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

[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 traveling 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.

 

[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.

 

[PeterDonis]

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

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 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.

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.

 

[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 traveling 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.

 

[PeterDonis]

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.

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.

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.

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

However, do you know why c is an unattainable speed? I don't think that it is a coincidence that it is true,

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.

but correct me if I'm wrong if I think light has 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.

since it comes in waves (Again, correct me if I'm wrong).

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.

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,

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.

and that the reason why things would appear different if you went at high speeds is because you are traveling faster than 0 m/s relative to the light,

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.

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.

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

 

[Saw]

relativity says that FTL travel is impossible because it would "break causality", as Mark M put it.

(...)

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 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.

 

[phinds]

... 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.

I think that is an excellent statement.

 

[PeterDonis]

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.

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?

 

[Saw]

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.

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?

is it, perhaps, that you don't regard the consequence as absurd?

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

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?

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.

 

[PeterDonis]

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?

I meant "measure" as you define it here.

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?

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.

Because an error must exist: if someone believes that FTL brings about absurdities, he or she must forcefully be mistaken.

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

the reason banning FTL travel would be some lower-level one, related to how things are accelerated, how causality is transmitted.

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

 

[Saw]

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

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.

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

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.

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.

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 traveled instantaneously. In frame B he has traveled forward in time. In frame C he has traveled 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 traveled 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 traveling 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.”

 

[Austin0]

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 traveled instantaneously. In frame B he has traveled forward in time. In frame C he has traveled 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 traveled 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 traveling 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.”

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. ;-)

 

[PeterDonis]

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.

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.

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.

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.

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.

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?

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.

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.

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.

Ok so far.

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?

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.

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?

In principle you could choose anyone 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...

- And if you arbitrarily choose any version of the story, why do you believe that the other versions are contradictory?...

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

 

[Saw]

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?

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?

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.

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.

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 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.

you would have to have a consistent causal theory of FTL travel. Do you?

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?

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.

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 learned 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.

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.

You have already seen it.

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.

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 traveled 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?

 

[PeterDonis]

How does causality operate in these cases? In my opinion, we do not know. In your opinion?

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.

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).

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.)

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.

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.

Suppose FTL is actually possible. What happens? Which version of simultaneity do you choose?

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.

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?

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.

We do not know what happens if a rocket flies FTL between two spacelike events.

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.

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 traveled 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?

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.

 

[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 traveled 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.)

 

[PeterDonis]

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

Some of the things you have expressed are about your particular scenario, not about "standard SR".

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

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.

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

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

* 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.

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

* Yet, despite that remarkable coincidence,

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.

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.

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.

For the sake of Lorentz invariance, this “view” is as valid as any other, even if it is physical inconsistent with the former.

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.

* 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.

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.

This means that our passenger arrives at the origin in this return-trip before he started the go-trip. He has traveled back in time. This is absurd.

* Hence we infer that FTL travel is impossible.

*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.

Did I express your view correctly?

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. [edit] 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.

(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?

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.

 

[Austin0]

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..

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

 

[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?

 

[PeterDonis]

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.

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.

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.

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.

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.

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

It certainly appears the FTL--->time travel idea implicitly assumes, and in fact requires, a model of block time or eternalism.

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.

In a presentist universe there is no "there" there to travel to. A singular universe where nothing exists outside the current instant.

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".

 

[PeterDonis]

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?

No. Gravity doesn't have to travel FTL to "get out" of the black hole, because the "gravity" you feel when you are outside the hole isn't coming from inside the hole; it's coming from the object that, sometime in the past, collapsed to form the hole. See this page on the Usenet Physics FAQ:

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html

There have also been a number of threads on PF about this; I can try to dig up some if you're interested, but the discussions on this topic tend to get rather involved. Feel free to ask more questions once you've read the FAQ entry.

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?

In GR, gravity isn't a force. See this Usenet Physics FAQ entry for a quick overview of a better way to look at gravity:

http://math.ucr.edu/home/baez/physics/Relativity/GR/gravity.html

There are a number of mathematical objects in GR that describe aspects of gravity, but none of them are vectors.

 

[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.

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.

Well I started out by stating I was talking about the observers who see the arrival before the takeoff and there is zero points of difference between my description and yours [except the fact that those observers would see the rocket both still on Earth as well as appearing on mars] Do you disagree with that?

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.

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

. Apparently you are a bit confused as i clearly said" At some point he would see, as you described, a retrograde trip back to Earth where it would appear to disappear" [look above]
If you do not see that there would clearly be different optical perceptions, effects as observed by the one seeing the reversed order then i would say you are not comprehending your own scenario.

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.

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

"If he had been observing the rocket on Earth as he approached Mars" [look above]
and yes I am talking about a single observers visual perceptions of events as that was what you indicated.

I'm sorry if I was not explicit enough. This is the chronology of the observations. The periods between the arrows are periods of simultaneous visual reception. His perception of the location(s) of the rocket

So the overall timeline is Earth =====> Mars with a lot of weird stuff in between

It certainly appears the FTL--->time travel idea implicitly assumes, and in fact requires, a model of block time or eternalism.

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.

Well so far in this scenario SR doesn't seem to enter into it. It is just another example of the visual distortions that occur with relativistic velocities like an approaching train appearing stretched . Simply due to the finite propagation time of light.
If we started extending frames and establishing chronology that way then it would be a different story
I am talking about the usual cast of characters. Messages sent from frame to frame and answers arriving before the questions are sent.Etc
don't you agree that none of this could possibly occur in a presentist universe as I described??

SO they necessarily require some kind of extended temporal reality I.e. Eternalism of some form

In a presentist universe there is no "there" there to travel to. A singular universe where nothing exists outside the current instant.

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".

You're of course quite right .SR doesn't have a concept of a universal , frame invariant instant.
But I disagree that this makes SR incompatible with a universal instant. It is only incompatible with some peoples interpretation of SR.
SR only says we can have no knowledge of any such instant or any way to ascertain or establish actual simultaneity.between disparate events. Obviously completely true. At the same time, in no way, either explicitly or logically, does it rule it out..
As I said I am not attached to any model of time and consider them all possible.

 

[PeterDonis]

Well I started out by stating I was talking about the observers who see the arrival before the takeoff and there is zero points of difference between my description and yours [except the fact that those observers would see the rocket both still on Earth as well as appearing on mars]

Which is what I was objecting to; if the "forward" observers don't see the rocket on both Earth and Mars at the same time, then neither will the "reverse" observers. If there are no weird "optical effects" for the first set of observers, there aren't any for the second set either. What you were describing seemed to indicate that the "reverse" observers would see a bunch of weird things that the "forward" observers didn't.

. Apparently you are a bit confused as i clearly said" At some point he would see, as you described, a retrograde trip back to Earth where it would appear to disappear" [look above]
If you do not see that there would clearly be different optical perceptions, effects as observed by the one seeing the reversed order then i would say you are not comprehending your own scenario.

It's not my scenario, it's Saw's, and yours in so far as you are defending it. I am simply pointing out that, by the terms of your own scenario, you can't have weird optical effects, or weird "retrograde trips", or the ship "appearing to disappear", for only one set of observers. If the observers who see the trip going from Earth to Mars don't see any of that weird stuff, the observers who see it going from Mars to Earth won't either. There's nothing about reversing the order of events that magically makes weird stuff happen.

So the overall timeline is Earth =====> Mars with a lot of weird stuff in between

Overall timeline for which set of observers? Again, I'm confused about whose observations you are describing here. There are some observers who see the rocket on Earth, then see it on Mars at a later time (by their clock, and allowing for light travel time, etc.). There are other observers who see the rocket on Mars, and then see it on Earth at a later time (by their clock, and allowing for light travel time, etc.). Either *both* kinds of observers see "weird stuff in between", or *neither* kind does. As I understood the original scenario, the observers who see the rocket on Earth, then on Mars at a later time, saw no weird stuff in between. That means the observers who see the rocket on Mars, then on Earth at a later time, won't see any weird stuff in between either.

don't you agree that none of this could possibly occur in a presentist universe as I described??

I don't understand your concept of "presentism" well enough to answer this.

SO they necessarily require some kind of extended temporal reality I.e. Eternalism of some form

I don't think "extended temporal reality" necessarily implies "eternalism". But I think this subtopic probably deserves its own thread.

You're of course quite right .SR doesn't have a concept of a universal , frame invariant instant.
But I disagree that this makes SR incompatible with a universal instant. It is only incompatible with some peoples interpretation of SR.
SR only says we can have no knowledge of any such instant or any way to ascertain or establish actual simultaneity.between disparate events. Obviously completely true. At the same time, in no way, either explicitly or logically, does it rule it out..

I can't come up with a definition of "instant" that has any observable physical consequences, but would not be inconsistent with SR. If your definition of "universal instant" doesn't have any observable consequences, then of course it can be consistent with any theory you like, including SR.

 

[danmay]

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?

Propagation of energy-momentum has an upper speed limit locally. Even locally, you don't need to exceed any speed limit to get sucked into something, as long as you have some non-zero velocity along that direction. I think black holes simply distort space-time while locally, c remains the same. Furthermore, in the case of light, I think it only bends; the magnitude of its velocity is not affected.

 

[danmay]

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?

In most derivations I've seen of the Lorentz transformation (the basis of special relativity effects), faster-than-light solutions (in some cases, c being a lower limit) are thrown out simply because they are not observed; i.e. causality is assumed to be in place and trumps over mathematical derivations. The other solution being thrown out is, of course, the Galileon transformation, in which there is no upper limit c.

But time is not really the same as a spatial coordinate. It's more of a statistical and thermodynamic "thing". If I were to imagine traveling back in time while being aware of it (i.e. isolated in my own frame/timeline different from the reversal of the rest of the world; not sure if that's specifically possible however), I think you would see something similar to traveling forward. Rare events would still be rare; frequent events would still be frequent. The order of any event is reversed (e.g. birth becomes death and death becomes birth); but that doesn't make any difference in terms of physical laws, because single events are symmetric with respect to time.

Edit: Corrected in posts #31 & 32

 

[danmay]

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.

In the alternate observer's frame, the rocket would be sucking, not pushing, and it would move you from Mars to Earth. No?

 

[PeterDonis]

In the alternate observer's frame, the rocket would be sucking, not pushing, and it would move you from Mars to Earth. No?

Actually, yes; I believe I corrected that in a later post. In the "reversed" frame, as the rocket went from Mars to Earth, its rocket "exhaust" would flow back into the nozzle, undergo the inverse reaction that turned it back into fuel, and put itself back into the rocket's tanks.

I answer this first because it is relevant to my response to your other post; see below.

