A Local Realistic Reconciliation of the EPR Paradox – Simulation
The Computer simulation: this Java program simulates the EPR correlations using a program written by Chantal Roth and modified by Michael Havas:
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.