# Will The Theory of Relativity allow me to travel Backwards in Time?

1. Jun 1, 2012

### Ferraridude

Hello, I have been wondering about this for a bit of time now, but forgive me for not being entirely clear with this, if that does happen.

I once heard that the relativity of space and time is like a graph. If you are not moving in space, that does not affect your time, with space being on the Y axis, and time being on the X axis. If you do not move in time, you are moving at the speed of light, and I hope you can visualize what the line would look like on the graph that shows the relativity between space and time.

So, I wondered that if you can hypothetically go faster than the speed of light, would you go backward in time?

Yes, I know, there are all of these paradoxes, and that may make it impossible and confusing, maybe.

But, it made me think of something. What if we could find some place in space that we could while we were in it, accelerate to a speed faster than the speed of light.

If that were something like a tunnel, this is what would happen from what I thought of.
If we were finally travelling at faster than the speed of light, when we hit the end of that tunnel, we would immediately go backwards in the tunnel, because once we hit the first contact with regular space, we would go backwards in space due to this explanation of The Theory of Relativity. Then, that same thing would happen when we got to the other side of the tunnel. If this was true, then we would be stuck inside the tunnel until we could possibly, if we could, slow down to slower than the speed of light.

Thank you for reading, and I would greatly appreciate opinions on this.

2. Jun 1, 2012

### Mark M

Well, FTL speeds don't directly lead to reverse time travel, but they allow you to exploit a loophole that does. Because the speed of light is the same for every observer, events that would normally be considered simultaneous may not be in another reference frame. For example, imagine two people on a train, and a third person on a platform. The two observers are standing on opposite ends of the train. In the center is an orb that emits a ray of light in both directions. When these observers see the light go off (when it reaches their eyes) they press a button emitting a sound. Since they are in an inertial frame of reference on the train, everything goes as normal, and they hear the sounds go off simultaneously. However, the observer on the platform sees something different. Since the train is moving in one direction, but the speed of light must be the same, he sees the light reaching the observer on one side before the other, hence breaking the simultaneity of the events.

Over larger distances, this effect becomes more dramatic. You can imagine a person on earth who is in contact with an alien on a distant planet. When the alien begins to move, the relativity of simultaneity takes effect, and what the person would have considered his past, is now the present for the alien. You would think that this may allow for reverse time travel. However, since the alien is restricted to sending slower-than-light signals, by the time a signal reaches the human, enough time has passed that nothing has been changed when the message is received. This hinges on the fact that the alien can not send a signal faster than light - however, if he could, he could send a message to the past of the human, or even travel there himself.

In a situation named the twin paradox, an observer leaves another observer on a rocket ship. Since they both see the other moving relative, they both say that each others clocks are ticking slower. This would seem to be a paradox, how could they meet up and see each other as being younger? Well, the resolution comes in the fact that the observer who left in the rocket will eventually have to turn around, which relinquishes his inertial reference frame, and he can no longer claim to be at rest.

This relies on the fact that it will take him a slower-than-light speed to return to the other observer. If he could instantly transmit his time to the observer on earth, then we would have a paradoxical situation where they both see each other as being younger.

So, we can see that faster than light travel not only allows for past time travel, but it breaks causality. This is, of course, impossible. So, we simply conclude that FTL speed are unattainable.

3. Jun 1, 2012

### Staff: Mentor

The short answer to this question is, if you could hypothetically go faster than light, then it would look like you were going backwards in time to some observers, but not others; it would depend on the state of motion of the observers, relative to you.

Actually, even that statement hides a subtlety. Suppose you activate your faster-than-light rocket and use it to fly from, say, the Earth to Mars, in such a way that an observer on Earth sees you moving faster than light between the two, but still forward in time (that is, you arrive at Mars after you leave Earth). Then another observer, moving at some substantial fraction of the speed of light relative to Earth, might see you "arrive" at Mars *before* you "leave" Earth. But he could equally well interpret this as you traveling from Mars to Earth--i.e., he would put the "direction of time" for you opposite to the way you and the first observer would.

In fact, that last observation illustrates why relativity says that FTL travel is impossible because it would "break causality", as Mark M put it. The second observer sees you going from Mars to Earth instead of from Earth to Mars--but he also sees your rocket pushing you in the direction from Earth to Mars! That doesn't make physical sense. The only way to avoid this sort of inconsistency (and others like it) is to say that the whole thing is impossible to begin with; nothing can move faster than light. As long as everything moves at light speed or slower, no such inconsistencies can arise; everyone will agree that you go from Earth to Mars, the same direction that your rocket is pushing you.

