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Quantum Measurement Problem and the Gravitational Field

J. Anandan

Published Apr 30, 1998• 4 citations
Publisher

Abstract

Abstract Department of Physics and Astronomy University of South Carolina, Columbia, SC 20208, USA [AF] Two of the most important unsolved problems in theoretical physics are the problem of quantizing gravitation and the measurement problem in quantum theory. It is possible that the solution of each one needs the other. Since we have successful quantum theories of electroweak, and strong interactions, the solution to the problem of the collapse of the wave function, known as the measurement problem, may lie in the yet unknown quantum theory of the remaining interaction, namely quantum gravity. On the other hand, the numerous unsuccessful attempts to construct a quantum theory of gravity for more than six decades on the assumption that the present linear quantum theory is correct suggests that perhaps not only general relativity but also quantum theory should be modified in order to construct of satisfactory quantum theory of gravity.

DOI
10.1093/oso/9780198500599.003.0026

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Abstract Department of Physics and Astronomy University of South Carolina, Columbia, SC 20208, USA [AF] Two of the most important unsolved problems in theoretical physics are the problem of quantizing gravitation and the measurement problem in quantum theory. It is possible that the solution of each one needs the other. Since we have successful quantum theories of electroweak, and strong interactions, the solution to the problem of the collapse of the wave function, known as the measurement problem, may lie in the yet unknown quantum theory of the remaining interaction, namely quantum gravity. On the other hand, the numerous unsuccessful attempts to construct a quantum theory of gravity for more than six decades on the assumption that the present linear quantum theory is correct suggests that perhaps not only general relativity but also quantum theory should be modified in order to construct of satisfactory quantum theory of gravity.
Two fundamental, and unsolved problems in physics are: i) the resolution of the "measurement problem" in quantum mechanics ii) the quantization of strongly nonlinear (nonabelian) gauge theories. The aim of this paper is to suggest that these two problems might be linked, and that a mutual, simultaneous solution to both might exist. We propose that the mechanism responsible for the "collapse of the wave function" in quantum mechanics is the nonlinearities already present in the theory via nonabelian gauge interactions. Unlike all other models of spontaneous collapse, our proposal is, to the best of our knowledge, the only one which does not introduce any new elements into the theory. A possible experimental test of the model would be to compare the coherence lengths - here defined as the distance over which quantum mechanical superposition is still valid - for, \textit{e.g}, electrons and photons in a double-slit experiment. The electrons should have a finite coherence length, while photons should have a much longer coherence length (in principle infinite, if gravity - a very weak effect indeed unless we approach the Planck scale - is ignored).
Abstract When about half a century ago the concept of universal spontaneous collapse of the wave function was conceived it was an attempt to alter standard non-relativistic quantum physics. As such, it was largely ignored by relativistic field theory and quantum gravity communities. A central motivation of spontaneous collapse community has been to replace the standard collapse-by-measurement that annoyed many. With few exceptions, it did not annoy the field theory and quantum gravity communities. Concept of certain general-relativity-related universal irreversibility in quantum field theory had been initiated very long ago by Wheeler, Hawking and a few others independently from the concept of spontaneous collapse. Lately the two concepts started to converge and support each other.
The measurement problem of quantum theory (QT) is the unsolved problem of how the probabilistic predictions of QT are turned into definite measurement results. A related question is whether a measurement in QT implies a collapse of the wave function and what the collapse of the wave function exactly means. Theories proposed on these subjects have not found general agreements among physicists. This paper proposes a solution to the QT measurement problem in terms of a functional model of the measurement process. A functional model describes the process of the dynamic evolution of a physical system. The model assumes that the interactions between the measured QT object and the measurement apparatus are normal interactions which adhere to the laws of quantum field theory.
“Despite almost a century’s worth of study, it is still unclear how general relativity (GR) and quantum theory (QT) should be unified into a consistent theory. The conventional approach is to retain the foundational principles of QT, such as the superposition principle, and modify GR. This is referred to as ‘quantizing gravity’, resulting in a theory of ‘quantum gravity’. The opposite approach is ‘gravitizing QT’ where we attempt to keep the principles of GR, such as the equivalence principle, and consider how this leads to modifications of QT. What we are most lacking in understanding which route to take, if either, is experimental guidance. Here we consider using the Dirac–Pauli representation of free Dirac equation to search for the clues. In particular, we study how the double-slit diffraction experiment, when only one Dirac particle (‘say’ electron) at a time is in the apparatus, could test a gravitizing QT proposal in which the wavefunction collapse emerges on the detector screen from the Dirac–Pauli representation, as an objective process, resolving the measurement problem of QT.” [1] We found that the Dirac–Pauli representation is inherently a unified theory embodying a gravitizing QT proposal that Dirac–Pauli representation as wave nature is manifestation of inertial mass and the Foldy-Wouthuysen representation as particle nature is manifestation of gravitational mass such that the fact, that same physics is involved in these two representations, is simply the validity and exhibition of the principle of equivalence, of GR, in QT. [1] Richard Howl et al 2019 New J. Phys. 21 043047 DOI 10.1088/1367-2630/ab104a
Abstract We discuss effects of loss of coherence in low energy quantum systems caused by or related to gravitation, referred to as gravitational decoherence. These effects, resulting from random metric fluctuations, for instance, promise to be accessible by relatively inexpensive table-top experiments, way before the scales where true quantum gravity effects become important. Therefore, they can provide a first experimental view on gravity in the quantum regime. We will survey models of decoherence induced both by classical and quantum gravitational fluctuations; it will be manifest that a clear understanding of gravitational decoherence is still lacking. Next we will review models where quantum theory is modified, under the assumption that gravity causes the collapse of the wave functions, when systems are large enough. These models challenge the quantum-gravity interplay, and can be tested experimentally. In the last part we have a look at the state of the art of experimental research. We will review efforts aiming at more and more accurate measurements of gravity ( G and g ) and ideas for measuring conventional and unconventional gravity effects on nonrelativistic quantum systems.