Multi-stage Stern–Gerlach experiment modeled

Abstract

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.

Numerical modeling of the multi-stage Stern–Gerlach experiment by Frisch and Segrè using co-quantum dynamics via the Schrödinger equation

“…Here, we present a numerical simulation using the Schrödinger equation based on the torque-averaged magnetic field ⃗ B n of the co-quantum with a continuous angular distribution, along with the branching condition, to yield a CQD model for the flip of electron spin in the Frisch-Segrè experiment. Our numerical simulation agrees with the Frisch-Segrè experimental observation and confirms our previous closedform analytical solution of CQD [12,13], which builds on the insightful analysis by Majorana [6].…”

“…We use |+z⟩ and |−z⟩ to denote the states where ⃗ µ e is aligned with +z or −z, respectively. Upon selecting the |+z⟩ branch from SG1, the associated co-quanta follow an anisotropic probability density function [12]:…”

“…In addition to the external field, the torque-averaged nuclear magnetic field given below also acts on the electron [12]:…”

“…To predict the experimental observation, the co-quantum dynamics (CQD) theory was developed by introducing the following concepts [12,13]. CQD considers the interaction between the electron (⃗ µ e ) and nuclear (⃗ µ n ) magnetic moments through the torque-averaged instead of self-averaged magnetic field, introduces an induction term, and treats ⃗ µ n as a non-collapsing co-quantum of the principal quantum ⃗ µ e .…”

“…The co-quantum guides the collapse of the principal quantum according to their relative orientations at the time of measurement, yielding the CQD branching condition [12,13]. CQD has been shown to statistically recover the quantum mechanical wave function from the continuous angular distribution of the co-quantum that is assumed to be isotropic for atoms immediately out of the oven (see figure 1) [12,13]. However, the angular distribution of the co-quantum is altered by the collapse of the principal quantum.…”