Bohmian Mechanics (BM) posits a deterministic quantum framework where particle trajectories are guided by a wave function within a preferred Lorentz frame, a dependence starkly revealed by a novel EPR-Bohm experiment with reversible measurements. Unlike Bell tests, where BM’s predictions align with standard quantum mechanics regardless of frame, this experiment demonstrates that the Born rule’s application in the preferred frame determines whether Alice’s intermediate measurement statistics are random or deterministic. This reliance on a preferred frame—a measure-zero set in the continuum of Lorentz frames—exposes BM’s fundamental deficiency, as it is experimentally undetectable, lacks physical justification, and violates special relativity’s frame equivalence. Collapse theories, such as GRW and CSL, face analogous issues, requiring a preferred frame for non-local collapse events. This analysis highlights the inherent tension between single-world quantum theories and relativistic constraints, raising significant doubts about their viability as alternative quantum theories. The findings underscore the need for quantum interpretations that reconcile realism with relativity, suggesting that the Many-Worlds Interpretation, which provides a Lorentz-invariant framework without requiring a preferred frame, may offer a more robust and consistent foundation for quantum mechanics.
Bohmian Mechanics (BM) posits a deterministic quantum framework where particle trajectories are guided by a wave function within a preferred Lorentz frame, a dependence starkly revealed by a novel EPR-Bohm experiment with reversible measurements. Unlike Bell tests, where BM’s predictions align with standard quantum mechanics regardless of frame, this experiment demonstrates that the Born rule’s application in the preferred frame determines whether Alice’s intermediate measurement statistics are random or deterministic. This reliance on a preferred frame—a measure-zero set in the continuum of Lorentz frames—exposes BM’s fundamental deficiency, as it is experimentally undetectable, lacks physical justification, and violates special relativity’s frame equivalence. Collapse theories, such as GRW and CSL, face analogous issues, requiring a preferred frame for non-local collapse events. This analysis highlights the inherent tension between single-world quantum theories and relativistic constraints, raising significant doubts about their viability as alternative quantum theories. The findings underscore the need for quantum interpretations that reconcile realism with relativity, suggesting that the Many-Worlds Interpretation, which provides a Lorentz-invariant framework without requiring a preferred frame, may offer a more robust and consistent foundation for quantum mechanics.
A non-relativistic quantum mechanical theory is proposed that combines elements of Bohmian mechanics and of Everett's "many-worlds" interpretation. The resulting theory has the advantage of resolving known issues of both theories, as well as those of standard quantum mechanics. It has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Most importantly, the Born rule can be derived by straightforward application of the Laplacian rule, without reliance on a "quantum equilibrium hypothesis" that is crucial for Bohmian mechanics, and without reliance on a "branch weight" that is crucial for Everett-type theories. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett's approach, without being actually reducible to these. In particular, there is no "splitting of worlds", which is a typical feature of Everett-type theories. Altogether, the theory explains 1) the subjective occurrence of probabilities, 2) their quantitative value as given by the Born rule, 3) the identification of observables as self-adjoint operators on Hilbert space, and 4) the apparently random "collapse of the wavefunction" caused by the measurement, while still being an objectively deterministic theory.
Bohmian mechanics (BM) draws a picture of nature, which is completely different from that drawn by standard quantum mechanics (SQM): Particles are at any time at a definite position, and the universe evolves deterministically. Astonishingly, according to a proof by Bohm the empirical predictions of these two very different theories coincide. From the very beginning, BM has faced all kinds of criticism, most of which are either technical or philosophical. There is, however, a criticism first raised by Correggi et al. (2002) and recently strengthened by Kiukas and Werner (2010), which holds that, in spite of Bohm's proof, the predictions of BM do not agree with those of SQM in the case of local position measurements on entangled particles in a stationary state. Hence, given that SQM has been proven to be tremendously successful in the past, BM could most likely not be considered an empirically adequate theory. My aim is to resolve the conflict by showing that 1) it relies on hidden differences in the conceptual thinking, and that 2) the predictions of both theories approximately coincide if the process of measurement is adequately accounted for. My analysis makes no use of any sort of wavefunction collapse, refuting a widespread belief that an "effective collapse" is needed to reconcile BM with the predictions of SQM.
The de Broglie-Bohm interpretation of quantum mechanics (BM) has been favored as the preferred alternative to standard quantum mechanics on the ground that it allows a realist construal of the quantum world. We examine in the present work whether BM is consistent with scientific realism. Indeed, Bohmian mechanics makes strong ontological claims but accepts in principle the impossibility of generating epistemic warrants in support of its assumptions. We will argue that such a situation gives rise, at best, to an unsolvable underdetermination dilemma. This leads in turn to the following paradox: although Bohmian mechanics has frequently been invoked to reconcile quantum mechanics with realism, its status as a valid interpretation of quantum mechanics hinges nonetheless on nonevidential epistemological arguments traditionally associated with antirealism.
Lorentz invariance is considered a fundamental property of relativistic quantum theory. However, in standard quantum theory this invariance is only partially realized: while relativistic wave equations like the Dirac equation are Lorentz invariant, the collapse postulate is not. In the non-relativistic domain, alternative theories have been formulated, like Bohmian mechanics and spontaneous collapse theories, which dispense with the problematic collapse postulate. Extending these theories to the relativistic domain appears challenging, particularly with respect to implementing Lorentz invariance, mainly due to the unavoidable non-locality implied by Bell’s theorem. However, space-time theories can also trivially be formulated in a Lorentz-invariant way. If Lorentz invariance is to impose a genuine constraint on the content of a physical theory, one should aim for what can be called substantive Lorentz invariance. However, articulating a precise definition of this notion is notoriously difficult. This paper investigates two candidate criteria: Anderson’s criterion based on the identification of absolute objects, and a relativity principle for isolated subsystems. These criteria are applied to evaluate several Lorentz-invariant Bohmian models, a spontaneous collapse model, and a version of the Many-Worlds theory. With the exception of two Bohmian approaches, these models satisfy both criteria. Nevertheless, some Bohmian models that meet these conditions still do not appear to be substantively Lorentz-invariant, suggesting that the proposed criteria may not fully capture the intended concept. Nevertheless, they help clarify what aspects of relativity theory may need to be given up in passing from classical to quantum theory.
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions about objects in a multiplicity of worlds. In this logical framework, the continuum of worlds is treated in analogy to the continuum of time points; both “time” and “world” are considered as mutually independent modes of existence. The theory combines elements of Bohmian mechanics and of Everett’s many-worlds interpretation; it has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Probability as given by the Born rule emerges as a consequence of insufficient knowledge of observers about which world it is that they live in. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett’s approach, without being actually reducible to these. In particular, there is no splitting of worlds, which is a typical feature of Everett-type theories. Altogether, the theory explains (1) the subjective occurrence of probabilities, (2) their quantitative value as given by the Born rule, and (3) the apparently random “collapse of the wavefunction” caused by the measurement, while still being an objectively deterministic theory.
We formulate Bohmian mechanics (BM) such that the main objects of concern are macroscopic phenomena, while microscopic particle trajectories only play an auxiliary role. Such a formulation makes it easy to understand why BM always makes the same measurable predictions as standard quantum mechanics (QM), irrespective of the details of microscopic trajectories. Relativistic quantum field theory (QFT) is interpreted as an effective long-distance theory that at smaller distances must be replaced by some more fundamental theory. Analogy with condensed-matter physics suggests that this more fundamental theory could have a form of nonrelativistic QM, offering a simple generic resolution of an apparent conflict between BM and relativistic QFT.