In most derivations I've seen of the Lorentz transformation (the basis of special relativity effects), faster-than-light solutions (in some cases, c being a lower limit) are thrown out simply because they are not observed;

What does this have to do with the derivation of the Lorentz transformations? They apply to spacelike curves just as well as to timelike and null curves, as I said in an earlier post. The only "restriction" imposed is that normally spacelike curves are not allowed to be causal, which means they can't be the worldlines of objects. But the Lorentz transformations themselves work for any kind of curve.

The other solution being thrown out is, of course, the Galileon transformation, in which there is no upper limit c.

This "solution" is not "thrown out" arbitrarily; it's falsified by the evidence.

But time is not really the same as a spatial coordinate. It's more of a statistical and thermodynamic "thing".

This sense of "time" is not the sense of "time" that's relevant here. In SR, there certainly is a coordinate that's usually labeled "time", and it has nothing to do with statistics or thermodynamics; it's one of four numbers that are used to label each event, i.e., a coordinate.

If I were to imagine traveling back in time while being aware of it (i.e. isolated in my own frame/timeline different from the reversal of the rest of the world; not sure if that's specifically possible however), I think you would see something similar to traveling forward. Rare events would still be rare; frequent events would still be frequent. The order of any event is reversed (e.g. birth becomes death and death becomes birth); but that doesn't make any difference in terms of physical laws, because single events are symmetric with respect to time.

These statements don't necessarily go together. Consider the rocket scenario, whose "reversed" version you describe, and I elaborated on your description above. It certainly doesn't look the same in reverse as it does in the forward direction; so if someone could "travel back in time" in the sense of seeing these events in reverse order, they would see something quite different from those who travel "forward" in time. (Btw, this is a separate issue from whether the rocket can travel FTL; if you hypothesize an observer who travels on a timelike worldline, but somehow their experience is "backwards" from the usual direction of time, you get the same problems.)

Furthermore, since rockets sucking up their own exhaust, which then goes through a reverse reaction and fills the rocket tanks, is extremely rare in our ordinary "forward" time, whereas it would have to be common in the "reversed" version, it is not true that "rare events would still be rare" or "frequent events would still be frequent".

It is true, however, that the fundamental physical laws governing the rocket's travel are time symmetric; at least, that's our best understanding. The only "law" that we know of that isn't time symmetric is the second law of thermodynamics, which is the law that makes it "reasonable" to see rockets burning fuel and ejecting exhaust, and "unreasonable" to see rockets sucking up exhaust and "unburning" fuel. And the standard understanding of the second law is that it's not really a "law" governing the microphysics of the individual particles, but a boundary condition: our universe started off in a very special, low-entropy state in the past. It's that past low entropy state that makes rockets, and indeed life on Earth, possible in the first place: the universe is not in thermodynamic equilibrium, and there is lots of available "work" that can be done in the process of it tending towards that equilibrium sometime in the distant future.

 

[Austin0]

Well I started out by stating I was talking about the observers who see the arrival before the takeoff and there is zero points of difference between my description and yours [except the fact that those observers would see the rocket both still on Earth as well as appearing on mars]

Which is what I was objecting to; if the "forward" observers don't see the rocket on both Earth and Mars at the same time, then neither will the "reverse" observers. If there are no weird "optical effects" for the first set of observers, there aren't any for the second set either. What you were describing seemed to indicate that the "reverse" observers would see a bunch of weird things that the "forward" observers didn't.

Yes it did clearly indicate that; the "reverse" observers would see a bunch of weird things that the "forward" observers didn't.


I am unclear why you would think that both observers would necessarily see the same phenomenon?
.

If you do not see that there would clearly be different optical perceptions, effects as observed by the one seeing the reversed order then i would say you are not comprehending your own scenario.

It's not my scenario, it's Saw's, and yours in so far as you are defending it. I am simply pointing out that, by the terms of your own scenario, you can't have weird optical effects, or weird "retrograde trips", or the ship "appearing to disappear", for only one set of observers. If the observers who see the trip going from Earth to Mars don't see any of that weird stuff, the observers who see it going from Mars to Earth won't either. There's nothing about reversing the order of events that magically makes weird stuff happen.

Sorry. I read it in one of your posts and mistakenly assumed. I am not defending it simply making observations as I had never encountered this specific scenario and found it interesting.

If you are convinced of your assumption and are saying my analysis is wrong, do you have any basis for this other than your preconceptions?

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.

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.

"If he had been observing the rocket on Earth as he approached Mars"
and yes I am talking about a single observers visual perceptions of events as that was what you indicated.

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.

This is the chronology of the observations. The periods between the arrows are periods of simultaneous visual reception. His perception of the location(s) of the rocket

So the overall timeline is earth =====> mars with a lot of weird stuff in between

Overall timeline for which set of observers? Again, I'm confused about whose observations you are describing here. There are some observers who see the rocket on Earth, then see it on Mars at a later time (by their clock, and allowing for light travel time, etc.). There are other observers who see the rocket on Mars, and then see it on Earth at a later time (by their clock, and allowing for light travel time, etc.). Either *both* kinds of observers see "weird stuff in between", or *neither* kind does. As I understood the original scenario, the observers who see the rocket on Earth, then on Mars at a later time, saw no weird stuff in between. That means the observers who see the rocket on Mars, then on Earth at a later time, won't see any weird stuff in between either.

1) Forward observers no weirdness. backward observer definite strangeness.

2) Both observers would agree on the ultimate chronology as calculated by their observations and watches.

I don't think "extended temporal reality" necessarily implies "eternalism". But I think this subtopic probably deserves its own thread.

Agreed

I can't come up with a definition of "instant" that has any observable physical consequences, but would not be inconsistent with SR. If your definition of "universal instant" doesn't have any observable consequences, then of course it can be consistent with any theory you like, including SR

.

of course , which is why i questioned your statement that it was incompatible as I described it ;-)what time model has any observable consequences?

 

[PeterDonis]

I am unclear why you would think that both observers would necessarily see the same phenomenon?

They will both see the same "sequence" of events, just in reversed order, because they are both seeing the same spacelike trajectory, just "projected" into different inertial frames.

If you are convinced of your assumption and are saying my analysis is wrong, do you have any basis for this other than your preconceptions?

It's not an "assumption", it's a necessary implication of the scenario I understood Saw (and you) to be describing, plus the Lorentz transformation.

1) Forward observers no weirdness. backward observer definite strangeness.

2) Both observers would agree on the ultimate chronology as calculated by their observations and watches.

You're continuing to use confusing terminology, so I'm not sure I correctly understand what you're trying to say. Does "strangeness" simply mean that the backward observer sees things like the rocket sucking up its exhaust and its fuel getting "unburned"? Or does it mean the backward observer sees things like the rocket "appearing to disappear" but the forward one does not? Does "chronology" mean a sequence of events, but not necessarily in the same time order? Or does it mean a sequence of events in a particular time order?

Here's a suggestion to Saw, and you if you are in agreement with his position, as you appear to be: Don't use English to describe your scenario; English is too fuzzy and imprecise. Use math. Pick some convenient inertial frame and write down the equation of the FTL rocket's trajectory in that frame, or something equivalent. Or draw a spacetime diagram showing the trajectory, along with any other events or worldlines of interest. Once you've done that, everything else is determined, including what the trajectory will "look like" in any other frame. If you do that, I think it will be a lot easier to understand where each of us is coming from.

I'll even help by giving an example. Understand, I am not saying this is a description of the scenario Saw (and you) have been describing; I'm just giving an example that might be a similar scenario (or might not--if it turns out to be, of course that will make things easier), but should illustrate the general method of using math instead of English to describe the scenario.

Suppose that there is some inertial frame in which the Earth and Mars are at rest. And suppose that at some time t = 0 in this frame, an FTL rocket "launches" from Earth. We'll scale the coordinates so the distance, in this frame, between Earth and Mars is 1, and Earth is at the origin, so the event of the FTL rocket "launching" from Earth is at the origin of the inertial frame, (x, t) = (0, 0). Call this event E.

For this example, I'll suppose that, in the frame just described, the FTL rocket's flight to Mars is instantaneous: that means that the FTL rocket's worldline, in this frame, is just the line t = 0, from x = 0 to x = 1. That is, it is a straight, horizontal line from (0, 0) to (1, 0). Call the event of the rocket "landing" on Mars, at (1, 0), event M.

Now consider a second frame which is moving in the direction from Earth to Mars at speed sqrt(3)/2 (as should be evident, we are using units where the speed of light is 1). The gamma factor at this speed is 2. We keep the origin the same, so event E is still at (x', t') = (0, 0) in this frame. We can derive the coordinates of event M in this frame easily by the Lorentz transformation equation; the result is that event M's coordinates are (x', t') = (4, - sqrt(3)). So in this second frame, the FTL rocket appears to go backwards in time; but its trajectory is still a straight line, and in this frame it looks just like a smooth motion from Mars to Earth--but with, of course, all the physically unreasonable stuff like the rocket nozzle sucking up the exhaust and the fuel being "unburned", which violates the second law of thermodynamics.

We can also consider a third frame which is moving from Mars to Earth at speed - .866 (relative to the original frame). Again we keep event E at the origin, (x'', t'') = (0, 0). It should then be obvious that the coordinates of event M in this frame are (x'', t'') = (4, sqrt(3)). So in this frame, it looks like the FTL rocket goes from Earth to Mars, but not instantaneously; it takes some time (but is still FTL).

 

[Austin0]

You're continuing to use confusing terminology, so I'm not sure I correctly understand what you're trying to say. Does "strangeness" simply mean that the backward observer sees things like the rocket sucking up its exhaust and its fuel getting "unburned"? Or does it mean the backward observer sees things like the rocket "appearing to disappear" but the forward one does not? Does "chronology" mean a sequence of events, but not necessarily in the same time order? Or does it mean a sequence of events in a particular time order?

.

]
There is nothing confusing in my terminology. Absolutely every one of these points has been explicitly stated. You mention one here "appearing to disappear" ; what is ambiguous about that?
I also stated that the forward observer does not see this.
yes agreement of chronology is meant in the normal sense of time ordering. Sequence of events.
Not on the proper time of any of the events of course.

Frames and transformations have nothing to do with this, it is purely visual perception of two individuals at different locations and perspectives.

If you simply assume I have a reasonable command of english and take my words at face value everything has been explicitly covered.
Those other scenarios you mention could be interesting but are completely different questions.
Have you actually given any thought to my description on the remote chance I might have some idea of what I am talking about? Consider it a little puzzle Visualizing my description and why it would be so. ;-)

 

[PeterDonis]

Frames and transformations have nothing to do with this, it is purely visual perception of two individuals at different locations and perspectives.

