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29 March 2024
 
  » arxiv » quant-ph/0403020

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On the Cyclotomic Quantum Algebra of Time Perception
Michel Planat ;
Date 2 Mar 2004
Journal Neuroquantology 2 (4) (2004) 292-308
Subject Quantum Physics; Mathematical Physics | quant-ph math-ph math.MP
AbstractI develop the idea that time perception is the quantum counterpart to time measurement. Phase-locking and prime number theory were proposed as the unifying concepts for understanding the optimal synchronization of clocks and their 1/f frequency noise. Time perception is shown to depend on the thermodynamics of a quantum algebra of number and phase operators already proposed for quantum computational tasks, and to evolve according to a Hamiltonian mimicking Fechner’s law. The mathematics is Bost and Connes quantum model for prime numbers. The picture that emerges is a unique perception state above a critical temperature and plenty of them allowed below, which are parametrized by the symmetry group for the primitive roots of unity. Squeezing of phase fluctuations close to the phase transition temperature may play a role in memory encoding and conscious activity.
Source arXiv, quant-ph/0403020
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