“The Heisenberg Method”: Geometry, Algebra, and Probability in Quantum Theory
The article reconsiders quantum theory in terms of the following principle, which can be symbolically represented as QUANTUMNESS → PROBABILITY → ALGEBRA and will be referred to as the QPA principle. The principle states that the quantumness of physical phenomena, that is, the speci...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-08-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/20/9/656 |
| _version_ | 1811185228890243072 |
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| author | Arkady Plotnitsky |
| author_facet | Arkady Plotnitsky |
| author_sort | Arkady Plotnitsky |
| collection | DOAJ |
| description | The article reconsiders quantum theory in terms of the following principle, which can be symbolically represented as QUANTUMNESS → PROBABILITY → ALGEBRA and will be referred to as the QPA principle. The principle states that the quantumness of physical phenomena, that is, the specific character of physical phenomena known as quantum, implies that our predictions concerning them are irreducibly probabilistic, even in dealing with quantum phenomena resulting from the elementary individual quantum behavior (such as that of elementary particles), which in turn implies that our theories concerning these phenomena are fundamentally algebraic, in contrast to more geometrical classical or relativistic theories, although these theories, too, have an algebraic component to them. It follows that one needs to find an algebraic scheme able make these predictions in a given quantum regime. Heisenberg was first to accomplish this in the case of quantum mechanics, as matrix mechanics, whose matrix character testified to his algebraic method, as Einstein characterized it. The article explores the implications of the Heisenberg method and of the QPA principle for quantum theory, and for the relationships between mathematics and physics there, from a nonrealist or, in terms of this article, “reality-without-realism” or RWR perspective, defining the RWR principle, thus joined to the QPA principle. |
| first_indexed | 2024-04-11T13:25:51Z |
| format | Article |
| id | doaj.art-961064a239bb41a98cd446f9bfbb1fd2 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T13:25:51Z |
| publishDate | 2018-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-961064a239bb41a98cd446f9bfbb1fd22022-12-22T04:22:04ZengMDPI AGEntropy1099-43002018-08-0120965610.3390/e20090656e20090656“The Heisenberg Method”: Geometry, Algebra, and Probability in Quantum TheoryArkady Plotnitsky0Literature, Theory, Cultural Studies Program, Purdue University, West Lafayette, IN 47907, USAThe article reconsiders quantum theory in terms of the following principle, which can be symbolically represented as QUANTUMNESS → PROBABILITY → ALGEBRA and will be referred to as the QPA principle. The principle states that the quantumness of physical phenomena, that is, the specific character of physical phenomena known as quantum, implies that our predictions concerning them are irreducibly probabilistic, even in dealing with quantum phenomena resulting from the elementary individual quantum behavior (such as that of elementary particles), which in turn implies that our theories concerning these phenomena are fundamentally algebraic, in contrast to more geometrical classical or relativistic theories, although these theories, too, have an algebraic component to them. It follows that one needs to find an algebraic scheme able make these predictions in a given quantum regime. Heisenberg was first to accomplish this in the case of quantum mechanics, as matrix mechanics, whose matrix character testified to his algebraic method, as Einstein characterized it. The article explores the implications of the Heisenberg method and of the QPA principle for quantum theory, and for the relationships between mathematics and physics there, from a nonrealist or, in terms of this article, “reality-without-realism” or RWR perspective, defining the RWR principle, thus joined to the QPA principle.http://www.mdpi.com/1099-4300/20/9/656algebracausalitygeometryprobabilityquantum information theoryrealismreality |
| spellingShingle | Arkady Plotnitsky “The Heisenberg Method”: Geometry, Algebra, and Probability in Quantum Theory Entropy algebra causality geometry probability quantum information theory realism reality |
| title | “The Heisenberg Method”: Geometry, Algebra, and Probability in Quantum Theory |
| title_full | “The Heisenberg Method”: Geometry, Algebra, and Probability in Quantum Theory |
| title_fullStr | “The Heisenberg Method”: Geometry, Algebra, and Probability in Quantum Theory |
| title_full_unstemmed | “The Heisenberg Method”: Geometry, Algebra, and Probability in Quantum Theory |
| title_short | “The Heisenberg Method”: Geometry, Algebra, and Probability in Quantum Theory |
| title_sort | the heisenberg method geometry algebra and probability in quantum theory |
| topic | algebra causality geometry probability quantum information theory realism reality |
| url | http://www.mdpi.com/1099-4300/20/9/656 |
| work_keys_str_mv | AT arkadyplotnitsky theheisenbergmethodgeometryalgebraandprobabilityinquantumtheory |