Lorentz transformation, time dilation, length contraction and Doppler Effect - all at once

TL;DR

This paper offers a straightforward derivation of Lorentz transformations, illustrating how length contraction, time dilation, and Doppler effects naturally emerge from the relative measurement of space-time intervals without assuming their specific nature.

Contribution

It provides a simple, assumption-free derivation of Lorentz transformations that simultaneously explains length contraction, time dilation, and Doppler shift as consequences of relative motion.

Findings

Derivation based on relative measurement modifies space-time intervals

Formulas for length contraction, time dilation, and Doppler shift are derived as outcomes

No prior assumptions about the nature of these effects are needed

Abstract

We present a simple derivation of the Lorentz transformations for the space-time coordinates of the same event. It is based on the relative character of length and time interval as measured by observes in relative motion. We begin by accepting that the relative motion modifies in some particular way the result of these measurements. However we do not postulate the character of this distortion i.e. whatever it is dilation or contraction. The formulas accounting for length contraction, time dilation and Doppler shift are a byproduct of this derivation.