I also wanted to comment on this, even though it's not directly related to your question about FTL travel. Actually there are two comments:

(1) Normally a spacetime diagram shows the time axis vertical and the space axis horizontal, so a more natural way to put it would be that the time axis is the "y" axis (but it's virtually always called the "t" axis) and the space axis is the "x" axis (which is what it's virtually always called). Also note that in such a diagram, two space dimensions have been suppressed; many problems can be analyzed this way because all of the motion of interest is along a single line. But a full "diagram" of spacetime would have to have 4 dimensions, t, x, y, and z. Unfortunately nobody has yet invented 4-dimensional graph paper.

Also, it's important to note that a standard spacetime diagram uses units in which the speed of light is 1; for example, time in years and distance in light-years, or distance in meters and time in "light-meters", i.e., the unit of time is the time it takes light to go 1 meter (about 3.3 nanoseconds). I'll refer to this again below.

(2) A number of popular treatments of relativity talk about "moving through spacetime at the speed of light", and how as your speed increases, more of the movement is "through space" instead of "through time", until light itself "doesn't move through time at all". I suspect that you have been exposed to some of these, so I wanted to take some time to explain why I think they are highly misleading.

First of all, on a standard spacetime diagram (like the kind I described above), light moves on 45 degree lines. I suspect that that was *not* what you were thinking of when you said that "I hope you can visualize what the line would look like on the graph". But it should be obvious that light moves on 45 degree lines from the fact I referred to above, that the units of the diagram are such that the speed of light is 1. If I had to describe this in the sort of terms you used, I would say that light moves through space "as fast as" it moves through time, whereas anything else, that moves slower than light, moves through space "more slowly than" it moves through time. However, I prefer not to put things in those terms at all; see further remarks below.

The reason why those popular treatments of relativity talk about "speed through spacetime" being constant is that the relativistic way to describe the motion of an object is to assign it a "4-velocity", which is a 4-dimensional vector whose t, x, y, and z components can be thought of as the "speed" of the object through each of the four dimensions. The key thing about this 4-velocity vector is that its length is constant: it is always 1 (or c, the speed of light, if we are using conventional units). As an object moves faster and faster, the "time" and "space" components of the 4-velocity change, but they change in such a way as to keep the length of the vector as a whole the same. So if we think of the length of the 4-velocity as "speed through spacetime", then we could say that every object "moves through spacetime" at the same speed, which, in the units we are using, can be thought of as the speed of light.

However, the above interpretation of the 4-velocity can be highly misleading, because it invites the inference that, as an object moves faster, more of its motion is "through space" and less is "through time", which leads to the inference that light is somehow a "limiting case" where the motion is all "through space" and none "through time". I've already shown how light does move "through time", above, but there's also another point: light can't be described by a "4-velocity" vector in the sense given above. You can describe the motion of light by a 4-vector, but it will be a *null* 4-vector: its length will be *zero*. (In spacetime, unlike normal Euclidean space, a 4-vector can have length zero and still be a vector, not a single point; in fact there are an infinite family of null, zero-length 4-vectors at any event in spacetime.) This means that the case of light can't be thought of as a "limiting case" of ordinary motion; there is no continuous way to go from a 4-vector of length 1 to a 4-vector of length 0. They're simply two fundamentally different things. The fact that light's 4-vector has length 0 is why some treatments talk about light "not moving through time", but I think you can see how why I think that is a highly misleading way of putting it.

Sorry for the long post, but this is one of my pet peeves and I wanted to get all that off my chest.

4. Jun 1, 2012

### Ferraridude

Thanks a lot, I think I understand the 4 vector topic that you described. I see how that if one of the variables in the 4 Velocity vector changes, it still has a constant length for the vector.
Lol, forgive me for being a little slow, for I am only a freshman in high school, and the extent of what I was taught is limited to Newtonian Laws and an off topic talk about string theory. And I do make the mistake of thinking too much about it without actually doing the research, but one of the solutions for that for me was joining Physics Forums.

However, do you know why c is an unattainable speed? I don't think that it is a coincidence that it is true, but correct me if I'm wrong if I think light has mass, since it comes in waves (Again, correct me if I'm wrong).
One of my thoughts on the question I asked was that there is the possibility that time doesn't really exist past the fact that things are given time to happen, and that the reason why things would appear different if you went at high speeds is because you are travelling faster than 0 m/s relative to the light, and things just appear to look different. However, that would mean that if you went in the opposite direction that the light was going, say towards a light source, not away from it, that things would appear to happen faster.
I don't necessarily believe in one of the theories that I just described, but I would like any feedback on it.

5. Jun 1, 2012

### Staff: Mentor

No problem at all. You're already well ahead of me; I didn't start learning about relativity until the summer after my junior year, and I didn't learn about Newton's Laws until my senior year. That was quite a while ago, so string theory didn't even exist yet.

Welcome! Of course I think that was a good move. Seriously, though, there are a lot of experts here who are happy to help, so by all means keep posting!

If you're really interested in relativity, I would also recommend trying to get a copy of a good introductory textbook, such as Taylor & Wheeler's Spacetime Physics. Also, there are some good FAQs here on PF, and another good resource is the Usenet Physics FAQ:

http://math.ucr.edu/home/baez/physics/index.html

It's not; it has to be true to fit in with the rest of the framework of relativity. I'll comment on this more below since it fits in with your next question about mass.

