A delightful quirk of relativity theory

Well, another way of looking at it is that the observer is not the same as the decider.

So ultimately your reference frame is only current within the locus of your own mind and any decisions you make get broadcasted out to observers in the universe. They make their own decisions about where to be, how fast to be, and so on, and from their perspective it could be yesterday from when the decider decided, but its irrelevant just as much as being farther away in 3d space gives a longer delay in ping time.

Whether or not the decider has free will or not I don't think can be argued by this specific example.

The description of relativistic movement by hyperbolic rotations is really neat. One way I like to think of it is that moving with respect to some other observer puts you into a different "world", where the x and t axes are rotated towards each other. You can see from the diagrams that for example different events happen in different orders in both "worlds". And this is not just due to signal propagation, but there really is no "true" ordering if the events are sufficiently separated.

Bit there is one thing I never understood, even though I have a PhD in physics. Why does relative movement put you into a different "world"? Or more precise, why does relative movement correspond to a lorentz boost? That is not a piori neccessary. A stupid example is a laser pointed to the moon. If you flick it quickly, the spot can move faster than light over the ground. But you can also imagine mass moving independent of boost. You have a rock at x=0, t=0. At t=1, cut it and paste it at x=1. At t=2, cut it and paste it at x=2. Now make the time steps infintely small. It is moving (in the sense of dx/dy>0) but not moving (in the sense of v or ß = 0).

My intuition is, if you look at electromagnetism, it takes some time for a changing electric field to create a magnetic field, and for the magnetic field to create an electric field. This is what Einstein meant when he said, time exists so that not everything happens at once. If you think of a relatively moving object - and I'm thinking of it completely in terms of EM for the sake of simplicity - what happens is that the fields are propagating. One field creates the next field not at the same space but slightly in front. So the whole thing is rotated towards the x axis. The "time" vector does not point completely in the time direction, but in the space direction. This gives you time dilation as well as the subjective experience of an intertial frame (because you are just moving forwards in time, but not in space from your POV). I think this microscopic perspective shows why motion must == boost. But does anybody here know if there is a canonical answer to this question?

Edit: I just realize this is basically electromagnetism of moving bodies which Einstein already solved in 1905 :-) but I still find it hard to wrap my head around

It is interesting that "real" observations of relativistic objects are quite different from what you expect them to be. For example, a cube passing by at relativistic speed would appear as if it is rotating towards you. This allows you to see some of its sides which you normally wouldn't [1].

[1] https://en.wikipedia.org/wiki/Terrell_rotation

At least when you think of objects moving slower than light there can't be reversing of casuality. But relativity allows for that, we just drop the faster than light solutions usually as non-physical.

Recently there's been an interesting paper about what happens when we don't drop these solutions: https://arxiv.org/abs/1910.02780

Imagine the Andromeda fleet can move faster than light. When you look at it from Earth POV suddenly it manifests near Earth out of nothing. Looks very similar to quantum mechanics indeterminism - if alien general decided to send the fleet it's there, if he didn't - it's not there, and there's no local cause for it appearing suddenly.

What the paper above explores is - starting from relativity including faster-than-light objects and trying to prevent paradoxes they derive quantum mechanics.

> "The more you move in space, the less you move in time."

Even better IMO: everything is moving at the max speed (c) through spacetime, and accelerating along one dimension means decelerating along other dimensions; for example, stationary objects have 0 speed in spatial dimensions but move at c through time, and photons move at c through space but are stationary along the time dimension.