As it stands now, I disagree. If you want to convince me, please relate what you are saying to either the precise description I posted, or to your own precise description made along similar lines. Until you do that, I can't comment further because I don't know precisely what scenario you think you are describing.

]If you simply assume I have a reasonable command of english and take my words at face value everything has been explicitly covered.

I tried that, it didn't work. That's why I've been continuing to ask questions and ask for more precise descriptions.

Those other scenarios you mention could be interesting but are completely different questions.

What "other scenarios"? Do you mean the precise description I posted does not match what you were visualizing? If so, can you post a similarly precise description of your scenario?

Have you actually given any thought to my description on the remote chance I might have some idea of what I am talking about?

I started out trying to do that, but as I said above, it didn't work. So unless you can post a precise description the way I did, giving explicit coordinates for events (or post a spacetime diagram), I'm afraid we're at a standstill.

 

[danmay]

What does this have to do with the derivation of the Lorentz transformations?

SR is the derivation, validation, and application of Lorentz transformations. The derivation of Lorentz transformations requires causality (one-way past-->present-->future) not be violated in order to dismiss the faster-than-c solutions and leave only SR (& its limiting case where v << c) standing.

This "solution" is not "thrown out" arbitrarily; it's falsified by the evidence.

Therefore, because "no upper limit c" is falsified by evidence, Galileon-transformation solutions were "thrown out". I didn't say "arbitrarily", however; let's not mince words.

This sense of "time" is not the sense of "time" that's relevant here. In SR, there certainly is a coordinate that's usually labeled "time", and it has nothing to do with statistics or thermodynamics; it's one of four numbers that are used to label each event, i.e., a coordinate.

SR as a model chooses not to deal with the sense of time, only its transformation due to motion. As explained earlier, the derivation of the SR model prohibits any violation of causality in the first place. Since a model cannot explain the assumptions on which it's based, it cannot explain the OP question, which is about traveling backwards in time. In order to answer it, we must break out of the SR model. Does GR allow traveling to the past? How can we tell/observe if causality were violated? What does it mean to travel backwards in time? Only thermodynamics seems to offer any relevant ideas as to what time is.

Furthermore, since rockets sucking up their own exhaust, which then goes through a reverse reaction and fills the rocket tanks, is extremely rare in our ordinary "forward" time, whereas it would have to be common in the "reversed" version, it is not true that "rare events would still be rare" or "frequent events would still be frequent".

I think you're right. I might have been thinking of a system already at equilibrium, or rare/frequent "microstates" and transitions among them being reversed. Right now I can't remember.

 

[Saw]

Sorry if I do not comment other posts. I just had time to answer PeterDonis':

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

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.

That is fine. I do not have any theory to fill this gap, either. That is what I was saying: we have a knowledge gap as to what happens (which spacelike trajectory succeeds) when FTL travel comes into the scene.

I'm not sure what that has to do with standard SR.

What is your problem with noting and even underlining this? I see two possibilities. Either SR knows or not. I thought we had just agreed that it does not know. And of course the issue has everything to do with the explanation of what standard SR is. It is a theory that solves all slower-than-light problems but has no answer as to what happens in a FTL thought experiment.

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

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

Nice. This means your interpretation of SR, like mine, adheres to the principle of reality.

* 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.

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

Perfect.

* Yet, despite that remarkable coincidence,

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.

I did not say that what you explain is a “remarkable coincidence”. The mere fact that observers disagree on the order of events is what relativity of simultaneity means. That does not surprise either you or me. What is a “coincidence” is that our magical rocket, which by definition travels instantaneously from its origin to its destination, does so as per the definition of simultaneity of a particular frame X, that is to say, chooses an instant of arrival that is the same instant as that of departure only in such frame X.

As I explained, my interpretation of SR and of relativity of simultaneity is not that all observers hold that their respective simultaneity versions are each of them “absolute”; I believe that each observer makes a relative judgment, not an absolute one. What is the difference? It is obvious. Each concept’s scope depends on the nature of the measurement operation with which you feed it. An absolute measurement of simultaneity would be one made with a signal like our magical rocket, that is to say, one displacing in no time, instantaneously. Instead a relative judgment is made ala Einstein-Poincaré, by halving the go and return trip of a real signal, either a light pulse or a massive object.

Hence if a (real) relative measurement made ala Einstein coincides by chance with a (hypothetical and magical) absolute operation, that is of course a coincidence and a very remarkable one, or not?

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.

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.

I am not sure what your criticism is here. The events are simultaneous in frame X, but they are ordered in frame Y. Have we not just said that they can only be simultaneous in one frame?

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.

I am puzzled here. Isn’t this what I… not only “meant to say” but actually said? I accept, if you wish, the wording “in another frame Y event B –arrival- is before A –departure-“ but I am not sure about the difference between that and my own wording.

this “view” is as valid as any other, even if it is physical inconsistent with the former.

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.

I think you misunderstood me here. I have no problem at all in general with SR and in particular with relativity of simultaneity. I love the fact that observers disagree on what events are simultaneous. I adore the idea that, when spacelike events are in play, observers can measure them in reverse order. I know that spacelike events are causally unconnected… as long there is no FTL agent around. And if I do consider the idea that such events can be causally connected through a FTL agent, well that is only because this queer hypothesis is the subject of the discussion!

To avoid inaccuracies I will just quote your words:

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.

This is what

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.

That is what I mean you mean: there are two “views” and (because of the FTL actor in play) those views are physically inconsistent with one another.

I think we can do without the rest of the thought experiment, where I considered the return trip and chose for this purpose (as some commentators do) another simultaneity line and hence a different spacelike path. That would only be a step up in the ladder of inconsistency, but as you say the first step is good enough to allow for the discussion.

So we can focus on a key issue, which plays a fundamental role in why the two views are inconsistent and that is “Lorentz invariance”.

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

Lorentz invariance is thus a condition for inconsistency. Put it in and FTL gets absurd; remove it and it becomes again possible, unless banned by other reasons.

Given this, I had guessed that “Lorentz invariance” is what makes you hold that the two views, despite being contradictory, are both valid, instead of simply preferring, for example, the view of the frame where the two relevant instants (departure and arrival) were simultaneous.

Now you add this clarification:

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.

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.

I wonder if you could elaborate more on this. It looks to me as if you were either contradicting yourself or simply confirming my initial understanding:

- Hypothesis of self-contradiction: If the mechanism governing FTL travel were Lorentz invariant, then all frames would explain what has happened on the basis of a single law, containing invariant concepts. There would be no discrepancy between their respective versions. Hence no inconsistency would arise.
- But maybe you mean that the inconsistency stems from the fact that you have only one trajectory but (based on your understanding of SR) two explanations: in one of them, the rocket travels from Earth to Mars, in the other it moves the other way round. In other words, your Lorentz invariant theory would like to offer a single law explaining what has happened but can’t. It would like to be invariant also in face of FTL but it is not.

 

[PeterDonis]

SR is the derivation, validation, and application of Lorentz transformations.

I wouldn't say that's *all* of SR, but it's certainly part of it.

The derivation of Lorentz transformations requires causality (one-way past-->present-->future) not be violated in order to dismiss the faster-than-c solutions and leave only SR (& its limiting case where v << c) standing.

I don't see this at all. Where in the derivation of the Lorentz transformations is causality assumed? Also, the "faster-than-c solutions" are not "dismissed"; as I said before, there are spacelike curves in SR as well as timelike and null curves. The spacelike curves aren't allowed to be the worldlines of objects in standard SR, but that's an assumption over and above the Lorentz transformations.

SR as a model chooses not to deal with the sense of time, only its transformation due to motion.

In the sense that you can apply a "time reversal" transformation to an SR coordinate chart and it will still be a valid SR coordinate chart, yes, this is true.

As explained earlier, the derivation of the SR model prohibits any violation of causality in the first place.

You haven't really "explained" this, as I said above.

Since a model cannot explain the assumptions on which it's based, it cannot explain the OP question, which is about traveling backwards in time.

If you are talking about timelike worldlines, yes, I agree; SR can equally well describe timelike worldlines that "flow" in either direction. But the OP was talking about FTL travel, i.e., letting *spacelike* curves be the worldlines of objects. That has a whole different set of consequences, which SR *can* predict, and which I've been discussing.

 

[PeterDonis]

Either SR knows or not. I thought we had just agreed that it does not know.

We agree that SR does not "know" which specific spacelike worldline an FTL rocket would travel on, assuming an FTL rocket were possible. We do *not* agree that SR can say nothing about what would happen if an FTL rocket could travel on a spacelike worldline in general. See below.

And of course the issue has everything to do with the explanation of what standard SR is. It is a theory that solves all slower-than-light problems but has no answer as to what happens in a FTL thought experiment.

Wrong. SR *can* say things about the general consequences of allowing *any* spacelike curve to be causal, i.e., to be the worldline of an object like an FTL rocket. Those consequences are what I've been talking about. Nothing I've said requires any assumption about which specific spacelike worldline the FTL rocket travels on. In my post #29, I did make a particular assumption about that, but that was only for concreteness, to illustrate the kind of general consequences I've been talking about. I could have assumed *any* other spacelike worldline for the FTL rocket and the general consequences would have been the same; it just would have taken more words to describe them.

What is a “coincidence” is that our magical rocket, which by definition travels instantaneously from its origin to its destination, does so as per the definition of simultaneity of a particular frame X, that is to say, chooses an instant of arrival that is the same instant as that of departure only in such frame X.

As I said, an FTL rocket would have to travel on *some* spacelike worldline. That means there has to be *some* frame in which the events of its "departure" and "arrival" are simultaneous. So it isn't a "coincidence" that you can find such a frame.

Hence if a (real) relative measurement made ala Einstein coincides by chance with a (hypothetical and magical) absolute operation, that is of course a coincidence and a very remarkable one, or not?

What you're basically saying is, normally we judge simultaneity indirectly, by measurements involving light signals; but if we allow FTL travel, we can judge some particular "simultaneity" directly, based on pairs of events linked by the FTL object's worldline. That's true, but it's not a "coincidence"; as I said, it's a logical consequence of allowing FTL travel at all.

I am not sure what your criticism is here. The events are simultaneous in frame X, but they are ordered in frame Y.

They are ordered one way in frame Y, but they are ordered in the opposite way in some other frame, Z. There is no frame invariant order to the events. Frame X is just a frame in which this lack of invariant order is particularly obvious, since the events happen at exactly the same instant.

Lorentz invariance is thus a condition for inconsistency. Put it in and FTL gets absurd; remove it and it becomes again possible, unless banned by other reasons.