It does in one sense, but not in another. The sense in which it does is the sense in which anything that has energy, has "mass". This sense of the word "mass" is more precisely called "relativistic mass", and a good starting point to read about it is here:

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

Some people like this use of the term "mass" and others don't; I tend to lean towards the latter.

The sense in which light does *not* have mass is that it does not have any "rest mass". (Another term for this is "invariant mass"; when you see the word "mass" used without qualification in the modern literature on relativity, it almost always means rest mass.) Rest mass is, in fact, simply the length of an object's 4-momentum vector, also sometimes called its "energy-momentum 4-vector" since its "time" component in a given inertial frame is the object's energy, and its space components are the components of the object's momentum.

For a timelike object, one with nonzero rest mass, the 4-momentum is just the rest mass times the 4-velocity vector that I described before; it should be obvious that the length of this vector will in fact be the object's rest mass. For a lightlike object, with zero rest mass, the 4-momentum is the 4-vector I described before, that has a length of zero but still describes the object's "motion through spacetime", times the object's energy. (In fact, for lightlike objects, the 4-momentum is pretty much the only 4-vector that's actually used to describe them; the other one, the 4-momentum divided by the energy, is hardly ever used.)

The reason this is important is that only objects with zero rest mass can move at the speed of light; objects with nonzero rest mass (which is pretty much any familiar object except light) can approach the speed of light but can never reach it. It's these objects for which c is an "unattainable speed", as you say. The latter fact follows from the fact that the length of a timelike object's 4-vector (either 4-velocity or 4-momentum) is nonzero, and that length is invariant; it doesn't depend on the object's state of motion. But for a timelike object to move at the speed of light, the length of its 4-vector would have to change to zero from a nonzero value. That can't happen, so a timelike object can never move at the speed of light.

I should say that the explanation I've just given is not the usual one. The usual one is to say that, in order to reach the speed of light, a timelike object would have to gain an infinite amount of energy. That is correct, and I can go into it in more detail if needed; but since we had already discussed 4-vectors and the fundamental difference between timelike and lightlike ones, I thought it would be good to show how c being an unattainable speed for timelike objects is connected to that.

You're correct, light comes in waves. However, it also comes in particles. That's really a question of quantum physics, not relativity, so questions about that should be posed in the quantum physics forums. But it's worth noting that, to a certain extent, both descriptions of light can be used in relativity, without having to go into the quantum details. For some purposes, it's sufficient to think of light as made of particles, called "photons", that have a particular energy and momentum and move on lightlike worldlines (their 4-vectors have length zero). For others, it's better to think of light as a set of wave crests in spacetime.

There's a *lot* of literature about the nature of time. The physicist John Wheeler (at least I think it was he) once said that "time is what keeps everything from happening at once, and space is what keeps everything from happening to me". For purposes of basic relativity theory, however, there are two senses of the word "time" that are used:

(1) "Time" is one of the four dimensions of spacetime; in a given inertial frame, one of the 4 coordinates we use to describe events will be the "time" coordinate.

(2) "Time" is also something that is directly experienced by observers traveling on particular worldlines in spacetime. This sense of time is called "proper time", and it corresponds to the (invariant) length of a particular worldline (a curve in spacetime) from a particular starting point to a particular end point.

There's a sense in which this is true, but you have to be careful. Suppose I shine a light beam in the same direction in which you are flying by me at high speed. Relative to me, the light beam is moving at c, and you are moving at some speed v < c. So to me, it seems like you are indeed moving faster than 0 m/s relative to the light. However, relative to you, the light beam is also moving at c, so you do *not* think you are moving faster than 0 m/s relative to the light.

Things do look different to you when you are moving relative to them and you receive light from them. One way they look different is that things do indeed appear to happen faster if you are moving towards the light source, and slower if you are moving away from it. Another way is that light from a source that is moving towards you is blueshifted, and light from a source that is moving away from you is redshifted. The latter is what is usually called the Doppler Shift, but it's worth noting that, in relativity, the former (things appearing to happen faster or slower) is also an aspect of the Doppler Shift. There are other effects as well; you can read more here:

http://en.wikipedia.org/wiki/Relativistic_Doppler_effect

6. Jun 2, 2012

### Saw

I thank you for these long posts, which have been very educational for me.

I would like to note, however, as to the part I have quoted, that there is another way to look at this issue. It is not that FTL must be ruled out to avoid absurdities. I do not like that statement because it seesm to imply sensu contrario that, if FTL actually existed, absurdities might arise. It is the other way round. Absurdities cannot arise because they are absurd. FTL is most probably impossible for other reasons, which must forcefully be physical reasons, related to how things work in the universe. But if those reasons were proved wrong, which I do not believe will ever happen but is a theoretical possibility, then absurd consequences (like backwards time travel or paradoxical contradictions) would still not arise.

