Squaring the circle: Gleb Wataghin and the prehistory of quantum gravity

Hagar, Amit

doi:10.1016/j.shpsb.2013.07.005

Cited by 5 publications

(3 citation statements)

References 64 publications

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“…As we see the uncertainty relations are intimately related to canonical commutation relations (10). To our best knowledge, Gleb Wataghin was the first [34,35] who suggested that both the commutation relations (10) and the uncertainty principle (1) might be modified at high relative impulses in such a way that…”

Section: Generalized Uncertainty Principlementioning

confidence: 79%

“…according to the Liouville equation ( 22). As we see from (35), the parameter α essentially coincides with time and the characteristics of the Liouville equation ( 22) are just classical Newtonian trajectories in the extended phase space. Moreover, the KvN wave function ψ(q, p, t) remains constant along these trajectories.…”

Section: Koopman-von Neumann Mechanicsmentioning

confidence: 87%

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On deformations of classical mechanics due to Planck-scale physics

Chashchina,

Sen,

Silagadze

2019

Preprint

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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.

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Section: Generalized Uncertainty Principlementioning

confidence: 79%

Section: Koopman-von Neumann Mechanicsmentioning

confidence: 87%

On deformations of classical mechanics due to Planck-scale physics

Chashchina,

Sen,

Silagadze

2019

Preprint

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“…Squaring the circle has been a metaphor for the effort to unify relativity and quantum theory [35]. Related to the squaring of the circle are more approximations involving the four fundamental coupling constants.…”

Section: Squaring the Circlementioning

confidence: 99%

Physical Mathematics and The Fine-Structure Constant

Sherbon¹

2018

JAP

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Research into ancient physical structures, some having been known as the seven wonders of the ancient world, inspired new developments in the early history of mathematics. At the other end of this spectrum of inquiry the research is concerned with the minimum of observations from physical data as exemplified by Eddington's Principle. Current discussions of the interplay between physics and mathematics revive some of this early history of mathematics and offer insight into the fine-structure constant. Arthur Eddington's work leads to a new calculation of the inverse fine-structure constant giving the same approximate value as ancient geometry combined with the golden ratio structure of the hydrogen atom. The hyperbolic function suggested by Alfred Landé leads to another result, involving the Laplace limit of Kepler's equation, with the same approximate value and related to the aforementioned results. The accuracy of these results are consistent with the standard reference. Relationships between the four fundamental coupling constants are also found.

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Introduction: Spacetime and Quantum Gravity

Crowther

2016

Effective Spacetime

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Squaring the circle: Gleb Wataghin and the prehistory of quantum gravity

Cited by 5 publications

References 64 publications

On deformations of classical mechanics due to Planck-scale physics

On deformations of classical mechanics due to Planck-scale physics

Physical Mathematics and The Fine-Structure Constant

Introduction: Spacetime and Quantum Gravity

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