Recovering Absolute Time in the Lorentz Transformation -The Apparent Nature of Relative Simultaneity

Relative simultaneity remains a highly debated issue. It is presented as a necessary physical consequence of the Lorentz transformation (LT). However, we demonstrate that the phenomenon is an artefact of 'mixed-coordinate' algebraic representation, which does not guarantee that the stationary system S 4-vector transformed to the moving system S’ are both covariant. A covariant representation of a transformed 4-vector which components are explicit functions of time, requires them to be expressed as functions of the local time in S and in the moving frame S'. While the one step multiplication of LT matrix by the 4-vector in S, yields correct algebraic expressions, the ‘raw’ resulting 4-vector retains the variable t throughout all components. This ‘mixed-coordinate’ representation is incomplete; it is not in a form covariant with the vector in S because its components are not functions of t'. The variable t must be replaced by equating the first component of the transformed vector to ct’ and substituting the resulting expression into all instances of t in the ‘raw’ 4-vector. After this procedure applied to two simultaneous events in S, the apparent time difference between the events in S’ becomes ∆t’=0. The effect of relative simultaneity, which appears in the ‘mixed-coordinate’ representation, is absent. This highlights the role of emergent ‘absolute-like time’ hidden within the structure of LT equations affecting temporal relations, suggests that the "Relative Now" discussed by Eddington in 1927 resulting from widely known conclusion ∆t’≠0 is a mathematical artefact of coordinates convention rather than the physical reality.