Foundations of Quantum Mechanics and Physical Chemistry

A Local Realistic Reconciliation of the EPR Paradox – Research Paper

Bryan — Tue, 14 May 2013 20:22:33 +0000

1. The following paper can be downloaded as a PDF (Submitted to Physical Review A):

A Local Realistic Reconciliation of the EPR paradox - Complete PDF

The 1935 paper that states the EPR paradox: “Is quantum mechanics complete?”

2. The following is a PDF that contains the derivations of all the major equations in the above paper.

These are my working notes and may contain typos or notation changes. If you have questions or queries, I am happy to try to answer them:

Summary of the paper

3. “Non-locality” is an absurd notion.

The motivation for this work is my inability to accept non-locality or instantaneous-action-at-a-distance. Since Bell’s theorem states that quantum mechanics violates local causality then unless one accepts non-locality, then it must be concluded that quantum mechanics is incomplete.

Bell’s conclusion was that special relativity is at fault and not quantum mechanics. This point of view is not considered here but rather by making a small change to the definition of spin, the quantum correlations in EPR experiments can be reconciled in a locally causal way.

Isaac Newton’s quote in 1693 on his recognition that his theory of gravity is incomplete because it violates instantaneous-action-at-a-distance :

“That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.”

The 1927 Solvay conference: the epistemological debate starts (did I discover this photo?).

The 1927 Solvay conference: the epistemological debate starts.

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A Local Realistic Reconciliation of the EPR Paradox – Simulation

Bryan — Tue, 14 May 2013 20:20:30 +0000

The Computer simulation: this Java program simulates the EPR correlations using a program written by Chantal Roth and modified by Michael Havas:

http://challengingbell.blogspot.ca/

Computer simulations of experimental data provide a way of testing models and theories. For example in classical statistical mechanics various simulations are done by starting with a collision model between particles, and then running computer simulations until the system becomes statistical under various approximations. The results from the simulation of properties are compared to the known experimental values.

A similar procedure is followed here. The spin model is defined (in my case as having two axes of quantization rather than one) and this model is treated with the methods of quantum mechanics. Since the model describes the spin of one particle only, the simulation calculates coincidences one by one. This leads to a value for the correlation between each Einstein Podolsky Rosen (EPR) pair. The quantum state is found by averaging over all the variables that define each pair.

If a model fails to give the right numbers for the correlation, or if it inadvertently violates local reality, then it is not worth pursuing. Since the simulation here agrees with quantum mechanics, then the model should be examined further to determine if quantum theory can be extended to accommodate a spin with two axes. This extension means that quantum theory needs admit states that cannot be measured.

In the application of quantum mechanics, the usual approach is to obtain analytic expressions through a mathematical development that undoubtedly includes approximations. In the case of the EPR paradox, many models have been suggested, later found to be incorrect or incomplete, with the consequence that few take new approaches seriously. Rather the question of the completeness of quantum mechanics does not detract (much) from its usefulness and applicability at the present time, so indeterminism and non-locality are accepted. However if spin indeed is confirmed to have two axes, and only half the correlation can be detected in one experiment, then this can have implications in many areas, for example like quantum information theory which considers entanglement as a resource. Since it is only possible to measure only half the value of spin property that depends on two non-commuting operators, then this might have implications to the limit of measurement for other properties. Being purely speculative, this could have implications to the dark matter question.

Computer simulations provide an alternate and independent method of assessment. The computer programs given below provide evidence that the EPR paradox can be reconciled in a local realistic way. It suggests that Bell’s inequalities, which are classical, do not take into account non-commutation (Heisenberg Uncertainty relation) and this lies at the root of the disagreement between the classical predictions and the quantum measurement of EPR correlation.

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A Local Realistic Reconciliation of the EPR Paradox – Some consequences

Bryan — Tue, 14 May 2013 20:19:55 +0000

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:

A Local Realistic Reconciliation of the EPR Paradox

CHSH: there lies a vector of length √2

Consistency of Bell’s (CHSH) Inequalities and two dimensional spin

The invisible side of quantum spin

When quantum mechanics fails in EPR experiments

Spin and Quantum Computers

Quantum Coherence – now Nature hides stuff from us

3. Further discussion and relationship to Joy Christian’s Clifford Algebra approach:

The Bloch Sphere and Spin in Quantum Mechanics

Disproof of Bell’s Theorem

The Sub-quantum spin

Two Dimensional spin model:

Great simulation of the Stern-Gerlach experiment at

http://phet.colorado.edu/en/simulation/stern-gerlach

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 n_x and n_z 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 experiment

The experimental setup to measure photon coincidences.

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Seminar: A local realistic reconciliation of the EPR paradox–Part 7 Video

Bryan — Thu, 07 Feb 2013 16:11:08 +0000

This is part 7 of a seminar I gave in the Department of Chemistry, McGill University, January 22, 2013

http://www.youtube.com/watch?v=tciCMKctekA

The following are segments of the talk are:

In this part after the seminar there is a question and answer period.

