Protective measurements which were defined by Aharonov and Vaidman in 1993 played an important role in the discussion about the interpretation of quantum mechanics. In 1999, following an early work by Englert et al., Aharonov et al. wrote an article in which they showed that protective measurements can be used to demonstrate the `surrealism' of Bohmian mechanics. Bohmian mechanics also known as pilot-wave interpretation is certainly the best-known hidden variable interpretation of quantum mechanics. It played a fundamental role in the discovery by Bell of his famous non locality theorem. Therefore, any attacks against pilot-wave interpretation is particularly interesting and instructive to learn something new about the mysterious quantum universe. It is the aim of this chapter to review the debate surrounding protective measurement and pilot-wave and to show if it is possible to reconciliate the different interpretations of the results given in the work by Aharonov et al.
Protective measurements which were defined by Aharonov and Vaidman in 1993 played an important role in the discussion about the interpretation of quantum mechanics. In 1999, following an early work by Englert et al., Aharonov et al. wrote an article in which they showed that protective measurements can be used to demonstrate the `surrealism' of Bohmian mechanics. Bohmian mechanics also known as pilot-wave interpretation is certainly the best-known hidden variable interpretation of quantum mechanics. It played a fundamental role in the discovery by Bell of his famous non locality theorem. Therefore, any attacks against pilot-wave interpretation is particularly interesting and instructive to learn something new about the mysterious quantum universe. It is the aim of this chapter to review the debate surrounding protective measurement and pilot-wave and to show if it is possible to reconciliate the different interpretations of the results given in the work by Aharonov et al.
The de Broglie–Bohm interpretation (Bohmian mechanics, hidden-variables theory, causal interpretation
or pilot-wave theory) is one of the interpretations of quantum mechanics which opposes
to the claim of standard interpretation on the completeness of description of the state of quantummechanical
system, that description in Bohmian mechanics is completed by defining positions of
the particles of the system i.e. hidden variables and their dynamics. These facts are the basis of motivation
for the introduction of a new theory that can describe dubious axiomatic requirements of
standard interpretation. The presented theory is deterministic and explicitly nonlocal. Originators
of Bohmian mechanics were L. de Broglie (1927.) and D. Bohm (1952.) who presented mathematically
more general and conceptual elaborate formulation. Along with the historical overview,
a note is given about the main properties of the theory, such as the issue of nonlocality and hidden
variables. The aim of this paper is to present and explain the main ideas and properties of the
theory as well as to give a systematic overview of present and historical mathematical construction
of the theory and most of all to discuss implications of de Broglie–Bohm theory on the ontology of
quantum-mechanical picture, showcasing examples of the equivalency of the description of a free
particle as a propagation of the plane wave in space or as the ensemble of the trajectories and of
the spreading of the Gaussian wave packet. The main example of the obvious conceptual clashing
of the interpretations is presented: the double-slit experiment, with a detailed examination of the
Bohmian mechanics’ predictions using presented formalism on the two double-slit experiment.
The graphs of trajectories for given examples are obtained.
Abstract David Bohm published his “Suggested Interpretation of Quantum Theory in Terms of Hidden Variables” some twenty five years after Louis de Broglie first presented his similar Pilot Wave theory of quantum mechanics. In the following 30 years what became known as the de Broglie–Bohm approach to quantum theory was to a large extent ignored within the physics community. Even David Bohm himself became somewhat disillusioned with the lack of impact of his interpretation of quantum theory and he directed his interest elsewhere. But some 27 years after Bohm had published his interpretation of quantum theory, interest was rekindled in part by new, detailed calculations that demonstrated clearly and graphically, exactly how his interpretation explained quantum phenomena in terms of well defined individual particle trajectories. These computations encompassed two-slit interference, quantum tunnelling, neutron interferometry, Wheeler’s delayed choice experiment, orbital and intrinsic angular momentum, quantum measurement and Einstein–Podolsky–Rosen nonlocal correlations for orbital angular momentum, intrinsic angular momentum and correlated particle interferometry. Since then, the acceptance of the validity of de Broglie–Bohm theory has steadily grown, as has the interest in the consequences of the approach. For my contribution to the current celebratory volume I was asked to provide a personal review specifically of this novel work within its historical context of the last quarter of the twentieth century.
