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Summary Bohmian mechanics is an alternative to quantum mechanics that is popular amongst philosophers of physics. In the non-relativistic n-particle domain, it is empirically equivalent to quantum mechanics despite being fully deterministic. The ontology of the theory includes a specification of 'local beables' - for example, corpuscles with precise positions - along with a guidance equation, with the structure of the quantum state, which determines the evolution of the beables. Recent work has extended the Bohmian treatment to quantum field theories.
Key works The approach is often called 'de Broglie-Bohm theory' after the early contribution of Louis deBroglie to the 1927 Solvay conference. It was rediscovered and set out in detail by David Bohm (Bohm 1952). It was again rediscovered, and ably championed within the foundations of physics community, by Bell 2004
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  1. David Albert & Barry Loewer (1989). Symposiums Papers: Two No-Collapse Interpretations of Quantum Theory. Noûs 23 (2):169-186.
  2. Valia Allori, Sheldon Goldstein, Roderich Tumulka & and Nino Zanghì (2008). On the Common Structure of Bohmian Mechanics and the Ghirardi–Rimini–Weber Theory: Dedicated to Giancarlo Ghirardi on the Occasion of His 70th Birthday. British Journal for the Philosophy of Science 59 (3):353-389.
    Bohmian mechanics and the Ghirardi–Rimini–Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about ‘matter’ moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of (...)
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  3. Valia Allori (2013). On the Metaphysics of Quantum Mechanics. In Soazig Lebihan (ed.), Precis de la Philosophie de la Physique. Vuibert.
    What is quantum mechanics about? The most natural way to interpret quantum mechanics realistically as a theory about the world might seem to be what is called wave function ontology: the view according to which the wave function mathematically represents in a complete way fundamentally all there is in the world. Erwin Schroedinger was one of the first proponents of such a view, but he dismissed it after he realized it led to macroscopic superpositions (if the wave function evolves in (...)
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  4. Valia Allori (2013). Primitive Ontology and the Structure of Fundamental Physical Theories. In Alyssa Ney & David Z. Albert (eds.), The Wave Function: Essays in the Metaphysics of Quantum Mechanics. Oxford University Press.
    For a long time it was believed that it was impossible to be realist about quantum mechanics. It took quite a while for the researchers in the foundations of physics, beginning with John Stuart Bell [Bell 1987], to convince others that such an alleged impossibility had no foundation. Nowadays there are several quantum theories that can be interpreted realistically, among which Bohmian mechanics, the GRW theory, and the many-worlds theory. The debate, though, is far from being over: in what respect (...)
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  5. Valia Allori, Detlef Duerr, Nino Zanghi & Sheldon Goldstein (2002). Seven Steps Toward the Classical World. Journal of Optics B 4:482–488.
    Classical physics is about real objects, like apples falling from trees, whose motion is governed by Newtonian laws. In standard quantum mechanics only the wave function or the results of measurements exist, and to answer the question of how the classical world can be part of the quantum world is a rather formidable task. However, this is not the case for Bohmian mechanics, which, like classical mechanics, is a theory about real objects. In Bohmian terms, the problem of the classical (...)
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  6. Valia Allori, Sheldon Goldstein, Roderich Tumulka & Nino Zanghi (2008). On the Common Structure of Bohmian Mechanics and the Ghirardi-Rimini-Weber Theory. British Journal for the Philosophy of Science 59 (3):353 - 389.
    Bohmian mechanics and the Ghirardi-Rimini-Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about 'matter' moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of (...)
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  7. Valia Allori & Nino Zanghi (2008). On the Classical Limit of Quantum Mechanics. Foundations of Physics 10.1007/S10701-008-9259-4 39 (1):20-32.
    Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the ¯h → 0 asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains in its own structure the possibility of describing (...)
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  8. Valia Allori & Nino Zanghi (2004). What is Bohmian Mechanics. International Journal of Theoretical Physics 43:1743-1755.
