Probability in quantum mechanics according to E. Schrödinger

Gordey B. Lesovik

The concept of the theory of measurement and choice of quantum alternative is considered, according to which the outcome of a particular measurement is determined by the reservoir (detector) state. The way of deducing standard (probabilistic) quantum-mechanical interpretation rules is discussed, with special emphasis on the theoretical demonstration of the wave-function reduction phenomenon. The method of resolving the “Schrodinger cat” paradox is suggested. The interrelation between the mechanisms of formation of shot and flicker noises and the role of reservoir in the formation of quantum-mechanical probability is discussed.

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Toshio Ishigaki

Maksim Sozonov

This paper presents a deterministic temporal interpretation of quantum mechanics. It proposes that a particle has multiple possible trajectories, but it does not move along them simultaneously. Instead, the particle switches between trajectories over time, spending more time on the trajectory where the probability of detection is higher according to the Schrödinger equation. The particle does not have a fixed position until it interacts with a detector. This approach explains the statistical patterns observed in quantum experiments, such as the double-slit experiment, while maintaining determinism and remaining fully consistent with quantum mechanics.

Abner Shimony

Alireza Jamali

According to our current understanding of quantum mechanics, a `measurement' violates unitarity. In other words as the act of measurement `resets' the probabilities described by the Schrödinger equation, in the very `moment' of the collapse of the wavefunction, conservation of probability does not hold. To make progress in our understanding of the measurement problem it is thus expected that one must encompass in a single equation both otherwise mutually-exclusive processes of measurement and unitary evolution. In this light, turning to the continuity equation, we realize the possibility that if we allow for existence of sources and sinks in the `fluid of probability' we get closer to such a theory by arriving at nonlinear generalizations of Schrödinger and Klein-Gordon equations. The generalized equations derived are then shown to satisfy all conditions that are expected from a proper generalization: simplification to their linear counterparts by a well-defined dynamical condition, and Galilean and Lorentz invariance.