Quantum Mechanics, Gravity and Modified Quantization Relations

Abstract

In this paper we investigate a possible energy scale dependence of the quantization rules and in particular, from a phenomenological point of view, an energy scale dependence of an effective $\hslash$. We set a bound on the deviation from the value of $\hslash$ at the muon scale from its usual value using measurements of the anomalous magnetic moment of the muon. Assuming that inflation took place, we can conclude that nature is described by a quantum theory at least up to an energy scale of about $10^{16}$ GeV.

14 pages

References in corpus (13)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• Minimal Length Scale Scenarios for Quantum Gravity
• Renormalization of Black Hole Entropy and of the Gravitational Coupling Constant
• Minimum Length from Quantum Mechanics and Classical General Relativity
• Classical Physics and Quantum Loops
• Towards an S-matrix Description of Gravitational Collapse
• The Inflationary Energy Scale
• An introduction to cosmological inflation
• Minimum Length from First Principles
• The Lightest of Black Holes
• The hbar Expansion in Quantum Field Theory
• The Cellular Automaton Interpretation of Quantum Mechanics
• On the Precision of a Length Measurement

Cited by in corpus (4)

• Inconstant Planck's constant
• The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario
• Generalised complex geometry in thermodynamical fluctuation theory
• Entropy, topological theories and emergent quantum mechanics