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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, Sheldon Goldstein, Roderich Tumulka & 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 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 space-time points. The (...)
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  8. 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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  9. 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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  10. 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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  11. 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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  12. Mahdi Atiq, Mozafar Karamian & Mahdi Golshani (2009). A New Way for the Extension of Quantum Theory: Non-Bohmian Quantum Potentials. [REVIEW] Foundations of Physics 39 (1):33-44.
    Quantum Mechanics is a good example of a successful theory. Most of atomic phenomena are described well by quantum mechanics and cases such as Lamb Shift that are not described by quantum mechanics, are described by quantum electrodynamics. Of course, at the nuclear level, because of some complications, it is not clear that we can claim the same confidence. One way of taking these complications and corrections into account seems to be a modification of the standard quantum theory. In this (...)
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  13. Guido Bacciagaluppi (2009). Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference. Cambridge University Press.
    The 1927 Solvay conference was perhaps the most important meeting in the history of quantum theory. Contrary to popular belief, the interpretation of quantum theory was not settled at this conference, and no consensus was reached. Instead, a range of sharply conflicting views were presented and extensively discussed, including de Broglie's pilot-wave theory, Born and Heisenberg's quantum mechanics, and Schrödinger's wave mechanics. Today, there is no longer an established or dominant interpretation of quantum theory, so it is important to re-evaluate (...)
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  14. C. Baladrón (2011). Study on a Possible Darwinian Origin of Quantum Mechanics. Foundations of Physics 41 (3):389-395.
    A sketchy subquantum theory deeply influenced by Wheeler’s ideas (Am. J. Phys. 51:398–404, 1983) and by the de Broglie-Bohm interpretation (Goldstein in Stanford Encyclopedia of Philosophy, 2006) of quantum mechanics is further analyzed. In this theory a fundamental system is defined as a dual entity formed by bare matter and a methodological probabilistic classical Turing machine. The evolution of the system would be determined by three Darwinian informational regulating principles. Some progress in the derivation of the postulates of quantum mechanics (...)
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  15. Jeffrey A. Barrett (1996). Empirical Adequacy and the Availability of Reliable Records in Quantum Mechanics. Philosophy of Science 63 (1):49-64.
    In order to judge whether a theory is empirically adequate one must have epistemic access to reliable records of past measurement results that can be compared against the predictions of the theory. Some formulations of quantum mechanics fail to satisfy this condition. The standard theory without the collapse postulate is an example. Bell's reading of Everett's relative-state formulation is another. Furthermore, there are formulations of quantum mechanics that only satisfy this condition for a special class of observers, formulations whose empirical (...)
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  16. 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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  17. Jeffrey A. Barrett (2005). Relativistic Quantum Mechanics Through Frame-Dependent Constructions. Philosophy of Science 72 (5):802-813.
    This paper is concerned with the possibility and nature of relativistic hidden-variable formulations of quantum mechanics. Both ad hoc teleological constructions of spacetime maps and frame-dependent constructions of spacetime maps are considered. While frame-dependent constructions are clearly preferable, they provide neither mechanical nor causal explanations for local quantum events. Rather, the hiddenvariable dynamics used in such constructions is just a rule that helps to characterize the set of all possible spacetime maps. But while having neither mechanical nor causal explanations of (...)
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  18. A. O. Barut, M. Božić & Z. Marić (1988). Joint Probabilities of Noncommuting Operators and Incompleteness of Quantum Mechanics. Foundations of Physics 18 (10):999-1012.
    We use joint probabilities to analyze the EPR argument in the Bohm's example of spins.(1) The properties of distribution functions for two, three, or more noncommuting spin components are explicitly studied and their limitations are pointed out. Within the statistical ensemble interpretation of quantum theory (where only statements about repeated events can be made), the incompleteness of quantum theory does not follow, as the consistent use of joint probabilities shows. This does not exclude a completion of quantum mechanics, going beyond (...)
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  19. Katherine Bedard (1999). Material Objects in Bohm's Interpretation. Philosophy of Science 66 (2):221-242.
    According to the traditional presentation of Bohm's interpretation, we have immediate epistemic access to particle properties but not wavefunction properties, and mental states, pointer states, and ink patterns supervene on particle properties alone. I argue that these claims do not make physical sense, and I offer an alternative account that does.