7. Jun 2, 2012

### phinds

I think that is an excellent statement.

8. Jun 2, 2012

### Staff: Mentor

I'm not sure I understand what you're saying here. Do you find some flaw in the reasoning I gave in my earlier post, which shows that if you could travel FTL from Earth to Mars, then there would be some observer who would see you on Mars before you were on Earth, meaning that to that observer, you were traveling from Mars to Earth, but would still see your rocket pushing you in the direction from Earth to Mars? If you do see a flaw, then please point it out.

If there is no flaw, then it seems to me that the absurd consequence is a good enough "physical reason" to say that FTL travel is impossible. If it doesn't seem that way to you, then what would you consider to be a "physical reason" for FTL being impossible? Or is it, perhaps, that you don't regard the consequence as absurd?

9. Jun 3, 2012

### Saw

No, I do not see any flaw. I have not thought over the example in detail but I am sure that what yo say is right. Just to understand it a little better, by "see" do you mean the literal meaning (the observer's eye receives light coming from one event earlier than the other) or "measure" (in her network of clocks, synched ala Eisntein, the clock witnessing one event shows an ealier time than the one by the other) or both things?

In any case, is the burden of proof for me? I could also ask you: Given this fact (observers disagree about the sequence of events, of spacelike events by the way), why do you think that -if the prohibition of FTL is removed- absurd consequences would arise? In oter words, what do you understand by "time" and "simutaneity" that makes you fear such consequences?

No, no, please, not me. I do regard absurd things as absurd.

Hmm. Good point. I suppose yours is also a "physical reason". What I am implying is that it is an abstract or high-level one, one that requires handling many abstract concepts. And I am also implying that during such long intellectual way there lies some intellectual error. Because an error must exist: if someone believes that FTL brings about absurdities, he or she must forcefully be mistaken. But I am not sure that we should go into the discussion as to whether one view or the other is better. I was just pointing that out that, together with yours, there is another interpretation, the one I outlined above. And in this view, the reason banning FTL travel would be some lower-level one, related to how things are accelerated, how causality is transmitted.

10. Jun 3, 2012

### Staff: Mentor

I meant "measure" as you define it here.

It's not just the disagreement about the sequence of events that causes the "absurdity"; it's the fact that only one sequence of events makes physical sense, while the other does not, so at least some observers are seeing a sequence of events that doesn't make physical sense. If both sequences of events make physical sense, then I don't see a problem with different observers observing different sequences.

This amounts to saying that you believe FTL is actually possible. Do you?

I'm not sure how this is different from saying that if FTL were possible, there would have to be "absurdity" at some level.

11. Jun 3, 2012

### Saw

No, not at all. I suppose you will agree that you can hold these two things at the same time without incurring in a logical contradiction:

- On the one hand, based on what we know about how the universe works, it is logical to deduct that FTL is impossible, a deduction which has been proved so far by overwhelming empirical evidence.
- On the other hand, if the universe worked differently from what we presume and FTL were possible, that would mean a major upheaval in physics but we should not fear absurd consequences.

In other words, FTL is a theoretical possibility, a legitimate speculation, albeit a most improbable one; to my taste, a quasi-impossible one.

That is not what I am saying. Again, a universe with FTL would break the laws of physics that we know but it would not be absurd in the sense, for example, of violating causality.

We both agree that the fact that under SR two observers disagree on the chronological order of spacelike events is not absurd, for the reason that those events are not causally connected, which in turn is true as long as causal influences cannot travel FTL.

However, if you remove that restriction, if you admit that the spacelike events can be causally linked through a FTL agent, then do you fear that one observer sees or measures a sequence of events that makes physical sense, whereas another sees another sequence that does not make sense? Well, I do not have that fear.

Let us complete your example with a little more detail. We assume that the Earth and Mars belong to the same frame, they are the rest wrt each other, the Earth on the left, Mars on the right (frame A). We consider two simultaneous events in the Earth-Mars frame. For example, from the mid-point of the distance between the two planets light signals are fired in opposite directions and hence they reach the planets simultaneously in that frame. However, in a frame B moving away from the Earth and to the left, the Earth receives its signal earlier and this event is simultaneous with another on Mars where the local observer has not yet seen its own signal. Instead in a frame C moving towards the Earth and to the right, the Earth receives its signal later and this event is simultaneous to another on Mars where the local observer has already received its own signal.

Now we introduce the FTL rocket. When a man on the Earth receives its signal, he jumps on a magical rocket which travels not only FTL but, for simplicity, instantaneously, that is to say, at infinite velocity.

Does he arrive at Mars just when the light signal is reaching this planet or rather earlier or rather later?

