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Say electron and positron are excited and emit photons with the same wavelength, somehow the two photons meet. I think the photon from positron is 180° out of phase and will cancel out with the photon from electron, does it work this way? If so what happens to the photons after they cancel each other?

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No, it does not happen this way. Matter and anti-matter emit the same photons, because the photon is its own anti-particle. The distructive interference happens when the photons are out of phase. This depends on the setup, such as on the distances and other parameters. However, the phase of the emitted photon is random (except in lasers), so it is not important if the photon is emitted by matter or anti-matter.

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