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Register a new userIs Bohmian Mechanics an empirically adequate theory?
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Added by
Kim Joris Bostr\\\"om
Publication date
2015
fields
Physics
and research's language is
English
Authors
Kim Joris Bostrom
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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 Bohms 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.
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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), irrespectively 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 non-relativistic QM, offering a simple generic resolution of an apparent conflict between BM and relativistic QFT.
It is shown that quantum entanglement is the only force able to maintain the fourth state of matter, possessing fixed shape at an arbitrary volume. Accordingly, a new relativistic Schrodinger equation is derived and transformed further to the relativistic Bohmian mechanics via the Madelung transformation. Three dissipative models are proposed as extensions of the quantum relativistic Hamilton-Jacobi equation. The corresponding dispersion relations are obtained.
Bohmian mechanics is a causal interpretation of quantum mechanics in which particles describe trajectories guided by the wave function. The dynamics in the vicinity of nodes of the wave function, usually called vortices, is regular if they are at rest. However, vortices generically move during time evolution of the system. We show that this movement is the origin of chaotic behavior of quantum trajectories. As an example, our general result is illustrated numerically in the two-dimensional isotropic harmonic oscillator.
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Irreversible processes are frequently adopted to account for the entropy increase in classical thermodynamics. However, the corresponding physical origins are not always clear, e.g. in a free expansion process, a typical model in textbooks. In this letter, we study the entropy change during free expansion for a particle with the thermal de Broglie wavelength ($lambda_{T}$) in a one-dimensional square trap with size $L$. By solely including quantum dephasing as an irreversible process, we recover classical result of entropy increase in the classical region ($Lgglambda_{T}$), while predict prominent discrepancies in the quantum region ($Llllambda_{T}$) because of non-equilibrium feature of trapped atoms after expansion. It is interesting to notice that the dephasing, though absent in classical system, is critical to clarify mysteries in classical thermodynamics.
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