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  20. J. S. Bell (2004). Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. Cambridge University Press.
    This book comprises all of John Bell's published and unpublished papers in the field of quantum mechanics, including two papers that appeared after the first edition was published. It also contains a preface written for the first edition, and an introduction by Alain Aspect that puts into context Bell's great contribution to the quantum philosophy debate. One of the leading expositors and interpreters of modern quantum theory, John Bell played a major role in the development of our current understanding of (...)
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  21. J. S. Bell (1992). Six Possible Worlds of Quantum Mechanics. Foundations of Physics 22 (10):1201-1215.
  22. J. S. Bell (1982). On the Impossible Pilot Wave. Foundations of Physics 12 (10):989-999.
    The strange story of the von Neumann impossibility proof is recalled, and the even stranger story of later impossibility proofs, and how the impossible was done by de Broglie and Bohm. Morals are drawn.
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  23. Js Bell (1992). 6 Possible Worlds of Quantum-Mechanics (Reprinted From Possible Worlds in Humanities Arts and Sciences, Pg 359-373, 1989. [REVIEW] Foundations of Physics 22 (10):1201-1215.
  24. Gordon Belot (2012). Quantum States for Primitive Ontologists. European Journal for Philosophy of Science 2 (1):67-83.
    Under so-called primitive ontology approaches, in fully describing the history of a quantum system, one thereby attributes interesting properties to regions of spacetime. Primitive ontology approaches, which include some varieties of Bohmian mechanics and spontaneous collapse theories, are interesting in part because they hold out the hope that it should not be too difficult to make a connection between models of quantum mechanics and descriptions of histories of ordinary macroscopic bodies. But such approaches are dualistic, positing a quantum state as (...)
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  25. Darrin W. Belousek (2003). Formalism, Ontology and Methodology in Bohmian Mechanics. Foundations of Science 8 (2):109-172.
    The relationship between mathematical formalism, physical interpretation and epistemological appraisal in the practice of physical theorizing is considered in the context of Bohmian mechanics. After laying outthe formal mathematical postulates of thetheory and recovering the historical roots ofthe present debate over the meaning of Bohmianmechanics from the early debate over themeaning of Schrödinger's wave mechanics,several contemporary interpretations of Bohmianmechanics in the literature are discussed andcritiqued with respect to the aim of causalexplanation and an alternative interpretationis proposed. Throughout, the over-arching aimis (...)
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  26. D. J. Bohm & B. J. Hiley (1982). The de Broglie Pilot Wave Theory and the Further Development of New Insights Arising Out of It. Foundations of Physics 12 (10):1001-1016.
    We briefly review the history of de Broglie's notion of the “double solution” and of the ideas which developed from this. We then go on to an extension of these ideas to the many-body system, and bring out the nonlocality implied in such an extension. Finally, we summarize further developments that have stemmed from de Broglie's suggestions.
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  27. D. Bohm & B. J. Hiley (1984). Measurement Understood Through the Quantum Potential Approach. Foundations of Physics 14 (3):255-274.
  28. 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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  29. David Bohm (1996). On the Role of Hidden Variables in the Fundamental Structure of Physics. Foundations of Physics 26 (6):719-786.
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  30. David Bohm (1993). The Undivided Universe: An Ontological Interpretation of Quantum Theory. Routledge.
    In the The Undivided Universe, David Bohn and Basil Hiley present a radically different approach to quantum theory.
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  31. 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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  32. David Bohm (1980/2002). Wholeness and the Implicate Order. Routledge.
    In this classic work David Bohm, writing clearly and without technical jargon, develops a theory of quantum physics which treats the totality of existence as an unbroken whole.
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  33. David Bohm (1973). Quantum Theory as an Indication of a New Order in Physics. B. Implicate and Explicate Order in Physical Law. Foundations of Physics 3 (2):139-168.
    In this paper, we inquire further into the question of the emergence of new orders in physics, first raised in an earlier paper. In this inquiry, we are led to suggest that the quantum theory indicates the need for yet another new order, which we call “enfolded” or “implicate.” One of the most striking examples of the implicate order is to be seen by considering the function of the hologram, which clearly reveals how a total content (in principle extending over (...)
