Quantum Interference on the Non-Commutative Plane and the Quantum-to-Classical Transition

• URL: http://arxiv.org/abs/2101.06108v2
• Date: Fri, 12 Aug 2022 12:54:56 GMT
• Title: Quantum Interference on the Non-Commutative Plane and the Quantum-to-Classical Transition
• Authors: IB Pittaway and FG Scholtz
• Abstract summary: We explore a possible link between the structure of space at short length scales and the emergence of classical phenomena at macroscopic scales. We explicitly compute the outcomes of a double slit experiment and a von Neumann measurement in the non-commutative plane.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We explore a possible link between the structure of space at short length scales and the emergence of classical phenomena at macroscopic scales. To this end we adopt the paradigm of non-commutative space at short length scales and explicitly compute the outcomes of a double slit experiment and a von Neumann measurement in the non-commutative plane. A very consistent picture of a continuous quantum-to-classical transition emerges. The mechanism driving this transition is standard decoherence, but here the ``environment'' arises quite naturally from the tensor product structure of the non-commutative quantum Hilbert space. The double slit calculation enables us to establish a lower bound on the non-commutative parameter for this transition to become effective at particle numbers of the order of Avogadro's number. Similarly, the result of the von Neumann measurement establishes a criterium involving the non-commutative parameter, apparatus size and coupling between system and apparatus for classicality to emerge.

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