A contextual Planck parameter and the classical limit in quantum cosmology

Abstract

We propose that whatever quantity controls the Heisenberg uncertainty relations (for a given complementary pair of observables) it should be identified with an effective Planck parameter. With this definition it is not difficult to find examples where the Planck parameter depends on the region under study, varies in time, and even depends on which pair of observables one focuses on. In quantum cosmology the effective Planck parameter depends on the size of the comoving region under study, and so depends on that chosen region and on time. With this criterion, the classical limit is expected, not for regions larger than the Planck length, $l_P$, but for those larger than $l_Q=(l_P^2{H}^{-1}{)}^{1/3}$, where $H$ is the Hubble parameter. In theories where the cosmological constant is dynamical, it is possible for the latter to remain quantum even in contexts where everything else is deemed classical. These results are derived from standard quantization methods, but we also include more speculative cases where ad hoc Planck parameters scale differently with the length scale under observation. Even more speculatively, we examine the possibility that similar complementary concepts affect thermodynamical variables, such as the temperature and the entropy of a black hole.

References in corpus (14)

• Planck evidence for a closed Universe and a possible crisis for cosmology
• Approaches to Quantum Cosmology
• How the huge energy of quantum vacuum gravitates to drive the slow accelerating expansion of the Universe
• Dynamics of a Quantum Reference Frame
• The Chern-Simons Invariant as the Natural Time Variable for Classical and Quantum Cosmology
• Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations
• The cosmology of minimal varying Lambda theories
• Parity violating Friedmann Universes
• A Zero-Parameter Extension of General Relativity with Varying Cosmological Constant
• Inconstant Planck's constant
• Nonlinear Schrödinger equations and generalized Heisenberg uncertainty principle violating the principle of estimation independence
• A Mesoscopic Quantum Gravity Effect
• Do we live in an eigenstate of the "fundamental constants" operators?
• No-signaling non-unitary modification of quantum dynamics within a deterministic model of quantization

Cited by in corpus (5)

• Quantum analysis of the recent cosmological bounce in the comoving Hubble length
• Quantum torsion and a Hartle-Hawking "beam''
• Unimodular Hartle-Hawking wave packets and their probability interpretation
• Lorentzian quantum cosmology with torsion
• Making a Quantum Universe: Symmetry and Gravity