    Bohmian mechanics is a quantum theory with a clear ontology. To make clear what we mean by this, we shall proceed by recalling first what are the problems of quantum mechanics. We shall then briefly sketch the basics of Bohmian mechanics and indicate how Bohmian mechanics solves these problems and clarifies the status and the role of of the quantum formalism.
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  9. D. M. Appleby (1999). Bohmian Trajectories Post-Decoherence. Foundations of Physics 29 (12):1885-1916.
    The role of the environment in producing the correct classical limit in the Bohm interpretation of quantum mechanics is investigated, in the context of a model of quantum Brownian motion. One of the effects of the interaction is to produce a rapid approximate diagonalisation of the reduced density matrix in the position representation. This effect is, by itself, insufficient to produce generically quasi-classical behaviour of the Bohmian trajectory. However, it is shown that, if the system particle is initially in an (...)
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  10. D. M. Appleby (1999). Generic Bohmian Trajectories of an Isolated Particle. Foundations of Physics 29 (12):1863-1883.
    The generic Bohmian trajectories are calculated for an isolated particle in an approximate energy eigenstate, for an arbitrary one-dimensional potential well. It is shown that the necessary and sufficient condition for there to be a negligible probability of the trajectory deviating significantly from the classical trajectory at any stage in the motion is that the state be a narrowly localised wave packet. The properties of the Bohmian trajectories are compared with those in the interpretation recently proposed by García de Polavieja. (...)
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  11. Guido Bacciagaluppi (2009). Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference. Cambridge University Press.
    This book will be of interest to graduate students and researchers in physics and in the history and philosophy of quantum theory.
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  12. Jeffrey A. Barrett (1995). The Distribution Postulate in Bohm's Theory. Topoi 14 (1):45-54.
    On Bohm''s formulation of quantum mechanics particles always have determinate positions and follow continuous trajectories. Bohm''s theory, however, requires a postulate that says that particles are initially distributed in a special way: particles are randomly distributed so that the probability of their positions being represented by a point in any regionR in configuration space is equal to the square of the wave-function integrated overR. If the distribution postulate were false, then the theory would generally fail to make the right statistical (...)
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  13. David Bohm (2003). The Essential David Bohm. Routledge.
    There are few scientists of the twentieth century whose life's work has created more excitement and controversy than that of physicist David Bohm (1917-1992). Exploring the philosophical implication of both physics and consciousness, Bohm's penchant for questioning scientific and social orthodoxy was the expression of a rare and maverick intelligence. For Bohm, the world of matter and the experience of consciousness were two aspects of a more fundamental process he called the implicate order. Without a working sensibility of what this (...)
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  14. David Bohm (1985). Unfolding Meaning: A Weekend of Dialogue with David Bohm. Foundation House.
    David Bohm argues that our fragmented, mechanistic notion of order permeates not only modern science and technology today, but also has profound implications ...
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  15. David Bohm (1962). Classical and Non-Classical Concepts in the Quantum Theory. An Answer to Heisenberg's Physics and Philosophy. British Journal for the Philosophy of Science 12 (48):265-280.
  16. David Bohm (1952). A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables, I and II. Physical Review (85):166-193.
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  17. Harvey Brown & David Wallace (2005). Solving the Measurement Problem: De Broglie-Bohm Loses Out to Everett. [REVIEW] Foundations of Physics 35 (4):517-540.
    The quantum theory of de Broglie and Bohm solves the measurement problem, but the hypothetical corpuscles play no role in the argument. The solution finds a more natural home in the Everett interpretation.
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  18. Craig Callender, Discussion: The Redundancy Argument Against Bohm's Theory.
    Advocates of the Everett interpretation of quantum mechanics have long claimed that other interpretations needlessly invoke "new physics" to solve the measurement problem. Call the argument fashioned that gives voice to this claim the Redundancy Argument, or ’Redundancy’ for short. Originating right in Everett’s doctoral thesis, Redundancy has recently enjoyed much attention, having been advanced and developed by a number of commentators, as well as criticized by a few others.[1] Although versions of this argument can target collapse theories of quantum (...)