Let us assume that the man lands on Mars right when the signal is hitting this planet. In the Earth-Mars frame or frame A the man has travelled instantaneously. In frame B he has travelled forward in time. In frame C he has travelled backward in time: as you say, the man’s departure from the Earth happened later than its arrival on Mars, making it look as if it were the other way round, as if he had travelled from Mars to Earth, which is against the evidence of how the spaceship was propelled.

Given this, my questions are:

- What makes you decide that the story happens like this? When we stipulated that the travel would be instantaneous, we implicitly decided that departure and arrival would be simultaneous. But then which simultaneity version do you choose? Frame A’s? But why not any other? If we had chosen frame C’s, the ship would have arrived at Mars after the light, thus travelling forward in time in A and B.

- And if you arbitrarily choose any version of the story, why do you believe that the other versions are contradictory? If I were for example the observer in frame C, I would reason as follows: “Ok, I never said I knew what was going to happen. Understand my words. When I said that in my frame the arrival of the light signal at Mars –arrival of the rocket- is simultaneous with an event earlier to the departure of the rocket from the Earth, what I meant is that on the basis of this info and thanks to the equations of SR I manage to solve causality problems where no FTL agent is involved. But I cannot predict what happens if you send a really instantaneous signal. That is not what *simultaneous* means in SR jargon.”

12. Jun 3, 2012

### Austin0

I agree completely. Given the unlikely physical phenomenon of actual instantaneous translation SR has no basis for predicting when such a traveler would appear in any frame.
Since it is absurd and outside the principles of SR to assume that any systems clocks were absolutely synchronized there is no rational reason whatsoever to think that an absolute physical occurrence would conform to a clock convention. Even less to assume it would conform to the simultaneity of whatever particular frame was chosen.

I also think that the reductio ad absurdem argument is itself somewhat absurd, as it rests on the assumption that the universe necessarily cares about human concerns regarding causality. Time travel is either a possibility of the physics of reality (which I seriously doubt),
in which case I don't think what we think matters
or
it isn't .
Not that I think FTL is likely. Although I have to point out that without it, the ultimate prospects for human exploration of the universe are very limited so I hope we are all wrong. ;-)

13. Jun 3, 2012

### Staff: Mentor

You're right that there is no logical contradiction between these two positions (at least, I can't see one). But that doesn't mean I agree with the second statement (of course I agree with the first). The only way we could know that we would not have to fear absurd consequences from FTL would be to either (1) observe it empirically, which we haven't, or (2) have a theory that included FTL travel without requiring any absurd consequences, which we don't. The theories we have all predict consequences of FTL that, while not logically contradictory, strictly speaking, are certainly not physically reasonable. If you want to say that only logical contradictions qualify as "absurd", that's fine; "absurd" was your word, not mine. I'm fine with "physically unreasonable" being a sufficient reason to think FTL is impossible.

You don't know that it wouldn't violate causality. To know that, you would have to have a consistent causal theory of FTL travel. Do you? If so, how does it explain the FTL Earth-Mars rocket scenario above, without requiring observers who see the rocket going from Mars to Earth to also see other physically unreasonable behavior from the rocket? I suppose I should point out that I didn't list all of the physically unreasonable consequences before; perhaps I should give some more. For example: the observer who sees the rocket going from Mars to Earth, also sees its rocket "exhaust" scooping up incoming matter that just happens to have exactly the right speed and direction to enter the nozzle; then, once inside, the incoming matter just happens to undergo exactly the right reactions to absorb all the excess energy in it and convert it back into fuel, which then just happens to flow back into the rocket's tanks.

No, I don't agree. If I can get in my FTL rocket and fly from Earth to Mars, then obviously the events of my leaving Earth and my arriving on Mars *are* causally connected. Otherwise I wouldn't be able to make the trip. Unless, as I said, you have some other theory of FTL travel that says how I can experience both those events, in the order I gave, without them being causally connected. Do you?

Then presumably you have an explanation of the physically unreasonable things I described earlier, that the observer who sees my FTL rocket going from Mars to Earth would observe. I would love to see it.

Ok so far.

Obviously, by hypothesis, he arrives at the instant the light signal does. Or at least, that's the most obvious hypothesis. I agree there are others, but it doesn't matter which one you choose; see further comments below.

In principle you could choose any one you wanted to. Presumably the actual physics governing which one was chosen--or, put another way, which specific spacelike trajectory the FTL rocket follows--would be part of that physical theory you are supposed to have that explains FTL travel without requiring anything physically unreasonable. I don't have such a theory, so I can only go by what the person making up the thought experiment--you--says.

However, according to standard SR, no matter *which* spacelike trajectory the FTL rocket follows, there will be *some* observer (some timelike observer, more precisely) who sees it going the opposite direction. Depending on which trajectory you choose, that observer might not be A, B, or C; that's true. But there must be *some* such observer, at least in principle--there must be *some* timelike worldline for which the order of events is reversed. So all the rest of your comments here...

