Wave interference and energy conservation

[Bill Minerick]

If the crest of one light wave meets the trough of another light wave of the same frequency and intensity they supposedly cancel each other resulting in no light (e.g., the dark areas that result on the screen when both slits are open on a dual slit experiment). In particle physics, why then does the collision of an electron and a positron result in the release of a photon vs. just no energy at all?

 

[Jakell]

When light interferes ,the energy does not just disappear. You will get spots where there is destructive interference, and spots with constructive interference; the energy is isolated into the bright bands. As for the collision of an electron and a positron, both have positive energy (ie it takes energy to make them, me*c^2 for both), and so when they meet, they annialate each other releasing energy in the form of two photons (for momentum conservation).
The closest you can get to the release of no energy is with virtual particles; they spring into existence and then annialate each other, consuming or releasing no energy in the process.