Are observables necessarily Hermitian?

TL;DR

This paper argues that quantum observables need not be Hermitian but can be more generally represented as normal operators, aligning with physical observations and potentially enriching the understanding of quantum measurement.

Contribution

It proposes reformulating quantum observables as normal operators instead of strictly Hermitian, maintaining consistency with current quantum theory and physical observations.

Findings

Reformulation as normal operators does not alter physical predictions.

The approach aligns with observed eigenstates and spectrum distributions.

It deepens the conceptual understanding of measurement in quantum mechanics.

Abstract

Observables are believed that they must be Hermitian in quantum theory. Based on the obviously physical fact that only eigenstates of observable and its corresponding probabilities, i.e., spectrum distribution of observable are actually observed, we argue that observables need not necessarily to be Hermitian. More generally, observables should be reformulated as normal operators including Hermitian operators as a subclass. This reformulation is consistent with the quantum theory currently used and does not change any physical results. The Clauser-Horne-Shimony-Holt (CHSH) inequality is taken as an example to show that our opinion does not conflict with conventional quantum theory and gives the same physical results. Reformulation of observables as normal operators not only coincides with the physical facts but also will deepen our understanding of measurement in quantum theory.