Does instantaneous travel *in a privileged frame of reference* cause paradoxes?

[Sermil]

So, I'm pretty sure that, in special relativity, having a transport or communication system which is instantanous in one particular frame of reference doesn't cause causality issues.

In other words, I'm proposing an instant transport system that is only instant relative to a certain observer -- a single special frame of reference for the entire universe. For all other observers traveling at different speeds, transmissions going in one direction will go back in time but transmissions going in the opposite direction will go forward in time by the same amount. The end point of the transmission will still always be outside the 'past' or 'future' light cones of the sending event, though, since everyone agrees on light cones, and the special frame of reference sees the transmission going outside the light cone. And attempting to violate causality by using a round-trip will fail because the return trip always takes as long as the initial trip went backwards.

Obviously, this violates the philosophical idea of relativity (that all frames of reference are equally valid), but I don't think it violates the actual math.

However, would this actually work for general relativity -- that is, once you throw in gravity? Could you even define a single frame of reference for a universe that includes black holes?

[Douglas]

However, would this actually work for general relativity -- that is, once you throw in gravity? Could you even define a single frame of reference for a universe that includes black holes?

Sure, it's easy. Pick a spacetime coordinate, any arbitrary one will do, and define your special reference frame as "the inertial reference frame of an observer at infinite distance who is at rest relative to the location part of your coordinate". All events have unambiguously defined coordinates in both space and time in this frame (or any arbitrary inertial reference frame, really) that will never change, and gravity doesn't change that fact. A restriction that the time coordinate in this frame of an FTL effect is always after the time coordinate (also in this frame) of its cause is enough to prevent causal loops.

[Anymage]

A privileged frame of reference means that simple FTL wouldn't automatically break causality. Having instantaneous warp gates, though, does open up the possibility of placing one in a deep gravity well while the other stays in generally flat spacetime. Time dilation will cause time at one end to progress slower than the other, and there are ways this could be exploited to create time travel. (E.G: let one end sit in slower time until it's a year behind the other, then bring both of the gates into the same room, and walking into one end will put you a year ahead or behind.)

Throwing out relativity entirely means that you can have whatever arbitrary speeds you want, up to and including infinite. Considering that relativity means that things like distance, time, and simultaneity all get mucked up, that's really the best move for a story/game setting that's not explicitly set up to explore relativity related ideas.

[Binks]

Obviously, this violates the philosophical idea of relativity (that all frames of reference are equally valid), but I don't think it violates the actual math.

It does actually. The concept of 'no preferred references' isn't just a philosophical idea, it's the foundation of all of relativity. Throw that out and you throw out everything, all the math is based on that concept holding true. Pretty much every formula in relativity is based on the postulate of no special reference frames. You need to start over again with a brand new system that will probably end up looking a lot like relativity, but won't be quite the same as it will rest on a different foundation. And yeah, in this new hypothetical system with a special reference frame, causality may be preserved even with FTL travel, but that's not the physics we have today.

Here's the problem with a preferred frame of reference, it means that there exists a non-preferred frame of reference, a four dimensional point where the laws of physics don't work the same as they do elsewhere. Under relativity (math and concept both) every point in the universe is equally valid for making physical observations. If I measure something, and you measure something, our results might disagree on the details, but both are equally valid measurements and will always line up in certain ways (events that cause other events always precede them, light always moves at c in a vacuum, etc). If we allows preferred and non-preferred frames though, that means that a frame of reference can exist where events flow backwards (effect->cause, causality violations) or light doesn't move at c in a vacuum. In your given example, for instance, if one set of observers see their messages going back in time, those observers are not seeing light move at c in a vacuum, which completely breaks all the math relativity is based on.