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  19. Craig Callender (2007). The Emergence and Interpretation of Probability in Bohmian Mechanics. Studies in History and Philosophy of Science Part B 38 (2):351-370.
    A persistent question about the deBroglie–Bohm interpretation of quantum mechanics concerns the understanding of Born’s rule in the theory. Where do the quantum mechanical probabilities come from? How are they to be interpreted? These are the problems of emergence and interpretation. In more than 50 years no consensus regarding the answers has been achieved. Indeed, mirroring the foundational disputes in statistical mechanics, the answers to each question are surprisingly diverse. This paper is an opinionated survey of this literature. While acknowledging (...)
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  20. James T. Cushing (1995). Quantum Tunneling Times: A Crucial Test for the Causal Program? [REVIEW] Foundations of Physics 25 (2):269-280.
    It is generally believed that Bohm's version of quantum mechanics is observationally equivalent to standard quantum mechanics. A more careful statement is that the two theories will always make the same predictions for any question or problem that is well posed in both interpretations. The transit time of a “particle” between two points in space is not necessarily well defined in standard quantum mechanics, whereas it is in Bohm's theory since there is always a particle following a definite trajectory. For (...)
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  21. James T. Cushing, Arthur Fine & Sheldon Goldstein (1996). Bohmian Mechanics and Quantum Theory: An Appraisal. Springer.
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  22. Martin Daumer, Detlef Dürr, Sheldon Goldstein & Nino Zanghì (1996). Naive Realism About Operators. Erkenntnis 45 (2-3):379 - 397.
    A source of much difficulty and confusion in the interpretation of quantum mechanics is a naive realism about operators. By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to the all too casual talk about measuring operators that occurs when the subject is quantum mechanics. Without a specification of what should be meant by measuring a quantum observable, such an expression can have no clear meaning. A definite specification is provided by (...)
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  23. Michael Dickson (1996). Antidote or Theory? Studies in History and Philosophy of Science Part B 27 (2):229-238.
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  24. W. Michael Dickson (1996). Determinism and Locality in Quantum Systems. Synthese 107 (1):55 - 82.
    Models of the EPR-Bohm experiment usually consider just two times, an initial time, and the time of measurement. Within such analyses, it has been argued that locality is equivalent to determinism, given the strict correlations of quantum mechanics. However, an analysis based on such models is only a preliminary to an analysis based on a complete dynamical model. The latter analysis is carried out, and it is shown that, given certain definitions of locality and determinism for completely dynamical models, locality (...)
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  25. Mauro Dorato & Federico Laudisa (forthcoming). Realism and Instrumentalism About the Wave Function. How Should We Choose? In Shao Gan (ed.), Protective Measurements and Quantum Reality: Toward a New Understanding of Quantum Mechanics. CUP.
    The main claim of the paper is that one can be ‘realist’ (in some sense) about quantum mechanics without requiring any form of realism about the wave function. We begin by discussing various forms of realism about the wave function, namely Albert’s configuration-space realism, Dürr Zanghi and Goldstein’s nomological realism about Ψ, Esfeld’s dispositional reading of Ψ Pusey Barrett and Rudolph’s realism about the quantum state. By discussing the articulation of these four positions, and their interrelation, we conclude that instrumentalism (...)
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  26. Cian Dorr, Finding Ordinary Objects in Some Quantum Worlds.
    cation we have in mind is that of formulating the laws of a classical meration space to the complex numbers. But what is it for such a function chanics of point-particles living in Newtonian absolute space, one espe-.
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  27. D. Durr, S. Goldstein & N. Zanghi (1995). Quantum Physics Without Quantum Philosophy. Studies in History and Philosophy of Science Part B 26 (2):137-149.
