Within the class of ontological interpretations of quantum theory where a physical system comprises a particle and a field (wavefunction) guiding it, an empty wave is a segment of the wavefunction not containing the particle. We examine the impact of this concept on the debate between the epistemological and ontological viewpoints. The theoretical merits of the empty wave in avoiding the wavefunction collapse hypothesis, and in supplying conceptual precision in the application of quantum mechanics, are emphasized. Particular reference is made to path detection in interferometry and it is shown how a consistent application of the particle and empty wave concepts dispels the suggestion that this is a theory. The problem of how the reality of an empty wave might be demonstrated by its effect on other systems is examined and general arguments advanced against this possibility. However, these arguments are not conclusive and we describe how the technique of protective measurement suggests a method to probe the empirical implications of empty waves and potentially distinguish between the epistemological and ontological perspectives.
Within the class of ontological interpretations of quantum theory where a physical system comprises a particle and a field (wavefunction) guiding it, an empty wave is a segment of the wavefunction not containing the particle. We examine the impact of this concept on the debate between the epistemological and ontological viewpoints. The theoretical merits of the empty wave in avoiding the wavefunction collapse hypothesis, and in supplying conceptual precision in the application of quantum mechanics, are emphasized. Particular reference is made to path detection in interferometry and it is shown how a consistent application of the particle and empty wave concepts dispels the suggestion that this is a theory. The problem of how the reality of an empty wave might be demonstrated by its effect on other systems is examined and general arguments advanced against this possibility. However, these arguments are not conclusive and we describe how the technique of protective measurement suggests a method to probe the empirical implications of empty waves and potentially distinguish between the epistemological and ontological perspectives.
Two roads diverged in a wood, and I – I took the one less traveled by , And that has made all the difference . Robert Frost (1916) The explanatory role of empty waves in quantum theory In this chapter we are concerned with two classes of interpretations of quantum mechanics: the epistemological (the historically dominant view) and the ontological. The first views the wave function as just a repository of (statistical) information on a physical system. The other treats the wave function primarily as an element of physical reality, whilst generally retaining the statistical interpretation as a secondary property. There is as yet only theoretical justification for the program of modelling quantum matter in terms of an objective spacetime process; that some way of imagining how the quantum world works between measurements is surely better than none. Indeed, a benefit of such an approach can be that “measurements” lose their talismanic aspect and become just typical processes described by the theory. In the quest to model quantum systems one notes that, whilst the formalism makes reference to “particle” properties such as mass, the linearly evolving wave function ψ( x ) does not generally exhibit any feature that could be put into correspondence with a localized particle structure. To turn quantum mechanics into a theory of matter and motion, with real atoms and molecules consisting of particles structured by potentials and forces, it is necessary to bring in independent physical elements not represented in the basic formalism. The notion of an “empty wave” is peculiar to those representatives of this class of extended theories which postulate that the additional physical element is a corpuscle-like entity or point particle. For clarity, we shall develop the discussion in terms of a definite model of this kind whose properties are well understood and which it is established reproduces the empirical content of quantum mechanics: the de Broglie–Bohm theory, a prominent representative of the class of ontological interpretations (Holland, 1993).
The quantum measurement problem remains a central unresolved issue in theoretical physics, arising from the incompatibility between unitary quantum dynamics and the emergence of definite measurement outcomes. Closely related is the question of the physical status of the wavefunction within contemporary quantum theory. This review critically surveys leading approaches to the measurement problem, focusing on their formal consistency, physical assumptions, and empirical implications. We examine the standard measurement framework, the role of environment-induced decoherence and quantum Darwinism, and the restrictions imposed by no-go theorems such as Bell, Kochen–Specker, and Pusey–Barrett–Rudolph. Interpretations including Everettian many-worlds, Bohmian mechanics, spontaneous collapse models, relational quantum mechanics, QBist approaches, and Copenhagen-type frameworks are assessed in terms of their ability to account for classical definiteness without sacrificing empirical adequacy. We also review experimental efforts probing macroscopic superpositions and collapse dynamics. The analysis indicates that, despite its predictive success, quantum theory lacks a complete physical account of outcome selection. This suggests that the measurement problem reflects a fundamental structural limitation of current theory, motivating either new physical principles or a redefinition of the wavefunction’s ontological role.
