Artwork illustration for the relativistic subject of The Lorentz Transformations Equations. Artwork: NaturPhilosophie with AI

The Lorentz Transformation

Measurements with respect to non-inertial reference frames can be transformed to an inertial frame by incorporating directly the acceleration of the non-inertial frame as that acceleration as seen from the inertial frame.

For this, we use a set of very simple equations, well-known to undergraduate students, called the Lorentz transformation equations:

t' = \gamma (t - \frac{vx}{c^2}) \\* x' = \gamma (x-vt) \\* y' = y \\* z' = z

where (t, x, y, z) and (t', x', y', z') are the coordinates of an event in two frames with their origins coinciding at t = t' = 0 , where the primed frame is seen from the unprimed frame as moving with speed v along the x -axis and

where c is the speed of light, and the factor \gamma = (\sqrt{1 - \frac {v^2}{c^2}})^{-1} is the Lorentz factor.

So that’s the technical background to this answer.

Because we need to consider this problem from different observers’ points of view, that is to say different frames of reference.

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