# Photon direction as hidden variable in a double slit expt?

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• Jiyong Chung
I'm just wondering if there is any way to measure which interpretation is more correct.In summary, the pilot wave theory proposes that each photon behaves as a wave, with no hidden variables. However, the experiment described above can be used to localize the waves.f

#### Jiyong Chung

I was wondering if it would be feasible to set up something like the following experiment to validate the pilot wave theory. The idea here is to set up a double slit experiment, but control the initial conditions of photons emitted from a source (i.e., their directions) such that one can specifically target a particular slit (of the two slits).

According to the pilot wave theory, since one has both a particle and a pilot wave for each photon, it seems that one should be able to aim the particle part of the photon precisely enough at the middle of a particular slit, such that the particle MUST pass through the slit. Although the experiment is done with two slits, one should end up with a non-interference pattern at the detector.

According to the Copenhagen interpretation, each photon should travel as a wave, and therefore, no matter how accurately one aim's the photons, one should still end up with the interference pattern. Since there are no hidden variables - no amount of directional adjustment should erase the interference pattern.

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So, my question is: Does the above experiment make any sense?

Is setting the initial conditions of the photons equivalent to a "measurement" and "collapsing the wave function? (i.e., forcing the photon to travel as particles)? Obviously, the experiment won't work if this were true. Or is there a possible way to set the directions of the photons but NOT collapse the wave function?

The idea here is to control the initial conditions of photons emitted from a source (i.e., their directions) such that one can specifically target a particular slit in a double slit experiment.
Then you get a single-slit pattern.
The distance between the slits would have to be much smaller than the wave fronts of the pilot waves.
That is in direct contradiction to what you wanted before.
You cannot control or even know where in the pilot wave the particle is.

de-Broglie-Bohm makes exactly the same predictions for measurements as other interpretations of quantum mechanics. You cannot distinguish between them experimentally.

bhobba and Jiyong Chung
You cannot control or even know where in the pilot wave the particle is.

de-Broglie-Bohm makes exactly the same predictions for measurements as other interpretations of quantum mechanics. You cannot distinguish between them experimentally.
Thanks for the reply. If I understand you correctly, you are saying that: (1) one cannot adjust the initial conditions to distinguish the pilot wave interpretation from the Copenhagen interpretation, and that (2) even if one could adjust the initial conditions, one would still end up with the same experimental results.

Using oil drops, it seems that one should be able to perform an experiment analogous to what I described above. Of course I realize that the oil drop experiment illustrates only few facets of the pilot wave theory.

According to the Copenhagen interpretation, each photon should travel as a wave, and therefore, no matter how accurately one aim's the photons, one should still end up with the interference pattern.

This is not correct. You have specified that the photons are aimed accurately enough that each one only goes through one slit. In wave terminology, that means you have narrowed the spread of the wave packet representing each photon so that it only impinges on one slit. There is nothing in any interpretation of QM that forbids you from doing this, in principle. (In practice I'm not sure how feasible it is, but that would again apply regardless of which interpretation of QM you adopt.)

This is not correct. You have specified that the photons are aimed accurately enough that each one only goes through one slit. In wave terminology, that means you have narrowed the spread of the wave packet representing each photon so that it only impinges on one slit. There is nothing in any interpretation of QM that forbids you from doing this, in principle. (In practice I'm not sure how feasible it is, but that would again apply regardless of which interpretation of QM you adopt.)

I see that now. Basically, I was pondering if there is any way that one can manipulate the hidden variables (i.e., the initial conditions) such that they cause the photons to behave differently from what is expected of them according to the standard QM. But setting the initial conditions as described above would just result in localizing the waves.

I also see that there is no direct way to tell whether the Pilot wave theory is "more correct" than the SQM through double-slit experiments (or other analogous experiments).