published article https://www.degruyter.com/downloadpdf/j/phys.2017.15.issue-1/phys-2017-0089/phys-2017-0089.pdf
Abstract: The general class, Λ, of Bell hidden variables is composed of two subclasses ΛR and ΛN such that ΛR⋃ΛN=Λ and ΛR∩ΛN={}. The class ΛN is very large and contains random variables whose domain is the continuum, the reals. There are an uncountable infinite number of reals. Every instance of a real random variable is unique. The probability of two instances being equal is zero, exactly zero. ΛN induces sample independence. All correlations are context dependent but not in the usual sense. There is no "spooky action at a distance". Random variables, belonging to ΛN , are independent from one experiment to the next. The existence of the class ΛN makes it impossible to derive any of the standard Bell inequalities used to define quantum entanglement.
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3 Conclusion
We have presented cases for four inequalities and one condition based on the existence of the hidden variable class ΛN which are capable of violating the inequalities and condition. Experimental violation does not discriminate between local hidden variable models and standard Hilbert space based quantum mechanics. The state of the local hidden variable model takes one and only one value at each point in time. In contrast the state of standard quantum mechanics takes all possible values at each point in time. Leonard Susskind mentioned in a recent lecture that Richard Feyman said "Hilbert space is so damn big!". We now see that such excess is unnecessary. Real local single valued hidden variables can violate Bell's inequalities. Complex nonlocal multivalued quantum mechanics can violate Bell's inequality. Inequality violation does not determine which model is correct.
The literature is vast on the implications of inequality violation. Much of that literature is made suspect by the hidden variable class ΛN.
The abstract of the EPR paper [10] says
In a complete theory there is an element corresponding to each element of reality. A suffiient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the kowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these quantities can not have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false. One is thus led to conclude that the description of reality given by a wave function is not complete.
John S Bell states in his paper [1]
THE paradox of Einstein, Podolsky and Rosen [8] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore the theory causality and locality.
We have presented evidence that Bell's formulation fails for nonrecurrent hidden variables. As such Einstein's program of completing quantum mechanics with hidden variables remains viable.
Abstract: The general class, Λ, of Bell hidden variables is composed of two subclasses ΛR and ΛN such that ΛR⋃ΛN=Λ and ΛR∩ΛN={}. The class ΛN is very large and contains random variables whose domain is the continuum, the reals. There are an uncountable infinite number of reals. Every instance of a real random variable is unique. The probability of two instances being equal is zero, exactly zero. ΛN induces sample independence. All correlations are context dependent but not in the usual sense. There is no "spooky action at a distance". Random variables, belonging to ΛN , are independent from one experiment to the next. The existence of the class ΛN makes it impossible to derive any of the standard Bell inequalities used to define quantum entanglement.
...
3 Conclusion
We have presented cases for four inequalities and one condition based on the existence of the hidden variable class ΛN which are capable of violating the inequalities and condition. Experimental violation does not discriminate between local hidden variable models and standard Hilbert space based quantum mechanics. The state of the local hidden variable model takes one and only one value at each point in time. In contrast the state of standard quantum mechanics takes all possible values at each point in time. Leonard Susskind mentioned in a recent lecture that Richard Feyman said "Hilbert space is so damn big!". We now see that such excess is unnecessary. Real local single valued hidden variables can violate Bell's inequalities. Complex nonlocal multivalued quantum mechanics can violate Bell's inequality. Inequality violation does not determine which model is correct.
The literature is vast on the implications of inequality violation. Much of that literature is made suspect by the hidden variable class ΛN.
The abstract of the EPR paper [10] says
In a complete theory there is an element corresponding to each element of reality. A suffiient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the kowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these quantities can not have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false. One is thus led to conclude that the description of reality given by a wave function is not complete.
John S Bell states in his paper [1]
THE paradox of Einstein, Podolsky and Rosen [8] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore the theory causality and locality.
We have presented evidence that Bell's formulation fails for nonrecurrent hidden variables. As such Einstein's program of completing quantum mechanics with hidden variables remains viable.
