Visualizing the Lorentz Transformation

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1 Lightyear at rest

1 Lightyear at current speed

Your Spaceship

1 Second

What is all this jibber jabber about?

Hendrik Lorentz being a badass

This is the result of my pondering on the Lorentz Transformation, which is the result of Hendrik Lorentz's pondering on how the speed of light is observed to be constant in all frames of reference. This constancy requires us to make variables out of things we once thought were constants. Those variables are space and time.

I came to the realization that as an observer approaches the speed of light, the distances that were once observed at rest now appear to be much shorter. As a matter of fact, all distances go to 0 as one approaches the speed of light. Could it really be that two observers traveling at different velocities would disagree on how long a meter is? This goes against all of my intution and I wanted to play with the relationship between velocity and space/time. That's why I made this. I don't study physics, but I find this relationship particularly profound.

Some things to note

The visualizations are a bit conflated in terms of reference frames. The Distance Visualizer shows how far one light year appears to you compared to observers at rest. The Clock Visualizer is from the reference frame of someone at rest looking at your "1 Second Clock". As you approach the speed of light, if they could possibly make out anything on your ship, they would see that all of the natural processes have slowed.

Oh, and the spaceship distortion is a sham. I wanted to implement the Penrose-Terrell Rotation, which would cause an elongation plus a rotation along the Z-axis, but given the spaceship is a 2D SVG, I can't really do that. Plus, as you approached the speed of light, the spaceship skews into infinity in the direction the ship is moving. It's really wild stuff.

Why does it skew into infinity? Think about it. Say you're the one at rest. This spaceship is about to fly by you from left to right at a considerable distance away. The way you see that ship is from light that is emitted and bounced off the ship and back into your eyes. The ship is going fast enough to hit a loooooong line of photons spanning many many miles in almost parallel. All of those photons come back to your eyes and the result is an elongated ship. Not only elongated, but you can also see some of the back of the ship, like it has been rotated. Really wild stuff.