Yes; when I gave my own summary, I said exactly this.

Given this, I had guessed that “Lorentz invariance” is what makes you hold that the two views, despite being contradictory, are both valid, instead of simply preferring, for example, the view of the frame where the two relevant instants (departure and arrival) were simultaneous.

I said that Lorentz invariance means you can't privilege either view, *if* FTL travel is possible; both views would have to be valid if FTL travel is possible and Lorentz invariance holds. But I also said that the two views were physically inconsistent; that's why I think FTL travel is impossible if Lorentz invariance holds.

I wonder if you could elaborate more on this. It looks to me as if you were either contradicting yourself or simply confirming my initial understanding:

See above. I wasn't contradicting myself; everything I've said has been consistent with the summary I gave several posts back and what I just said here.

- Hypothesis of self-contradiction:
...
- But maybe you mean that the inconsistency stems from the fact that you have only one trajectory but (based on your understanding of SR) two explanations:
...

Neither of these really captures what I meant. See above.

 

[danmay]

I don't see this at all. Where in the derivation of the Lorentz transformations is causality assumed? Also, the "faster-than-c solutions" are not "dismissed"; as I said before, there are spacelike curves in SR as well as timelike and null curves. The spacelike curves aren't allowed to be the worldlines of objects in standard SR, but that's an assumption over and above the Lorentz transformations.

Well, check these out.
(1) http://en.wikipedia.org/wiki/Lorentz_transformation#Derivation
(2) http://arxiv.org/pdf/gr-qc/0107091v2.pdf
Note especially the discussion on whether FTL violates causality, benign versus paradoxical tachyons, and the candidate definition of "cause and effect" using the "arrow of time" from thermodynamics.
(3) http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf
(4) http://o.castera.free.fr/pdf/One_more_derivation.pdf
Note that in all of these derivations of SR/LorentzT, the case where the value of alpha or kappa violates of causality is dismissed before arriving at the conclusion that the other cases are Lorentz (<0, or in the limiting case, =0) and constitue what we usually know as SR. Alternatively, SR can be broadened to include transformations that are not Lorentz, or LorentzT can be re-defined to include all values of alpha or kappa, but I don't think either option is the consensus defition of SR/LorentzT.

If you are talking about timelike worldlines, yes, I agree; SR can equally well describe timelike worldlines that "flow" in either direction. But the OP was talking about FTL travel, i.e., letting *spacelike* curves be the worldlines of objects. That has a whole different set of consequences, which SR *can* predict, and which I've been discussing.

Well, we can say if you could travel "backwards" in time as well as "forwards", then time would lose its "arrow"/asymmetry/causality, and be just like space. In which case you wouldn't be traveling "backwards" or "forwards" in time, but only along or opposite relative to the direction of other time travelers/or whatever reference you choose. In essence, if you were to travel both ways in time under SR, it would be just like traveling in space, and you would lose causality.

 

[PeterDonis]

Well, check these out.

Ah, I see; you are referring to alternate derivations of the Lorentz transform that don't assume the constancy of the speed of light; instead they make some alternate assumption that's related in some way to causality (link 2 calls it "pre-causality", for example). Yes, if you use one of the alternate derivations, then you're basically deriving the constancy of the speed of light from some kind of "causality", instead of deriving propositions about causality from the constancy of the speed of light. Since the constancy of the speed of light is an actual observable, I would tend to prefer using it as an axiom to trying to formulate "causality" as an axiom; but that's a judgment call.

Interesting papers, btw; I've only briefly skimmed them and will have to read them in more detail when I get a chance.

Alternatively, SR can be broadened to include transformations that are not Lorentz, or LorentzT can be re-defined to include all values of alpha or kappa, but I don't think either option is the consensus defition of SR/LorentzT.

Agreed.

Well, we can say if you could travel "backwards" in time as well as "forwards", then time would lose its "arrow"/asymmetry/causality, and be just like space. In which case you wouldn't be traveling "backwards" or "forwards" in time, but only along or opposite relative to the direction of other time travelers/or whatever reference you choose. In essence, if you were to travel both ways in time under SR, it would be just like traveling in space, and you would lose causality.

Not necessarily; allowing timelike observers to go "backwards" along timelike worldlines is not the same as getting rid of timelike (and null) curves altogether and making all curves spatial. The latter changes the metric of spacetime to a positive definite one; the former keeps a non-positive definite metric. The two types of metric are physically different.

 

[Austin0]

As it stands now, I disagree. If you want to convince me, please relate what you are saying to either the precise description I posted, or to your own precise description made along similar lines. .

OK We are the reverse observer approaching Mars< We have been observing the rocket on Earth. Suddenly the rocket appears on Mars because of course it has arrived there faster than the image of it's journey can reach us. So by the time we see it it has been on Mars the length of time it took for that image to reach us in space. At the same time we are still receiving images of the rocket on Earth because at the time it left Earth there was a complete string of images transmitting through space toward us.

As soon as we see the rocket appear on Mars we begin to receive the images of the trip in reverse order. So we are seeing the ship on Mars and still seeing it on Earth and at the same time receiving the reverse path images of the trip.

As soon as we receive the last image of the trip (I.e.The takeoff) the image of the ship completely disappears because this instant is coincident with the last image of the rocket on Earth that was strung out in space at ignition.

At the time we receive the first image of it's arrival on Mars we note the time. A simple calculation D/c returns the time of arrival on Mars At the time we observe the takeoff we note the time. Again a simple calculation based on distance from Earth gives us the time of takeoff.
It seems clear that this time would have to be earlier than the time calculated for arrival
So both visually and as a calculated chronology the temporal sequence is Earth to Mars.

Interestingly at small velocities above c the visual image of the reverse trip would appear to be much faster (take less time) than the actual trip. at very low c+ v's appearing almost instantaneous. The sonic boom analog I mentioned.
At greater velocities it could appear to take longer than the actual trip.

BTW i think you are mistaken in your description of the rocket exhaust appearing to be sucked back into the rocket.
It would still appear to flow backward from the engine , It would be the whole system appearing to move in reverse, No part of it would appear to move backward relative to the general motion toward Earth (as you described)
Not that is any less strange an image.

So let me know if this description is sufficient or if you see any flaws in this analysis.

 

[PeterDonis]

So let me know if this description is sufficient or if you see any flaws in this analysis.

I see a number of flaws. But first of all, since you continue to refuse to give the sort of precise specifications I've been asking for, I'm going to give what I think are the precise specifications corresponding to the scenario you describe. If you think I've got the specs wrong, feel free to correct me, so I can be sure I'm analyzing the correct scenario.

OK We are the reverse observer approaching Mars< We have been observing the rocket on Earth. Suddenly the rocket appears on Mars because of course it has arrived there faster than the image of it's journey can reach us.

Ok, so in the frame of what you are calling the "reverse observer", the rocket travels from Earth to Mars instantaneously? You don't say that explicitly but it looks like that from your description. So in this frame, with coordinates I will call (X, T), event E ("launch" from Earth) has coordinates (-XE, 0) and event M ("landing" on Mars) has coordinates (+XM, 0). I have to leave the X coordinates unspecified for now because you haven't said how far away we are from Earth or Mars at any specific event; but I'll specify them in a moment. The only thing we can say is that, since we are at the spatial origin, Earth's X coordinate must be negative (as shown), and Mars' must be positive (as shown).

(Note that this frame is *not* a frame in which Earth and Mars are at rest; they are both moving in the minus X direction, since you say this observer is "approaching Mars", meaning moving towards Mars and away from Earth. So this scenario is different from the one I described before, where events E and M were simultaneous in the frame in which Earth and Mars were at rest.)

So by the time we see it it has been on Mars the length of time it took for that image to reach us in space.

Let's call the event where the first light signal from event M reaches us, at rest in the frame we're talking about, event S. You haven't specified how far away from Mars we are, in this frame, at time t = 0, when events E and M occur; so I'll assume that at that instant, we are exactly halfway between Earth and Mars, i.e., XE = XM = 0.5. So event E has coordinates (-0.5, 0) and event M has coordinates (0.5, 0). That means event S has coordinates (0, 0.5), since we are at rest in this frame and the light travel time equals the distance.

At the same time we are still receiving images of the rocket on Earth because at the time it left Earth there was a complete string of images transmitting through space toward us.

Actually, as should now be obvious from the above, event S is also the event at which the *last* light signal reaches us from Earth--i.e., the signal from event E, where the rocket "leaves" Earth. So event S is the event at which we stop receiving light signals from the rocket on Earth, and start receiving them from the rocket on Mars.

As soon as we see the rocket appear on Mars we begin to receive the images of the trip in reverse order.

Half right. The "trip" worldline, at least on the assumption that it's a straight line, must be the line from event E to event M; i.e., the line (-0.5, 0) to (0.5, 0). Which immediately tells us the following:

* We receive our first information about the trip at event O, coordinates (0, 0), which is when the rocket instantaneously flies past us (since that event is on the straight line I just described, and in fact is its midpoint). The light signal from the rocket at event O reaches us instantly, since we are right there.

* During the period from event O to event S, (0, 0) to (0.5, 0), we receive light signals from both halves of the rocket's worldline, from points gradually spreading outward from event O to events E and M. That is, we see signals from the rocket flying towards Mars, *and* from the rocket flying towards Earth; we see it appear to fly in both directions--towards the Earth in "reverse" order, towards Mars in "forward" order.

So we are seeing the ship on Mars and still seeing it on Earth and at the same time receiving the reverse path images of the trip.

Half right again. We are seeing images from Earth, but *not* from Mars; event S is the first event where we get a signal from Mars, but the last where we get a signal from Earth. So between event O and event S, we get signals from Earth "overlapping" with signals from the Earthbound half of the trip (in reverse). We also get signals from the Mars-bound half of the trip (in forward order), as above, but not yet from Mars itself.

As soon as we receive the last image of the trip (I.e.The takeoff) the image of the ship completely disappears because this instant is coincident with the last image of the rocket on Earth that was strung out in space at ignition.

For the Earth images, yes, this is correct. But only for the Earth images.

At the time we receive the fifst image of it's arrival on Mars we note the time. A simple calculation D/c returns the time of arrival on Mars At the time we observe the takeoff we note the time. Again a simple calculation based on distance from Earth gives us the time of takeoff.

It seems clear that this time would have to be earlier than the time calculated for arrival

Wrong. We see the images from the takeoff and the arrival at the same instant, and they are equidistant from us, so we conclude that the two events are simultaneous.

Note, however, that Earth and Mars are not at rest in this scenario, so we have to use previous light signals from both planets to conclude that we are exactly halfway between them at event O, the instant we receive the takeoff and arrival light signals from events E and M.

