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I'm playing this "Quantum Game":

http://play.quantumgame.io

I'm not an expert physicist but I'd like to get more understanding of quantum mechanics. The game has helped with that. I'm on level 22, and the screen looks like this:

enter image description here

The objects are:

  • orange/gray bars: simple mirrors, which reflect the photon
  • light blue bar: a 50/50 beam splitter
  • thing in the top row: photon detector
  • the other thing: photo emitter

If you run the simulation, some of the particle/wave will get caught in a mirror loop, while some will escape and bounce to the detector.

Is there a limit to how long the photon can get stuck in the loop, or is it always a 50% chance it will escape at each contact with the beam splitter? In that case, it would mean you could fire the photon and possibly detect it a long time later.

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First off, we're going to assume perfect physics here. In reality, effects like decoherenece, or even garden variety absorption will provide limits.

In a real loop like this, there's a propagation delay. Each pass around the loop takes time before it can interact with itself (once it reaches the beam splitter again).

If you were to timebox the experiment, limiting how long you're willing to keep the detector running, you could calculate a theoretical maximum number of loops that could be taken.

However, if we push this to the extreme, with our perfect mirrors and spherical cows, some interesting results do appear. Given any time limit, no matter how long, there is a non-zero probability that the photon will not be detected. The probability becomes vanishingly small, but it always exists.

In real experiments, of course, with every bounce off of imperfect, real mirrors there's a probability that something will happen to prevent the photon from being on the correct path. That, and noisy sensors, will eventually prevent the infinities from bugging you.

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  • $\begingroup$ This answer taught me the term spherical cows. Thanks. $\endgroup$ – Rob N Jul 9 '17 at 18:37

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