...are simply irrelevant. If there is *any* timelike worldline that sees the events in reversed order, then the physically unreasonable consequences I described follow.

14. Jun 4, 2012

### Saw

No. I do not object this. If you introduce FTL, two spacelike events become causally connected. Of course! That is the problem! How does causality operate in these cases? In my opinion, we do not know. In your opinion?

There is another possibility (3): have a theory that excludes FTL but admits that, should that postulate be wrong, still no absurd consequences would arise. That is SR, or at least a certain way of reading SR, which apparently is not yours.

You are embarking here on a subtle distinction that I am not sure you would like to pursue. If you admit the “physically unreasonable” (like the example you built), then you also have to admit that you run into the “blatantly absurd” (like time travel, grandfather paradox and so on). In any case, it is not my intention to discuss the right adjective for those situations. Whatever the adjective, it was negative enough for you to use it as a logical argument to reject FTL. I am just saying that we do not need to believe that FTL would bring about those “unreasonable or whatever-you-want-to-call-them” consequences.

My only point, I do not know if that amounts to a theory, is that SR must be interpreted in the sense that it does not predict and it does not even intend to predict, what would happen in case of FTL travel. Our knowledge has a “gap”, which is in practice irrelevant, because it seems that FTL is impossible.

What is a mystery to me is what your own interpretation of SR is. You have avoided to comment the key part of my previous post. Suppose FTL is actually possible. What happens? Which version of simultaneity do you choose? If you reject my view (“we do not know what happens”), there is only one other possibility (“we do know”). And if we do know, what do we know? Is it by chance that all versions of simultaneity actually happen, even if they are contradictory among themselves?

I already answered this in my previous post. We do not know what happens if a rocket flies FTL between two spacelike events. Obviously, however, only one thing happens, but we do not know which. If we learnt it by experience, then all reasonable interpreters would describe such thing in a reasonable and harmonious manner. In particular, as I said, an observer who had assumed that the arrival to Mars happened earlier than the departure from the Earth would explain that scenario in the manner which put between quotes in my previous post and which I am not going to repeat.

Why so? As I said, that observer who “sees” or (to be more precise, in my opinion) “measures” a reversed order of events gives a perfectly unambiguous explanation, which rules out any absurdity, any physically unreasonable consequence. He admits that his concept "order of events" is only aimed at solving causality problems in a non-FTL world. Therefore, if the FTL rocket's arrival at Mars is an event which (in his simultaneity line) coincides with another event happening on Earth earlier than the departure, he says: "ok, anyhow, I admit that the rocket travelled from Earth to Mars. I never said my measurement should be interpreted as a prediction of what was going to happen."

Austin0, for example, shares this explanation.

What is, in your opinion, the problem with it?

15. Jun 4, 2012

### Staff: Mentor

In my opinion, our current theories strongly suggest that causality *can't* operate in these cases; that's why I think our current theories strongly suggest that FTL travel is impossible.

Not necessarily; that would depend on the physical law that governed which particular spacelike trajectory an FTL object followed. The blatantly absurd consequences only follow if closed timelike curves (CTCs) are allowed. It is possible to imagine laws that would not allow CTCs while still allowing FTL travel. For example, the law could be that FTL objects always follow trajectories that look instantaneous from some particular "preferred" frame (such as, for example, the mutual rest frame of Earth and Mars in your example). The order of events on the object's trajectories would still look different for different observers, but the objects would not be able to travel into their own past.

Such a law would not be consistent with standard SR because it would break Lorentz invariance, but it's certainly logically possible. So if you want to say that standard SR requires FTL travel to lead to the absurd as well as the unreasonable, I suppose that's true; at least, I can't immediately see how to cobble together a Lorentz invariant law that would allow FTL travel but still make CTCs impossible. (I can see how to make CTCs highly unlikely with a Lorentz invariant law, but that's not the same thing.)

That's incorrect; SR does make predictions about FTL travel, because it makes predictions about the geometric properties of spacelike curves as well as timelike and null curves.

Of course I don't know; I said repeatedly that I don't have a theory of FTL travel, so I don't know what physical law would govern which simulaneity to choose (or, as I put it, which particular spacelike trajectory an FTL object follows). But as I showed in my last post, that's irrelevant to the deduction that physically unreasonable consequences would follow if FTL travel were allowed (and even absurd ones, given what you pointed out above); those consequences follow from the simple fact that FTL travel implies a spacelike worldline, regardless of which spacelike worldline it is.

Of course not; that would require the same object to travel on multiple worldlines. If the assumption that a single object travels on a single worldline counts as an "interpretation" of SR, then OK, it's part of my interpretation.

No, that's not correct. We do not know *which specific spacelke worldline* an FTL rocket follows. But we *do* know, based on standard SR, what would be observed if a rocket traveled on *any spacelike worldline whatever*, regardless of which one it was. The only premise I used to deduce the physically unreasonable consequences was that the rocket traveled on *some* spacelike worldline; I didn't have to use any information about which one it was.

