Something I don't understand about FTL travel

Fredrik

To produce a message that's going back in time in all inertial coordinate systems, you need two devices that can send and receive FTL messages, and there must be a large velocity difference or large distance between them.

Fredrik

It's contradictory and doesn't make sense, but only because the OP used the word "person" instead of "tachyon". Since there was an easy way to change the question into one that does make sense, I chose to answer the question that made sense instead. See my comment in the "Edit" part of post #4.

Dadface

If there is a real possibility that a particle can move FTL then the question can make sense. Sorry for not noticing your edit.

stevendaryl

The point of discussing what would happen if there were FTL is to prove that it is impossible. Logically, to prove something is impossible means showing that it leads to a contradiction.

Thinker007

I don't see the question like that. I believe he's saying that in one IRF (the IRF he's most familiar with - approximately at rest relative to Earth/Sun) FTL travel seems to create no paradoxes of the type he's heard about (arrival before departure, etc.)

The answers seem to me to be just about right on point - explaining what FTL travel looks like in other IRFs.

I'm certainly not convinced that SR, standing alone, rules out FTL. I'm not convinced that physics today rules out time travel. For all I know, some combination of the Many Worlds Theory of QM coupled with SR would obviate all the contradictions that appear. The contradictions are separated into different split-off worlds. As such, understanding the contradictions from FTL is an important step.

Shifting away from the MWT idea- when I think about the meaning of "now" in the Andromeda Galaxy, I'm often tugged towards the idea that the future is fixed and unchangeable - that free will is nothing but an illusion. In such a universe there can be no time paradoxes of the type that challenge us when thinking about FTL. The message to kill my grandfather never arrives, etc.

Or perhaps there are tachyons, but they are on the other side of a light speed barrier and just can't interact with an STL universe.

The question was quite reasonable from my point of view. We all have to start somewhere and we all can travel farther down the road of knowledge from where we are now.

Fredrik

That's not what we've been doing in most of this thread. If we replace the word "person" with "some weird particle" in the OP's question (in order to make sense of the question), it's just asking whether a particle that moves FTL from Earth to the Sun is really moving back in time. And the answer is that that it's only going back in time in some coordinate systems. In others, like the inertial coordinate system that's comoving with Earth, the particle reaches the Sun after it left Earth.

A theory of both FTL matter and normal matter in Minkowski spacetime would have to have some counterintuitive features, but I don't think there's a theorem that says that all such theories can be ruled out.

nitsuj

In all this hypothetical FTL talk; how would the natural units for time & length change?

I always find FTL talk really strange as they often are discussed in a context where c is a constant, and the metric is still +++-.

To say "On this Mink' diagram you see the message has arrived sometime before it was sent." seems to completely ignore the relationship, or representation of orthogonal time & length axis on said diagram and from where it was derived.

To say that different, c is a geometric constant as much as an invariant speed limit.

stevendaryl

It seems to me that you couldn't prevent closed time-loops if FTL were possible in all reference frames. If it's possible to send a particle from the Earth to the Sun that is backward in time relative to one frame, then what would prevent sending one back-in-time relative to the Earth's frame? And if it's possible to send a message back-in-time from the Earth to the Sun, what would prevent sending a message back-in-time from the Sun to the Earth? It seems to me that FTL + relativity implies the possibility of closed time loops. I don't see what could prevent it.

Long ago, I read a paper that resolved the paradoxes from closed time loops by invoking noise. If you try to communicate with yourself in the past using tachyons, then you will find, on the receiving end, that there will be tachyon "noise" that will drown out any message that you might receive from your own future. I couldn't figure out whether this made sense, or not.

PeterDonis

You could prevent it by introducing a preferred frame into the law that determines the worldlines of FTL particles: in other words, an FTL particle's velocity is not defined relative to the emitter, but relative to the same preferred frame regardless of the emitter's state of motion. This arguably violates the principle of relativity, but it could be modeled within the framework of SR; the model would just have an ugly "privileged" frame in it.

stevendaryl

Yeah. I would consider that a violation of the "spirit" of relativity, which is the equivalence of all inertial frames. If you are willing to give up that equivalence, then FTL doesn't necessarily lead to a contradiction.

Fredrik

Think about what we do when we use SR to find the the correct final ages in the twin paradox scenario. All we do is to consider Minkowski spacetime and two curves in it. Physics is usually like this. We use an extremely idealized theory that doesn't describe everything that's going on in the real world. In this case, the theory describes a universe that's empty save for two particles, one of which changes its direction at one point, for reasons not explained by the theory. So the theory doesn't even fully describe the scenario we're trying to study. In addition to things that are left out of the theory by choice, there are also things in the real world that can't exist in the fictional universe described by the theory. For example, a classical theory of point particles in Minkowski spacetime can't describe an atomic clock.

If we try to describe the "message back in time" scenario with an idealized classical theory of point particles, like we did with the twin paradox, and the real world contains objects like emitters and receivers of FTL particles, devices that can't exist in the theory we're using, as well as humans who are willing and able to do all the things we've talked about, then we run into the problem that you see. By assumption, there's nothing that prevents us from doing something self-contradictory, like sending a message that starts a chain of events that prevents us from sending that message in the first place.

I think that this line of reasoning rules out a large class of idealized theories, but maybe not all. You mentioned noise as a way out. I haven't heard that one, but yeah, why not? There could be other ways out, like having the time it takes to reliably detect a particle grow linearly with the distance it has traveled, or something like that. Maybe that's essentially the same idea, because what does noise do other than make it harder to detect the particle?

There's also a tiny chance that a theory of all the matter in the universe could involve FTL particles. In this case, since a theory wouldn't be a "theory" if it's logically inconsistent, the equations of motion would only have solutions in which none of these paradoxial experiments we have thought of is ever carried out. (If it's a quantum theory, that possibility is assigned probability 0). I know that this sounds ridiculous, but it's logically possible. There could be a solution in which humans never discover the technology. There could be a solution in which we do, but never choose to use it. There could be a solution in which we decide to use it, and then get wiped out by a meteor that's been on its way towards us for billions of years, before we have had a chance to finish the experiment. But there can't exist a solution in which we invent the technology, choose to use it, and then do the experiment, because a "solution" with a paradox isn't actually a solution. It's just nonsense.