Limitations of Determinism in Classical Mechanics

Hrvoje Nikolić

Ruggero María Santilli

In this paper, we continue the study initiated in preceding works of the argument by A. Einstein, B. Podolsky and N. Rosen according to which quantum mechanics could be “completed” into a broader theory recovering classical determinism. By using the previously achieved isotopic lifting of applied mathematics into isomathematics and that of quantum mechanics into the isotopic branch of hadronic mechanics, we show that extended particles appear to progressively approach classical determinism in the interior of hadrons, nuclei and stars, and appear to recover classical determinism at the limit conditions in the interior of gravitational collapse

John Earman

Suyu Li, Canneng Liang, Mingxing Jin

Identity principle is a fundamental postulate of quantum mechanics. In this paper, from a philosophical point of view, we revisit the identity principle of quantum mechanics. We attribute the identity to the existence of a precision limit for observation: the microscopic objects become indistinguishable when the difference between them is lower than the precision limit. This precision limit is determined not by the measuring apparatus, but by the action quantum h behand the objective physical law. We deduce logically how to relate the identity principle with the probabilistic interpretation, uncertainty principle, quantization in quantum mechanics, attempting to sorting out some logic for quantum theory. The indistinguishability of identical particles makes it impossible to accurately obtain all the details about the microscopic objects at the same time, and consequently the microscopic objects can only be described statistically, leading to the probabilistic determinism and indeterminacy of initial state in quantum mechanics. By reviewing Bohmian mechanics, one of the nonlocal hidden variable theories, we discuss the possibility of restoring determinism and causality in quantum mechanics by restoring the determinacy of initial state. However, any hidden variable theory constructed by using only the terminologies of classical physics cannot reproduce the quantum mechanical predictions. It is the identity principle that makes it impossible to restore causality and determinism, and is the root that makes quantum mechanics different from classical physics. Finally, the boundary between the so-called classical and quantum worlds is discussed. We hope these philosophical arguments can provide a kind of epistemic understanding for quantum mechanics.

John Earman

William Hughes Miller

Using a classical phase space integral to approximate certain quantum mechanical operations, the classical limit of the Fredholm determinant for a general multichannel scattering system is derived. This statistical form of the classical limit of scattering is found to give exactly the same ``classical S matrix'' for the case of potential scattering as does a dynamical treatment of the classical limit. For inelastic scattering, however, the classical S matrix which results from this Fredholm determinant is only an approximation to that obtained by exact classical dynamics. Reasons for this failure of the statistical version of the classical limit for inelastic scattering are discussed.