Violation of conservation of energy?

Question

When the photon/partical two slit experiment is performed you get a pattern of alternating lines on the screen. I've read that in the dark area that's where the waves have cancelled each other out and in the light area is where the waves have peaked. So how can two photons or electrons cancell each other out and still not break the law of energy conservation?

What has happened to this energy?

Ok if one wave-ical gets cancelled out where did the energy go?

Unless my memory is failing or there are new discoveries - A wave or particle will pass through both slits at the same time.

http://en.wikipedia.org/wiki/Double-slit_experiment

Please read up on the CopenHagen interpretation.

Answer 1

There are two ways to look at this, and they both give the same results.

1) Quantum View

Technically speaking, the photons do not wave. The thing that "waves" is probability. The probability waves destructively interfere to produce regions of zero probability. These are the dark fringes. The photons do not "cancel out" in any sense. Rather, they just never show up to begin with.

2) Electromagnetic View

The energy that would have gone into a dark fringe instead finds itself in a bright fringe. The peaks in the bright areas are twice as bright as they would have been without any interference. This makes up for the "lost" energy in the dark fringes.

Answer 2

Firstly, the interference pattern for the single-particle/two-slit experiment appears gradually as the buildup of little dots as each particle hits the detection screen. The point is that the dots form this pattern, but you can't tell which dot is due to which slit.

No particles are getting "cancelled". They are just being distributed as if they were waves.

Now two classical waves will also form an interference pattern. Notice that along the nodes there is very little energy, while along the maxima there is more energy than for just one wave. The lack in the node is made up for by the surplus in the maxima. So energy is conserved here, too.

Answer 3

There is no violation of conservation of energy. It does NOT take two photons or electrons to cancel each other out. It takes just one. Each photon will act as a wave and interfere with itself to create the interference pattern. So the energy of the photon is NOT lost.

BTW, it is the wave that's canceling each other, not the particles. You are mixing up particle and wave properties of the photon to create this scenario, and that is incorrect. If you want to treat it as a particle, then it must behave like a particle all the time, and not suddenly start to behave like a wave, just so to create some violation scenario.

Answer 4

You are thinking classically about a quantum effect. The particles are passing through either one of the slits individually, and each one passes through a distinct part of the detection screen, the PATTERN that emerges from the aggregate of particles impacting the screen forms the interference pattern. No particles are being destroyed or created. Quantum mechanics can't tell which particle will land where, it can only give us a probability of where that particle will land, this probability function produces the interference pattern as the two probability functions from each slit create nodes or dark spots where the probability of any one particle hitting that spot drops to zero.

Hope this helps, QM produces some decidedly unintuitive effects.