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Physica E Low-dimensional Systems and Nanostructures

On physical and mathematical causality in quantum mechanics

Arkady Plotnitsky

Published Jun 24, 2009• 1 citation
Publisher
DOI
10.1016/j.physe.2009.06.046

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To study which are the most general causal structures which are compatible with local quantum mechanics, Oreshkov et al. [1] introduced the notion of a process: a resource shared between some parties that allows for quantum communication between them without a predetermined causal order. These processes can be used to perform several tasks that are impossible in standard quantum mechanics: they allow for the violation of causal inequalities, and provide an advantage for computational and communication complexity. Nonetheless, no process that can be used to violate a causal inequality is known to be physically implementable. There is therefore considerable interest in determining which processes are physical and which are just mathematical artefacts of the framework. Here we make key progress in this direction by proposing a purification postulate: processes are physical only if they are purifiable. We derive necessary conditions for a process to be purifiable, and show that several known processes do not satisfy them.

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The political attitude and the ideology of a very small elite of physicists (Niels Bohr, Werner Heisenberg, Max Born and view other) played a major role in the construction of the Copenhagen Interpretation of quantum mechanics in the 1920s.Lastly, the hegemonic standard acausal Copenhagen Interpretation of quantum mechanics abandoned the principle of causality in quantum mechanics and opened a very wide door to mysticism, logical fallacies and wishful thinking in physics and in science as such.Historically, the Second International Congress for the Unity of Science (Copenhagen, June 21-26, 1936) tried to solve the problem of causality within physics but without a success.Thus far, 80 years after the Second International Congress for the Unity of Science this publication will expel Bohr's and Heisenberg's dogma of non-causality out of quantum mechanics and re-establish the unrestricted validity of the principle of causality at quantum level and under conditions of relativity theory by mathematizing the relationship between cause and effect in the form of the mathematical formula of the causal relationship k.In contrast to Bohr, Heisenberg and other representatives of the Copenhagen interpretation quantum mechanics, a realistic interpretation of quantum theory grounded on the unrestricted validity of the principle of causality will expel any kind of mysticism from physics and enable a quantization of the gravitational field too.
To study which are the most general causal structures which are compatible with local quantum mechanics, Oreshkov et al. [1] introduced the notion of a process: a resource shared between some parties that allows for quantum communication between them without a predetermined causal order. These processes can be used to perform several tasks that are impossible in standard quantum mechanics: they allow for the violation of causal inequalities, and provide an advantage for computational and communication complexity. Nonetheless, no process that can be used to violate a causal inequality is known to be physically implementable. There is therefore considerable interest in determining which processes are physical and which are just mathematical artefacts of the framework. Here we make key progress in this direction by proposing a purification postulate: processes are physical only if they are purifiable. We derive necessary conditions for a process to be purifiable, and show that several known processes do not satisfy them.