    Quantum philosophy, a peculiar twentieth-century malady, is responsible for most of the conceptual muddle plaguing the foundations of quantum physics. When this philosophy is eschewed, one naturally arrives at Bohmian mechanics, which is what emerges from Schrodinger's equation for a nonrelativistic system of particles when we merely insist that 'particles' means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. The quantum formalism emerges when measurement situations are (...)
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  28. Detlef Dürr, Sheldon Goldstein & Nino Zanghí (1993). A Global Equilibrium as the Foundation of Quantum Randomness. Foundations of Physics 23 (5):721-738.
    We analyze the origin of quantum randomness within the framework of a completely deterministic theory of particle motion—Bohmian mechanics. We show that a universe governed by this mechanics evolves in such a way as to give rise to the appearance of randomness, with empirical distributions in agreement with the predictions of the quantum formalism. Crucial ingredients in our analysis are the concept of the effective wave function of a subsystem and that of a random system. The latter is a notion (...)
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  29. Shan Gao, Protective Measurement and the de Broglie-Bohm Theory.
    We investigate the implications of protective measurement for de Broglie-Bohm theory, mainly focusing on the interpretation of the wave function. It has been argued that the de Broglie-Bohm theory gives the same predictions as quantum mechanics by means of quantum equilibrium hypothesis. However, this equivalence is based on the premise that the wave function, regarded as a Ψ-field, has no mass and charge density distributions. But this premise turns out to be wrong according to protective measurement; a charged quantum system (...)
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  30. Shan Gao, Why the de Broglie-Bohm Theory is Probably Wrong.
    We investigate the validity of the field explanation of the wave function by analyzing the mass and charge density distributions of a quantum system. It is argued that 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. This is also a consequence of protective measurement. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously (...)
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  31. Sheldon Goldstein, On the Weak Measurement of Velocity in Bohmian Mechanics.
    In a recent article [1], Wiseman has proposed the use of so-called weak measurements for the determination of the velocity of a quantum particle at a given position, and has shown that according to quantum mechanics the result of such a procedure is the Bohmian velocity of the particle. Although Bohmian mechanics is empirically equivalent to variants based on velocity formulas different from the Bohmian one, and although it has been proven that the velocity in Bohmian mechanics is not measurable, (...)
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  32. Sheldon Goldstein, Bohmian Trajectories as the Foundation of Quantum Mechanics.
    Bohmian trajectories have been used for various purposes, including the numerical simulation of the time-dependent Schr¨ odinger equation and the visualization of time-dependent wave functions. We review the purpose they were invented for: to serve as the foundation of quantum mechanics, i.e., to explain quantum mechanics in terms of a theory that is free of paradoxes and allows an understanding that is as clear as that of classical mechanics. Indeed, they succeed in serving that purpose in the context of a (...)
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  33. Sheldon Goldstein (2010). Bohmian Mechanics and Quantum Information. Foundations of Physics 40 (4):335-355.
    Many recent results suggest that quantum theory is about information, and that quantum theory is best understood as arising from principles concerning information and information processing. At the same time, by far the simplest version of quantum mechanics, Bohmian mechanics, is concerned, not with information but with the behavior of an objective microscopic reality given by particles and their positions. What I would like to do here is to examine whether, and to what extent, the importance of information, observation, and (...)
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  34. Sheldon Goldstein, Bohmian Mechanics. Stanford Encyclopedia of Philosophy.
    Bohmian mechanics, which is also called the de Broglie-Bohm theory, the pilot-wave model, and the causal interpretation of quantum mechanics, is a version of quantum theory discovered by Louis de Broglie in 1927 and rediscovered by David Bohm in 1952. It is the simplest example of what is often called a hidden variables interpretation of quantum mechanics. In Bohmian mechanics a system of particles is described in part by its wave function, evolving, as usual, according to Schrödinger's equation. However, the (...)