So both visually and as a calculated chronology the temporal sequence is Earth to Mars.

Wrong. We conclude that the travel was instantaneous, so *all* events between E and M happen simulataneously. We cannot assign a "temporal sequence" to *any* portion of this line.

Interestingly at small velocities above c the visual image of the reverse trip would appear to be much faster (take less time) than the actual trip. at very low c+ v's appearing almost instantaneous. The sonic boom analog I mentioned.

At greater velocities it could appear to take longer than the actual trip.

I won't try to calculate whether this is correct or not, since I've already shown that you got some key things wrong above.

BTW i think you are mistaken in your description of the rocket exhaust appearing to be sucked back into the rocket.

It would still appear to flow backward from the engine , It would be the whole system appearing to move in reverse, No part of it would appear to move forward relative to the general motion (as you described)

Not sure how you're coming up with that. In the "forward" temporal sequence, the rocket exhaust moves backward from the nozzle while the rocket moves forward. In the "reversed" sequence, the exhaust would therefore move forward into the nozzle, while the rocket would move backward to "suck up" the exhaust.

 

[PeterDonis]

OK We are the reverse observer approaching Mars< We have been observing the rocket on Earth. Suddenly the rocket appears on Mars because of course it has arrived there faster than the image of it's journey can reach us.

So both visually and as a calculated chronology the temporal sequence is Earth to Mars.

I'll post separately on these two statements in particular, for reasons that should soon become evident. When you say the rocket "appears" on Mars, do you mean that's when it arrives there, or that's when the light from its arrival reaches us? It seems to be the former because "it has arrived there faster than the image...can reach us". But that leaves three possibilities, none of which appear to disagree with anything I've been saying.

The first possibility is the one I analyzed in my last post: you intended for events E and M to be simultaneous, in the frame of the "reverse observer". My last post shows that, if that is the case, what that observer will actually observe, by means of light signals, is not what you thought.

The second possibility is that you intended for event E to be earlier than event M, but for the travel to still be FTL. That would be consistent with the second statement I quoted above, that "both visually and as a calculated chronology" the trip is from Earth to Mars. I assume that by "calculated chronology" you mean "the actual coordinates assigned to events in the reverse observer's frame". But this possibility is precisely the one that we have never disagreed on to begin with! I have never said that an observer who sees event E before event M will observe anything physically unreasonable. I have only said that, if the curve from event E to event M is spacelike, there will be *some* observer who sees event M before event E, and *that* observer will see things that are physically unreasonable. Everything in your post talks only about what one particular observer will see, the "reverse observer"--but if this second possibility is correct, that is a misnomer, because this so-called "reverse" observer sees the "forward" version of the trip. So if this possibility is correct, you were looking at the wrong observer; you should have looked at some other observer, moving relative to the "reverse" observer, who sees event M before event E. Such an observer must always exist, so if you don't analyze what he observes, you're missing the whole point. (The analysis I'll give in a moment of the third possibility is what you would come up with if you analyzed what that other observer observes.)

The third possibility is that you intended for event M to be earlier than event E, in the frame of the "reverse observer". This would make that observer correctly named, but it would be inconsistent with the second quote above, since by hypothesis the "calculated chronology" would be that the trip was from Mars to Earth. However, I'll go ahead and briefly analyze this scenario as well. It works much the same as the one where the events are simultaneous; the only difference is that now there are two events, SM and SE, instead of a single event S. Event SM is the first event where signals from the "landing" on Mars reach the observer; event SE is the last event where signals from the "takeoff" from Earth reach the observer. Event SM comes first (because event M is earlier), so there is a period between events SM and SE where the observer is receiving signals from the ship on Mars (after "landing"), from the ship on Earth (before "takeoff"), *and* from the Earthbound half of the trip itself (in "reverse" order).

What would the observer conclude from this? He would conclude that there were two ships and one "antiship"! He would conclude that there was a ship on Earth; then, at some instant, a ship and an "antiship" appeared on Mars out of the vacuum; the ship stayed on Mars, while the "antiship" flew to Earth and annihilated the Earth ship, vanishing with it into the vacuum.

You may say that that doesn't make sense--wouldn't it make more sense to say that a single ship started on Earth, went backwards in time to Mars, and then stayed on Mars? The problem with that is that it isn't physically reasonable for at least two reasons:

(1) The portion of the ship's worldline between events E and M violates the second law of thermodynamics; the ship's entropy decreases from event M to event E, which is the forward direction of time.

(2) The whole portion of the spacetime between the time of event M and the time of event E violates energy conservation: there are three ships there, whereas at other times there is only one.

The "antiship" version I gave above avoids these problems because the "antiship" would have negative energy, canceling the energy of one of the ships to keep total energy conserved; and its entropy would run in reverse (because of the negative energy), so there would be no violation of the second law. However, that doesn't (IMO) make an "antiship" physically reasonable either; it just illustrates why FTL travel is disallowed if you want to keep Lorentz invariance.

 

[Austin0]

I'll post separately on these two statements in particular, for reasons that should soon become evident. When you say the rocket "appears" on Mars, do you mean that's when it arrives there, or that's when the light from its arrival reaches us? It seems to be the former because "it has arrived there faster than the image...can reach us". But that leaves three possibilities, none of which appear to disagree with anything I've been saying.

The first possibility is the one I analyzed in my last post: you intended for events E and M to be simultaneous, in the frame of the "reverse observer". My last post shows that, if that is the case, what that observer will actually observe, by means of light signals, is not what you thought.

The second possibility is that you intended for event E to be earlier than event M, but for the travel to still be FTL. That would be consistent with the second statement I quoted above, that "both visually and as a calculated chronology" the trip is from Earth to Mars. I assume that by "calculated chronology" you mean "the actual coordinates assigned to events in the reverse observer's frame". But this possibility is precisely the one that we have never disagreed on to begin with! I have never said that an observer who sees event E before event M will observe anything physically unreasonable. I have only said that, if the curve from event E to event M is spacelike, there will be *some* observer who sees event M before event E, and *that* observer will see things that are physically unreasonable. Everything in your post talks only about what one particular observer will see, the "reverse observer"--but if this second possibility is correct, that is a misnomer, because this so-called "reverse" observer sees the "forward" version of the trip. So if this possibility is correct, you were looking at the wrong observer; you should have looked at some other observer, moving relative to the "reverse" observer, who sees event M before event E. Such an observer must always exist, so if you don't analyze what he observes, you're missing the whole point. (The analysis I'll give in a moment of the third possibility is what you would come up with if you analyzed what that other observer observes.)

The third possibility is that you intended for event M to be earlier than event E, in the frame of the "reverse observer". This would make that observer correctly named, but it would be inconsistent with the second quote above, since by hypothesis the "calculated chronology" would be that the trip was from Mars to Earth. However, I'll go ahead and briefly analyze this scenario as well. It works much the same as the one where the events are simultaneous; the only difference is that now there are two events, SM and SE, instead of a single event S. Event SM is the first event where signals from the "landing" on Mars reach the observer; event SE is the last event where signals from the "takeoff" from Earth reach the observer. Event SM comes first (because event M is earlier), so there is a period between events SM and SE where the observer is receiving signals from the ship on Mars (after "landing"), from the ship on Earth (before "takeoff"), *and* from the Earthbound half of the trip itself (in "reverse" order).

What would the observer conclude from this? He would conclude that there were two ships and one "antiship"! He would conclude that there was a ship on Earth; then, at some instant, a ship and an "antiship" appeared on Mars out of the vacuum; the ship stayed on Mars, while the "antiship" flew to Earth and annihilated the Earth ship, vanishing with it into the vacuum.

You may say that that doesn't make sense--wouldn't it make more sense to say that a single ship started on Earth, went backwards in time to Mars, and then stayed on Mars? The problem with that is that it isn't physically reasonable for at least two reasons:

(1) The portion of the ship's worldline between events E and M violates the second law of thermodynamics; the ship's entropy decreases from event M to event E, which is the forward direction of time.

(2) The whole portion of the spacetime between the time of event M and the time of event E violates energy conservation: there are three ships there, whereas at other times there is only one.

The "antiship" version I gave above avoids these problems because the "antiship" would have negative energy, canceling the energy of one of the ships to keep total energy conserved; and its entropy would run in reverse (because of the negative energy), so there would be no violation of the second law. However, that doesn't (IMO) make an "antiship" physically reasonable either; it just illustrates why FTL travel is disallowed if you want to keep Lorentz invariance.

Since the scenario under discussion was for two observers. One seeing the normal forward motion of the ship. This observer naturally being in a frame traveling toward Earth on a trajectory parallel to the Earth Mars line (but outside the Earth-Mars interval), traveling in the positiv3e x direction. But able to see the takeoff,,, so as this wasn't specified I assumed take off was from an equatorial position orthogonal to Earth -Mars line and thus visible to such on observer.
The observer seeing the reverse translation being on a parallel course in the -x direction approaching Mars from outside the Earth-Mars interval with the landing likewise being visible on the equator.
Otherwise the scenario made no sense.
There was no mention of being in the middle or both observers traveling in the same direction which makes no sense in any such scenario.
Does this clear it up?

i made no mention of instantaneous although I did specifically mention various velocities greater than c. SO when I said appeared I meant as said that the light from the intermediate trip had not arrived not that the trip was instantaneous..

If this is not enough information I will get back to you

 

[danmay]

Ah, I see; you are referring to alternate derivations of the Lorentz transform that don't assume the constancy of the speed of light; instead they make some alternate assumption that's related in some way to causality (link 2 calls it "pre-causality", for example). Yes, if you use one of the alternate derivations, then you're basically deriving the constancy of the speed of light from some kind of "causality", instead of deriving propositions about causality from the constancy of the speed of light. Since the constancy of the speed of light is an actual observable, I would tend to prefer using it as an axiom to trying to formulate "causality" as an axiom; but that's a judgment call.

Actually, they had all assumed constancy of c before even getting into the point on causality.

Not necessarily; allowing timelike observers to go "backwards" along timelike worldlines is not the same as getting rid of timelike (and null) curves altogether and making all curves spatial. The latter changes the metric of spacetime to a positive definite one; the former keeps a non-positive definite metric. The two types of metric are physically different.

I only meant in terms of freedom of travel. Space is not actually turning into time or vice versa.

 

[Austin0]

I'll post separately on these two statements in particular, for reasons that should soon become evident. When you say the rocket "appears" on Mars, do you mean that's when it arrives there, or that's when the light from its arrival reaches us? It seems to be the former because "it has arrived there faster than the image...can reach us". But that leaves three possibilities, none of which appear to disagree with anything I've been saying.

