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Sozzo, A. Tang, A. Moro, S. Sozzo, Z. Aerts, S. Garola, S. Sozzo, J. This book is a revised and expanded edition of …. Book Dispositionalism Meincke, A. Book Quanta and Mind de Barros, J. In it, an international group of contributors focus on …. Ed This volume offers selected papers exploring issues arising from scientific discovery in the social sciences. It features a range of disciplines including behavioural sciences, ….
Ed This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations.
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For at least one century, the study of logical form has been widely adopted as a …. Bohmian mechanics is not simply classical mechanics with an additional force term. In Bohmian mechanics the velocities are not independent of positions, as they are classically, but are constrained by the guiding equation. Arguably, the most serious flaw in the quantum potential formulation of Bohmian mechanics is that it gives a completely false impression of the lengths to which we must go in order to convert orthodox quantum theory into something more rational. It should be clear that this view is inappropriate.
After all, the quantum potential need not even be mentioned in the formulation of Bohmian mechanics, and it in any case merely reflects the wave function, which Bohmian mechanics shares with orthodox quantum theory. In reality it contains the only mystery. Feynman How does it really work?
What machinery is actually producing this thing? Nobody knows any machinery. Nobody can give you a deeper explanation of this phenomenon than I have given; that is, a description of it. But Bohmian mechanics is just such a deeper explanation. It resolves in a rather straightforward manner the dilemma of the appearance of both particle and wave properties in one and the same phenomenon: Bohmian mechanics is a theory of motion describing a particle or particles guided by a wave. Here we have a family of Bohmian trajectories for the two-slit experiment. Figure 1: An ensemble of trajectories for the two-slit experiment, uniform in the slits.
While each trajectory passes through only one slit, the wave passes through both; the interference profile that therefore develops in the wave generates a similar pattern in the trajectories guided by the wave. Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle?
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And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes.
And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored. Bell  c: Perhaps the most puzzling aspect of the two-slit experiment is the following: If, by any means whatsoever, it is possible to determine the slit through which the particle passes, the interference pattern will be destroyed. This dramatic effect of observation is, in fact, a simple consequence of Bohmian mechanics.
To see this, one must consider the meaning of determining the slit through which the particle passes. This must involve interaction with another system that the Bohmian mechanical analysis must include. The destruction of interference is related, naturally enough, to the Bohmian mechanical analysis of quantum measurement Bohm For an accessible presentation of the behavior of Bohmian trajectories in scattering and tunneling phenomena, see Norsen The measurement problem is the most commonly cited of the conceptual difficulties that plague quantum mechanics.
Indeed, for many physicists the measurement problem is not merely one conceptual difficulty of quantum mechanics; it is the conceptual difficulty. The problem is as follows. Suppose that the wave function of any individual system provides a complete description of that system. In this description of the after-measurement situation it is difficult to discern the actual result of the measurement—e. But the whole point of quantum theory, and the reason we should believe in it, is that it is supposed to provide a compelling, or at least an efficient, account of our observations, that is, of the outcomes of measurements.
In short, the measurement problem is this: Quantum theory implies that measurements typically fail to have outcomes of the sort the theory was created to explain. In contrast, if we, like Einstein, regard the description provided by the wave function as incomplete, the measurement problem vanishes: There is no measurement problem with a theory or interpretation in which, as in Bohmian mechanics, the description of the after-measurement situation includes, in addition to the wave function, at least the values of the variables that register the result.
In Bohmian mechanics pointers always point. Often, the measurement problem is expressed a little differently. However, the objection continues, textbook quantum theory does not explain how to reconcile these two apparently incompatible rules.
Dr Sandro Sozzo
Hence the collapse rule. But it is difficult to take seriously the idea that different laws than those governing all other interactions should govern those interactions between system and apparatus that we happen to call measurements. Hence the apparent incompatibility of the two rules. The second formulation of the measurement problem, though basically equivalent to the first, raises an important question: Can Bohmian mechanics itself reconcile these two dynamical rules? What would nowadays be called effects of decoherence, which interaction with the environment air molecules, cosmic rays, internal microscopic degrees of freedom, etc.
This overlap refers to the configuration space of the very large system that includes all systems with which the original system and apparatus come into interaction. But without such overlap that component all by itself generates to a high degree of accuracy the future evolution of the configuration of the system and apparatus. Many proponents of orthodox quantum theory believe that decoherence somehow resolves the measurement problem itself.
It is not easy to understand this belief. In the first formulation of the measurement problem, nothing prevents us from including in the apparatus all sources of decoherence.
Related Mechanics: Classical and Quantum (International Series in Natural Philosophy, Volume 82)
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