[XorNot]

It did recently occur to me that it's not a hard requirement that FTL be impossible, just that causality not be violated. There may be solutions to FTL where naively they could violate causality, but in practice other effects ensure that no usage of them ever will.

[captn3m0]

The Atomic Rockets website[0] describes the issue clearly:

Relativity proves that FTL travel is identical to Time travel.

Time travel makes Causality impossible, since it can be used to create paradoxes. Note that to a physicist, it is not enough that time travel never happens to be used to make a paradox. The mere fact it is possible is enough to utterly destroy Causality.

1. So if you have Relativity and FTL, Causality is impossible

2. If you do not have Relativity, then FTL is not Time travel, so you can have Causality.

3. Or more mundanely you can have Relativity and Causality, but no FTL/Time travel

∴ Causality, Relativity, FTL travel: chose any two.

[0]: http://www.projectrho.com/public_html/rocket/fasterlight.php...

[codethief]

> The Atomic Rockets website[0] describes the issue clearly:

I don't find their description very clear. In particular, they don't even define

- what "faster-than-light" is supposed to mean in a non-relativistic setting (Newtonian mechanics) where there's no such thing as a universal velocity and you're dealing with Galilean velocity transformations.

- what causality is supposed to mean exactly outside the relativistic setting where you have a universal velocity which induces the causal structure.

All in all, their definitions are very inter-dependent, so the "trichotomy" they present as truth doesn't make much sense to begin with. From my POV, they're not even wrong[0].

Moreover, they seem to only consider Special Relativity and completely ignore General Relativity where the speed-of-light bound is only a local bound. Basically, even if what they say were true, it would still not apply to the General Relativistic setting we're looking at here.

> Time travel makes Causality impossible, since it can be used to create paradoxes

This is not so clear, either, compare e.g. https://en.wikipedia.org/wiki/Novikov_self-consistency_princ...

[0]: https://en.wikipedia.org/wiki/Not_even_wrong

[XorNot]

This is missing the point though: it's not "optional" per se - it's that naively, if we simply go "what if FTL" then yeah, based on current physics we have a problem.

But the logic doesn't then mean "can't FTL" - it's still "can't have paradoxes". An FTL system, theoretically incapable of creating paradoxes, has no such problems.

An FTL system which prevents you from going faster then light in directions which allow violating causality would be totally fine, provided this was a theoretical restriction: i.e. your FTL engine just plain can't thrust in causality violating vectors, because it encounters some temporal restriction field or similar.

So the problem isn't "FTL is a causality violation", it's FTL without a mechanism to prevent causality violation is probably impossible.

The sci-fi conceit of it being difficult to plot efficient paths through hyperspace or whatever might well be quite a real thing, and simply related to charting causality-allowed courses through FTL-space.

[dragonwriter]

> Time travel makes Causality impossible

No, it makes the idea that causal sequence and temporal sequence are identical and that the former mapped against the latter can’t have cycles impossible.

Making causality more complex than we'd like to think it is isn't making it impossible.

[codethief]

Relevant link: https://en.wikipedia.org/wiki/Novikov_self-consistency_princ...