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arXiv:2108.08222

The Mach-Zehnder Interferometer and Photon Dualism: with an Analysis of Nonlocality

Paul A. Klevgard

Published Jul 2, 2021• 1 citation
arXivHTMLPDF

Abstract

The Mach-Zehnder Interferometer (MZI) is chosen to illustrate the long-standing wave particle duality problem. Why is which-way (welcher weg) information incompatible with wave interference? How to explain Wheeler's delayed choice experiment? Most crucially, how can the photon divide at the first beam splitter and yet terminate on either arm with its undiminished energy? The position advanced is that the photon has two identities, one supporting particle features and the other wave features. There is photon kinetic energy that never splits (on half-silvered mirrors) or diffracts (in pinholes or slits). Then there are photon probability waves that do diffract and can reinforce or cancel. Photon kinetic energy is oscillatory; its cycles require/occupy time. E = mc2 suggests that kinetic energy is physically real as occurrence in time just as rest mass is physically real as existence in space; both are quantized and both occupy/require a dimension for their occurrence or existence. Photon kinetic energy (KE) thus resides in time, but is still present/available for interactions (events) in space; rest mass (e.g., your desk) resides in space but is still present/available for interactions (events) in time. While photon probability waves progress in space and diffract there, photon KE resides in time and never diffracts in space; at reception it always arrives whole and imitates particle impact without being a particle. Photon probability waves are real; they diffract in space. Acknowledging that the photon has two identities (residing energy and progressing probability), explains photon dual nature. And wave-particle duality is central to quantum mechanics. Understanding it leads to new insights into entanglement, nonlocality and the measurement problem. Supporting video: https://youtu.be/A1Wabkr0YFE

