Quantum Mechanics Without State Vectors

TL;DR

This paper proposes a shift from state vector ensembles to solely using density matrices for quantum states, exploring new symmetry transformation properties and implications for quantum theory.

Contribution

It introduces a novel approach to quantum states using only density matrices and investigates their transformation properties under symmetry groups.

Findings

Density matrices can describe quantum states without ensembles.

New symmetry transformation behaviors for density matrices are identified.

Loopholes exist in extending traditional symmetry actions to density matrices.

Abstract

It is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying instead solely on the density matrix as the description of reality. With this definition of a physical state, even in entangled states nothing that is done in one isolated system can instantaneously effect the physical state of a distant isolated system. This change in the description of physical states opens up a large variety of new ways that the density matrix may transform under various symmetries, different from the unitary transformations of ordinary quantum mechanics. Such new transformation properties have been explored before, but so far only for the symmetry of time translations into the future, treated as a semi-group. Here new transformation properties are studied for general symmetry transformations forming groups, rather than semi-groups. Arguments are given that such symmetries should act on the density matrix as in ordinary quantum mechanics, but loopholes are found for all of these arguments.