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.
KEYWORDS: Quantum experiments, Modeling, Magnetism, Chemical species, Potassium, Monte Carlo methods, Data modeling, Quantum physics, Quantum phenomena, Quantization
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.
Visualization of the spatiotemporal dynamics of propagation is fundamental to understanding dynamic processes ranging from action potentials to electromagnetic pulses, the two ultrafast processes in biology and physics, respectively. Here, we demonstrate differentially enhanced compressed ultrafast photography to directly visualize propagations of passive current flows at approximately 100 m/s along internodes from Xenopus laevis sciatic nerves and of electromagnetic pulses at approximately 5×107 m/s through lithium niobate. The spatiotemporal dynamics of both propagation processes are consistent with the results from computational models, demonstrating that our method can span these two extreme timescales while maintaining high phase sensitivity.
We introduce a three-dimensional photoacoustic computed tomography (3D-PACT) system with unparalleled imaging depth, clarity, and speed, and demonstrate that the imaged structural and functional optical contrast provide a unique tool for preclinical research and an appealing prototype for clinical translation. 3D-PACT allows for multipurpose imaging of biological tissues ranging from the rodent brain to the human breast. In the rat brain, we visualized whole brain vasculatures, oxygenation dynamics, intrinsic functional connectivity, and electrical-stimulation-induced hemodynamics. In the human breast, an in vivo imaging depth of 4 cm has been achieved by scanning the breast within a single breath hold of 10 seconds. 3D-PACT holds a high reliability to reproducibly generate detailed images with a contrast similar to that provided by contrast enhanced magnetic resonance imaging, yet with higher spatiotemporal resolution and without using exogenous contrast agents.
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