TOPOLOGY CHANGE AND QUANTUM PHYSICS

TL;DR

This paper explores how classical topology emerges from quantum states and how boundary conditions can induce topology change, suggesting a deeper microstructure underlying gravity with additional degrees of freedom.

Contribution

It demonstrates that classical topology arises from quantum state properties and boundary conditions, and shows topology can change smoothly or exist in superpositions within quantum physics.

Findings

Classical topology emerges from quantum state properties.

Topology can be changed smoothly via boundary conditions.

Quantum superpositions of different topologies are possible.

Abstract

The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge from considerations on the domain of the quantum Hamiltonian, this domain being often specified by boundary conditions in elementary quantum physics. Several examples are presented where classical topology is changed by smoothly altering the boundary conditions. When the parameters labelling the latter are treated as quantum variables, quantum states need not give a well-defined classical topology, instead they can give a quantum superposition of such topologies. An existing argument of Sorkin based on the spin-statistics connection and indicating the necessity of topology change in quantum gravity is recalled. It is suggested therefrom and our results here that Einstein gravity and its minor variants are effective theories of a deeper description with additional novel degrees of freedom. Other reasons for suspecting such a microstructure are also summarized.