Schroedinger's cat and the clock: Lessons for quantum gravity

Abstract

I review basic principles of the quantum mechanical measurement process in view of their implications for a quantum theory of general relativity. It turns out that a clock as an external classical device associated with the observer plays an essential role. This leads me to postulate a ``principle of the integrity of the observer''. It essentially requires the observer to be part of a classical domain connected throughout the measurement process. Mathematically this naturally leads to a formulation of quantum mechanics as a kind of topological quantum field theory. Significantly, quantities with a direct interpretation in terms of a measurement process are associated only with amplitudes for connected boundaries of compact regions of space-time. I discuss some implications of my proposal such as in-out duality for states, delocalization of the ``collapse of the wave function'' and locality of the description. Differences to existing approaches to quantum gravity are also highlighted.

12 pages, 3 figures, LaTeX + AMS + eps; introduction, section numbers and two references added

References in corpus (5)

• Loop Quantum Gravity
• Spin Foam Models for Quantum Gravity
• Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity
• A "general boundary" formulation for quantum mechanics and quantum gravity
• Quantum Gravity as Topological Quantum Field Theory

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• Background independence in a nutshell
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• General boundary quantum field theory: Timelike hypersurfaces in Klein-Gordon theory
• Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation
• Spin foams with timelike surfaces
• Spatially asymptotic S-matrix from general boundary formulation
• The perturbative Regge-calculus regime of Loop Quantum Gravity
• States on timelike hypersurfaces in quantum field theory
• Probabilities in the general boundary formulation
• Three-dimensional Quantum Supergravity and Supersymmetric Spin Foam Models
• Two-dimensional quantum Yang-Mills theory with corners
• Generalized Tomonaga-Schwinger equation from the Hadamard formula
• A positive formalism for quantum theory in the general boundary formulation
• General boundary quantum field theory in de Sitter spacetime
• Generalized Schroedinger equation in Euclidean field theory
• Quantum general relativity and the classification of smooth manifolds
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Locality and General Vacua in Quantum Field Theory
• Second-order amplitudes in loop quantum gravity
• Spin-Spacetime Censorship
• Diffeomorphisms from finite triangulations and absence of 'local' degrees of freedom
• A predictive framework for quantum gravity and black hole to white hole transition
• Entanglement entropy between virtual and real excitations in quantum electrodynamics
• Compositional Quantum Field Theory: An axiomatic presentation
• General Boundary Quantum Field Theory in Anti de Sitter Spacetimes
• Codimension-2 surfaces and their Hilbert spaces: low-energy clues for holography from general covariance