Probability and Uncertainty - the Quantum Mechanical view of Nature

Reiji Sugano

John Hemp

In this short paper, we point out that the interference of probabilities in the double slit experiment, or in a particle interferometer, should not necessarily lead us to think that a quantum mechanical particle’s position is a meaningless concept or that continuous motion of a quantum mechanical particle is an impossibility. We do not need to conclude that a particle must sometimes be in two places at once, or that nature herself does not know exactly where a particle is etc. We show that the argument leading to that kind of conclusion, based on the interference of probabilities, is illogical when probability is viewed in a rational Bayesian fashion i.e. as accounting for rational degree of belief in an occurrence rather than the relative frequency of that occurrence in many trials. We lend support to the view that much progress may be made in the interpretation of the quantum formalism and in the formation of physical pictures of processes in quantum mechanics by viewing probability in a rational Bayesian manner. Keywords Quantum Mechanics, uncertainty principle, Bayesian probability, Realism, QBism.

Zhonghao Lu

The deterministic nature of EQM (the Everett Interpretation of Quantum Mechanics) seems to be inconsistent with the use of probability in EQM, giving rise to what is known as the “incoherence problem”. In this paper, I explore approaches to solve the incoherence problem of EQM via pre-measurement uncertainty. Previous discussions on the validity of pre-measurement uncertainty have leaned heavily on intricate aspects of the theory of semantics and reference, the embrace of either four-dimensionalism or three-dimensionalism of personhood, or the ontology of EQM. In this paper, I argue that, regardless of the adoption of three-dimensionalism or four-dimensionalism of personhood, the overlapping view or the divergence view of the ontology of EQM, the pre-measurement uncertainty approach to the incoherence problem of EQM can only achive success while contradicting fundamental principles of physicalism. I also use the divergence view of EQM as an example to illustrate my analyses.

Tim Freegarde

Bryce de Witt