Imaginary Time and the Arrow of Time: Interplay Between Relativity and Quantum Mechanics

The existence and directionality of time are fundamental issues in modern physics. Special relativity is based on two principles: the invariance of physical laws in all inertial frames and the constancy of the speed of light in vacuum\cite{SRPostulates}. These principles lead naturally to a four‑dimensional spacetime with a distinct time coordinate. In quantum mechanics and quantum field theory the imaginary unit~$i$ appears essentially in dynamical equations such as the Schrödinger equation and in path‑integral formulations. Mathematically, multiplying real time by~$i$—a so‑called Wick rotation—transforms the Minkowski spacetime metric into a Euclidean metric\cite{WickRotation}. This paper analyses how the requirement of imaginary numbers in quantum theory and the postulates of relativity together imply the existence of a one‑way time axis associated with the imaginary direction. We review the role of imaginary time in relativistic geometry and quantum dynamics, discuss the thermodynamic arrow of time and its link to entropy increase\cite{ArrowOfTime}, and present theoretical considerations supporting the claim that time exists and is oriented along a one‑directional imaginary axis.