The central problem with such any system that can allow for FTL without causality violations is that you must discard relativity to get there though. Now, if you're writing speculative sci-fi, nothing wrong with that, as you can just explain how relativity isn't true and 'insert your theory that looks like relativity in all circumstances we've tested but differs in one specific way' is. Pretty much every piece of sci-fi out there does this, some more blatantly than others. But if you're talking actual physics as we know it today, relativity is the best we've got, and it precludes FTL travel without causality violations. Period. No exceptions. The math of any system where information can move faster than light inevitably allows time travel within the rules of relativity because relativity presupposes that all references frames are equally valid, and that some are in the past/future of others, so allowing communication between them at FTL velocities is time travel.

EDIT: Worth noting, some scientists are floating the idea of a privileged frame of reference actually existing and working through what that means for the math, specifically the Cosmic Microwave Background radiation being the preferred frame of reference for observations. It hasn't gone anywhere yet, and relativity still has mountains of evidence that it holds true, but it's not like no one is considering this possibility.

[Satinavian]

Yes, with FTL and a privileged frame of referrence you don't get time travel in special elativity.

But keep in mind how symmetries and conservation laws are linked to each other. If you have a privileged frame of referrence, a huge part of the regular physics suddenly doen't work anymore as we are used to.

[Bohandas]

I'm not sure instantaneous travel would ever cause paradoxes, at least, depending on the precise meaning of "Instantaneous travel". If it passed through the intervening points there might be a problem, but if it were simply translocated directly from one point on the hypersurface of the present to another that wouldn;t seem to involve any velocity or acceleration and thus no time dialation

[DavidSh]

I'm not sure instantaneous travel would ever cause paradoxes, at least, depending on the precise meaning of "Instantaneous travel".

We've gone through this in excruciating detail in another thread. "Instantaneous travel" is a relatively easy case for causing paradoxes. The issue is that, under special relativity, different frames of reference disagree on what events are simultaneous, and all inertial frames of reference are equally valid. I will use "event" as the standard terminology for "point in space-time". In one frame of reference F1, event A and distant event B may be simultaneous, while in another frame of reference F2, event A may be slightly in the future relative to B. So, if you start in frame F1, you can use your magic instantaneous hopper to hop from A to B. Then accelerate to frame F2, and hop to a point near A in space, but in its past.

This does require that Special Relativity be true, and that you can hop sufficiently far that the time needed to accelerate to frame F2 and start the next hop is negligible.

With a privileged frame of reference, a major axiom of special relativity is false, and these loops in time are avoided.

But I see you've posted in that other thread. Is the issue then, what constitutes a paradox?


On the connection between symmetries and conservation laws, I ask: What conservation laws are tied to CPT symmetry, and what conservation laws were believed tied to CP symmetry, before CP violations were discovered?

[Bohandas]

Wait a sec, I just remembered something. The first paragraph of the topic post is definitely true (although I don't know about the rest of it). IIRC won't anything observed by an outsider to be moving at the speed of light complete it's journey instantaneously from it's own frame of reference (in which, IIRC, the universe will also be contracted into basically a flat [and thus instantly transversible without breaking the cosmic speed limit or bypassig passage through intervening spaces] 2+1 dimensional sheet)?

[jayem]

On the connection between symmetries and conservation laws, I ask: What conservation laws are tied to CPT symmetry, and what conservation laws were believed tied to CP symmetry, before CP violations were discovered?

I think for CP it's
Total(Matter)-Total(Antimatter) ?

Though that seems a little too trite, compared with the Time-Energy, Displacement-Momentum ones.
Although we're giving symmetry on multiplying by one value rather than symmetry on adding any, so maybe that's why.
Hmm what about symmetry on reflection, would that be something like centre of mass?

[Bohandas]

The central problem with such any system that can allow for FTL without causality violations is that you must discard relativity to get there though.

What about the Alcubierre metric? I understand it can get you to proxima centauri and back in under a year, but it was never my understanding it could get you back before you left. Because it doesn't involve actually moving, as such. Shouldn't it fall into the same category as how time in general doesn;t reverse due to the universe expanding at faster than the speed of light because the distance changes don't involve actual motion but rather expansion of the intervening space?