# Lorentz Transformation in Mathematica appears wrong.

1. Mar 27, 2013

### Floating Info

So, I'm trying (keyword trying) to learn a bit of special relativity on my own via the Stanford lectures on Youtube by Leonard Susskind, but I'm running into a problem.

According to the lectures, for two different reference frames with co-ordinates marked (x, t) and (x', t'), the latter moving, x' = x cosh(ω) - t sinh(ω), and t' = t cosh(ω) - x sinh(ω). (The velocity of the moving reference frame is sinh(ω)/cosh(ω). c = 1.). I've tried to graph this in Mathematica as an animation with omega (and thus velocity) increasing per frame.

Here is my code:

List1 = {};
List2 = {};
For[ω = 0, ω <= 1, ω = ω + 0.1,
For[x = -5, x <= 5, ++x,
For[t = -5, t <= 5, ++t,
AppendTo[
List1, {x Cosh[ω] - t Sinh[ω], -x Sinh[ω] +
t Cosh[ω]}]]]; AppendTo[List2, List1]; List1 = {}]
Animate[ListPlot[Part[List2, n]], {n, 1, 11, 1}]

The problem is, what I get is that, over time, the square turns into a gradually thinner parallelogram-like shape, but the "further" vertices are in the top left and lower right quadrants. According to the Wolfram Demonstrations Project, they should be in the top right and lower left quadrants. What did I do wrong?

Last edited: Mar 27, 2013
2. Mar 28, 2013

### Hepth

You have the inverse transformation. So take the inverse of your matrix:

The inverse of {{cosh,-sinh},{-sinh,cosh}} is {{cosh,sinh},{sinh,cosh}}

Its all about in which direction you're rotating.

What it boils down to is to switch the signs on the Sinh's