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I did some reaserch into this and after a lot of reading I came acrose a site with a good description of what you are talking about so here's a link.… If you go to this site it should answer your question and I hope it helps. –  Richard Sisson Jun 25 '12 at 20:03
this video from MIT shows very clearly what happens to the energy when there exists destructive interference in electromagnetic waves. –  anna v Nov 16 '14 at 15:57
I just thought of this question and logged on here to get an answer. Thanks for beating me to asking it :) –  dsollen Mar 14 at 21:51

12 Answers 12

We treated this a while back at University...



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up vote 19 down vote









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You really would have to construct an example.

Since non-dissipative waves whose equations of motions can be formulated by a Lagrangian will have an energy associated to them, as you say, you'd have to find a situation/theory without an energy quantity. The energy is related to the wave by its relation to the equation of motion. So if the energy is defined as that which is constant because of time symmetry and you don't have such a thing, then there is no question.

Also don't make the mistake and talk about about two different waves with different energy. If you have a linear problem, the wave will be "one wave" in the energy expression, wherever its parts may wander around.


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More engineer-like explanations can be found here:

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I had prepared this answer for a question that was made duplicate, so here it comes, because I found an instructive MIT video. (the second link) This answer is for electromagnetic waves mainly

Have a look at this video to get an intuition how interference appears photon by photon in a two slit experiment.

It comes because the probability distribution for the photons, as accumulated on the screen, has destructive and and constructive patterns, ruled by the underlying quantum mechanical solution of "photon + two slits".

The classical electromagnetic wave emerges from a great plethora of photons which have phases and such that they build up the electric and magnetic fields. The nu in the E=h*nu of the photon is the frequency of the electromagnetic wave that emerges from the confluence of the individual photons. In order to get an interference pattern the photons have to react with a screen, or some some matter, as in the laser experiments.

The reason that matter is needed for light interference phenomena is due to the very small electromagnetic coupling constant. Photon photon interactions due to the 1/137 end up having a probability of interaction of order of ~10^-16 . With respect to photon electron interactions, which to first order is ~ 10^-4,( and is the main photon-matter interaction) there are 12 orders of magnitude. To all intents two laser beams crossing will go through each other without any measurable interaction, interferences included. (Keep this in mind when you reach the last question at the end of the next video.)

This MIT video is instructive and a real experiment that shows that in destructive interference set up with interferometers there is a return beam, back to the source, as far as classical electromagnetic waves go. So the energy is balanced by going back to the source.

What is happening at the photon level? If the laser emitted photons one by one as in the two slit video? I will hand wave as there is no corresponding video to show:

The quantum mechanical solution with the complicated boundary values of the interferometer allows the elastic scattering ( not small, that is how we get reflections) of photons also back to the source. You can see in the video that there always exists a beam going back to the source, that beam is carried by individual photons scattering elastically backwards through the system of the optics of the interferometer. In total destructive interference all the energy is reflected back ( minus some due to absorption and scattering in the matter of the optical system).

In essence this experiment is a clear demonstration that the system laser-optical-bench is in a coherent quantum mechanical state, the returning photons joining the ensemble of photons within the laser action , which also includes reflections to be generated.

In this video, the first beam carries the information of the phases such that in space interference patterns will form if a screen or other matter intervenes. The energy of the final beam after it leaves the interferometer system and falls on the screen and is redistributed according to the pattern of the interference. The amount of energy carried by the beam there depends on the proportion of energy that manages to leave the interferometer/laser system, i.e. if all of the energy is returned to the laser (destructive interference) , or a part of it goes out of the lasing system to impinge on the screen.

In the case of waves in matter, as sound waves or water waves:

In the case of two sound waves interfering destructively, the temperature of the medium will go up and energy is conserved because it turns into incoherent kinetic energy of the molecules of the medium.

For two water waves, ditto.

