Time Dilation in Lorentzian and Modified Euclidean Metrics of Space–time

Abstract

In the relativistic Lorentzian metric transformation, Minkowski (The Principle of Relativity, 1908 [1]) realised the possibility for a two-dimensional representation of the interrelationships between bodies having large relative velocities. This realisation paved the way for the concept of spacetime in Einstein’s Special Theory of Relativity. Hartle and Hawking’s proposal (Phys. Rev. D 28:2960, 1983 [2]) employed Wick’s rotation transformation to transform the Lorentzian metric to a Euclidean metric in an attempt to resolve the issue of singularity in the light cone. This work is an attempt to show that the concept of spacetime, involving light cone in two dimensions, based on the Lorentzian and Euclidean metrics is rather a mathematical artifact than a physical reality and may lead to conflicting results as far as time dilation is concerned.