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Motion with respect to the extra independent time τ is instantaneous relative to the usual time t and is used to restore determinism, account for Zitterbewegung without invoking virtual antimatter, and predict a relativistic correction to the uncertainty principle. The work summarizes the model’s defining features and applies it to spherical atomic orbits and a particle-in-a-box scenario, then discusses related spin and astrophysical implications and the role of TTBM in defining time in quantum mechanics.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/two-time-relativistic-bohmian-model-of-quantum-mechanics/142131/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/two-time-relativistic-bohmian-model-of-quantum-mechanics/142131.png","ImageObject",300,407,{"name":92,"@type":93},"Theodora","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-23","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does the Two-Time Relativistic Bohmian Model (TTBM) introduce to explain quantum behavior?","Question",{"text":112,"@type":113},"TTBM postulates an extra unobservable time dimension τ, independent from the usual time t. Motions in τ generate quantum uncertainties while appearing instantaneous with respect to t.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does TTBM aim to restore determinism and address Zitterbewegung?",{"text":117,"@type":113},"By attributing paradoxical quantum aspects to hidden τ-motion, the model restores determinism. It explains Zitterbewegung through a more general law that avoids invoking virtual antimatter.",{"name":119,"@type":110,"acceptedAnswer":120},"What predictions does TTBM make about the uncertainty principle and where could it be tested?",{"text":121,"@type":113},"TTBM predicts a relativistic anisotropic correction of the uncertainty principle. The document notes this could be tested in high-energy accelerators.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},142131,1787675635,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144,"preview_page_count":4},687197207919,"https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552","arXiv :2409 .09049v12 [physics .gen-ph] 5 Mar 2026  \nTwo-Time Relativistic Bohmian Model of Quantum Mechanics  \nGiuseppe Ragun´ı∗  \nDepartamento de F´ısica, Universidad de Murcia, E-30071 Murcia, Spain.  \nTwo-Time relativistic Bohmian Model (TTBM) is a theory in which the apparently paradoxical aspects of Quantum Mechanics are the effect of the existence of an extra unobservable time dimension. The hypothesis that matter is capable of motion with respect to an additional independent time (thus resulting instantaneous with respect to usual time) is capable of restoring determinism, explaining the Zitterbewegung without evoking virtual antimatter. The model also predicts a relativistic correction of the uncertainty principle.  \nHere the model is first summarized (definition, salient properties and empiricism) and after applied to a generic spherical atomic orbit, obtaining electron oscillations in the new time dimension, τ , which demonstrate the static nature of the orbitals. Something very similar happens in the case of a particle in a box, where τ-oscillations cause the particle to spread out at steady states. Some astrophysical and about spin speculations follow. Finally, it is discussed how the model fits into the fundamental problem of the definition of time in Quantum Mechanics.  \nKeywords: Quantum Mechanics Foundations; de Broglie-Bohm Theory; Zitterbewegung; Uncertainty principle verification; Extra dimensions; Atomic orbitals; Spin; Definition of time in Quantum Mechanics.  \nI. INTRODUCTION  \nIn Feynman’s sum of histories interpretation [1–3] -a formulation equivalent to the standard one-all the apparent paradoxes of Quantum Mechanics converge into a single surprising aspect: the ubiquity of matter. Yet, to resolve it and restore determinism, all that’s needed is to introduce an extra temporal dimension: a measure that, though shocking at first glance, is physically equivalent to the introduction of additional spatial dimensions, already contemplated by several modern theories. This is achieved in the recently introduced TTBM theory [4, 5], linked to the attempts at relativistic generalization of the de Broglie-Bohm mechanics [6–11] . The crucial point in this effort is the definition of simultaneity [12] . Until a couple of years ago, the most successful strategy for this purpose was to introduce models which, while respecting Lorentz invariance, must admit superluminal speeds and complex space-time structures [13–20] . The approach of TTBM is more elementary: an additional time τ, independent of the usual time t is introduced. Motions in τ are instantaneous with respect to t time and, while not directly observable, are supposed to generate the quantum uncertainties of the observables. They are caused by a Bohmian-type Quantum Potential and find the basic example in the famous Zitterbewegung motion [21, 22], of which a more general law, free from the call of antimatter, is achieved. Beyond the empiricism of standard Quantum Mechanics, the model foresees a relativistic anisotropic modification of the uncertainty principle, which could be tested in high-energy accelerators.  \nHere we dedicate the following two sections to define and present the main features of the model, while the third one elucidates the empiricism of the theory. A section follows where the τ-movements of the atomic electrons are determined, thus justifying origin and staticity of the orbitals. Particles in box and a possible astrophys-  \nical consequence are covered in section VI, while the VII one outlines some basic points about spin in relation to the proposed model. This is followed by section VIII, which contains the aid of TTBM in the context of the issue of defining time in Quantum Mechanics, and Section IX with final remarks.  \nII. TTBM DEFINITION AND PROPERTIES  \nTwo-time physics has been considered in various contexts. An additional temporal parameter is considered, e.g., in [23–29] and, with a different approach, in [30–35] in order to mor","cbCaieTQ0WTUKjJ7","https://ap.wps.com/l/cbCaieTQ0WTUKjJ7","pdf",1128988,11,"English","# Introduction\n# TTBM Definition and Properties\n## Summary of the model’s rationale\n## Intrinsic time τ and its effects\n## Connection to Zitterbewegung and determinism\n# Applications and Predictions\n## Atomic orbitals and electron τ-oscillations\n## Particle in a box and steady-state spreading\n## Relativistic uncertainty principle correction\n# Spin and Astrophysical Implications\n# Defining Time in Quantum Mechanics\n## Final remarks","[{\"question\":\"What does the Two-Time Relativistic Bohmian Model (TTBM) introduce to explain quantum behavior?\",\"answer\":\"TTBM postulates an extra unobservable time dimension τ, independent from the usual time t. Motions in τ generate quantum uncertainties while appearing instantaneous with respect to t.\"},{\"question\":\"How does TTBM aim to restore determinism and address Zitterbewegung?\",\"answer\":\"By attributing paradoxical quantum aspects to hidden τ-motion, the model restores determinism. It explains Zitterbewegung through a more general law that avoids invoking virtual antimatter.\"},{\"question\":\"What predictions does TTBM make about the uncertainty principle and where could it be tested?\",\"answer\":\"TTBM predicts a relativistic anisotropic correction of the uncertainty principle. The document notes this could be tested in high-energy accelerators.\"}]","Two-Time Relativistic Bohmian Model of Quantum Mechanics | PDF",28]