Wednesday, August 5, 2009

Studying Quantum Mechanics: the Delayed Choice example

Most descriptions of QM are not very good. In particular, the configuration-space-wave-mechanical aspects of QM are usually not fully taken into account; instead, a nearly incomprehensible description is given in more classical terms.

Delayed Choice experiment:

For example, consider a delayed-choice thought experiment in which a photon can take two paths simultaneously. If the experimenter wants, he can "determine which path the photon took" by letting it hit a pair of detectors; it will register in only one detector, randomly chosen, as far as he can tell. The paths are laid out in such a way that in order for it to hit a detector, it must have taken the corresponding path. Taking the other path would cause it to sail past that detector and into the other one.

(image from http://scienceblogs.com/principles/2007/02/thought_experiments_made_real_1.php)

Or, he can insert a 'beamsplitter' (BS2; conceptually, a half-silvered mirror) to recombine the beams, in a way that results in the photon always going to the rightmost detector due to wave interference - in which case it must have taken both paths. He can choose whether to insert the mirror just before the photon reaches the detectors, after most of the paths would have already occurred!

Mysterious stuff, right? It looks like the experimenter reached back in time, changing whether the photon took both paths or chose one randomly!

Sure - if you think about it the wrong way.

In terms of wave mechanics (which is the MWI), the photon took both paths in all cases. If the beam recombiner is not present, the photon becomes entangled with the detectors - that is, becomes correlated with their degrees of freedom in configuration space. In one 'branch' of the wavefunction, one detector clicked; in the other, the other did. There is no 'delayed choice' mystery. [There is only the standard question for the MWI of what explains the appearance of probabilities - the old Born Rule problem.]

Most of the mysterious aspects of QM make a lot more sense when viewed as just wave mechanics in configuation space. But it's hard (impossible?) to find an introductory treatment of QM that even mentions configuration space. An advanced treatment of QM is unlikely to be much better - the equations will be there, but with little explanation.

The next post will be a basic glossary of common QM terms such as 'entangled'. Then I should be getting on to start discussing MWIs in more detail.

4 comments:

  1. I cannot see how to make PS2 work as described. However removing it and rearranging the detectors should make the experiment work just fine. - Charles

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  2. Charles,

    It looks to me like it would work fine as is.

    Going to the top detector along path 1, there are 3 reflections, each at a 45 degree angle. The net result should be a 270 degree phase shift. (Perpendicular reflection results in a 180 degree shift, but at a 45 degree angle of incidence, it's a 90 degree shift - I think. The initial polarization can be a factor.)

    Going to the top detector along path 2, there is one reflection, for a 90 degree phase shift. These two paths to the top detector therefore interfere destructively.

    Going to the rightmost detector, there are 2 reflections along each path, so they will interfere constructively.

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  3. I don't know what mirrors or beam splitters do to polarization. The Brewster trick is not being used. I was instead considering only the wave phase in the direction of propagation. That is what I always used to get the interference pattern in the Michaelson interferometer.

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  4. As I explained (in person) to Charles, I refer above to wave phase, not polarization.

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