The first possibility is the one I analyzed in my last post: you intended for events E and M to be simultaneous, in the frame of the "reverse observer". My last post shows that, if that is the case, what that observer will actually observe, by means of light signals, is not what you thought.

The second possibility is that you intended for event E to be earlier than event M, but for the travel to still be FTL. That would be consistent with the second statement I quoted above, that "both visually and as a calculated chronology" the trip is from Earth to Mars. I assume that by "calculated chronology" you mean "the actual coordinates assigned to events in the reverse observer's frame". But this possibility is precisely the one that we have never disagreed on to begin with! I have never said that an observer who sees event E before event M will observe anything physically unreasonable. I have only said that, if the curve from event E to event M is spacelike, there will be *some* observer who sees event M before event E, and *that* observer will see things that are physically unreasonable. Everything in your post talks only about what one particular observer will see, the "reverse observer"--but if this second possibility is correct, that is a misnomer, because this so-called "reverse" observer sees the "forward" version of the trip. So if this possibility is correct, you were looking at the wrong observer; you should have looked at some other observer, moving relative to the "reverse" observer, who sees event M before event E. Such an observer must always exist, so if you don't analyze what he observes, you're missing the whole point. (The analysis I'll give in a moment of the third possibility is what you would come up with if you analyzed what that other observer observes.)

The third possibility is that you intended for event M to be earlier than event E, in the frame of the "reverse observer". This would make that observer correctly named, but it would be inconsistent with the second quote above, since by hypothesis the "calculated chronology" would be that the trip was from Mars to Earth. However, I'll go ahead and briefly analyze this scenario as well. It works much the same as the one where the events are simultaneous; the only difference is that now there are two events, SM and SE, instead of a single event S. Event SM is the first event where signals from the "landing" on Mars reach the observer; event SE is the last event where signals from the "takeoff" from Earth reach the observer. Event SM comes first (because event M is earlier), so there is a period between events SM and SE where the observer is receiving signals from the ship on Mars (after "landing"), from the ship on Earth (before "takeoff"), *and* from the Earthbound half of the trip itself (in "reverse" order).

What would the observer conclude from this? He would conclude that there were two ships and one "antiship"! He would conclude that there was a ship on Earth; then, at some instant, a ship and an "antiship" appeared on Mars out of the vacuum; the ship stayed on Mars, while the "antiship" flew to Earth and annihilated the Earth ship, vanishing with it into the vacuum.

You may say that that doesn't make sense--wouldn't it make more sense to say that a single ship started on Earth, went backwards in time to Mars, and then stayed on Mars? The problem with that is that it isn't physically reasonable for at least two reasons:

(1) The portion of the ship's worldline between events E and M violates the second law of thermodynamics; the ship's entropy decreases from event M to event E, which is the forward direction of time.

(2) The whole portion of the spacetime between the time of event M and the time of event E violates energy conservation: there are three ships there, whereas at other times there is only one.

The "antiship" version I gave above avoids these problems because the "antiship" would have negative energy, canceling the energy of one of the ships to keep total energy conserved; and its entropy would run in reverse (because of the negative energy), so there would be no violation of the second law. However, that doesn't (IMO) make an "antiship" physically reasonable either; it just illustrates why FTL travel is disallowed if you want to keep Lorentz invariance.

It sounds like you are starting to get the picture. But your anti-ship ,and entropy violation etc.,etc. don't make any sense whatsoever. There is no 2nd and 3rd ship.Merely optical illusions as I said much earlier.
There is no time travel unless you adopt a nonsensical interpretation of visual perceptions.

so do you understand my description?

Or do you require more explication?

Would you now say it was inaccurate in any way??

 

[PeterDonis]

Since the scenario under discussion was for two observers. One seeing the normal forward motion of the ship. This observer naturally being in a frame traveling toward Earth on a trajectory parallel to the Earth Mars line (but outside the Earth-Mars interval), traveling in the positiv3e x direction. But able to see the takeoff,,, so as this wasn't specified I assumed take off was from an equatorial position orthogonal to Earth -Mars line and thus visible to such on observer.
The observer seeing the reverse translation being on a parallel course in the -x direction approaching Mars from outside the Earth-Mars interval with the landing likewise being visible on the equator.

Ok, so we have two observers, and they are located somewhat differently from what I assumed. Fair enough; see revised analysis below. None of the key conclusions change.

Observer A is moving in the positive X direction and is further in the negative X direction than Earth is; observer B is moving in the negative X direction and is further in the positive X direction than Mars is. Event E is still the event of the ship's "takeoff" from Earth; event M is still the event of the ship's "landing" on Mars. I'll define other important events in the new scheme below.

(Btw: when you use the word "see" in the above, I believe you mean "receive light rays from", because otherwise you have the observers backwards. As we will see, Observer A will assign an earlier time to event M than event E; his "calculated chonology" has the trip going from Mars to Earth, even though he receives light rays from the Earth end of the trip first. Observer B will assign an earlier time to event E than to event M; his "calculated chronology" has the trip going from Earth to Mars, even though he receives light rays from the Mars end of the trip first. This doesn't really affect my conclusions below, but I wanted to make clear how I'm interpreting what I quoted.)

It will be easiest here to adopt a reference frame in which events E and M are simultaneous, and to assume, as I did in my original elaboration on Saw's scenario, that this is the frame in which the Earth and Mars are mutually at rest. You didn't specify any of this in your statement, but nothing you specified contradicts it, and it makes the analysis simpler without affecting any of the key conclusions (which, as I've said several times now, apply regardless of which particular spacelike curve you choose for the trip). In this frame, we set the origin halfway between Earth and Mars at the instant the trip occurs (since the trip is instantaneous in this frame), so event E, once again, has coordinates (-0.5, 0), and event M has coordinates (0.5, 0).

At time t = 0 in this frame, I'll also assume that Observer A is at coordinates (-1, 0), moving in the positive X direction. You didn't specify a speed, so I'll assume it's 0.5. Similarly, I'll assume that Observer B at time t = 0 is at coordinates (1, 0), moving in the negative X direction, with speed -0.5.

Observer A will therefore see the light signal from event E at event EA = (-.833, .333), and from event M at event MA = (-0.5, 1); in between those two events, he sees light signals from intermediate points on the trip, in "forward" order. Since he is further away from Mars than Earth, he sees *no* "overlapping" light signals from the rocket being on Earth or Mars during this period; he sees light signals only from one "segment" of the rocket's total worldline at a time.

However, Observer A's "calculated chronology" concludes that event M happened *before* event E. This is easiest to see if we keep the origins of all the frames the same (meaning that observer A is *not* at the origin of the "moving frame" in his direction); then we can run a simple Lorentz transformation with v = 0.5 to find (X', T') for event E = 1.15 (-0.5, 0.25), and for event M = 1.15 (0.5, -0.25).

Observer B sees the light signal from event M at event MB = (.833, .333), and from event E at event EB = (0.5, 1). In between those two events, he sees the light signals from intermediate points on the trip, in "reverse" order. He also sees "overlapping" light signals from the rocket being on Earth before the "launch", in "forward" order, during this entire period (and, of course, he sees the rocket on Earth before that period as well).

However, Observer B's "calculated chronology" concludes that event E happened before event M; a similar procedure to the above but with v = -0.5 gives (X'', T'') for event E = 1.15 (-0.5, -0.25), and for event M = 1.15 (0.5, 0.25).

So after all this, I'm still not sure what you think it's all supposed to prove. There is an observer who sees (receives light signals from) the rocket's entire history in "forward" order--but that observer concludes, after allowing for light speed time delay, that the trip actually occurred in "reverse" order, from Mars to Earth, which raises all the issues I raised in my previous posts (either he concludes that there are two ships and an "antiship", or he concludes that the trip portion of the ship's history violates energy conservation and the second law of thermodynamics).

There is also an observer who sees "weird" stuff like light signals from the trip "overlapping" with light signals from the rocket's period on Earth before "launch", and the trip light signals arriving in "reverse" order. But *this* observer is the one who concludes, after allowing for light speed time delay, that the trip occurred FTL, but the rocket's entire history happened in ordinary "forward" order in time--no violations of anything, once he allows the possibility of FTL travel. So the observer who sees (receives light signals from) the "weird" stuff is *not* the same one who has to conclude that physical laws have been violated.

And in any case, there *is* an observer who has to conclude that physical laws have been violated; and it shouldn't be too hard to see, after the analyses I've already posted, that there will be some such observer regardless of which particular spacelike trajectory the trip is assumed to follow. So I'm still seeing this scenario as a good reason to disallow FTL travel in the first place.

 

[PeterDonis]

It sounds like you are starting to get the picture. But your anti-ship ,and entropy violation etc.,etc. don't make any sense whatsoever. There is no 2nd and 3rd ship.Merely optical illusions as I said much earlier.

No, they're not. They are conclusions those observers are *forced* to, after allowing for light speed time delay and all other optical effects.

There is no time travel unless you adopt a nonsensical interpretation of visual perceptions.

What other interpretation would you give? Would you have the observer say that the events from which "optical illusion" light rays are received weren't real? Then you have the problem that the rocket's worldline has "gaps"--it disappears from one event in spacetime and appears at another, without traversing any intervening events. That also violates energy conservation.

 

[Austin0]

So after all this, I'm still not sure what you think it's all supposed to prove.

As I said so far I was only interested in the visual perceptions. I had only examined the question through coordinate events and charts and never thought FTL objects would be visible so when I read your description , (it was your scenario not saw's)
talking about seeing exhaust in reverse being sucked up etc. it seemed to be referring to visual perceptions , not coordinate calculations and it got me thinking.
Since the case of the observer that saw forward motion was uninteresting i restricted my thought to observer B and the optical effects

It is just another example of the visual distortions that occur with relativistic velocities like an approaching train appearing stretched . Simply due to the finite propagation time of light.
If we started extending frames and establishing chronology that way then it would be a different story

Frames and transformations have nothing to do with this, it is purely visual perception of two individuals at different locations and perspectives.

it seemed so straight forward I assumed it would be obvious simply from a verbal description. I wasn't trying to be difficult.

I never imagined you would go to the trouble you did defining possible scenarios and I apologize for that . I should know better and not assume anything is obvious when dealing with these questions. I will remember in the future.

event M to be earlier than event E, in the frame of the "reverse observer". However, I'll go ahead and briefly analyze this scenario as well. It works much the same as the one where the events are simultaneous; the only difference is that now there are two events, SM and SE, instead of a single event S. Event SM is the first event where signals from the "landing" on Mars reach the observer; event SE is the last event where signals from the "takeoff" from Earth reach the observer. Event SM comes first (because event M is earlier), so there is a period between events SM and SE where the observer is receiving signals from the ship on Mars (after "landing"), from the ship on Earth (before "takeoff"), *and* from the Earthbound half of the trip itself (in "reverse" order).