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I think a good way to approach this question is with a Mach-Zehnder interferometer:Mach-Zehnder interferometer

The field landing on detector 1 is the interference between two waves, one from the lower path, and one from the upper path. Let's suppose the field in each arm is a collimated beam of coherent light, well-approximated as a plane wave, and the interferometer is well-aligned, so the two outputs are almost perfectly overlapped. By changing the thickness of the sample, we can change the relative phase between the two waves, changing our interference from destructive (less energy on detector 1) to constructive (more energy on detector 1). Where did this energy come from? If the beams are nicely matched, this interference can even be completely destructive, and detector 1 will register zero signal. Where does the energy go?

The short answer is: detector 2. The total energy hitting the two detectors is constant, as you vary the phase shift caused by the sample. Constructive interference at detector 1 goes hand-in-hand with destructive interference at detector 2.

If you only look at one detector or the other, it might seem like energy is created or destroyed by interference, but as other answers mention, we must consider the whole system.

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This figure shows two common situations.



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The Poynting_vector





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See the antilaser experiment.

We dont have theory? Then we must rethink.

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When there is a complete destructive interference of two light beams, Maxwell’s equations predict that the energy becomes zero. Let’s have the case of two coherent collinear beams, out of phase 180 degrees, like the case of the antilaser.

\begin{align} E_1 = E_m \sin (kx - \omega t);\quad E_2 = E_m \sin (kx - \omega t + p) \\ B_1 = B_m \sin (kx - \omega t); \quad B_2 = B_m \sin (kx - \omega t + p) \end{align}

$E = E_1 + E_2$ and $B = B_1 + B_2$ \begin{align} E &= E_m \sin (kx - \omega t) + E_m \sin (kx - \omega t + p) \\ B &=B_m \sin (kx - \omega t) + B_m \sin (kx - \omega t + p) \end{align} But, $\sin (kx - \omega t + p) = - \sin (kx – \omega t)$ , Then, $E = 0$ and $B = 0$ and,

\begin{align} UT &= U_E + U_B \\ &= \frac12ԑ_0E^2 + \frac1{2\mu_0}B^2 \\ &= 0 \end{align} This is the classical interpretation of the waves electromagnetism during total destructive interference, following Maxwell. Maxwell's description of the energy of the light wave is of an undulating energy that predictably reaches a maximum and later becomes zero. The proposed solution to this problem is to calculate the mean of the energy when the fields are maxima.

What is the physical meaning of an energy that have to be averaged in order to have the real magnitude. If the principle of conservation of energy is to be applied to this phenomenon, the energy must be constant, have an unique value for each instant during the movement of the wave. What is the meaning of that situation that has not been recognized for more than a century?

What almost nobody want to admit is that electromagnetism is incomplete, because cannot describe the electromagnetic radiation adequately, and generate a violation of the principle of conservation of energy.

As Helder Velez said: “We don’t have theory?”. NO Then we must rethink.” He has a proposition: EM energy is not transported, only is an excitation of the medium, the quantum vacuum, or the quantum plenum as I prefer to call it. But this is only an idea, an intuition, without support or evidence.

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Lots of copy-pasting from poster's other (flawed) answers. –  Kyle Kanos Feb 13 at 21:21
I made one and only one reference: Helder Velez. The fact that his comment have negative punctuation does not mean that he is incorrect; only that they disagree with him. I support him in the violation of the conservation of energy. I support the "EMG theory of the foton" by Diogenes Aybar that can be found at He thinks that the photon has another inherent field, the gravitational field, where the energy goes from the two electromagnetic fields to the gravitational field, keeping then, at every moment the energy constant. –  luis fondeur Feb 15 at 18:39

the waves will obliterate each other but they will still exist, they just won't be moving they would just change form (energy cannot be destroyed it can only change form) so when the waves meet they will cancel each other so sound will change to potential and kinetic will change to sound or whatever

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protected by Qmechanic Aug 15 at 5:47


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