Hypnotizing Lorentz Transformation

Hey all,

Today’s math art is an animated one! What you’re seeing is an animated spherical standing wave system undergoing a Lorentz transformation. Now, say that previous sentence all at one go. Without fudging up. Okay… today’s math-art is created by Gabriel LaFreniere.

Okay… now for the techy part where you can skip… So what is a Lorentz transformation? Wikipedia tells me it “…converts between two different observers’ measurements of space and time, where one observer is in constant motion with respect to the other.” General physics majors, if you don’t already know what a Lorentz transform is but yet the definition sounds familiar, its because something called the Doppler effect is quite similar to this.

The Doppler effect is the change of frequencies and wavelengths relative to the observer. An example would be if you’re a house burglar, and you just burgled a house that has a silent alarm to the police station. Just as you are going through the safe looking for pearl necklaces and diamond rings, you hear from a distance a sound of a police siren. It’s quite low pitched at first, but then you hear it getting louder, and the sound distorts into a higher pitched sound. Before you can calculate the ? of the sound, you find yourself being read your rights. That of course, is the Doppler effect. The pitch change is caused by the ‘compressing’ of wavelengths v = f? (since v is assumed constant), so the frequency appears to change.

The Doppler effect doesn’t only work on sound, it also works on light. I’m sure at the very least, in high school physics, you’ve heard of blue-shift and red-shifts? Same concept, applied to different wave forms.

While the Doppler effect is an ‘effect’, the Lorentz transformation can be seen as the ‘process’ which causes the effect. Again, this is only under very controlled circumstances. Take today’s math art for example. The Lorentz transformation is applied to an electron (its a simulation of course). According to Gabriel, when a Lorentz transformation is applied to a matter wave, its result is a Doppler effect. Right. I’d explain more, but just take Gabriel’s word for it yea?

Well.. if you skipped the above techy nonsense… good. You’re just as bored as I am. So get yourself hypnotized by the electron undergoing a Lorentz transformation then. I know I am hypnotized. Quack quack.