The quantum measurement problem and various unsuccessful attempts to resolve it are reviewed. A suggestion by Diosi and Penrose for the half life of the quantum superposition of two Newtonian gravitational fields is generalized to an arbitrary quantum superposition of relativistic, but weak, gravitational fields. The nature of the ``collapse'' process of the wave function is examined.
The quantum measurement problem and various unsuccessful attempts to resolve it are reviewed. A suggestion by Diosi and Penrose for the half life of the quantum superposition of two Newtonian gravitational fields is generalized to an arbitrary quantum superposition of relativistic, but weak, gravitational fields. The nature of the ``collapse'' process of the wave function is examined.
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.
The stability of a quantum superposition f two different stationary mass distributions is examined, where the perturbing effect of each distribution on the space-time structure is taken into account, in accordance with the principles of general relativity. It is argued that the definition of the time-translation operator for the superposed space-times involves an inherent ill-definedness, leading to an essential uncertainty in the energy of the superposed state which, in the Newtonian limit, is proportional to the gravitational self-energy EA of the difference between the two mass distributions. This is consistent with a suggested finite lifetime of the order of?t/ELx for the superposed state, in agreement with a certain proposal made by the author for a gravitationally induced spontaneous quantum state reduction, and with closely related earlier suggestions by Di6si and by Ghirardi et al. 1. THE PROBLEM OF QUANTUM STATE REDUCTION The fundamental problem of quantum mechanics, as that theory is presently understood, is to make sense of the reduction of the state vector (i.e. collapse of the wavefunction), denoted here by R. This issue is usually addressed in terms of the "quantum measurement problem", which is to comprehend how, upon measurement of a quantum system, this (seem-ingly) discontinuous R-process can come about. A measurement, after all, merely consists of the quantum state under consideration becoming en-tangled with a more extended part of the physical universe, e.g. with a
This article is a brief survey of some approaches to implementing the suggestion that collapse of the wave function is mediated by gravity. These approaches include: a possible connection between the problem of time and problem of quantum measurement, decoherence models based on space-time uncertainty, the Schrödinger-Newton equation, attempts to introduce gravity into collapse models such as CSL, ideas based on the black hole - elementary particle complementarity, and the possible role of a complex space-time metric.
Quantum mechanics famously posits two distinct evolution rules for the state of a system: a deterministic, unitary time evolution under the Schr¨odinger equation, and a probabilistic “collapse” of the wavefunction upon measurement as dictated by the Born rule. The apparent inconsistency of these two dynamical laws – one continuous and one discontinuous – constitutes the quantum measurement problem. This foundational problem, which underlies the emergence of definite outcomes from quantum superpositions, has persisted since the theory’s inception. In this review, we present a comprehensive and rigorous examination of the measurement problem and survey the leading approaches that seek to resolve or circumvent it. We begin by formulating the measurement problem and its conceptual challenges. We then discuss in detail the major interpretations of quantum mechanics and theoretical frameworks addressing the problem: the Copenhagen interpretation, Everett’s many-worlds interpretation, de Broglie–Bohm pilot-wave theory, objective collapse models, the role of decoherence and environment-induced superselection, and epistemic approaches such as QBism. For each interpretation, we describe the core principles and mathematical formalism, assessing how (and whether) it attempts to solve the measurement problem. We also review modern developments and experiments relevant to quantum measurements, including tests of Bell inequalities, observations of decoherence and macroscopic superpositions, weak measurements and quantum eraser experiments, and thought experiments ‘a la Wigner’s friend. We highlight how these results inform the ongoing debate. Finally, we discuss open problems and challenges that remain in fully resolving the measurement problem.
According to Penrose, the fundamental conflict between the superposition principle of quantum mechanics and the principle of general covariance of general relativity entails the existence of wavefunction collapse, e.g. a quantum superposition of two different space-time geometries will collapse to one of them due to the ill-definedness of the time-translation operator for the superposition. In this paper, we argue that Penrose's conjecture on gravity's role in wavefunction collapse is debatable. First of all, it is still a controversial issue what the exact nature of the conflict is and how to resolve it. Secondly, Penrose's argument by analogy is too weak to establish a necessary connection between wavefunction collapse and the conflict as understood by him. Thirdly, the conflict does not necessarily lead to wavefunction collapse. For the conflict or the problem of ill-definedness for a superposition of different space-time geometries also needs to be solved before the collapse of the superposition finishes, and once the conflict has been resolved, the wavefunction collapse will lose its physical basis relating to the conflict. In addition, we argue that Penrose's suggestions for the collapse time formula and the preferred basis are also problematic.
According to Penrose, the fundamental conflict between the superposition principle of quantum mechanics and the general covariance principle of general relativity entails the existence of wavefunction collapse, e.g. a quantum superposition of two different space-time geometries will collapse to one of them due to the ill-definedness of the time-translation operator for the superposition. In this paper, we argue that Penrose's conjecture on gravity's role in wavefunction collapse is debatable. First of all, it is still a controversial issue what the exact nature of the conflict is and how to resolve it. Secondly, Penrose's argument by analogy is too weak to establish a necessary connection between wavefunction collapse and the conflict as understood by him. Thirdly, the conflict does not necessarily lead to wavefunction collapse. For the conflict or the problem of ill-definedness for a superposition of different space-time geometries also needs to be solved before the collapse of the superposition finishes, and once the conflict has been resolved, the wavefunction collapse will lose its physical basis relating to the conflict. In addition, we argue that Penrose's suggestions for the collapse time formula and collapse states are also problematic.