• Corpus ID: 118487861

Quantum Gravity and a Time Operator in Relativistic Quantum Mechanics

  title={Quantum Gravity and a Time Operator in Relativistic Quantum Mechanics},
  author={M. Bauer},
  journal={arXiv: General Relativity and Quantum Cosmology},
  • M. Bauer
  • Published 5 May 2016
  • Physics
  • arXiv: General Relativity and Quantum Cosmology
The problem of time in the quantization of gravity arises from the fact that time in Schroedinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time" in QM and "time" in General Relativity (GR) are seen as mutually incompatible notions. The introduction of a dy- namical time operator in relativistic quantum mechanics (RQM), that in the Heisenberg representation is also a function of the parameter t (iden… 
A different perspective on the problem of time in quantum gravity.
The perspective is advanced that the time parameter in quantum mechanics corresponds to the time coordinate in a Minkowski flat spacetime local approximation to the actual dynamical curved spacetime
Tunneling in attosecond optical ionization and a dynamical time operator
The conundrum parameter-operator of time in quantum mechanics, as well as the time-energy uncertainty relation and the tunneling delay time, have recently been addressed in attosecond optical
The Pauli Objection Addressed in a Logical Way
A deeper understanding of how elementary particles can be seen, themselves, as ticking clocks, and to examine more broadly how they relate to time is developed.
Time and energy operators in the canonical quantization of special relativity
Based on Lorentz invariance and Born reciprocity invariance, the canonical quantization of special relativity is shown to provide a unified origin for (i) the complex vector space formulation of
The problem of time in quantum mechanics
The problem of time in quantum mechanics concerns the fact that in the Schrödinger equation time is a parameter, not an operator. Pauli’s objection to a time-energy uncertainty relation analogue to


Time in quantum mechanics: a story of confusion
Time dependence in quantum mechanics
Abstract:It is shown that the time-dependent equations (Schrödinger and Dirac) for a quantum system can be derived from the time-independent equation for the larger object of the system interacting
A dynamical time operator in Dirac's relativistic quantum mechanics
A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the
Time and the interpretation of canonical quantum gravity.
  • UnruhWald
  • Physics
    Physical review. D, Particles and fields
  • 1989
It is argued that the interpretive problems of quantum gravity are not alleviated by the incorporation of observers into the theory, and a proposal for a formulation of canonical quantum gravity in which an appropriate nondynamical time parameter is present is made.
Time Paradox in Quantum Gravity
The aim of this work is to review the concepts of time in quantum mechanics and general relativity to show their incompatibility. We show that the absolute character of Newtonian time is present in
Concept of time in canonical quantum gravity and string theory
The accommodation of gravity into the quantum framework will entail changes for the concepts of space and time at the most fundamental level. Here I shall review the concept of time, but include also
Problem of time in quantum gravity
The Problem of Time occurs because the ‘time’ of GR and of ordinary Quantum Theory are mutually incompatible notions. This is problematic in trying to replace these two branches of physics with a
The derivation of time-dependent Schrödinger equations
Beginning with an entangled state of a time-independent (TI) quantum system coupled to its TI quantum environment, we show that a time-dependent Schrödinger equation (TDSE) for the quantum system
General Principles of Quantum Mechanics
I The Uncertainty Principle and Complementarity.- 1. The Uncertainty Principle and Complementarity.- 2. The Measurement of Position and Momentum.- II Schrodinger Equation and Operator Calculus.- 3.
Prima Facie Questions in Quantum Gravity
The long history of the study of quantum gravity has thrown up a complex web of ideas and approaches. The aim of this article is to unravel this web a little by analysing some of the {\em prima