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  35. Sheldon Goldstein (1996). Bohmian Mechanics and the Quantum Revolution. [REVIEW] Synthese 107 (1):145 - 165.
    When I was young I was fascinated by the quantum revolution: the transition from classical definiteness and determinism to quantum indeterminacy and uncertainty, from classical laws that are indifferent, if not hostile, to the human presence, to quantum laws that fundamentally depend upon an observer for their very meaning. I was intrigued by the radical subjectivity, as expressed by Heisenberg’s assertion [3] that “The idea of an objective real world whose smallest parts exist objectively in the same sense as stones (...)
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  36. Sheldon Goldstein, James Taylor, Roderich Tumulka & Nino Zanghi (2005). Are All Particles Real? Studies in History and Philosophy of Science Part B 36 (1):103-112.
    In Bohmian mechanics elementary particles exist objectively, as point particles moving according to a law determined by a wavefunction. In this context, questions as to whether the particles of a certain species are real---questions such as, Do photons exist? Electrons? Or just the quarks?---have a clear meaning. We explain that, whatever the answer, there is a corresponding Bohm-type theory, and no experiment can ever decide between these theories. Another question that has a clear meaning is whether particles are intrinsically distinguishable, (...)
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  37. Amit Hagar (2012). Veiled Realism? Review of B d'Espagnat's On Physics and Philosophy. [REVIEW] Physics in Perspective (x).
  38. Michael Huemer, Quantum Mechanics for Philosophers.
    You pass an electron through an inhomogeneous magnetic field (this is produced by a type of magnet, but don’t worry about the details). The field causes the electron to swerve. It is found that all electrons swerve by the same amount, and half of them swerve up, while the other half swerve down. See a video illustration of this.
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  39. Nick Huggett & Tiziana Vistarini, Entanglement Exchange and Bohmian Mechanics.
    This paper analyses the phenomenon of entanglement exchange in Bohm's pilot wave interpretation of quantum mechanics. The interesting feature of the phenomenon is that systems become entangled without causal interaction; hence it is a useful situation for investigating the unique nature of interaction in Bohmian mechanics. The first two sections introduce, respectively, entanglement exchange in the standard interpretation of quantum mechanics, and the basic principles of Bohmian mechanics. The next section shows that the Bohmian interpretation makes the same experimental predictions (...)
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  40. Moncy V. John & Kiran Mathew (2013). Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories. Foundations of Physics 43 (7):859-871.
    This paper examines the nature of classical correspondence in the case of coherent states at the level of quantum trajectories. We first show that for a harmonic oscillator, the coherent state complex quantum trajectories and the complex classical trajectories are identical to each other. This congruence in the complex plane, not restricted to high quantum numbers alone, illustrates that the harmonic oscillator in a coherent state executes classical motion. The quantum trajectories we consider are those conceived in a modified de (...)
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  41. Vassilios Karakostas & Michael Dickson (1995). Decoherence in Unorthodox Formulations of Quantum Mechanics. Synthese 102 (1):61 - 97.
    The conceptual structure of orthodox quantum mechanics has not provided a fully satisfactory and coherent description of natural phenomena. With particular attention to the measurement problem, we review and investigate two unorthodox formulations. First, there is the model advanced by GRWP, a stochastic modification of the standard Schrödinger dynamics admitting statevector reduction as a real physical process. Second, there is the ontological interpretation of Bohm, a causal reformulation of the usual theory admitting no collapse of the statevector. Within these two (...)
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  42. Ruth E. Kastner (2013). De Broglie Waves as the “Bridge of Becoming” Between Quantum Theory and Relativity. Foundations of Science 18 (1):1-9.
    It is hypothesized that de Broglie’s ‘matter waves’ provide a dynamical basis for Minkowski spacetime in an antisubstantivalist or relational account. The relativity of simultaneity is seen as an effect of the de Broglie oscillation together with a basic relativity postulate, while the dispersion relation from finite rest mass gives rise to the differentiation of spatial and temporal axes. Thus spacetime is seen as not fundamental, but rather as emergent from the quantum level. A result by Solov’ev which demonstrates that (...)
