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Optical and Quantum Sensing and Precision Metrology II

Modeling of the multi-stage Stern–Gerlach experiment by Frisch and Segrè using co-quantum dynamics via the Bloch equation

Kelvin Titimbo, David C. Garrett, S. Suleyman Kahraman, Zhe He, Lihong V. Wang

Published Mar 12, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.3002093

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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.
Abstract We numerically study the spin flip in the Frisch–Segrè experiment, the first multi-stage Stern–Gerlach experiment, within the context of the novel co-quantum dynamics (CQD) theory. 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 simulation shows that CQD closely reproduces, without using any fitting parameters, the experimental observations reported by Frisch and Segrè in 1933, which have so far lacked theoretical predictions.
We numerically study the spin flip in the Frisch$\unicode{x2013}$Segrè experiment, the first multi-stage Stern$\unicode{x2013}$Gerlach experiment, within the context of the novel co-quantum dynamics theory. 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. Our results show that, without using any fitting parameters, the co-quantum dynamics closely reproduces the experimental observation reported by Frisch and Segrè in 1933, which has so far lacked theoretical predictions.
The 1922 experiment of Stern and Gerlach that initially provided evidence of the quantization of the angular momentum is now a prototypical example of quantum measurement. Frisch and Segrè in 1932 extended the experiment to include two Stern–Gerlach apparatuses separated by an inner rotation chamber, in which a varying magnetic field produces partial electron spin flipping. To this day, quantum mechanical treatments inadequately predict the experimental observations. Here, we use a theory termed co-quantum dynamics (CQD) to numerically model spin flip in the multi-stage Stern–Gerlach experiment conducted by Frisch and Segrè. Our simulation solves the Schrödinger equation with electron-nuclear interactions according to CQD and utilizes a branching condition (extended Pauli exclusion principle) postulated by CQD to predict the collapse of electron spins; the outcome agrees with the measurements of the fraction of spin flipping and supports CQD as a potential model for electron spin evolution and collapse.
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.
We use a theory termed co-quantum dynamics (CQD) to numerically model spin flip in the multi-stage Stern$\unicode{x2013}$Gerlach (SG) experiment conducted by R. Frisch and E. Segrè. This experiment consists of two Stern$\unicode{x2013}$Gerlach apparatuses separated by an inner rotation chamber that varies the fraction of spin flip. To this day, quantum mechanical treatments inadequately predict the Frisch$\unicode{x2013}$Segrè experiment. Here, we account for electron-nuclear interactions according to CQD and solve the associated Schrödinger equation. Our simulation outcome agrees with the Frisch$\unicode{x2013}$Segrè experimental observation and supports CQD as a potential model for electron spin evolution and collapse.
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.