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Seminar: A local realistic reconciliation of the EPR paradox–Part 6 Video

Bryan — Wed, 06 Feb 2013 15:55:12 +0000

This is part 6 of a seminar I gave in the Department of Chemistry, McGill University, January 22, 2013

http://www.youtube.com/watch?v=Wn_sS3f_w1M

The following are segments of the talk are:

Coming Soon
Part 7: Questions
In this part the following points are made:

In this part it is shown that the two dimensional spin model predicts the filter angles that give the maximum violation of the CHSH form of Bell’s Inequalities. It is also shown that the 2D spin is consistent with the non-commutative trigonometry by Karl Gustafson who found that a vector of length √2 is needed for the violation. This vector his has the same properties of the 2D structured spin presented here.

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Seminar: A local realistic reconciliation of the EPR paradox–Part 5 Video

Bryan — Tue, 05 Feb 2013 15:51:05 +0000

This is part 5 of a seminar I gave in the Department of Chemistry, McGill University, January 22, 2013

http://www.youtube.com/watch?v=ixRdWSnZ89k

The following are segments of the talk are:

Coming Soon

Part 6: Corroboration and summary
Part 7: Questions
In this part the following points are made:

In this part my two dimensional spin model in introduced. The model treats one of the many spins that makes up the statistical ensemble that is the quantum state. It is shown how averaging over all the Local Hidden Variables agrees completely with the correlation found in EPR experiments in a local and realistic way.

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Seminar: A local realistic reconciliation of the EPR paradox–Part 4 Video

Bryan — Mon, 04 Feb 2013 14:19:17 +0000

This is part 4 of a seminar I gave in the Department of Chemistry, McGill University, January 22, 2013

http://www.youtube.com/watch?v=4kmDawnbLPQ

The following are segments of the talk are:

Coming Soon
Part 5: The Two Dimensional spin model
Part 6: Corroboration and summary
Part 7: Questions
In this part the following points are made:

Two aspects of quantum mechanics that are not understood are non-locality and the persistence of entanglement to space-like separations. In this part entanglement is explained and non-locality is shown to be a concept that no-one understands. Non-locality is called quantum weirdness.

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Seminar: A local realistic reconciliation of the EPR paradox–Part 3 Video

Bryan — Fri, 01 Feb 2013 17:57:40 +0000

This is part 3 of a seminar I gave in the Department of Chemistry, McGill University, January 22, 2013

http://www.youtube.com/watch?v=KY9ezx3ZKP0

The following are segments of the talk:

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

Coming Soon:
Part 4: Entanglement and Non-locality
Part 5: The Two Dimensional spin model
Part 6: Corroboration and summary
Part 7: Questions
In this part the following points are made:

The longest standing unsolved problem in quantum mechanics is the EPR paradox. In this part of the seminar it is pointed out that quantum mechanics is a theory of measurement of the microscopic. This means that a probe of some sort must be used to “see” spin. However it is pointed out that states exist in the completely isotropic environment in the absence of a probe.

These new states carry the correlation that accounts for the violation of Bell’s Inequalities, as discussed in parts 4 and 5 that are coming soon.

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Seminar: A local realistic reconciliation of the EPR paradox–Part 2 Video

Bryan — Thu, 31 Jan 2013 16:43:21 +0000

This is part 2 of a seminar I gave in the Department of Chemistry, McGill University, January 22, 2013

http://www.youtube.com/watch?v=CUwytweOTAg

The following are segments of the talk are:

In this part the following points are made:

The longest standing unsolved problem in quantum mechanics is the EPR paradox. Its history is traced from the 1927 Solvay Conference to the present time. Today non-locality is firmly entrenched in physics and in spite of various experiments on teleportation, quantum cryptography and quantum computing, no one understands now entanglement persists to space like separation.

The only explanation is quantum weirdness, which is, of course, no explanation at all.

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Seminar: A local realistic reconciliation of the EPR paradox–Part 1 Video

Bryan — Mon, 28 Jan 2013 17:45:05 +0000

This is part 1 of a seminar I gave in the Department of Chemistry, McGill University, January 22, 2013

http://www.youtube.com/watch?v=axaoecmYhtU

As soon as I can I will post the following segments of the talk:

In this part the following points are made:

Local realism is heresy. It is a misconception that local realism is classical. It is not.

This talk is about the foundations of quantum mechanics. I do not change anything in quantum mechanics. Rather I use quantum ideas only. Heisenberg uncertainty relations play and important part in my model.

A spin model is proposed and this accounts for the quantum correlation in a simulation using 10 millions coincidences.

The model treats one spin that makes up a quantum ensemble.

Both the research paper and the simulation program will soon be available.

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