What would the observer conclude from this? He would conclude that there were two ships and one "antiship"! He would conclude that there was a ship on Earth; then, at some instant, a ship and an "antiship" appeared on Mars out of the vacuum; the ship stayed on Mars, while the "antiship" flew to Earth and annihilated the Earth ship, vanishing with it into the vacuum

.I call this Case 2) later in this post

You may say that that doesn't make sense--wouldn't it make more sense to say that a single ship started on Earth, went backwards in time to Mars, and then stayed on Mars? The problem with that is that it isn't physically reasonable for at least two reasons:

(1) The portion of the ship's worldline between events E and M violates the second law of thermodynamics; the ship's entropy decreases from event M to event E, which is the forward direction of time.

(2) The whole portion of the spacetime between the time of event M and the time of event E violates energy conservation: there are three ships there, whereas at other times there is only one

.I call this Case 1) later in this post
.
OBSERVER A

There is an observer who sees (receives light signals from) the rocket's entire history in "forward" order--but that observer concludes, after allowing for light speed time delay, that the trip actually occurred in "reverse" order, from Mars to Earth, which raises all the issues I raised in my previous posts (either he concludes that there are two ships and an "antiship", or he concludes that the trip portion of the ship's history violates energy conservation and the second law of thermodynamics).

OBSERVER B

There is also an observer who sees "weird" stuff like light signals from the trip "overlapping" with light signals from the rocket's period on Earth before "launch", and the trip light signals arriving in "reverse" order. But *this* observer is the one who concludes, after allowing for light speed time delay, that the trip occurred FTL, but the rocket's entire history happened in ordinary "forward" order in time--no violations of anything, once he allows the possibility of FTL travel. So the observer who sees (receives light signals from) the "weird" stuff is *not* the same one who has to conclude that physical laws have been violated.

So here you are now applying the anti-ship interpretation to observer A
You are quite right. It works in many interesting ways

Case 1) There is forward spatial motion wrt both frames A, sees forward motion in space but calculates that it is translating backward in time.
B sees backward spatial motion through optical effect but calculates the motion is forward in both dimensions. A single ship.

Case 2) The ship jumps directly to the destination at an earlier time without passing through the intermediate space and then translates in reverse motion back to the origin and the moment of launch. In this instance the A observer does not see the motion until the ship reaches the launch and then it only appears to move towards the destination through the same optical effect that takes place in B in the reverse direction. Amazing symmetry.
B sees an effect and it appears strange being in reverse. A sees the same effect but as it conforms to expectations it is deemed ordinary.
Here there are multiple ships.

If we place intermediate observers throughout both of the frames the observations will be equivalent:
the ship appearing out of thin air and racing off in both directions With no clue to determine direction.
In case 1) in both frames the optical part would be directed back to Earth and the normal visual towards Mars.

In Case 2) B's optical effect would point to Earth while A's would point to Mars

this all appears symmetrical and consistent but there is a point of contradiction.

If we have all the observers in both frames set off a flare at the instant the ship is collocated:

In case 1) we can assume that the flares would progress from Earth to Mars in both frames

case 2) it would seem that the flares in B would progress E--->M but the flares in A would have to progress in the opposite direction.

A clear lack of frame agreement on proximate events. I would think that this alone would be enough to eliminate case 2) as a possible option. Would you agree??

In addition case 2) has the problem you mentioned of having two or three ships existing at once , not as optical effects, as in case 1), but as actualities.

What would the observer conclude from this? He would conclude that there were two ships and one "antiship"! He would conclude that there was a ship on Earth; then, at some instant, a ship and an "antiship" appeared on Mars out of the vacuum; the ship stayed on Mars, while the "antiship" flew to Earth and annihilated the Earth ship, vanishing with it into the vacuum. (case 2)

You may say that that doesn't make sense--wouldn't it make more sense to say that a single ship started on Earth, (case 1) went backwards in time to Mars, and then stayed on Mars? The problem with that is that it isn't physically reasonable for at least two reasons:

(1) The portion of the ship's worldline between events E and M violates the second law of thermodynamics; the ship's entropy decreases from event M to event E, which is the forward direction of time.

(2) The whole portion of the spacetime between the time of event M and the time of event E violates energy conservation: there are three ships there, whereas at other times there is only one

.

I am confused here. You say a single ship ((case 1) doesn't make sense but them proceed to give reasons that only seem apply to case 2) Am i missing something here?
Why you think the single ship is less reasonable that case 2) ?

What other interpretation would you give? Would you have the observer say that the events from which "optical illusion" light rays are received weren't real? Then you have the problem that the rocket's worldline has "gaps"--it disappears from one event in spacetime and appears at another, without traversing any intervening events. That also violates energy conservation.

Again this seems to apply to case 2)

So i hope we are on the same track now and can go on to the interoretation. ;-)

 

[PeterDonis]

I had only examined the question through coordinate events and charts and never thought FTL objects would be visible

Why wouldn't they be? They're still there; they're just moving FTL. Wouldn't the simplest assumption be that they act like ordinary objects in all other respects?

So here you are now applying the anti-ship interpretation to observer A

I am saying that observer A's "calculated chronology" has event M before event E--the ship is on Mars before it is on Earth, yes. The "anti-ship" interpretation is the only way I can see for observer A to interpret that chronology without violating energy conservation and the second law of thermodynamics; but that doesn't mean I think the "anti-ship" interpretation is physically reasonable.

It works in many interesting ways.

I'm not sure I follow these alternate "cases"; some of what you're saying doesn't appear to make sense, other things just seem to be restatements of things we've already said and (I think) agreed on. Rather than try to comment in detail, let me just make a few general remarks:

(1) Once you have specified the worldline of the FTL rocket and of observers A and B, the scenario is entirely fixed; there's no further room for anything to vary as far as the spacetime coordinates of events are concerned. Once the worldlines are defined, all of the events of interest are fixed and their coordinates in all of the frames of interest are also fixed.

(2) Once you assume that the rocket can emit light rays, so it can be seen, and that observers A and B receive those light rays, you can map out the paths of all those light rays in spacetime and tell exactly at what events on A's and B's worldlines they will receive light rays from what events on the rocket's worldline. That's what I did in putting together my descriptions. There is no way for A or B to label some of those light rays as "just optical effects" and others as "normal visual". They're all bona fide light rays and they all have the same status when the observers see them.

(3) A and B can each construct a "calculated chronology" for their frames, from the optical data they receive and knowledge of the worldlines of Earth and Mars. Each of their chronologies is also fixed by the scenario; there's no room for either one to vary once the above items are fixed. Also, each calculated chronology is a chronology of "real" events; the observer is committed to the belief that those events actually happened, at the time and space coordinates, in his frame, that the chronology assigns to them. We are ruling out hallucinations and false data for this scenario.

(4) The above things are *prior* to any "interpretation" of what's going on by A or B; they are fixed data that any "interpretation" must be consistent with. That means, again, that there is no room for an interpretation to somehow declare that "well, my chronology makes it *seem* like one portion of the rocket's worldline is physically unreasonable, but that's just an optical illusion". If an observer's calculated chronology says that something physically unreasonable has to have happened, then that's the inescapable consequence of the scenario.

In this scenario, as I've said, there *must* be some observer--observer A, in the specific case we've been discussing--who will construct a calculated chronology that includes physically unreasonable events, *if* we allow FTL travel and also retain all the rest of standard SR, including Lorentz invariance. The only residual discussion, it seems to me, is over how to describe the physical unreasonableness. Do we say that observer A would have to believe that an "antiship" existed, and since "antiships" are not physically reasonable, that rules out this scenario? Or do we say that observer A would have to conclude that conservation of energy and the second law of thermodynamics were violated, and that rules out this scenario?

Some of what you say in your cases 1 and 2 could be seen as trying to pin down how to describe the unreasonableness; but to me that's a side issue. The question is, is there *any* way observer A could interpret his calculated chronology which *isn't* physically unreasonable? I don't see how there can be, and that's the critical point.

 

[Saw]

I said that Lorentz invariance means you can't privilege either view, *if* FTL travel is possible; both views would have to be valid if FTL travel is possible and Lorentz invariance holds. But I also said that the two views were physically inconsistent; that's why I think FTL travel is impossible if Lorentz invariance holds.

Well, the subject of our discussion is precisely the (unlikely) hypothesis that FTL is possible. So for simplicity we can leave out that IF and thus your statement boils down to the following:

Lorentz invariance means that both views are valid, despite being physically inconsistent.

Hmm. This looks quite similar to the way I had tried to express your opinion on this occasion:

For the sake of Lorentz invariance, this “view” is as valid as any other, even if it is physical inconsistent with the former.

Never mind. Anyhow, if you substituted “consistence” for invariance, the sentence could be rephrased as follows:

Lorentz consistence means that both views are consistent, despite being physically inconsistent.

Obviously, I assume you would reject this rephrasing on the grounds that “invariance” and “consistence” have in this context different meanings...

Since this is not clear to me, I will try to delve into the definition of Lorentz invariance (or covariance?). I think we can equate it with the principle of relativity = laws of physics are the same in all inertial frames, so that:

(a) If in two different inertial frames the same TWO experiments (same initial conditions) are carried out, then you get in both frames the same results (same final conditions).

Once that you describe such results in terms of physical laws, this means that in both frames those results could have been predicted by application of the same equations.

(b) If only a SINGLE experiment is carried out and it is analyzed in two different inertial frames, then the initial conditions may be equal but forcefully the final conditions will differ.

But these final conditions can be related through transformations, in particular Lorentz transformations. Thus if you know the final coordinates in frame X and its relative velocity wrt frame Y, then you can guess the final coordinates in frame Y.

In any case, both frames, based on their respective sets of coordinates, should be able to reach a common conclusion about what happens, by feeding their coordinate and frame-dependent values into equations that give out invariant or frame-independent conclusions. For example, if you send a moun from event A to B, you should be able to predict in any frame, by application of the same formula, the length of its timelike spacetime interval, i.e. its proper time and hence whether it reaches event B before disintegration.

In our case, we have situation (b), a SINGLE experiment = something that is on the Earth at event A and travels to Mars, arriving at event B.

Unfortunately here events A and B are simultaneous in the frame Earth-Mars (frame X), so we talk about a spacelike trajectory, requiring FTL travel.

We assume that in spite of that, the final coordinates in frame X and Y or any other one ARE related by the Lorentz transformations.

