can work without needing access to future timesteps.

A bit harder to realize with electronics or mechanics than software though...

Same here! I once came across a similar question that asked where energy goes when light red-shifts from distant galaxies.

Same. I love that feeling.

That reminds me of this article: https://www.quantamagazine.org/puzzling-quantum-scenario-app...

Catch the point where you have the most constructive interference and you might get more energy out than you put in

My view of things is that photons try all paths, and take ones that end up with a positive probability once they're integrated.

Another possibility is that they bounce backward in time, and try again.. which is silly.

> Another possibility is that they bounce backward in time, and try again.. which is silly.

This sounds like the single-electron universe theory[0]

But in the electron case, we experience the single electron in multiple places at once.

In your case, if the photon were trying all possibilities by going forward and backward in time, wouldn't we experience the photon in all places at once?

[0] https://en.m.wikipedia.org/wiki/One-electron_universe

From Wave_interference#Quantum_interference https://en.wikipedia.org/wiki/Wave_interference#Quantum_inte... :

> Here is a list of some of the differences between classical wave interference and quantum interference:

> - In classical interference, two different waves interfere; In quantum interference, the wavefunction interferes with itself.

> Classical interference is obtained simply by adding the displacements from equilibrium (or amplitudes) of the two waves; In quantum interference, the effect occurs for the probability function associated with the wavefunction and therefore the absolute value of the wavefunction squared.

> The interference involves different types of mathematical functions: A classical wave is a real function representing the displacement from an equilibrium position; a quantum wavefunction is a complex function. A classical wave at any point can be positive or negative; the quantum probability function is non-negative.

> In classical optical interference the energy conservation principle is violated as it requires quanta to cancel. In quantum interference energy conservation is not violated, the quanta merely assume paths per the path integral. All quanta for example terminate in bright areas of the pattern.

From Conservation_of_energy https://en.wikipedia.org/wiki/Conservation_of_energy :

> Classically, conservation of energy was distinct from conservation of mass. However, special relativity showed that mass is related to energy and vice versa by E = mc2, and science now takes the view that mass-energy as a whole is conserved. Theoretically, this implies that any object with mass [e.g. photons, and other massful particles] can itself be converted to pure energy, and vice versa. However this is believed to be possible only under the most extreme of physical conditions, such as likely existed in the universe very shortly after the Big Bang or when black holes emit Hawking radiation.

From Conservation_of_energy#Quantum_theory https://en.wikipedia.org/wiki/Conservation_of_energy#Quantum... :

> In quantum mechanics, energy of a quantum system is described by a self-adjoint (or Hermitian) operator called the Hamiltonian, which acts on the Hilbert space (or a space of wave functions) of the system. If the Hamiltonian is a time-independent operator, emergence probability of the measurement result does not change in time over the evolution of the system. Thus the expectation value of energy is also time independent. The local energy conservation in quantum field theory is ensured by the quantum Noether's theorem for energy-momentum tensor operator. Due to the lack of the (universal) time operator in quantum theory, the uncertainty relations for time and energy are not fundamental in contrast to the position-momentum uncertainty principle, and merely holds in specific cases (see Uncertainty principle). Energy at each fixed time can in principle be exactly measured without any trade-off in precision forced by the time-energy uncertainty relations. Thus the conservation of energy in time is a well defined concept even in quantum mechanics.

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