Comment by greysphere
7 hours ago
One oddity of Lorentz invariance is that two non-parallel boosts decompose into a boost and spatial rotation.
I've never quite wrapped my head around this and was hoping to get some insight from this simulation. But afaict, I'm not seeing this effect (press W for a bit, the A for a bit and it's not obvious I'm at a different orientation - if I look down at the ground the gridlines are still axial).
I don't know if I'm misinterpreting the math, or the simulation, or maybe the simulation is doing something to 'correct' for this behavior so things are more natural, or something else. Does anyone have any insight?
go past the cubes at near lightspeed, you'll see them rotated; you can see their back planes even before you passed them.
That’s just the aberration, no? I.e., you can simply smash A and observe some rotation. Since there are no non-collinear accelerations in this case, it’s certainly not the required effect (which is called Wigner rotation).
In the sources I see that the acceleration is applied simply by utilizing a velocity‐addition formula (see https://github.com/dbrant/relativity/blob/fcc20fb18381959ac2...), so no Wigner rotation appears. I guess all the fancy stuff related to how time passes in an accelerating frame (like https://en.wikipedia.org/wiki/Twin_paradox#Difference_in_ela...) is also wrong in this simulation because of that.
You can however observe a mathematically equivalent effect in hyperbolic games, e.g., in Hyperbolica. Hyperbolica even has a quest about rotating a chest by moving it along the axes. On the hyperbolic plane it’s of course not about acceleration but about a winding number you’re doing around some point, but it’s still fun.