A Local Realistic Reconciliation of the EPR Paradox – Some consequences
1. The following is a research lecture given on January 22nd, 2013 at McGill Chemistry:
Part 1: Introduction and the Statistical Ensemble Interpretation of quantum mechanics
Part 2: The EPR paradox and problems with quantum mechanics
Part 3: Measurement and EPR experiments
Part 4: Entanglement and Non-locality
Part 5: The Two Dimensional spin model
Part 6: Corroboration and summary
Part 7: Questions
2. Some discussions of the spin model:
3. Further discussion and relationship to Joy Christian’s Clifford Algebra approach:
Two Dimensional spin model:
Great simulation of the Stern-Gerlach experiment at
Contrast quantum ensemble (the statistical quantum state) with single particle of that ensemble.
I assume that this particle has two orthogonal and equivalent axes of spin quantization. Then all of the EPR paradox is reconciled.
Usually spin is described by the Fano density operator which is treated here a a quantum ensemble:
and which gives the states after a statistically large number of spins have passed the Stern-Gerlach filter.
This is changed for a single spin before it arrives at the filter and is in free flight. The state of this one particle is assumed to be (A is for Alice, there is another one for Bob with the plus changed to minus):
where the unit vector is generally oriented differently for every one generated from the source:
Every spin has local variables, θ, φ, which are angles that orient it relative to the laboratory frame. Using straight forward diagonalization of the above state, one arrives at a horizontal and vertical component as the possible eigenstates. The hidden variables that describe these are nx and nz which can take values of plus or minus one, and are shown in the following image.
It is believed that entanglement persists after separation. This “instantaneous-action-at-a-distance” makes no physical sense. Assuming a spin has two dimensions gives the same correlation but in a local realistic way. The following “quantum channels” or “EPR channels” do not exist in the 2D spin model.
The filter settings that maximize the CHSH form of Bell’s inequalities are predicted from the 2D spin model.
Half correlation: the correlation from one axis of quantization
Full correlation: The correlation from both axes of quantization
The relationship between EPR correlation and coincidences for one axis of quantization
The relationship between EPR correlation and coincidences for two axes of quantization
Flatland: the two dimensional spin: an anyon? A model of spin with two axes of quantization means that a spin is not a point particle but has a 2D planar structure. The relationship to anyons should be examined.
The experimental setup to measure photon coincidences.