{"title":"Pascual Jordan: from matrix multiplication to interference law","authors":"Domenico Costantini, Carlo Ferigato","doi":"10.1140/epjh/s13129-024-00073-8","DOIUrl":null,"url":null,"abstract":"<div><p>Pascual Jordan was the first to propose the law of interference of probability amplitudes as a principle of quantum mechanics. We analyze the role of probabilistic ideas played in this proposal from a historical perspective. In particular, we point out the relation between the usual theory of probability that Jordan called elementary and quantum mechanics. Jordan was the first to stress the analogy between the law of total probability and the law of interference. In this regard, we speculate about the intellectual path Jordan might have followed in order to arrive at the interference law. We do not oppose the usual probability to quantum probability. Instead, we are convinced, as Jordan was, that the rules of quantum mechanics are the rules of a probability theory that has ceased to be elementary.\n</p></div>","PeriodicalId":791,"journal":{"name":"The European Physical Journal H","volume":"49 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1140/epjh/s13129-024-00073-8.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal H","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjh/s13129-024-00073-8","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}
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Abstract
Pascual Jordan was the first to propose the law of interference of probability amplitudes as a principle of quantum mechanics. We analyze the role of probabilistic ideas played in this proposal from a historical perspective. In particular, we point out the relation between the usual theory of probability that Jordan called elementary and quantum mechanics. Jordan was the first to stress the analogy between the law of total probability and the law of interference. In this regard, we speculate about the intellectual path Jordan might have followed in order to arrive at the interference law. We do not oppose the usual probability to quantum probability. Instead, we are convinced, as Jordan was, that the rules of quantum mechanics are the rules of a probability theory that has ceased to be elementary.
期刊介绍：
The purpose of this journal is to catalyse, foster, and disseminate an awareness and understanding of the historical development of ideas in contemporary physics, and more generally, ideas about how Nature works.
The scope explicitly includes:
- Contributions addressing the history of physics and of physical ideas and concepts, the interplay of physics and mathematics as well as the natural sciences, and the history and philosophy of sciences, together with discussions of experimental ideas and designs - inasmuch as they clearly relate, and preferably add, to the understanding of modern physics.
- Annotated and/or contextual translations of relevant foreign-language texts.
- Careful characterisations of old and/or abandoned ideas including past mistakes and false leads, thereby helping working physicists to assess how compelling contemporary ideas may turn out to be in future, i.e. with hindsight.
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