Could we hear the pop of a wave-function collapse, and if so, what would it sound like? There exist reconstructions or modifications of quantum mechanics (collapse models) where this archetypal signature of randomness exists and can in principle be witnessed. But, perhaps surprisingly, the resulting sound is disappointingly banal, indistinguishable from any other click. The problem of finding the right description of the world between two completely different classes of models -- where wave functions jump and where they do not -- is empirically undecidable. Behind this seemingly trivial observation lie deep lessons about the rigidity of quantum mechanics, the difficulty to blame unpredictability on intrinsic randomness, and more generally the physical limitations to our knowledge of reality.
Could we hear the pop of a wave-function collapse, and if so, what would it sound like? There exist reconstructions or modifications of quantum mechanics (collapse models) where this archetypal signature of randomness exists and can in principle be witnessed. But, perhaps surprisingly, the resulting sound is disappointingly banal, indistinguishable from any other click. The problem of finding the right description of the world between two completely different classes of models -- where wave functions jump and where they do not -- is empirically undecidable. Behind this seemingly trivial observation lie deep lessons about the rigidity of quantum mechanics, the difficulty to blame unpredictability on intrinsic randomness, and more generally the physical limitations to our knowledge of reality.
This is the first single volume about the collapse theories of quantum mechanics, which is becoming a very active field of research in both physics and philosophy. In standard quantum mechanics, it is postulated that when the wave function of a quantum system is measured, it no longer follows the Schrödinger equation, but instantaneously and randomly collapses to one of the wave functions that correspond to definite measurement results. However, why and how a definite measurement result appears is unknown. A promising solution to this problem are collapse theories in which the collapse of the wave function is spontaneous and dynamical. Chapters written by distinguished physicists and philosophers of physics discuss the origin and implications of wave-function collapse, the controversies around collapse models and their ontologies, and new arguments for the reality of wave function collapse. This is an invaluable resource for students and researchers interested in the philosophy of physics and foundations of quantum mechanics.
Among several possibilities for what reality could be like in view of the empirical facts of quantum mechanics, one is provided by theories of spontaneous wave function collapse, the best known of which is the Ghirardi–Rimini–Weber (GRW) theory. We show mathematically that in GRW theory (and similar theories) there are limitations to knowledge, that is, inhabitants of a GRW universe cannot find out all the facts true of their universe. As a specific example, they cannot accurately measure the number of collapses that a given physical system undergoes during a given time interval; in fact, they cannot reliably measure whether one or zero collapses occur. Put differently, in a GRW universe certain meaningful, factual questions are empirically undecidable. We discuss several types of limitations to knowledge and compare them with those in other (no-collapse) versions of quantum mechanics, such as Bohmian mechanics. Most of our results also apply to observer-induced collapses as in orthodox quantum mechanics (as opposed to the spontaneous collapses of GRW theory). 1 Introduction 1.1 Known examples of limitations to knowledge 1.2 Remarks2 Brief Review of GRW Theories 2.1 The GRW process 2.2 GRWm 2.3 GRWf3 First Examples of Limitations to Knowledge in GRW Theories4 Measurements of Flashes in GRWf, or of Collapses in GRWm 4.1 An example in which ψ is known 4.2 Other choices of ψ 4.3 Experiments beginning before t 2 4.4 If ψ is random 4.5 Optimal way of distinguishing two density matrices 4.6 If ψ is unknown5 Measurements of m(x) in GRWmAppendix
Quantum mechanics is grounded on the superposition principle, which is the source both of its tremendous success and technological power, as well as of the problems in understanding it. The reason why superpositions do not propagate from the microscopic to the macroscopic world are subject to debate. Spontaneous wave function collapse models have been formulated to take into account a progressive breakdown of quantum superpositions when systems are large enough; they do so by modifying the Schrödinger dynamics, and therefore they are empirically testable. Deviations are tiny, and require precision measurements. I will review collapse models, and present the most recent experimental tests.
If we have to go on with these damned quantum jumps, then I'm sorry that I ever got involved. E. Schrödinger Introduction I have borrowed the title of a characteristic paper by Schrödinger (Schrödinger, 1952). In it he contrasts the smooth evolution of the Schrödinger wavefunction with the erratic behaviour of the picture by which the wavefunction is usually supplemented, or ‘interpreted’, in the minds of most physicists. He objects in particular to the notion of ‘stationary states’, and above all to ‘quantum jumping’ between those states. He regards these concepts as hangovers from the old Bohr quantum theory, of 1913, and entirely unmotivated by anything in the mathematics of the new theory of 1926. He would like to regard the wavefunction itself as the complete picture, and completely determined by the Schrödinger equation, and so evolving smoothly without ‘quantum jumps’. Nor would he have ‘particles’ in the picture. At an early stage, he had tried to replace ‘particles’ by wavepackets (Schrödinger, 1926). But wavepackets diffuse. And the paper of 1952 ends, rather lamely, with the admission that Schrödinger does not see how, for the present, to account for particle tracks in track chambers … nor, more generally, for the definiteness, the particularity, of the world of experience, as compared with the indefiniteness, the waviness, of the wavefunction. It is the problem that he had had (Schrödinger, 1935 a ) with his cat. He thought that she could not be both dead and alive.
We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. In a realistic interpretation, the wave function of a quantum system can be taken as a description of either a physical field or the ergodic motion of a particle. The essential difference between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time‐divided way. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist gravitational and electrostatic self‐interactions of its wave function. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus the wave function cannot be a description of a physical field but be a description of the ergodic motion of a particle. For the later there is only a localized particle with mass and charge at every instant, and thus there will not exist any self‐interaction for the wave function. It is further argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. Based on the negative result, we suggest that the wave function is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wave function not only gives the probability of the particle being found in certain locations, but also gives the probability of the particle being there. The suggested new interpretation of the wave function provides a natural realistic alternative to the orthodox interpretation, and it also implies that the de Broglie‐Bohm theory and many‐worlds interpretation are wrong and the dynamical collapse theories are in the right direction by admitting wavefunction collapse.