The original version of the de Broglie-Bohm pilot-wave theory, also called Bohmian mechanics, attempted to treat the wave function or pilot wave as a part of the physical ontology of nature. More recent versions of the de Broglie-Bohm theory appearing in the last few decades have tried to regard the pilot wave instead as an aspect of the theory's nomology, or dynamical laws. This paper argues that neither of these views is correct, and that the de Broglie-Bohm pilot wave is best understood as a collection of latent variables in the sense of a hidden Markov model, a construct that was not available when de Broglie and Bohm originally formulated what became their pilot-wave theory. This paper also discusses several other challenges for the ontological view of the pilot wave. One such challenge is due to Foldy-Wouthuysen gauge transformations, which connect up with the Deotto-Ghirardi ambiguity in the de Broglie-Bohm theory. Another challenge arises from the freedom to carry out canonical transformations in the wave function's own notion of phase space, as defined by Strocchi and Heslot.
There are three possible interpretations of the wave function in the de Broglie-Bohm theory: taking the wave function as corresponding to a physical entity or a property of the Bohmian particles or a law. In this paper, we argue that the first interpretation is favored by an analysis of protective measurements. The de Broglie-Bohm theory is an alternative to standard quantum mechan-ics initially proposed by de Broglie (1928) and later developed by Bohm (1952). According to the theory, a complete description of a quantum system is provided by the configuration defined by the positions of its particles together with its wave function. The wave function follows the linear Schrödinger equation and never collapses. The motion of the particles, which are usually called Bohmian particles, follows the so-called guiding equation. Although the de Broglie-Bohm theory is mathematically equivalent to quantum mechanics, there is no clear consensus with regard to its physical interpretation. In particular, the interpre-
Abstract The pilot-wave theory of de Broglie and Bohm has a special place in the history of contemporary physics, being it the very first alternative formulation of quantum mechanics. As is well-known, such a framework established itself as a leading interpretation of the quantum formalism in virtue of the solutions provided to the major technical and conceptual challenges affecting the orthodox view. The de Broglie-Bohm theory in fact not only solves the famous measurement problem, one of the most cogent issues faced by standard quantum mechanics, but also it clarifies the formal structure of the latter theory as a consequence of a consistent set of principles and an precise, unambiguous ontology. This volume aims to provide the reader with a discussion of the pilot-wave perspective which is as informative, comprehensive and accessible as possible, while at the same time clarifying confusions and misunderstandings that are unfortunately still common in literature despite the long history of this theoretical framework. The book features chapters about the various perspectives on the pilot-wave theory, its extensions to relativity and quantum field theory, and its experimental applications to various branches of physics, as for instance quantum electrodynamics, quantum chemistry, and quantum engineering. Moreover, the volume includes essays on the history and philosophy of de Broglie-Bohm theory in order to delineate its developments and the vicissitudes of its pioneers, as well as to understand the scientific image of the universe it provides.
Bohmian mechanics, also referred to as the de Broglie-Bohm pilot-wave theory, represents a deterministic and nonlocal interpretation of quantum mechanics. Central to this framework is a description of quantum motion in terms of particle trajectories, whose reconciliation with relativity remains a fundamental challenge. Although relativistic guidance laws have been proposed, their predicted dynamics has remained experimentally untested. Here we use weak measurements in a single-photon interferometer to jointly reconstruct the photon energy and momentum weak values and the associated relativistic velocity field. The reconstructed average trajectories agree with theoretical predictions. Near destructive interference, the flow exhibits local reconstructed velocities exceeding the speed of light and negative values of the effective squared-mass parameter. Our results establish an experimental basis for investigating the physical meaning of quantum trajectories and their role in describing motion in relativistic spacetime.