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New Light on the Objective Indefiniteness or Literal Interpretation of Quantum Mechanics
TL;DR: In this paper, the authors show that the mathematics of QM is the math of indefiniteness and thus, literally and realistically interpreted, it describes an objectively indefinite reality at the quantum level, which corrects the historical wrong turn of seeing QM as "wave mechanics" rather than the mechanics of particles with indefinite/definite properties.
Abstract: The development of the new logic of partitions (= equivalence relations) dual to the usual Boolean logic of subsets, and its quantitative version as the new logical theory of information provide the basic mathematical concepts to describe distinctions/indistinctions, definiteness/indefiniteness, and distinguishability/indistinguishability. They throw some new light on the objective indefiniteness or literal interpretation of quantum mechanics (QM) advocated by Abner Shimony. This paper shows how the mathematics of QM is the math of indefiniteness and thus, literally and realistically interpreted, it describes an objectively indefinite reality at the quantum level. In particular, the mathematics of wave propagation is shown to also be the math of the evolution of indefinite states that do not change the degree of indistinctness between states. This corrects the historical wrong turn of seeing QM as "wave mechanics" rather than the mechanics of particles with indefinite/definite properties. For example, the so-called "wave-particle duality' for particles is the juxtaposition of the evolution of a particle having an indefinite position ("wave-like" behavior) with a particle having a definite position (particle-like behavior).
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TL;DR: The uncertainty principle was introduced by Heisenberg as mentioned in this paper, who argued that by the very act of measuring a variable factor, it disqualifies the evidence by virtue of altering the thing measured.
Abstract: I do not recall having met an educated person who claims to know less about contemporary physics than I do. Nevertheless, it has been my contention that as physicians living in the early part of the second half of the twentieth century we have very strong obligations to understand as much as we can of the world we live in. Perhaps if this could be done on a large scale events might be bent somewhat to wise purposes rather than just letting them happen. The introduction of the uncertainty principle, for which Heisenberg received the Nobel Prize, may be of some comfort in its oversimplified form as applied to research in biology. As I understand it, his essential belief is that by the very act of measuring a variable factor is introduced which disqualifies the evidence by virtue of altering the thing measured. Certainly, in clinical investigation and in biology
265 citations
82 citations
TL;DR: Weyl's philosophy of mathematics and philosophy of science as mentioned in this paper was published in 1949 and translated by Olaf Helmer (Princeton, NJ: Princeton University Press, 1949, 2009).
Abstract: By Hermann Weyl. Translated by Olaf Helmer (Princeton, NJ: Princeton University Press, 1949, 2009), xvii +311 pp. $19.95/£27.95 paper.The reprinting of Hermann Weyl’s Philosophy of Mathematics and ...
66 citations
01 Jan 2016
TL;DR: In this paper, the authors describe how people search numerous times for their favorite readings like this interpreting bodies classical and quantum objects in modern physics, but end up in infectious downloads, rather than reading a good book with a cup of coffee in the afternoon.
Abstract: Thank you very much for downloading interpreting bodies classical and quantum objects in modern physics. As you may know, people have search numerous times for their favorite readings like this interpreting bodies classical and quantum objects in modern physics, but end up in infectious downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they cope with some harmful bugs inside their laptop.
7 citations
References
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Book•
01 Jan 1955
TL;DR: The Mathematical Foundations of Quantum Mechanics as discussed by the authors is a seminal work in theoretical physics that introduced the theory of Hermitean operators and Hilbert spaces and provided a mathematical framework for quantum mechanics.
Abstract: Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth century, shows that great insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. He begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which von Neumann regards as the definitive form of quantum mechanics. Using this theory, he attacks with mathematical rigor some of the general problems of quantum theory, such as quantum statistical mechanics as well as measurement processes. Regarded as a tour de force at the time of publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.
4,908 citations
01 Jan 1996
TL;DR: The Mathematical Foundations of Quantum Mechanics as discussed by the authors is a seminal work in theoretical physics that introduced the theory of Hermitean operators and Hilbert spaces and provided a mathematical framework for quantum mechanics.
Abstract: Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth century, shows that great insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. He begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which von Neumann regards as the definitive form of quantum mechanics. Using this theory, he attacks with mathematical rigor some of the general problems of quantum theory, such as quantum statistical mechanics as well as measurement processes. Regarded as a tour de force at the time of publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.
4,043 citations
1,391 citations
Book•
01 Jan 1985
TL;DR: Feynman's "QED" as mentioned in this paper is an edited version of four lectures on quantum electrodynamics that Feynman gave to the general public at UCLA as part of the Alix G. Mautner Memorial Lecture series.
Abstract: Famous the world over for the creative brilliance of his insights into the physical world, Nobel Prize-winning physicist Richard Feynman also possessed an extraordinary talent for explaining difficult concepts to the nonscientist. "QED" - the edited version of four lectures on quantum electrodynamics that Feynman gave to the general public at UCLA as part of the Alix G. Mautner Memorial Lecture series - is perhaps the best example of his ability to communicate both the substance and the spirit of science to the layperson. The focus, as the title suggests, is quantum electrodynamics (QED), the part of the quantum theory of fields that describes the interactions of the quanta of the electromagnetic field-light, X rays, gamma rays - with matter and those of charged particles with one another. By extending the formalism developed by Dirac in 1933, which related quantum and classical descriptions of the motion of particles, Feynman revolutionized the quantum mechanical understanding of the nature of particles and waves. And, by incorporating his own readily visualizable formulation of quantum mechanics, Feynman created a diagrammatic version of "QED" that made calculations much simpler and also provided visual insights into the mechanisms of quantum electrodynamic processes. In this book, using everyday language, spatial concepts, visualizations, and his renowned "Feynman diagrams" instead of advanced mathematics, Feynman successfully provides a definitive introduction to QED for a lay readership without any distortion of the basic science. Characterized by Feynman's famously original clarity and humor, this popular book on QED has not been equaled since its publication.
1,058 citations
01 Jan 1976
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.
909 citations
"New Light on the Objective Indefini..." refers background in this paper
...And just as the Boolean logic of subsets has the dual logic of partitions, so the usual notion of the quantum logic of (closed) subspaces of a Hilbert space [4] will have a dual form in the quantum logic of direct-sum decompositions [17]....
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