{"title":"Weak Ratios","authors":"Yakov Bloch","doi":"10.1007/s10701-025-00871-0","DOIUrl":null,"url":null,"abstract":"<div><p>Weak values characterize a quantum system in the period of time between preparation and measurement and may lie outside the eigenvalue spectrum of the measured operator. The probability of such “superweak\" values for random quantum states has been calculated and applied to Klein–Gordon and Dirac waves, where the maximal probability for superluminal propagation was shown to be 1/2. In a recent paper, a different definition for the velocity of a relativistic quantum particle was proposed in terms of a ratio of two weak values. In this paper, we find the probability distribution of such ratios. With the new definition, the superluminal probability of photons is found to be bounded between <span>\\(1-1/\\sqrt{2}\\)</span> and <span>\\(1/\\sqrt{2}\\)</span>, while for general eigenvalue distributions the superluminal probability can take any value between 0 and 1.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":"55 4","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-025-00871-0.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Foundations of Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10701-025-00871-0","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Weak values characterize a quantum system in the period of time between preparation and measurement and may lie outside the eigenvalue spectrum of the measured operator. The probability of such “superweak" values for random quantum states has been calculated and applied to Klein–Gordon and Dirac waves, where the maximal probability for superluminal propagation was shown to be 1/2. In a recent paper, a different definition for the velocity of a relativistic quantum particle was proposed in terms of a ratio of two weak values. In this paper, we find the probability distribution of such ratios. With the new definition, the superluminal probability of photons is found to be bounded between \(1-1/\sqrt{2}\) and \(1/\sqrt{2}\), while for general eigenvalue distributions the superluminal probability can take any value between 0 and 1.
期刊介绍：
The conceptual foundations of physics have been under constant revision from the outset, and remain so today. Discussion of foundational issues has always been a major source of progress in science, on a par with empirical knowledge and mathematics. Examples include the debates on the nature of space and time involving Newton and later Einstein; on the nature of heat and of energy; on irreversibility and probability due to Boltzmann; on the nature of matter and observation measurement during the early days of quantum theory; on the meaning of renormalisation, and many others.
Today, insightful reflection on the conceptual structure utilised in our efforts to understand the physical world is of particular value, given the serious unsolved problems that are likely to demand, once again, modifications of the grammar of our scientific description of the physical world. The quantum properties of gravity, the nature of measurement in quantum mechanics, the primary source of irreversibility, the role of information in physics – all these are examples of questions about which science is still confused and whose solution may well demand more than skilled mathematics and new experiments.
Foundations of Physics is a privileged forum for discussing such foundational issues, open to physicists, cosmologists, philosophers and mathematicians. It is devoted to the conceptual bases of the fundamental theories of physics and cosmology, to their logical, methodological, and philosophical premises.
The journal welcomes papers on issues such as the foundations of special and general relativity, quantum theory, classical and quantum field theory, quantum gravity, unified theories, thermodynamics, statistical mechanics, cosmology, and similar.
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