Space-Time in Quantum Theory

TL;DR

This paper explores the necessity of redefining space-time in quantum theory due to the quantization of action, leading to a view where classical notions of continuous time and space are replaced by discrete, quantum jump-based concepts.

Contribution

It introduces a new conceptual framework for space-time in quantum physics, emphasizing the role of quantized action and the resulting discrete nature of physical quantities.

Findings

Classical space-time notions are replaced by a manifold of transition rates.

Quantum uncertainties arise naturally from action quantization.

Discreteness of physical quantities is fundamental to quantum laws.

Abstract

Quantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of light $c$ not being infinite calls for a redefinition of space-time on large and cosmological scales, quantization of action in terms of a finite, i.e. non vanishing, universal constant $h$ requires a redefinition of space-time on very small scales. Most importantly, the classical notion of "time", as one common continuous time variable and nature evolving continuously "in time", has to be replaced by an infinite manifold of transition rates for discontinuous quantum transitions. The fundamental laws of quantum physics, commutation relations and quantum equations of motion, resulted from Max Born's recognition of the basic principle of quantum physics: {\bf To each change in nature corresponds an integer number of quanta of action}. Action variables may only change by integer values of $h$, requiring all other physical quantities to change by discrete steps, "quantum jumps". The mathematical implementation of this principle led to commutation relations and quantum equations of motion. The notion of "point" in space-time looses its physical significance; quantum uncertainties of time, position, just as any other physical quantity, are necessary consequences of quantization of action.