Bound State Internal Interactions as a Mechanism for Exponential Decay

Bound State Internal Interactions as a Mechanism for Exponential Decay | 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 Research Article Bound State Internal Interactions as a Mechanism for Exponential Decay Peter W. Bryant This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7410576/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 04 Oct, 2025 Read the published version in Foundations of Physics → Version 1 posted 7 You are reading this latest preprint version Abstract We hypothesize that the binding interactions among the components of bound systems and the background fields, sometimes known as virtual particle exchange, affect the state of the systems as do typical scattering interactions. Then with the assumption that the interior environment of unstable particles is disordered, we derive in the limit of continuous binding both an exactly exponential non-decay probability and Fermi's Golden Rule for the decay rates. The result suggests resolutions to several long-standing theoretical challenges associated with exponential decay in quantum mechanics, without appealing directly to non-Hermitian, approximate Hamiltonians or complex energies. It also contributes to a conceptual understanding of the apparent continuum between controlled interactions that induce deviations from exponential decay, such as those in the Quantum Zeno Effect, and the uncontrolled internal dynamics of excited atoms and nuclei, which exhibit no such deviations. Finally, we examine how the binding interactions responsible for the general exponential character of decay for bound systems differ from the couplings with decay products that control decay rates, providing insight into challenges in quantum computing and information processing. Exponential Decay Fermi's Golden Rule Bound States Quantum Zeno Effect Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 04 Oct, 2025 Read the published version in Foundations of Physics → Version 1 posted Editorial decision: Accepted 19 Sep, 2025 Reviews received at journal 19 Sep, 2025 Reviewers agreed at journal 29 Aug, 2025 Reviewers invited by journal 29 Aug, 2025 Editor assigned by journal 28 Aug, 2025 Submission checks completed at journal 19 Aug, 2025 First submitted to journal 19 Aug, 2025 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-7410576","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":507561351,"identity":"99869e8d-7918-48ba-ba9e-eeebf8ed1a22","order_by":0,"name":"Peter W. Bryant","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAw0lEQVRIiWNgGAWjYFACHgjFz3AARDETr0VCsoFkLQZgHcRoMZfIPfaZp+ZOnfHB488kGCqsExsIabGckZc8m+fYMwmzA2fMJBjOpBPWYnA7x5iZh+0wSAubBGPbYWK1/DssYdwAdBjjP2K18LYdljBgOGAmwdhAhBbL+e+SGef2HZacceCMsUXCsXRjglrMec4eZnjz7TA//4zjD298qLGWJewwIGYCR43EAQaGBELKYVoYf4BY/ASNHwWjYBSMgpEKAG3CQDtQdn+CAAAAAElFTkSuQmCC","orcid":"","institution":"Jacksonville State University","correspondingAuthor":true,"prefix":"","firstName":"Peter","middleName":"W.","lastName":"Bryant","suffix":""}],"badges":[],"createdAt":"2025-08-19 16:38:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7410576/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7410576/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10701-025-00889-4","type":"published","date":"2025-10-04T15:56:50+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":92883632,"identity":"3fa94612-efb3-47fd-8c40-b17243a1e8d8","added_by":"auto","created_at":"2025-10-06 16:06:39","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":276193,"visible":true,"origin":"","legend":"","description":"","filename":"boundstatebryant.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7410576/v1_covered_332025c1-d483-44bd-8d74-7c210719d020.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Bound State Internal Interactions as a Mechanism for Exponential Decay","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"foundations-of-physics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"foop","sideBox":"Learn more about [Foundations of Physics](http://link.springer.com/journal/10701)","snPcode":"10701","submissionUrl":"https://submission.nature.com/new-submission/10701/3","title":"Foundations of Physics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Exponential Decay, Fermi's Golden Rule, Bound States, Quantum Zeno Effect","lastPublishedDoi":"10.21203/rs.3.rs-7410576/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7410576/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe hypothesize that the binding interactions among the components of bound systems and the background fields, sometimes known as virtual particle exchange, affect the state of the systems as do typical scattering interactions. Then with the assumption that the interior environment of unstable particles is disordered, we derive in the limit of continuous binding both an exactly exponential non-decay probability and Fermi's Golden Rule for the decay rates. The result suggests resolutions to several long-standing theoretical challenges associated with exponential decay in quantum mechanics, without appealing directly to non-Hermitian, approximate Hamiltonians or complex energies. It also contributes to a conceptual understanding of the apparent continuum between controlled interactions that induce deviations from exponential decay, such as those in the Quantum Zeno Effect, and the uncontrolled internal dynamics of excited atoms and nuclei, which exhibit no such deviations. Finally, we examine how the binding interactions responsible for the general exponential character of decay for bound systems differ from the couplings with decay products that control decay rates, providing insight into challenges in quantum computing and information processing.\u003c/p\u003e","manuscriptTitle":"Bound State Internal Interactions as a Mechanism for Exponential Decay","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-08 03:57:16","doi":"10.21203/rs.3.rs-7410576/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Accepted","date":"2025-09-19T17:35:09+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-19T16:48:40+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"35629952772117637127223312462260261465","date":"2025-08-29T16:01:31+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-08-29T08:10:53+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-08-28T15:42:32+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-19T20:54:40+00:00","index":"","fulltext":""},{"type":"submitted","content":"Foundations of Physics","date":"2025-08-19T16:35:38+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"foundations-of-physics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"foop","sideBox":"Learn more about [Foundations of Physics](http://link.springer.com/journal/10701)","snPcode":"10701","submissionUrl":"https://submission.nature.com/new-submission/10701/3","title":"Foundations of Physics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"c3767f6e-cd69-44f3-b78b-cffcd87e973a","owner":[],"postedDate":"September 8th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-10-06T15:59:29+00:00","versionOfRecord":{"articleIdentity":"rs-7410576","link":"https://doi.org/10.1007/s10701-025-00889-4","journal":{"identity":"foundations-of-physics","isVorOnly":false,"title":"Foundations of Physics"},"publishedOn":"2025-10-04 15:56:50","publishedOnDateReadable":"October 4th, 2025"},"versionCreatedAt":"2025-09-08 03:57:16","video":"","vorDoi":"10.1007/s10701-025-00889-4","vorDoiUrl":"https://doi.org/10.1007/s10701-025-00889-4","workflowStages":[]},"version":"v1","identity":"rs-7410576","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7410576","identity":"rs-7410576","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}