Probability in the deterministic theory known as quantum mechanics.

Itamar Pitowsky

A deterministic model that accounts for the statistical behavior of random samples of identical particles is presented. The model is based on some nonmeasurable distribution of spin values in all directions. The mathematical existence of such distributions is proved by set-theoretical techniques, and the relation between these distributions and observed frequencies is explored within an appropriate extension of probability theory. The relation between quantum mechanics and the model is specified. The model is shown to be consistent with known polarization phenomena and the existence of macroscopic magnetism. Finally the possibility of a thought experiment which indicates a deviation from the predictions of quantum mechanics is described.

Itamar Pitowsky

Meir Hemmo, Orly Shenker

Roy C. Weatherford

Behaviorism has taught people a lot, and has helped move psychology towards the status of a science, but that science, when it finally arrives, will not be thoroughly behavioristic. The Classical Theory of Probability had the odd difficulty that it functioned properly only when nothing was known about the way the system to which it was applied actually worked. Albert Einstein rejected the popular view that quantum mechanics (QM) was the final word in physical theory and believed that it would eventually be replaced with a more fundamental, deterministic theory. He denied that there was any fundamental randomness in the universe and believed that the time at which any individual atom emits radiation is really determined in advance and that there would be some future theory, which he did not specify, that would allow people to predict when this would happen, even though the quantum theory did not.

Jincheng Zhang

Quantum-enhanced probability theory seeks to reconcile the seemingly paradoxical nature of quantum mechanics with the framework of probability theory. This paper explores a novel approach, extending standard probability theory to incorporate dynamically evolving landscapes with non-deterministic parameters, ultimately aiming to provide a more realistic model of quantum phenomena. We introduce a "landscape adjustment algorithm" that subtly alters the probabilities of different outcomes within the landscape, creating a probabilistic evolution. This mechanism represents a significant step towards bridging the gap between quantum mechanics and probability theory, offering a potentially transformative perspective on uncertainty and the inherent randomness within quantum systems.

Toshio Ishigaki