On the Einstein Podalsky Rosen Paradox - by J.S. Bell 1964 - Article review

This document contains article review "On the Einstein Podalsky Rosen Paradox" by J.S. Bell written in 1964
To order to read the article select: https://journals.aps.org/ppf/pdf/10.1103/PhysicsPhysiqueFizika.1.195



1. Introduction

THE paradox of Einstein, Podolsky and Rosen was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables.
Why are these specific (?) additional variables necessary?
these additional variables were to restore to the theory causality and locality [2]
causality has nothing to do with quantum theory. Causality means that all changes (all what exists) are caused by something.
Why is locality an issue? What is the clear definition of locality?
It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty.
This requires a clear definition in this respect of what means a measurement.

2. 2. Formulation

Consider a pair of spin one-half particles formed somehow in the singlet spin state and moving freely in opposite directions.
This seems simple, but it is not.
A better start is this: "Consider two identical elementary particles, which have spin. (for example: electrons) " This implies that previous experiments have identified, that all electrons, each spins around a common axis.
The idea that they move in opposite directions is removed.
Measurements can be made, say by Stern-Gerlach magnets, on selected components of the spins -sigma1-> and -sigma2->.
If measurement of the component -sigma1->.-a-> where -a-> is some unit vector, yields the value + 1 then, according to quantum mechanics, measurement of -sigma2->.-a-> must yield the value -1 and vice versa.
Quantum mechanics can not make this claim. The only thing that a physicus can do is perform experiment-1 that creates two electrons, measure the spin of both electrons and establish that the spins of both are 'correlated'. Next he or she can repeat experiment-1 1000 times and establish that this correlation is true in 995 cases.
Now we make the hypothesis, and it seems one at least worth considering, that if the two measurements are made at places remote from one another the orientation of one magnet does not influence the result obtained with the other.
This implies that the orientation does not matter as long as they are identical. This has to be verified by means of experiments.
For example: in experiment-1 the direction of the of the two magnets is both -a-> or both -b-> or both -c->. The correlation is 1. For example: in experiment-2 the direction of the of the two magnets is different one -a-> and one -b-> . The correlation is 0.
Since we can predict in advance the result of measuring any -sigma2-> chosen component of by previously measuring the same component of -sigma1-> it follows that the result of any such measurement must actually be predetermined
The only thing that you know in case of experiment-1 (as demonstrated by many experiments-1) that if you perform one experiment-1 and you keep the result secret that if person A observes his result and sees +1 that he knows that person B will observe -1.
However before A observes his result he has a 50% chance of observing a 1. Nothing is predetermined
Since the initial quantum mechanical wave function does not determine the result of an individual measurement, this predetermination implies the possibility of a more complete specification of the state.
To understand the outcome of this experiment does not require the concept of a wave function.
The reason of the correlation lies completely in the reaction, when the two electrons were created.
If there is also a correlation in the direction of the two electrons, than the cause lies also in the reaction.
Let this more complete specification be effected by means of parameters lambda.

3. Illustration

4. Contradiction

5. Generalization

6. Conclusion

In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote.
This sentence is very difficult to understand.
A measurement, general means, to establish the value of a quantity or situation. The general way is to compare that with a standard.
Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant.
Signals don't propagate, so we have a problem.

Reflection 1 - Physical interpretation.

Is there any physical fact which makes a measurement in any way special?
No there is not. A measurement is the same as any event, in which a certain physical changes take place
An event can be an explosion in which one object explodes in 1000 parts or in 2 parts, but generally speaking all the parts involved are physical different. That is all.
The same is the case for any chemical reaction involving two components. In A + B gives C + D. In general the products or particles involved before the reaction (or collision) are different before the reaction as after the reaction. A general case is the HSS at CERN were collisions are studied resulting in an avalance of elementary particles. In many case identical reactions are studied resulting in the same avalache of elementary particles. Also some times, a group of different reactions is studied, each resulting in one particle which is identical for all.

  1. Now suppose we have a reaction which results in two X particles and measurements indicate that the two particles are correlated (entangled),
  2. A different reaction which also results in two X particles and measurements indicate that the two particles are not correlated
  3. A different reaction which results in only one X particle.
In all reactions measurement devices are used to establish that X particles are involved. In reaction 1 and 2 at least two because more X particles are involved. But does that mean, specific in case 1, that there exist a special physical connection between the two measurement devices, which causes this correlation?
A different way to investigate is to build a sphere of photon detectors around the reaction.
  1. In the case of reaction 1 each time of a reaction two photon detectors opposite each other should respond, but the direction of the axis connecting both, will be random.
  2. In the case of reaction 2 each time of a reaction two photon detectors should respond, but the position on the sphere will be random.
  3. In the case of reaction 3 each time of a reaction atleast one photon detectors should respond. The position on the sphere is of no importance.
What is the explanation? The full explanation lies at the origin and details of reaction.

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Created: 25 January 2022

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