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The MEEF Model-Based Complex Numbers, the Point-Like Paradox and Time as Emergent

Mohammad Reza Movahed Shariat Panahi

Published Oct 14, 2026• 0 citations
Publisher

Abstract

This paper addresses, based on the Movahed Energy Escape Factor (MEEF), three foundational questions: why quantum mechanics requires complex numbers, why particles appear point-like, and how time emerges. In the MEEF picture, complex phase reflects the energy phase of a confined state, the apparent point-likeness is an artefact of extreme confinement, and time arises as a consequence of energy confinement, with implications for measurement and for macroscopic objects

DOI
10.5281/zenodo.23353445

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Introduction

A. O. Caldeira

Since its very beginning, quantum mechanics has been developed to deal with systems on the atomic or sub-atomic scale. For many decades, there has been no reason to think about its application to macroscopic systems. Actually, macroscopic objects have even been used to show how bizarre quantum effects would appear if quantum mechanics were applied beyond its original realm. This is, for example, the essence of the so-called Schrödinger cat paradox (Schrödinger, 1935). How-ever, due to recent advances in the design of systems on the meso- and nanoscopic scales, as well as in cryogenic techniques, this situation has changed drastically. It is now quite natural to ask whether a specific quantum effect, collectively involving a macroscopic number of particles, could occur in these systems. In this book it is our intention to address the quantum mechanical effects that take place in properly chosen or built “macroscopic” systems. Starting from a very naïve point of view, we could always ask what happens to systems whose classical dynamics can be described by equations of motion equivalent to those of particles (or fields) in a given potential (or potential energy density). These can be represented by a generalized “coordinate” φ( r , t ) which could either describe a field variable or a “point particle” if it is not position dependent, φ( r , t ) = φ( t ).

Cambridge University Press eBooks•Mar 20, 2014•0 citations
This paper addresses, based on the Movahed Energy Escape Factor (MEEF), three foundational questions: why quantum mechanics requires complex numbers, why particles appear point-like, and how time emerges. In the MEEF picture, complex phase reflects the energy phase of a confined state, the apparent point-likeness is an artefact of extreme confinement, and time arises as a consequence of energy confinement, with implications for measurement and for macroscopic objects
Abstract This paper, based on the Movahed Energy Escape Factor (MEEF), explains wave–particle duality and the double-slit experiment within the confinement picture: unobserved energy propagates as an unconfined wave, while measurement confines the energy and produces particle-like behaviour. The Mo transition at measurement is derived, and the de Broglie relation is recovered for confined systems. The framework's account of the collapse of the wavefunction is compared with standard interpretations.
Abstract In the standard quantum–field–theoretic description of unstable particles, exponential decay with width is encoded by promoting the energy (or mass) to a complex quantity . This prescription works extremely well in practice, but its imaginary part has no direct counterpart in the usual real–valued notion of energy, and it raises a natural question: where does the imaginary unit really belong? In this letter we show that the same physics can be reformulated in a complex–time framework in which the rest mass remains real and the decay is absorbed into a complex phase associated with the time direction. For a stable relativistic particle, the proper–time action can be written so that the mass controls the rate of phase rotation along a complex extension of time. For a quasi–stable state with width , the standard replacement is equivalently realized by a complex phase whose real part encodes the mass–controlled oscillation and whose imaginary part encodes the exponential damping. As a concrete example we apply this construction to the Higgs boson, whose mass arises from the Higgs vacuum expectation value while its finite lifetime is generated by interactions. In the complex–time picture these two aspects appear as the real and imaginary components of a single geometric object, providing a unified way to relate mass, width and the arrow of time without complexifying the energy spectrum itself. Running Title Unstable States in Complex Time Key Words unstable quantum states; complex time; complex energy; Higgs boson; vacuum structure
Since its very beginning, quantum mechanics has been developed to deal with systems on the atomic or sub-atomic scale. For many decades, there has been no reason to think about its application to macroscopic systems. Actually, macroscopic objects have even been used to show how bizarre quantum effects would appear if quantum mechanics were applied beyond its original realm. This is, for example, the essence of the so-called Schrödinger cat paradox (Schrödinger, 1935). How-ever, due to recent advances in the design of systems on the meso- and nanoscopic scales, as well as in cryogenic techniques, this situation has changed drastically. It is now quite natural to ask whether a specific quantum effect, collectively involving a macroscopic number of particles, could occur in these systems. In this book it is our intention to address the quantum mechanical effects that take place in properly chosen or built “macroscopic” systems. Starting from a very naïve point of view, we could always ask what happens to systems whose classical dynamics can be described by equations of motion equivalent to those of particles (or fields) in a given potential (or potential energy density). These can be represented by a generalized “coordinate” φ( r , t ) which could either describe a field variable or a “point particle” if it is not position dependent, φ( r , t ) = φ( t ).