The collapse postulate in quantum mechanics is problematic. In standard presentations of the theory, the state of a system prior to a measurement is a sum of terms, with one term representing each possible outcome of the measurement. Many dynamical collapse theories imply that the quantum wavefunction is fundamental, and that particles are just a temporary “bunching up” of the fundamental wave-like entity. Quantum mechanics is often taken to be an indeterministic theory. Quantum mechanics represents the state of a system in various ways, but the representation that is most perspicuous for understanding collapse theories uses a wavefunction. Consistency with special relativity is, therefore, a problem for dynamical collapse theories, but perhaps not an insuperable one. Some have argued that the wavefunction needs to be supplemented to counteract the effects of the novel quantum vagueness introduced by dynamical collapse theories. The ontological consequences of dynamical collapse theories remain an area of active debate.
We examine the entanglement and state disturbance arising in a protective measurement and argue that these inescapable effects doom the claim that protective measurement establishes the reality of the wave function. An additional challenge to this claim results from the exponential number of protective measurements required to reconstruct multi-qubit states. We suggest that the failure of protective measurement to settle the question of the meaning of the wave function is entirely expected, for protective measurement is but an application of the standard quantum formalism, and none of the hard foundational questions can ever be settled in this way. Introduction From the start, the technical result of protective measurement has been suggested to have implications for the interpretation of quantum mechanics. Consider how Aharonov and Vaidman [2] chose to begin their original paper introducing the idea of protective measurement: We show that it is possible to measure the Schrödinger wave of a single quantum system. This provides a strong argument for associating physical reality with the quantum state of a single system.… Since then, the pioneers of protective measurement seem to have taken a more moderate stance. Vaidman [42], in a recent synopsis of protective measurement, concedes that the protective measurement procedure is not a proof that we should adopt one interpretation instead of the other, but it is a good testbed which shows advantages and disadvantages of various interpretations. Notwithstanding this more subtle perspective and a number of critical studies of the technical and foundational aspects of protective measurement, Gao [21] has maintained, if not amplified, the force of Aharonov and Vaidman's original argument: An immediate implication is that the result of a protective measurement, namely the expectation value of the measured observable in the measured state, reflects the actual physical property of the measured system, as the system is not disturbed after this result has been obtained. […]
Waves and particles are alternative modes of being for the elements of atomic dimensions. This feature appears to be evident at the experimental level but remains a conundrum at the theoretical level. The squared wavefunction |Ψ|2 yields the probability of finding a particle at a particular position and time, namely, the wave is conceived as a derivation or a physical condition of the particle and not a condition of the quantum. What the wavefunction represents, whether it really exists, whether it is a purely formal representation and if the observer influences the wavefunction are the major arguments of quantum mechanics (QM). The double nature of electrons, photons, and so on has been clearly recognized, and the two natures should be established by precise formulations. This work adheres totally to this methodological criterion and puts forward two formal definitions. The measurement process and wave collapse problems are also discussed. Finally, we verify the theoretical conclusions using the double slit experiment and the photoelectric effect. Probability plays a crucial role in the quantum literature, and the definitions of the wave and the particle should be illustrated by exploiting the probability theory; however, the various probability theories are not univocal and propose irreconcilable views. Therefore, in a preliminary stage, we unify the ontological and epistemic interpretations of probability using four theorems that have been already published. In summary, this work is developed on the basis of two methodological criteria, which seek to improve the probability theory and fix the definitional formulas of QM.
Introduction One of the crucial issues about protective measurements is the extent to which they provide (additional) grounds for some realist understanding of the wave function. This issue is notoriously subject to debate, which is not the aim of this chapter. Rather, this chapter aims at clarifying the further issue of the ontological picture corresponding to the realist understanding of the wave function possibly suggested by protective measurements. Oddly enough, proponents of a realist reading of protective measurements remain in general rather vague about ontology (see for instance Aharonov et al. (1993, 4624), who assimilate the wave function to an “extended object” without further details, or the brief and somewhat unprecise discussion in Dickson (1995, 135–136) of the interpretation of the wave function within Bohmian mechanics (BM) and within the theoretical framework elaborated by Ghirardi, Rimini and Weber (GRW); in this volume, Gao does propose a more elaborated ontological model for quantum mechanics (QM) based on protective measurements). Despite this vagueness (or maybe because of it), it seems that the most obvious ontological intuition resulting from protective measurements points towards some form of straightforward realism about the wave function understood in the sense of a real, physical field: indeed, protective measurements are claimed to allow measuring expectation values of observables on a single quantum system, thereby providing the possibility of reconstructing (i.e. “measuring” in some sense) the wave function of a single quantum system. Aharonov et al. (1996, 125) clearly express this intuition: “We can observe the expectations values of operators, and we can observe the density and the current of the Schrödinger wave. We can “see” in some sense the Schrödinger wave. This leads us to believe that it has physical reality.” Therefore, this kind of intuition seems in line with a realist conception of the wave function, according to which the wave function is considered as a real substantial, material in some sense) entity on its own (this view is often called “wave function realism”).