The physical interpretation of the fine-structure constant α≈1/137.036…

The physical interpretation of the fine-structure constant α≈1/137.036… | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Physical Sciences - Article The physical interpretation of the fine-structure constant α≈1/137.036… Luca Varani, Federico Intini, Lino Reggiani This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7903948/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The fine-structure constant α is a fundamental, dimensionless constant in physics, introduced by Sommerfeld in 1916, that is still an empirical parameter in the Standard Model for physical particles, the most advanced theory of modern physics. Its numerical value 1/137 is continuosly receiving wide attention in respect of the accuracy of its value, now claimed to stay at 11 digits in fair agreement with the Sommerfeld expression. This number was physically interpreted as a way of quantifying the strength of the electromagnetic interaction. Since then, several physicists (like Dirac, Pauli, Feynman and others) expressed their unsatisfaction of this situation waiting for a more direct interpretation of this number. Here we address this problem by giving a direct microscopic meaning to 137. We show the existence of a one-to-one correspondence between 137 and the variance of the photon average number N inside a black-body of given volume and temperature. The explicit expression writes: δN 2 =γ N =1/ α with the variance and the average determined by the Planck's law applied to a cubic cavity of side L = 3.3 cm exact and an equilibrium temperature of 0.516 K corresponding to the equivalent energy of the measured fine-structure line of about 45 μeV, with γ =1.37 being the Fano factor. As a broader perspective we propose that any atomic spectral line be associated with a structure-constant that provides the statistical information on the photon gas inside the corresponding black-body. From this point of view, the expression of the Sommerfeld constant is viewed as a particular case that coincides exactly with our results when the emission line is of 45 μeV. Present findings open new experimental possibilities to measure the statistical properties of thermal photons and in particular of the fine-structure constant by using a recently developed counting-statistics technique. Physical sciences/Physics Physical sciences/Physics/Quantum physics fine structure constant quantumrelativistic statistics black-body properties generalized state equation of a quantum gas Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7903948","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Physical Sciences - Article","associatedPublications":[],"authors":[{"id":535671325,"identity":"4d670047-2448-4011-a994-4e060fdf74eb","order_by":0,"name":"Luca Varani","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFElEQVRIiWNgGAWjYBACPgSTsfEBjHXggQGQYj6AVQsbkpZmkDoGHiA+kABisiUQ0sLAJoHQwoBHi0Tyww+MbXb5/LOb26p5c2zy7KWbDxxIKLDJZ2DjfYBdS5qxBGNbsuWMOwfbbvNuSyvmkTmWAHRYmmUDG7sBdi05DBIMZ5gNGG4kgrQcTuyRyDEAajlswCDfhsNhOcw/GM7UG8gDtRRDtOR/AGr5b8DAxoZLC9DXFYcNDIBamKG2gELsAG4tPM/MLBIqjhsY3khslpy7LS2x584xkMOSDdhwaOFnT35844NBtYHcjfSHH95us0lsn9388MGHP3YG/Di0gEECCk8C5gDcGtCBBGElo2AUjIJRMLIAANtLWdWHxBkrAAAAAElFTkSuQmCC","orcid":"","institution":"University of Montpellier","correspondingAuthor":true,"prefix":"","firstName":"Luca","middleName":"","lastName":"Varani","suffix":""},{"id":535671326,"identity":"c957b2a7-c8e0-45cd-bb34-875abade8351","order_by":1,"name":"Federico Intini","email":"","orcid":"","institution":"University of Modena and Reggio Emilia","correspondingAuthor":false,"prefix":"","firstName":"Federico","middleName":"","lastName":"Intini","suffix":""},{"id":535671327,"identity":"8df4197e-9b5d-4056-95c3-fc6952dbbb1d","order_by":2,"name":"Lino Reggiani","email":"","orcid":"","institution":"University of Salento","correspondingAuthor":false,"prefix":"","firstName":"Lino","middleName":"","lastName":"Reggiani","suffix":""}],"badges":[],"createdAt":"2025-10-20 08:55:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7903948/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7903948/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":94985124,"identity":"cf803e53-6bf7-4321-859c-b75476190ed8","added_by":"auto","created_at":"2025-11-03 06:57:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":271473,"visible":true,"origin":"","legend":"Article File","description":"","filename":"nature11.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7903948/v1_covered_1f007df7-3e7f-4cec-a02e-0159fb0d08a3.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"\u003cp\u003eThe physical interpretation of the fine-structure constant α≈1/137.036…\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"fine structure constant, quantumrelativistic statistics, black-body properties, generalized state equation of a quantum gas","lastPublishedDoi":"10.21203/rs.3.rs-7903948/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7903948/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The fine-structure constant α is a fundamental, dimensionless constant in physics, introduced by Sommerfeld in 1916, that is still an empirical parameter in the Standard Model for physical particles, the most advanced theory of modern physics.\r\nIts numerical value 1/137 is continuosly receiving wide attention in respect of the accuracy of its value, now claimed to stay at 11 digits in fair agreement with the Sommerfeld expression. \r\n\r\nThis number was physically interpreted as a way of quantifying the strength of the electromagnetic interaction. Since then, several physicists (like Dirac, Pauli, Feynman and others) expressed their unsatisfaction of this situation waiting for a more direct interpretation of this number. \r\n\r\nHere we address this problem by giving a direct microscopic meaning to 137. We show the existence of a one-to-one correspondence between 137 and the variance of the photon average number N inside a black-body of given volume and temperature. The explicit expression writes: δN\u003csup\u003e2\u003c/sup\u003e =γ N =1/ α\r\nwith the variance and the average determined by the Planck's law applied to a cubic cavity of side L = 3.3 cm exact and an equilibrium temperature of 0.516 K corresponding to the equivalent energy of the measured fine-structure line of about 45 μeV, with γ =1.37 being the Fano factor.\r\n\r\nAs a broader perspective we propose that any atomic spectral line be associated with a structure-constant that provides the statistical information on the photon gas inside the corresponding black-body. 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