[choeger]

What even is the speed of causality? Is there any way to determine that causality has made it halfway from cause to effect?

Or is this just a metaphysical way of saying that no particle can move faster than the speed of light, assuming that causality is just an abstraction of moving particles around?

[hughesjj]

Network propagation delay ;-)

Imagine the world without a speed of causality, where everything was updated instantaneously. No CAP theorm, no Byzantine generals.

Being a programmer/information theorist would be so much easier lol

[crdrost]

It kind of is that (a metaphysical restatement), but it's more precisely understood as a kind of half-statement of the theory.

That is, if you assume relativity, then for anything which moves faster than speed c, there exists some reference frame where it appears to move backwards in time. (This needs to be slightly qualified because it's kind of like when you're looking in a mirror and you intuitively don't think it does what it actually does -- flip front to back -- but you mentally rotate and then think that it flips left-to-right. So to be clear, if someone on a hyperluminal rocket cracks an egg into a pan, there exists someone else whose best understanding of this situation is a rocket that is traveling "backwards" engine-first, onboard of which an egg is flying up from the pan into an eggshell. But you would mentally reorient to say that the rocket is traveling "forwards" and that "forwards" direction is backwards in time.)

Now, this doesn't directly violate causality by itself, it depends on whether you can move faster than light according to an arbitrary observer. So if Carol goes faster than light according to Alice and then turns and goes faster than light according to Bob, and Bob is moving relative to Alice, only then can Carol potentially meet up with her "past self" according to Alice & Bob. The idea is that the first time she moves, Alice says she's moving very fast, but forward in time, and Bob says she's moving backward in time. Then the second time she moves, Bob says she's moving very fast, but forward in time, and Alice says she's moving backward in time. You combine these two to find that both agree that she has objectively moved backward in time.

The way this manifests in the mathematics is that in relativity, after something happens, light kind of "announces" that it happened to the rest of the world, via an expanding bubble of photons traveling away from the event at speed c. This expanding bubble is formally known as a "light cone". There is another light cone as well: before the event happens you can understand a contracting bubble of photons traveling towards the event. And basically these partition the world into five regions: The contracting bubble is the "objective past" of the event, that bubble itself is the "null past" of the event, the spacetime between the bubbles is the "general present" of the event, the expanding bubble is the "null future" of the event, and the points inside of the bubble are the "objective future" of the event. Moving faster than light, is moving from the objective future of an event, into its general present. This is "general" because different reference frames regard these points as either before or after the event in time. You need a second trajectory to then go from the general present of the event, to its objective past.