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  43. Frederick M. Kronz (1998). Bohm's Ontological Interpretation and its Relations to Three Formulations of Quantum Mechanics. Synthese 117 (1):31-52.
    The standard mathematical formulation of quantum mechanics is specified. Bohm's ontological interpretation of quantum mechanics is then shown to be incapable of providing a suitable interpretation of that formulation. It is also shown that Bohm's interpretation may well be viable for two alternative mathematical formulations of quantum mechanics, meaning that the negative result is a significant though not a devastating criticism of Bohm's interpretation. A preliminary case is made for preferring one alternative formulation over the other.
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  44. C. R. Leavens (2005). Weak Measurements From the Point of View of Bohmian Mechanics. Foundations of Physics 35 (3):469-491.
    The theory of weak measurements developed by Aharonov and coworkers has been applied by them and others to several interesting problems in which the system of interest is both pre- and post-selected. When the probability of successful post-selection is very small the prediction for the weak value of the measured quantity is often “bizarre” and sometimes controversial, lying outside the range of possibility for a classical system or for a quantum system in the absence of post-selection (e.g. negative kinetic energies (...)
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  45. E. Levy, A. Chernavska & R. I. G. Hughes (1977). Book Review:The Interpretation of Quantum Mechanics Jeffrey Bub. [REVIEW] Philosophy of Science 44 (2):332-.
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  46. Peter J. Lewis (2007). Empty Waves in Bohmian Quantum Mechanics. British Journal for the Philosophy of Science 58 (4):787 - 803.
    There is a recurring line of argument in the literature to the effect that Bohm's theory fails to solve the measurement problem. I show that this argument fails in all its variants. Hence Bohm's theory, whatever its drawbacks, at least succeeds in solving the measurement problem. I briefly discuss a similar argument that has been raised against the GRW theory.
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  47. Steve Mackman & Euan Squires (1995). Lorentz Invariance and the Retarded Bohm Model. Foundations of Physics 25 (2):391-397.
    We show how a recently introduced retarded version of the Bohm Model evades the Hardy proof that hidden-variable models must violate Lorentz Invariance. We also discuss a possible test of such models.
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  48. O. Maroney & B. J. Hiley (1999). Quantum State Teleportation Understood Through the Bohm Interpretation. Foundations of Physics 29 (9):1403-1415.
    Quantum state teleportation has focused attention on the role of quantum information. Here we examine quantum teleportation through the Bohm interpretation. This interpretation introduced the notion of active information and we show that it is this information that is exchanged during teleportation. We discuss the relation between our notion of active information and the notion of quantum information introduced by Schumacher.
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  49. Hrvoje Nikolić (2009). Boson-Fermion Unification, Superstrings, and Bohmian Mechanics. Foundations of Physics 39 (10):1109-1138.
    Bosonic and fermionic particle currents can be introduced in a more unified way, with the cost of introducing a preferred spacetime foliation. Such a unified treatment of bosons and fermions naturally emerges from an analogous superstring current, showing that the preferred spacetime foliation appears only at the level of effective field theory, not at the fundamental superstring level. The existence of the preferred spacetime foliation allows an objective definition of particles associated with quantum field theory in curved spacetime. Such an (...)
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  50. Hrvoje Nikolić (2008). Probability in Relativistic Bohmian Mechanics of Particles and Strings. Foundations of Physics 38 (9):869-881.
    Even though the Bohmian trajectories given by integral curves of the conserved Klein-Gordon current may involve motions backwards in time, the natural relativistic probability density of particle positions is well-defined. The Bohmian theory predicts subtle deviations from the statistical predictions of more conventional formulations of quantum theory, but it seems that no present experiment rules this theory out. The generalization to the case of many particles or strings is straightforward, provided that a preferred foliation of spacetime is given.
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