Lorentz Transformation Equations in Galilean Form

TL;DR

This paper reformulates Lorentz transformation equations in a simplified, Galilean-like form using vector space representations with different inner products for each reference frame, highlighting a new perspective on relativistic transformations.

Contribution

It introduces a novel approach to express Lorentz transformations in a Galilean form by employing vector space representations with frame-dependent inner products.

Findings

Lorentz transformations can be expressed in a simple Galilean-like form.

Different reference frames can share a vector space with distinct inner products.

The inner products are determined by each frame's observational setup.

Abstract

Using the notion, developed in an earlier paper, of "representation" of "position" by a vector in a vector space with an inner product, we show that the Lorentz Transformation Equations relating positions in two different reference frames can be put in a particularly simple form which could be said to be "Galilean". We emphasize that two different reference frames can use a common vector space for representation but with two different inner products. The inner products are defined through the observational set-up of each frame.