A linear theory underlying quantum mechanics

TL;DR

This paper proposes a linear theoretical framework underlying quantum mechanics, suggesting that wave functions alone explain particle properties and that quantum field theory emerges from this foundational perspective.

Contribution

It introduces a linear, pre-representational theory that underpins quantum mechanics and explains particle properties without requiring objective particles.

Findings

Wave functions account for all particle-like properties.

Quantum field theory can be derived as a representation of the underlying theory.

No evidence supports the objective existence of particles.

Abstract

Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in conjunction with group representation theory, that the particle-like properties of mass, energy, momentum, spin and charge are attributes of the state vectors. These results can be used to show there is no evidence for the objective existence of particles. The properties of the wave function are sufficient to explain all the particle-like properties of matter. Representation theory is also extensively employed in the Standard Model, with gauge fields transforming as representations of the internal symmetry group. And when applied to the permutation group, it is essential for understanding symmetric and antisymmetric states. In fact all of quantum mechanics is set up exactly as if it were the representation of an underlying pre-representational theory. A linear equation structure for the underlying theory is suggested, and it is shown in outline how quantum field theory emerges as a representational form of the pre-representational theory.