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Journal of Physics B Atomic Molecular and Optical Physics

Multi-stage Stern–Gerlach experiment modeled

Lihong V. Wang

Published Mar 3, 2023• 6 citations
Publisher

Abstract

Abstract In the classic multi-stage Stern–Gerlach experiment conducted by Frisch and Segrè, the Majorana (Landau–Zener) and Rabi formulae diverge far from the experimental observation while the physical mechanism for electron-spin collapse remains unidentified. Here, introducing the physical co-quantum concept provides a plausible physical mechanism and predicts the experimental observation in absolute units without fitting (i.e. no parameters adjusted), with a p-value less than one per million, which is the probability that the co-quantum theory happens to match the experimental observation purely by chance. Further, the co-quantum concept is corroborated by exactly statistically reproducing the wave function, density operator, and uncertainty relation for electron spin in Stern–Gerlach experiments.

DOI
10.1088/1361-6455/acc149

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Abstract In the classic multi-stage Stern–Gerlach experiment conducted by Frisch and Segrè, the Majorana (Landau–Zener) and Rabi formulae diverge far from the experimental observation while the physical mechanism for electron-spin collapse remains unidentified. Here, introducing the physical co-quantum concept provides a plausible physical mechanism and predicts the experimental observation in absolute units without fitting (i.e. no parameters adjusted), with a p-value less than one per million, which is the probability that the co-quantum theory happens to match the experimental observation purely by chance. Further, the co-quantum concept is corroborated by exactly statistically reproducing the wave function, density operator, and uncertainty relation for electron spin in Stern–Gerlach experiments.
In the classic multi-stage Stern−-−Gerlach experiment conducted by Frisch and Segrè, the Majorana (Landau−-−Zener) and Rabi formulae diverge afar from the experimental observation while the physical mechanism for electron-spin collapse remains unidentified. Here, introducing the physical co-quantum concept provides a plausible physical mechanism and predicts the experimental observation in absolute units without fitting (i.e., no parameters adjusted) with a p-value less than one per million, which is the probability that the co-quantum theory happens to match the experimental observation purely by chance. Further, the co-quantum concept is corroborated by statistically reproducing exactly the wave function, density operator, and uncertainty relation for electron spin in Stern−-−Gerlach experiments.
The 1922 Stern–Gerlach experiment quickly proved fundamental to quantum physics. The benchmark experiment led to the quantization of angular momenta, discovery of electron spin, and study of the measurement problem and superposition. Immediately, Heisenberg and Einstein proposed multi-stage Stern–Gerlach experiments to explore deeper mysteries of directional quantization. In the classic multi-stage Stern–Gerlach experiment conducted by Frisch and Segrè, the Majorana (Landau–Zener) and Rabi formulae diverge afar from the experimental observation while the physical mechanism for electron-spin collapse remains unidentified. Here, introducing the physical co-quantum concept provides a plausible physical mechanism and predicts the experimental observation in absolute units without fitting (i.e., no parameters adjusted) with a p-value less than one per million, which is the probability that the co-quantum theory happens to match the experimental observation purely by chance. Further, the co-quantum concept is corroborated by statistically reproducing exactly the wave function, density operator, and uncertainty relation for electron spin in Stern–Gerlach experiments.
The Stern–Gerlach experiment stands as one of the fundamental demonstrations of quantum phenomena. A successive combination of Stern–Gerlach apparatuses was first explored as a gedankenexperiment by Heisenberg to study angular momentum quantization further; later a detailed experiment was proposed by Einstein to Stern and Ehrenfest. Here, we numerically study the spin flip in the Frisch–Segrè experiment, the first successful multi-stage Stern–Gerlach experiment, within the context of the novel co-quantum dynamics theory. Despite early attempts by P. Güttinger, E. Majorana, I.I. Rabi, L. Landau, C. Zener, and E. Stückelberg among others, theoretical descriptions deviate from the Frisch and Segrè observations. We model the middle stage responsible for spin rotation by sampling the atoms with the Monte Carlo method and solving the dynamics of the electron and nuclear magnetic moments numerically according to the Bloch equation. The simulated dynamics shows that co-quantum dynamics closely reproduces, without using any fitting parameters, the experimental observations reported by Frisch and Segrè in 1933, which have so far lacked theoretical predictions using the standard theories.
The multi-stage Stern–Gerlach experiment conducted by Frisch and Segrè has been modeled analytically using quantum mechanics by Majorana and revised by Rabi by including the hyperfine interaction. However, the closed-form analytical predictions, which rely on approximations, do not match the experimental observation well. To avoid the approximations, we numerically solve the standard quantum mechanical model, via the von Neumann equation, which includes the hyperfine interaction for the time evolution of the spin. The outcome is compared with the experimental observation and the predictions by Majorana, Rabi, and an alternative model called co-quantum dynamics. Thus far, the coefficients of determination from the standard quantum mechanical model, which does not use free parameters, are still below zero. Non-standard variants that improve the match are explored.
Abstract We use a theory termed co-quantum dynamics (CQD) to numerically model spin flip in the multi-stage Stern–Gerlach (SG) experiment conducted by R. Frisch and E. Segrè. This experiment consists of two SG apparatuses separated by an inner rotation chamber that varies the fraction of spin flip. To this day, quantum mechanical treatments inadequately predict the Frisch–Segrè experiment. Here, we account for electron-nuclear interactions according to CQD and solve the associated Schrödinger equation. Our simulation utilizes a branching condition to predict the collapse of electron spins, and the outcome agrees with the Frisch–Segrè experimental observation and supports CQD as a potential model for electron spin evolution and collapse.
Abstract The multi-stage Stern–Gerlach experiment conducted by Frisch and Segrè includes two cascaded quantum measurements with a nonadiabatic flipper in between. The Frisch and Segrè experiment has been modeled analytically by Majorana without the nuclear effect and subsequently revised by Rabi with the hyperfine interaction. However, the theoretical predictions do not match the experimental observation accurately. Here, we numerically solve the standard quantum mechanical model, via the von Neumann equation, including the hyperfine interaction for the time evolution of the spin. Thus far, the coefficients of determination from the standard quantum mechanical model without using free parameters are still low, indicating a mismatch between the theory and the experiment. Non-standard variants that improve the match are explored for discussion.