Hmm...I missed this aspect of your previous posts. This doesn't make sense, at least not in standard SR. An observer sees the events "rocket on Mars" and "rocket on Earth" in that order, yet he somehow concludes that the rocket is traveling from Earth to Mars? How? Because he communicates with other observers who saw the events in the opposite order? Why should he believe them? What makes their viewpoint more valid than his? There is no answer in standard SR.

You could, I suppose, say that the frame in which Earth and Mars are at rest is a "preferred frame", and that the order of events in that frame is the "real" order of events, regardless of what any other observer sees. That would violate standard SR since it would violate Lorentz invariance; you would have to have some physical law that only held true in the "preferred" frame (similar to the proposed law I gave above, for allowing FTL travel while still prohibiting CTCs). So I still don't see a way to reconcile your viewpoint with standard SR.

16. Jun 4, 2012

### Saw

Let us see if I express well your view, which you call standard SR:

* We do not know which spacelike trajectory or worldline a FTL (say “instantaneous”) rocket would follow.

* However, in practice it would follow only one, not many or infinite trajectories.

* This trajectory would coincide with the “simultaneity version” of only one particular frame X, meaning that the departure event and the arrival events are simultaneous in and only in that frame X.

* Yet, despite that remarkable coincidence, another frame Y would be entitled to hold that the said events have happened in reverse order, that is to say, arrival has preceded departure. For the sake of Lorentz invariance, this “view” is as valid as any other, even if it is physical inconsistent with the former.

* Now the passenger of our rocket mounts on another ship that travels back, also instantaneously, to the origin.

* Again we have to decide which spacelike trajectory the rocket will follow. For the sake of Lorentz invariance, we do not want to hold that X is a preferred frame. So we arbitrarily choose now that departure and arrival are simultaneous in Y frame, instead of X frame. This means that our passenger arrives at the origin in this return-trip before he started the go-trip. He has travelled back in time. This is absurd.

* Hence we infer that FTL travel is impossible.

Did I express your view correctly?

(What I do not understand, in any case, is why you call this travel to the past phenomenon a CTC. Why is it a “timelike” curve, if it is spacelike? I thought that the CTC expression was reserved for cases where the traveler moves slower than light, that is to say, timelike, but benefits from a GR phenomenon, like a traversable wormhole, which is a shortcut in spacetime created by its curvature.)

17. Jun 4, 2012

### Staff: Mentor

We don't know because we don't have any physical theory that tells us, and you, who made up your particular scenario, didn't specify. I'm not sure what that has to do with standard SR.

Yes, since standard SR assigns a unique worldline to any object, this is fine.

Yes, by standard SR, this is true of any pair of spacelike separated events; they are simultaneous in one and only one inertial frame.

I'm not sure why you describe it this way. As just noted, it has to be true by standard SR of any pair of spacelike separated events. There's no "coincidence" involved. Different pairs of spacelike separated events may be simultaneous in different frames, but given any specific pair of spacelike separated events, that pair will be simultaneous in one and only one frame.

You should be more careful about your wording. If the events are simultaneous there is no "order"--they both happen at the same instant, so they are not "ordered". For them to be "ordered", one would have to happen before the other.

But that's a relatively minor point; I think what you meant to say is that there are frames in which the events happen in a particular order that you prefer, namely, that the rocket is on Earth, and then it is on Mars. But by standard SR, for any pair of spacelike separated events A and B, there are frames in which A is before B, *and* frames in which B is before A. The ordering of the events is not frame invariant; it depends on the observer's state of motion.

As far as the statements about the ordering of spacelike separated events, no, there is no inconsistency. There is only an "inconsistency" if you insist that spacelike separated events can be causally connected, so that the ordering of the events has some physical meaning, even though it is not frame invariant. *That* is what is inconsistent with Lorentz invariance.

How is the arbitary choice of the Y frame any better than the arbitrary choice of the X frame? Neither one is expressed in terms of invariants.

Perhaps I need to elaborate on what a Lorentz invariant theory requires: it requires that any physical law, such as the law that would tell us what particular spacelike trajectory an FTL rocket would follow, has to be capable of being expressed purely in terms of invariant quantities. For example: the law that determines what energy a given observer will measure a given object, say a light ray, to have, is expressed as follows:

$$E = \eta_{ab} u^{a} p^{b}$$

where $\eta_{ab}$ is the Minkowski metric, $u^{a}$ is the 4-velocity of the observer, and $p^{b}$ is the 4-momentum of the light ray. I say this law is invariant because it holds regardless of which frame you use to determine the components of the 4-vectors; you will get the same number E out regardless.

