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.
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.
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.
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.
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 forspin
andlinear 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.
- 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.
- These models of
- 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.
- Testing Bell’s Theorem with Circular Polarization
- Disproof of Bell's Theorem
- Reference to a book that can be requested from the Library of Congress, or downloaded for $38.