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  34. 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.
  35. David Bohm (1957/1999). Causality and Chance in Modern Physics. University of Pennsylvania Press.
    CHAPTER ONE Causality and Chance in Natural Law. INTRODUCTION IN nature nothing remains constant. Everything is in a perpetual state of transformation, ...
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  36. 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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  37. María C. Boscá (2013). Some Observations Upon “Realistic” Trajectories in Bohmian Quantum Mechanics. Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 28 (1):45-60.
    Experimental situations in which we observe quantum effects that deviate from the intuitive expectations of the classical world call for an interdisciplinary discussion, and one fundamental issue to be considered is the compatibility between the description of phenomena and the assumption of an objective reality. This paper discusses the ontological interpretation of Bohmian quantum mechanics, focusing on the use of the term “trajectory” and the difficulties associated with its connection to a “real” (objective) trajectory. My conclusion is that the intended (...)
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  38. Gary E. Bowman (2005). On the Classical Limit in Bohm's Theory. Foundations of Physics 35 (4):605-625.
    The standard means of seeking the classical limit in Bohmian mechanics is through the imposition of vanishing quantum force and quantum potential for pure states. We argue that this approach fails, and that the Bohmian classical limit can be realized only by combining narrow wave packets, mixed states, and environmental decoherence.
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  39. Mirjana Božić & Zvonko Marić (1995). Compatible Statistical Interpretation of a Wave Packet. Foundations of Physics 25 (1):159-173.
    A compatible statistical interpretation of a wave packet is proposed. De Broglian probabilities which unite wave and particle features of quantons are evaluated for free wave packets and Jor a superposition of wave packets. The obtained expressions provide a very plausible and physically appealing explanation of coherence in apparently incoherent beams and of the characteristic modulation of the momentum distribution, found recently in neutron interferometry combined with spectral filtering. Certain conclusions about dualism and objectivity in quantum domain are also derived.
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  40. 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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  41. Jeremy Butterfield, On Hamilton-Jacobi Theory as a Classical Root of Quantum Theory.
    This paper gives a technically elementary treatment of some aspects of <span class='Hi'>Hamilton</span>-Jacobi theory, especially in relation to the calculus of variations. The second half of the paper describes the application to geometric optics, the optico-mechanical analogy and the transition to quantum mechanics. Finally, I report recent work of Holland providing a Hamiltonian formulation of the pilot-wave theory.
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  42. 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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  43. 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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  44. Michael E. Cuffaro (2014). Review Of: Christopher G. Timpson, Quantum Information Theory and the Foundations of Quantum Mechanics. [REVIEW] Philosophy of Science 81 (4):681-684,.
  45. 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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  46. James T. Cushing, Arthur Fine & Sheldon Goldstein (1996). Bohmian Mechanics and Quantum Theory: An Appraisal. Springer.
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  47. M. Daumer & S. Goldstein, On the Flux-Across-Surfaces Theorem.
    The quantum probability flux of a particle integrated over time and a distant surface gives the probability for the particle crossing that surface at some time. We prove the free fluxacross-surfaces theorem, which was conjectured by Combes, Newton and Shtokhamer [1], and which relates the integrated quantum flux to the usual quantum mechanical formula for the cross section. The integrated quantum flux is equal to the probability of outward crossings of surfaces by Bohmian trajectories in the scattering regime.
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  48. 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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  49. J. Acacio de Barros, J. P. R. F. de Mendonça & N. Pinto-Neto (2007). Realism in Energy Transition Processes: An Example From Bohmian Quantum Mechanics. Synthese 154 (3):349-370.
    In this paper we study in details a system of two weakly coupled harmonic oscillators from the point of view of Bohm’s interpretation of quantum mechanics. This system may be viewed as a simple model for the interaction between a photon and a photodetector. We obtain exact solutions for the general case. We then compute approximate solutions for the case where one oscillator is initially in its first excited state (a single photon) reaching the other oscillator in its ground state (...)
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  50. Michael Dickson (1996). Antidote or Theory? Studies in History and Philosophy of Science Part B 27 (2):229-238.
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