2021/01/15 by I B Pittaway, Pittaway, IB, F. G. Scholtz +1
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2101.06108
openalex publication_date 2021/01/15 · openalex created_date 2022/08/16 · openalex updated_date 2026/07/28
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.