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Imagine we have a wave with a certain frequency. We can calculate the energy of this wave with the equation

$E=hf$, where $h$ is the Planck constant and $f$ the frequency

Now, we can create a second wave, with the same frequency but a phase of $\pi$, so when we add the two waves they cancel out.

However both waves have positive energy, so their energies should add up, giving twice the energy.

In reality, the waves might not perfectly cancel, giving a residual with the added energy of the two waves, but in a pure conceptual design, how can "nothing" have energy?

Or am I missing something?

Elerium115
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    If you manage to make the wave superposition with zero amplitude everywhere, then the energy will be zero too because it is calculated as a the total field strenght (zero in your case) squared and integrated over the space. – Vladimir Kalitvianski Jun 28 '18 at 16:26
  • So, then the question is: where does the energy go? It cannot be destroyed. – Elerium115 Jun 29 '18 at 13:47
  • While calculating the photon energy ($h\nu$), you imply there is no other wave (photon) here; otherwise your calculation is wrong. Thus, if you have initially two photons, there are regions where they do not add up their amplitudes. In this case there may be region with destructive and constructive interference described in other posts. The energy does not disappear in any case. – Vladimir Kalitvianski Jun 29 '18 at 15:01

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