Abstract
Originally conceived as a thought experiment, an apparatus consisting of two Stern–Gerlach apparatuses joined in an inverted manner touched on the fundamental question of the reversibility of evolution in quantum mechanics. Theoretical analysis showed that uniting the two partial beams requires an extreme level of experimental control, making the proposal in its original form unrealizable in practice. In this work, we revisit the above question in a numerical study concerning the possibility of partial-beam recombination in a spin-coherent manner. Using the Suzuki–Trotter numerical method of wave propagation and a configurable, approximation-free magnetic field, a simulation of a transversal Stern–Gerlach interferometer under ideal conditions is performed. The result confirms what has long been hinted at by theoretical analyses: the transversal Stern–Gerlach interferometer quantum dynamics is fundamentally irreversible even when perfect control of the associated magnetic fields and beams is assumed.
Highlights
The experiment by Stern and Gerlach performed in 1921 [1,2]proved to be of fundamental importance for the development of quantum mechanics
There is Wigner’s scheme, in which the inhomogeneous magnetic field from an electric current recombines the beams that emerge from the Stern–Gerlach apparatus (SGA) [19]; it has not been used for a quantitative model
The results of our simulation confirm the intuition that the quantum dynamics of a Stern–Gerlach apparatus is not reversed by the application of inverse magnetic fields even if one has perfect control over the experimental apparatus
Summary
The experiment by Stern and Gerlach performed in 1921 (a centennial this year) [1,2]. The analysis of Bohm’s proposal gave rise to what is known as the Humpty-Dumpty problem [20,21,22] of the coherent recombination of spatially separated partial atomic beams (i.e., the spin-up and spin-down components of the spinor wave function) from an SGA as well as to a plethora of experimental techniques within the domain of matter-wave interferometry, all of which use different approaches to work around the fantastic precision required to realize the original proposal by Bohm. The results of our simulation confirm the intuition that the quantum dynamics of a Stern–Gerlach apparatus is not reversed by the application of inverse magnetic fields even if one has perfect control over the experimental apparatus
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