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BellExperments

Explorations in Bell's Inequality

In part, these are models of various Bell Inequality experiments I've read about.

But also, in part, they are test of a few hidden variable models in an attempt to re-create some of the QM behaviour.

Polarizable

This base generic class handles all the hidden variables involved in polarization.

It is woefully inadequate to describe all of the QM behavior involving polarization. For instance, it only describes linear polarization not circular polarization, let alone elliptical polarization.

But simple tests (such as the 0|120|240 polarization tests) it is adequate for.

More rigorous tests (like the CHSH) ... not so much.

Spinnable

This base generic class handles all the hidden variables involved in spin around the three spacial axes.

I suspect it is inadequate to describe all the QM behavior involving spin. But most Bell Inequality Tests documented are about photons, and only a few about electrons.

CAVEATS:

  • My spin model requires measurement on exactly the X, Y or Z axis.
    • A better model would allow measurement on any rotated axis.

Unit Tests

I have chosen to use the unit test structure to validate and test my models.

First, there are those that verify that the model meets the bare minimum requirements for the behavior of random particles and entangled particles.

Then there are those which try to check my models against some Bell test Experiment I found documented out in the real world.

Conclusions

Well, as of 2019.08.18, when I documented all this and put it up on github for the first time. <):-)

  • My hidden variable models for spin and linear polarization and how measurements are done adequately handles:
    • randomized particles behave as randomized particles ought to.
    • entangled particles behave (in simple tests) as entangled particles ought to.
      • Measuring spin on one axis is stable no matter how many time you measure it, nor on which entangled particle you measure it.
      • Measuring spin on one axis destroys entanglement on the other two axes.
      • Measuring polarization on any axis has 50% chance of passing.
      • If it does pass, then it also changes the particle's polarization to that axis.
  • My hidden variable models are not adequate for all demonstrated QM behavior. (not unexpected)
    • I would actually have been quite surprised if all my tests had passed.

CAVEATS:

  • I do not bother with Complex values or arithmetic.
    • These models of hidden variables didn't happen to require it.
    • If I develop other models, they might. We'll have to see.
  • It is possible that I have not correctly coded some of the tests.
    • I will review both those that passed and those that failed to be sure I have modeled the relevent math properly.

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