Quantum Mechanical Indeterminacy and Conservation Laws

TL;DR

This paper explores how quantum indeterminacies relate to conservation laws, showing that energy conservation can be complex and context-dependent, especially in entangled systems and superpositions.

Contribution

It analyzes the nuanced relationship between quantum indeterminacy and conservation laws, highlighting cases where energy conservation is not straightforward.

Findings

Energy and indeterminacy can be intricately connected.

Entangled superpositions can yield definite net observables.

Energy conservation is context-dependent and not universally defined.

Abstract

Conservation laws are discussed in conjunction with quantum-mechanical indeterminacies of the corresponding observables. The considered examples show that the connections between energy and its indeterminacy may be quite intricate. The indeterminacies of the parts of a composite system may be correlated in such a way that the net value of the considered observable is definite. This may be the case with specific entangled superposition of eigenstates in a composite system. In some cases the fact of energy conservation cannot be convincingly established and generally the concept of conserving observable is not universally defined to embrace all possible situations under one rule. Keywords: energy, conservation, indeterminacy, photon