Similarly, a Lorentz invariant law that told you which spacelike trajectory an FTL rocket would follow would have to be expressible in invariant form, as above. It would certainly not just be an "arbitrary choice". I don't have such a law, so I have no way of telling, in your scenario, what spacelike trajectory any of these FTL rockets are supposed to follow. It's up to you, who are making up the scenario, to provide the law that does so. You certainly can't just arbitrarily draw conclusions about what I would say, or implications for my viewpoint, when it's your scenario and you just made it up out of whole cloth.

*If* you adopt the particular arbitrary choice of the return trajectory, then yes, the passenger travels into his own past, which allows the paradoxes that you, not I, called "absurd". But I agree they should be sufficient reason to rule out this kind of scenario, so they should be sufficient reason to disallow any kind of physical law that allows FTL travel scenarios in which such things occur.

Not really; see above comments. But perhaps I should try to summarize since I raised objections to your summary:

* You say that if FTL travel were possible, we should not "fear" absurd consequences.

* I have pointed out that if FTL travel were possible, and the laws governing it were Lorentz invariant, I see no way to avoid the absurd consequences.

* Therefore, it seems to me that the only way for FTL travel to be possible without absurd consequences is for Lorentz invariance to be violated.  And since standard SR requires Lorentz invariance, FTL travel would only be possible without absurd consequences if standard SR were violated.

That's as simple a summary as I can give.

This is a good point; the actual trajectories we've been discussing, such as that of the passenger above, have spacelike segments. But the actual prohibition addressed by Hawking's Chronology Protection Conjecture is on closed *causal* curves--the CPC says that such curves are impossible. Normally that prohibition is taken to apply only to timelike and null curves; but you are basically saying we can somehow redefine "causal" to include certain spacelike curves as well, so that by your version of physics, we could have closed causal curves that had spacelike segments. But the fact that they are closed *causal* curves is what causes the problems; so saying that "spacelike curves aren't normally causally connected" doesn't help, since you have redefined physics so that in your version, they are.

18. Jun 4, 2012

### Austin0

In the original trip to mars it seems that an observer that would see the arrival before the departure might see something like this:
If he had been observing the rocket on earth as he approached Mars he would suddenly see the rocket appear on Mars while it still appeared to be on earth. At some point he would see, as you described, a retrograde trip back to earth where it would appear to disappear.
Strange to be sure. But we can imagine it would be interpreted as a weird visual effect. Equivalent to a visual sonic boom. but not grounds for an interpretation of actual violation of causality.
Historical chronology would be ; it was on earth --->.then it was on earth and mars---> then it was on mars and earth and moving back to earth- ----> and then only on mars.
Although it is questionable if an FTL anything would be visible

As far as a physical principle preventing time travel;
It certainly appears the FTL--->time travel idea implicitly assumes, and in fact requires, a model of block time or eternalism.
In a presentist universe there is no "there" there to travel to. A singular universe where nothing exists outside the current instant. While this is no more logically provable than block time it does exclude the possibility of time travel while retaining the FTL option.
I am not committed to either model BTW

19. Jun 4, 2012

### Ferraridude

I have a question about FTL speed.

If not even light can escape most black holes because a black hole has too high of an escape velocity, is that implying that maybe the gravity is exceeding something? Does that mean that there can't be higher velocities, with velocity being a vector, but there can be higher magnitudes of gravity, with gravity being a force, which is a vector?

20. Jun 4, 2012

### Staff: Mentor

So far we haven't talked at all about the specifics of the rocket's trajectory between Earth and Mars. But whatever that trajectory is, as seen by observers who see the rocket on Earth before it's on Mars, the observers who see those events in reverse order will see the entire trajectory in reverse. So if the first set of observers see the rocket take off from Earth, fly smoothly to Mars, and land on Mars, the second set of observers will see the rocket "unland" (i.e., they see the landing happen backwards) from Mars, fly smoothly (but backwards, and sucking up its own rocket exhaust as it goes) all the way to Earth, and "untakeoff" on Earth.

Not if the trajectory looks normal in the "forward" direction, to observers who see the rocket going from Earth to Mars. It looks like you are not fully comprehending what reversing the time order of those events means. It means reversing the *entire* trajectory, as above. If there are no weird optical effects in the "forward" version, then there aren't in the "reversed" version either.

I'm confused: which observers are supposed to see this chronology? I thought you were talking about the observers that see the rocket on Mars first, then on Earth. In this chronology, the rocket is on Earth first and on Mars at the end.

Although it is questionable if an FTL anything would be visible

Are you talking about FTL --> some observers see events on the FTL object's worldline in the opposite time order? Or do you mean something more elaborate by "time travel"?

If you're just talking about FTL implying that some observers will see a reversed time order for the FTL object's events, that doesn't require "block time"; it just requires standard SR and what it says about spacelike curves.

If you mean something more elaborate by "time travel", such as people traveling into their own past (or future), then that may require something more like a "block time" viewpoint, but I'm still not sure it would.

As you state it, this version of "presentism" is incompatible with SR, because SR does not have a frame-invariant concept of "the current instant".