On the temporal wavefunction in quantum physics - a short note

TL;DR

This paper explores the role of time as a wavefunction variable in quantum mechanics, proposing a symmetric treatment of space and time, and analyzing how this affects nonlocality and interference phenomena.

Contribution

It introduces a temporal wavepacket framework that treats time symmetrically with space in quantum wavefunctions, offering new insights into nonlocality and measurement.

Findings

Temporal wavepackets can explain nonlocality as a spread in time.

Position in two-slit experiments relates to independent phases of space and time.

The approach extends Born's law to include temporal variables.

Abstract

Experiments involving single or few elementary particles are completely described by Quantum Mechanics. Notwithstanding the success of that quantitative description, various aspects of observations, as nonlocality and the statistical randomness of results, remain as mysterious properties apart from the quantum theory, and they are attributed to the strangeness of the microscopic world. Here we restart from the fundamental relations of uncertainty to reformulate the probability law of Born including the temporal variable. Considering that both the spatial and the temporal variables play a symmetric role in the wave-function \Psi (x,t) , a temporal wavepacket is built and analysed. The probability density is written as p(x,t) = | \Psi (x,t) |^2, where the probabilistic interpretation for the temporal wavepacket is equivalent to Born's law for the spatial variable, x. For the convenience of the discussion of the role of the temporal variable, we write p(x_0,t) = | \Psi (x_0,t) |^2 for a free particle, expressing only the temporal wavepacket, then we discuss its spread. In the light of the evolution of this temporal wavepacket we analyse basic processes of matter-wave interaction, involving single and entangled entities. Nonlocality appears then as a consequence of the spread of the temporal wavepacket; and the position of each detected event in two-slits interferometry as due to the independent phases of the spatial and temporal wavepackets.