DOI
10.48550/arxiv.2108.08222

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The Mach-Zehnder Interferometer (MZI) is chosen to illustrate the long-standing wave particle duality problem. Why is which-way (welcher weg) information incompatible with wave interference? How to explain Wheeler's delayed choice experiment? Most crucially, how can the photon divide at the first beam splitter and yet terminate on either arm with its undiminished energy? The position advanced is that the photon has two identities, one supporting particle features and the other wave features. There is photon kinetic energy that never splits (on half-silvered mirrors) or diffracts (in pinholes or slits). Then there are photon probability waves that do diffract and can reinforce or cancel. Photon kinetic energy is oscillatory; its cycles require/occupy time. E = mc2 suggests that kinetic energy is physically real as occurrence in time just as rest mass is physically real as existence in space; both are quantized and both occupy/require a dimension for their occurrence or existence. Photon kinetic energy (KE) thus resides in time, but is still present/available for interactions (events) in space; rest mass (e.g., your desk) resides in space but is still present/available for interactions (events) in time. While photon probability waves progress in space and diffract there, photon KE resides in time and never diffracts in space; at reception it always arrives whole and imitates particle impact without being a particle. Photon probability waves are real; they diffract in space. Acknowledging that the photon has two identities (residing energy and progressing probability), explains photon dual nature. And wave-particle duality is central to quantum mechanics. Understanding it leads to new insights into entanglement, nonlocality and the measurement problem. Supporting video: https://youtu.be/A1Wabkr0YFE
The Mach-Zehnder Interferometer (MZI) is used to illustrate the long-standing wave-particle duality problem. How can the photon divide at the first beam splitter and yet terminate on either arm with its undiminished energy? Why is which-way (welcher weg) information incompatible with wave interference? How do we explain Wheeler’s delayed choice experiment? The position adopted is that the photon has two identities, one supporting particle features and the other wave features. There is photon kinetic energy that never splits (on half-silvered mirrors) or diffracts (in pinholes or slits). Then there is photon probability waves that do diffract and can reinforce or cancel. Interpretations of these two identities are suggested.
Many delayed-choice experiments based on Mach-Zehnder interferometers (MZI) have been thought and made to address the fundamental problem of wave-particle duality. Conventional wisdoms long hold that by inserting or removing the second beam splitter (BS2) in a controllable way, microscopic particles (photons, electrons, etc.) transporting within the MZI can lie in the quantum superposition of the wave and particle state as ψ=a_wψ_wave+a_pψ_particle. Here we present an alternative interpretation to these delayed-choice experiments. We notice that as all composite devices of MZI including BS2 are purely classical, the inserting and removing operation of BS2 imposes a time-modulated Hamiltonian H_mod(t)=a(t)H_in+b(t)H_out, instead of a quantum superposition of H_in and H_out as H=a_wH_in+b_pH_out, to act upon the incident wave function. Solution of this quantum scattering problem, rather than the long held quantum eigen-problem yields a synchronically time-modulated output wave function as ψ_mod=a(t)ψ_wave+b(t)ψ_particle. As a result, the probability of particle output from the MZI behaves as if they are in the superposition of the wave and particle state when many events over time accumulation are counted and averaged. We expect these elementary but insightful analyses will shed a new light on exploring basic physics beyond the long-held wisdom of wave-particle duality and principle of complementarity.
The photon is typically regarded as a unitary object that is both particle-discrete and wave-continuous. This is a paradoxical position and we live with it by making dualism a fundamental feature of radiation. It is argued here that the photon is not unitary; rather it has two identities, one supporting discrete behavior and the other supporting continuous (wave) behavior. There is photon kinetic energy that is always discrete/localized on arrival; it never splits (on half-silvered mirrors) or diffracts (in pinholes or slits). Then there is the photon’s probability wavefront that is continuous and diffractable. Acknowledging that the photon has two identities explains the photon’s dual nature. And wave-particle duality is central to quantum mechanics. Understanding it leads to new insights into the photon’s constant velocity and its entanglement with another photon.
Many delayed-choice experiments based on Mach–Zehnder interferometers (MZI) have been considered and made to address the fundamental problem of wave-particle duality. Conventional wisdom long holds that by inserting or removing the second beam splitter (BS2) in a controllable way, microscopic particles (photons, electrons, etc.) transporting within the MZI can lie in the quantum superposition of the wave and particle state as ψ = a w ψ wave + a p ψ particle . Here we present an alternative interpretation to these delayed-choice experiments. We notice that as the BS2 is purely classical, the inserting and removing operation of the BS2 imposes a time-modulated Hamiltonian H mod (t) = a(t)H in + b(t)H out , instead of a quantum superposition of H in and H out as H = a w H in + a p H out , to act upon the incident wave function. Solution of this quantum scattering problem, rather than the long held quantum eigen-problem yields a synchronically time-modulated output wave function as ψ mod (t) = a(t)ψ wave + b(t)ψ particle , instead of the stationary quantum superposition state ψ = a w ψ wave + a p ψ particle . As a result, the probability of particle output from the MZI behaves as if they are in the superposition of the wave and particle state when many events over time accumulation are counted and averaged. We expect that these elementary but insightful analyses will shed a new light on exploring basic physics beyond the long-held wisdom of wave-particle duality and the principle of complementarity.
The chapter discusses the Mach–Zehnder interferometer (MZI), which uses beam splitters in combination with mirrors to place a photon into a superposition of paths. In a final beam splitter, the two paths may be recombined to interfere, showing wave behavior. If the final beam splitter is removed, the photon is definitely in one path or the other, showing particle behavior. The polarization of light allows additional applications—one can use a polarizing beam splitter to separate and reconstitute the wave functions of a photon polarized at an angle. In a delayed-choice experiment, one decides which kind of experiment one is to do, particle or wave, after the photon has already entered the arms of the MZI. The chapter discusses a version of this that puts the MZI and a second-detector photon in an entangled state of particle and wave results.
\n\nThe Mach-Zehnder interferometer (MZI) is a regular yet simple instrument to test wave-particle duality. One key device in a standard MZI is the beam splitter 2 (BS2). Here we make a simple quantum mechanics analysis about the wave function evolution and find that the strong and exclusive interaction of BS2 with the incident microscopic particle beam (photons, electrons, etc.) is the fundamental reason why standard MZIs could not allow for the simultaneous observation of wave and particle properties of these particles. A weak-measurement (WM) MZI setup is then proposed, where BS2 is replaced with a deliberately designed highly transparent interference screen operating via either weak absorption or weak-scattering effect. Quantum-mechanical analysis on this WM-MZI shows that the overall power to make simultaneous observation of interference fringe (wave nature) and which-path information (particle nature) of microscopic particles can be significantly enhanced compared with the standard MZIs.\n