Extended space-time and the interpretation of wave functions

Thomas Filk A

It is argued that many of the so‐called “mysteries” of quantum mechanics like the “particle‐wave duality” or the “spooky action at a distance” loose their weirdness if space itself, the “embedding” of quantum objects into space, and the entanglement among quantum objects are interpreted as relational concepts. Extended to space‐time, this approach may allow for a new interpretation of Haag’s localization of events.

Wolfram Schommers

Ovidiu Cristinel Stoica

One of the major concerns of Schr\"odinger, Lorentz, Einstein, and many others about the wave function is that it is defined on the $3\mathbf{N}$-dimensional configuration space, rather than on the three-dimensional (3D) physical space. This gives the impression that quantum mechanics cannot have a $3\mathrm{D}$ space or space-time ontology, even in the absence of quantum measurements. In particular, this seems to affect interpretations which take the wave function as a physical entity, in particular, the many-worlds and the spontaneous collapse interpretations, and some versions of the pilot wave theory. Here, a representation of the many-particle states is given, as multilayered fields defined on the three-dimensional physical space. This representation is equivalent to the usual representation on the configuration space, but it makes it explicit that it is possible to interpret the wave functions as defined on the physical space. As long as only unitary evolution is involved, the interactions are local. I intended this representation to capture and formalize the nonexplicit and informal intuition of many working quantum physicists, who, by considering the wave function sometimes to be defined on the configuration space and sometimes on the physical space, may seem to researchers in the foundations of quantum theory as adopting an inconsistent view about its ontology. This representation does not aim to solve the measurement problem, and it allows for Schr\"odinger cats just like the usual one. But, it may help various interpretations to solve these problems, through inclusion of the wave function as (part of) their primitive ontology. In appendices, it is shown how the multilayered field representation can be extended to quantum field theory.

Xinchuan Zeng

J. Anandan, Harvey R. Brown

Yan Breek

This article proposes a unified theory framework encompassing a discrete topological interpretation of physical forces, wave functions, and the nature of space and time. It provides novel explanations for the collapse of wave functions, quantum entanglement, and offers insights into the origins of quantum probabilities. This article also explains the nature of mass, Higgs field, and suggests a path for unifying quantum mechanics and gravity. Elementary particles are represented as defects in discrete topological spaces. Entangled particles are directly connected to each other through a puncture in discrete space, separated by a distance of one Planck length. Wave functions are explained as mechanical stress waves within elastic discrete space. The results of the double-slit experiment are interpreted as wave functions maximizing the probability of rupture in high-stress areas of discrete space with obvious analogies to solid state mechanics. Wave-particle duality is explained as discrete topological defects causing extended distributed stress within space lattice.