Nonconservation of Energy and Loss of Determinism II: Colliding with an Open Set

TL;DR

The paper argues that classical mechanics laws should be limited to finite or potentially infinite systems to avoid logical inconsistencies, which also resolves issues of indeterminism and energy non-conservation.

Contribution

It introduces a finite domain restriction for mechanical laws and demonstrates how this prevents non-conservation of energy and indeterminism.

Findings

Finite systems exhibit predictable asymptotic behavior.

Restrictions on system size eliminate logical inconsistencies.

Energy conservation is maintained under the proposed limitations.

Abstract

An actual infinity of colliding balls can be in a configuration in which the laws of mechanics lead to logical inconsistency. It is argued that one should therefore limit the domain of these laws to a finite, or only a potentially infinite number of elements. With this restriction indeterminism, energy non-conservation and (creatio ex nihilo) no longer occur. A numerical analysis of finite systems of colliding balls is given, and the asymptotic behavior that corresponds to the potentially infinite system is inferred.