Logic of Quantum Mechanics
01 Jan 1976-pp 368-370
TL;DR: “When the authors go far in the direction of the very small, quantum theory says that their forms of thought fail, so that it is questionable whether they can properly think at all”.
Abstract: “When we go far in the direction of the very small, quantum theory says that our forms of thought fail, so that it is questionable whether we can properly think at all”. These words of Bridgman express the main problem of quantum logic.
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TL;DR: The Mathematical Foundations of Quantum Mechanics as mentioned in this paper were the first to provide a rigorous mathematical formulation of quantum theory and a systematic comparison with classical mechanics so that the full ramifications of the quantum revolution could be clearly revealed.
Abstract: Classical mechanics was first envisaged by Newton, formed into a powerful tool by Euler, and brought to perfection by Lagrange and Laplace. It has served as the paradigm of science ever since. Even the great revolutions of 19th century phys icsnamely, the FaradayMaxwell electro-magnetic theory and the kinetic t h e o r y w e r e viewed as further support for the complete adequacy of the mechanistic world view. The physicist at the end of the 19th century had a coherent conceptual scheme which, in principle at least, answered all his questions about the world. The only work left to be done was the computing of the next decimal. This consensus began to unravel at the beginning of the 20th century. The work of Planck, Einstein, and Bohr simply could not be made to fit. The series of ad hoc moves by Bohr, Eherenfest, et al., now called the old quantum theory, was viewed by all as, at best, a stopgap. In the period 1925-27 a new synthesis was formed by Heisenberg, Schr6dinger, Dirac and others. This new synthesis was so successful that even today, fifty years later, physicists still teach quantum mechanics as it was formulated by these men. Nevertheless, two foundational tasks remained: that of providing a rigorous mathematical formulation of the theory, and that of providing a systematic comparison with classical mechanics so that the full ramifications of the quantum revolution could be clearly revealed. These tasks are, of course, related, and a possible fringe benefit of the second task might be the pointing of the way 'beyond quantum theory'. These tasks were taken up by von Neumann as a consequence of a seminar on the foundations of quantum mechanics conducted by Hilbert in the fall of 1926. In papers published in 1927 and in his book, The Mathemat ical Foundations of Quantum Mechanics, von Neumann provided the first completely rigorous
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TL;DR: In this article, the authors consider a reformulation of quantum mechanics in terms of information theory, where all systems are assumed to be equivalent, there is no observer-observed distinction, and the theory describes only the information that systems have about each other.
Abstract: I suggest that the common unease with taking quantum mechanics as a fundamental description of nature (the “measurement problem”) could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer-independent time. I suggest that this incorrect notion that generates the unease with quantum mechanics is the notion of “observer-independent state” of a system, or “observer-independent values of physical quantities.” I reformulate the problem of the “interpretation of quantum mechanics” as the problem of deriving the formalism from a set of simple physical postulates. I consider a reformulation of quantum mechanics in terms of information theory. All systems are assumed to be equivalent, there is no observer-observed distinction, and the theory describes only the information that systems have about each other; nevertheless, the theory is complete.
887 citations
Cites background or methods from "Logic of Quantum Mechanics"
...Experimental propositions This “deconstructivist” strategy was championed by Birkhoff and von Neumann in a seminal paper of 1936 [32]....
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...On the contrary, one of the two ‘suggested questions’ put forward by these authors in the conclusion of [32] reads: “What experimental meaning can one attach to the meet and join of two given experimental propositions?”....
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TL;DR: In this article, the authors present an exhaustive review of the recent attempt to overcome the difficulties that standard quantum mechanics meets in accounting for the measurement (or macro-objectification) problem, an attempt based on the consideration of nonlinear and stochastic modifications of the Schrodinger equation.
761 citations
Journal Article•
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Book•
26 Jul 2012TL;DR: The foundations for modelling probabilistic-dynamic systems using two aspects of quantum theory, 'contextuality' and 'quantum entanglement', are introduced, which allow cognitive phenomena to be modeled in non-reductionist ways.
Abstract: Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modelling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, 'quantum entanglement', allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision.
745 citations