On deformations of classical mechanics due to Planck-scale physics

Olga I. Chashchina, Abhijit Sen, Zurab K. Silagadze

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

3 Цитирования (Scopus)

Аннотация

Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification may imply a modification of the canonical commutation relations and hence quantum mechanics at the Planck scale. The corresponding modification of classical mechanics is usually considered by replacing modified quantum commutators by Poisson brackets suitably modified in such a way that they retain their main properties (antisymmetry, linearity, Leibniz rule and Jacobi identity). We indicate that there exists an alternative interesting possibility. Koopman-von Neumann's Hilbert space formulation of classical mechanics allows, as Sudarshan remarked, to consider the classical mechanics as a hidden variable quantum system. Then, the Planck scale modification of this quantum system naturally induces the corresponding modification of dynamics in the classical substrate. Interestingly, it seems this induced modification in fact destroys the classicality: classical position and momentum operators cease to be commuting and hidden variables do appear in their evolution equations.

Язык оригиналаанглийский
Номер статьи2050070
Число страниц38
ЖурналInternational Journal of Modern Physics D
Том29
Номер выпуска10
DOI
СостояниеОпубликовано - 1 июл 2020

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