However, we do not have the other advantage. We have assumed for the sake of discussion that the spacetime spacelike trajectory in question ends in event B, but we could not predict it. Furthermore, if we place a moun on the FTL rocket, we cannot guess whether it will “survive” to reach the target: the length of the spacetime interval (which is its proper time in timelike trajectories) is now an imaginary number, ie no solution to the question.

Conclusion: our life is more complicated now. We have two sets of coordinates, frame X’ and frame Y’s, describing the same events. They are Lorentz-invariant in that they meet the first requirement: they can be mutually related by Lorentz transformations. But they fail to meet the second, which is also part of the usual meaning of Lorentz invariance: they have no predictive value.

Given this, my reaction is quite straight-forward:

- Those space and time coordinates differ because they have to. They are measured from different states of motion, which has a bearing on the result, so it is no surprise they are frame-variant.
- However, they are good as clues for guessing what happens because when you mix them into spacetime formulae, they all lead to the same predictions. That is Lorentz invariance. “Consistence” in predictions.
- If we now refer to FTL travel, we could talk about building clocks and rods based on the FTL mechanism, if that were possible. Then we should see how the diagram is re-constructed and whether the same equations apply. In the (impossible) limit, if we had a really instantaneous agent traveling at infinite velocity from two places, we could synch clocks thereby and would thus have absolute simultaneity and Galilean invariance, at least for an instant. (I cannot even think of how to build an absolute system for registering durations, since an agent of infinite velocity enclosed in a box would not “change”.)
- That is not our assumption, however. We assume that the diagram is the same as before FTL came into play. But then we must also acknowledge that it is not apt for the analysis of the FTL (theoretical) challenge. Remember: the coordinates are not, strictly speaking, “views” about what happens with the rocket or the muon, they are primarily measurements or views about what happens with the clocks and rods. Normally speaking, they are also good indirect clues about what happens with the rocket and its passengers, but not when faced with FTL travel. They are not “valid” for this more ambitious purpose, because by definition non-FTL instruments do not “mirror” FTL agents.

Instead, I do not understand your statement. The two “views” (actually, to be accurate, “measurements”) cannot be both valid in some mysterious sense. They are valid or not in the sense that they meet together at the goal, they are consistent in providing the same predictions. If they do not, then the statement that they are still valid does not make any sense. So you cannot even say that that they are “physically inconsistent”.

PS: A different thing is whether *one* frame could hold that only its (non-FTL) measurements are valid for predicting what happens FTL. That would be for example an aether frame, which would thus be “preferable” only in this specific domain (FTL maters), relativity still holding for the rest of problems (non-FTL ones). Such frame would be undetectable in the non-FTL world. I suppose that in a FTL thought experiment you can argue that such frame is the one where the instantaneous trajectories, regardless direction, always coincide with that frame’s line of simultaneity. I would not find all that abnormal, though. SR (IMO) holds that all frames are equal (in their predicting capabilities) assuming that FTL is impossible, it has no problem with admitting a theoretical preferred frame in a theoretical world.

 

[PeterDonis]

Obviously, I assume you would reject this rephrasing on the grounds that “invariance” and “consistence” have in this context different meanings...

I would say this: Lorentz invariance requires that the "views" of a given scenario from all inertial frames must be valid--i.e., they must be physically reasonable and consistent with the laws of physics. In this case, we have at least one inertial frame whose "view" of the scenario is *not* physically reasonable and/or not consistent with the laws of physics. So Lorentz invariance says that this scenario is not possible. This seems pretty straightforward to me.

Since this is not clear to me, I will try to delve into the definition of Lorentz invariance (or covariance?). I think we can equate it with the principle of relativity = laws of physics are the same in all inertial frames, so that:

You could view Lorentz invariance as a more specific statement of the POR, yes; Lorentz invariance tells you more about what "laws of physics are the same" means. But you still have to be careful about applying the principle.

(a) If in two different inertial frames the same TWO experiments (same initial conditions) are carried out, then you get in both frames the same results (same final conditions).

By "same initial conditions" I assume you mean "same conditions relative to the two different inertial frames". For example, if we start the experiment in frame A with the apparatus at rest in frame A, then we must start the experiment in frame B with the apparatus at rest in frame B. If this is what you meant, then yes, Lorentz invariance says the final results should be the same, when expressed relative to each frame.

But there is a proviso to this: *all* of the physical objects participating in the experiment must have their motion, etc. specified relative to each frame. I think you recognize this; see further comments below.

Once that you describe such results in terms of physical laws, this means that in both frames those results could have been predicted by application of the same equations.

As long as the equations are expressed in terms of invariant and covariant quantities, yes. Again, you seem to realize this; see further comments, below.

(b) If only a SINGLE experiment is carried out and it is analyzed in two different inertial frames, then the initial conditions may be equal but forcefully the final conditions will differ.

I'm not sure *all* of the initial conditions could be the same; there would have to be some that varied, because of the relative velocity of the frames.

But these final conditions can be related through transformations, in particular Lorentz transformations. Thus if you know the final coordinates in frame X and its relative velocity wrt frame Y, then you can guess the final coordinates in frame Y.

Yes, except that instead of "guess" I would say "calculate", which has a much stronger connotation of the result being determined by the laws of physics.

In any case, both frames, based on their respective sets of coordinates, should be able to reach a common conclusion about what happens, by feeding their coordinate and frame-dependent values into equations that give out invariant or frame-independent conclusions.

Yes.

We assume that in spite of that, the final coordinates in frame X and Y or any other one ARE related by the Lorentz transformations.

Yes.

However, we do not have the other advantage. We have assumed for the sake of discussion that the spacetime spacelike trajectory in question ends in event B, but we could not predict it.

I think you are confusing conditions that specify a scenario with physical laws. For example:

if we place a moun on the FTL rocket, we cannot guess whether it will “survive” to reach the target: the length of the spacetime interval (which is its proper time in timelike trajectories) is now an imaginary number, ie no solution to the question.

That's not because we can't Lorentz transform the muon's trajectory, or because we can't define what it would mean for the muon to travel FTL. It's because the physical law for muon decay depends on proper time. Obviously any law that includes proper time as one of the invariants on which it depends won't work as it stands if you allow FTL travel. But one could imagine other laws that would not involve proper time.

(Actually, strictly speaking, we *could* use the muon decay law even with an imaginary proper time; the decay law involves an exponential, and you can exponentiate imaginary numbers. When you do, you get sines and cosines; so basically, you would find that an FTL muon "oscillates" between the decayed and non-decayed states. But this is really a side issue; you would still be adjusting the law to accommodate FTL travel, not just using it "as is".)

So if you allowed FTL travel, you would have to adjust some physical laws, yes. For example, as I commented in previous posts, you would have to find a physical law that told you what specific trajectory an FTL rocket would follow. We *assumed* such a law, implicitly, when we assumed for purposes of our scenario that event E and event M were simultaneous in the Earth-Mars mutual rest frame. But to have a full theory of FTL travel we would have to actually find such a law. But so what? We also have to know physical laws to predict the trajectories of non-FTL objects like muons.

Basically, you are observing that some of our current physical laws would have to be modified if we wanted to accommodate FTL travel. That's true, but I don't see how it changes our reasoning about whether to allow FTL travel in the first place; that reasoning is based on the consequences of allowing *any* pair of spacelike separated events to be causally connected (see further comments at the end of this post). Nothing about that reasoning depends on *which* particular spacelike separated events are causally connected in a particular scenario, as I've said before.

We have two sets of coordinates, frame X’ and frame Y’s, describing the same events. They are Lorentz-invariant in that they meet the first requirement: they can be mutually related by Lorentz transformations. But they fail to meet the second, which is also part of the usual meaning of Lorentz invariance: they have no predictive value.

No, that's not correct. As above, any "predictive value" over and above relating the coordinates in different frames by Lorentz transformations does *not* come from Lorentz invariance; it comes from the specific physical laws involved, which must be expressible in Lorentz invariant form, but that still leaves a lot of latitude in *which* specific Lorentz invariant/covariant quantities are included in the law. Some quantities (like proper time) cause more problems if you want to allow FTL travel than others do.

- If we now refer to FTL travel, we could talk about building clocks and rods based on the FTL mechanism, if that were possible.

It isn't possible. Allowing FTL travel doesn't change which dimensions of the underlying spacetime are timelike and which are spacelike. Therefore it doesn't change along which dimensions you can define a "time" coordinate vs. "space" coordinates. So nothing about spacetime diagrams are constructed can change when you allow FTL travel. That also means that you can't construct a "frame" with a spacelike worldline as its "time" axis; it won't work, regardless of how you try to jigger the behavior of "rods" and "clocks" based on an "FTL mechanism".

In the (impossible) limit, if we had a really instantaneous agent traveling at infinite velocity from two places, we could synch clocks thereby and would thus have absolute simultaneity and Galilean invariance, at least for an instant.

All of which gives further reasons to believe that FTL travel is not possible.

- That is not our assumption, however. We assume that the diagram is the same as before FTL came into play.

Yes, I agree; see above.

But then we must also acknowledge that it is not apt for the analysis of the FTL (theoretical) challenge. Remember: the coordinates are not, strictly speaking, “views” about what happens with the rocket or the muon, they are primarily measurements or views about what happens with the clocks and rods.

No, this is not correct. Coordinates are numbers (4-tuples of numbers) that are used to label events. The events are events that happen to rockets and muons and other things we're interested in. The rods and clocks are imaginary; we use them to help visualize how we could physically measure numbers that were either identical to or closely related to the coordinate numbers we assign. But if you don't believe that the coordinates are "views" about what happens to rockets and muons and so forth, why would you care about coordinates at all?

Normally speaking, they are also good indirect clues about what happens with the rocket and its passengers, but not when faced with FTL travel. They are not “valid” for this more ambitious purpose, because by definition non-FTL instruments do not “mirror” FTL agents.

Nope; this is not true. The coordinates are *direct* descriptions, in a given inertial frame, of the spacetime locations at which things happen to rockets, etc. And the reasoning we use based on imaginary rods and clocks to visualize how we would measure numbers that are either identical to or closely related to the coordinate values works the same if the rockets, etc. move FTL. The only difference is that the worldlines we end up assigning to FTL objects are spacelike instead of timelike; everything else stays the same.

I can't really comment more on most of the rest of your post since it just seems to be circling around the same misconception as above. But I do want to comment on this:

SR (IMO) holds that all frames are equal (in their predicting capabilities) assuming that FTL is impossible, it has no problem with admitting a theoretical preferred frame in a theoretical world.

No, this is wrong. SR (I assume here that "SR" includes "Lorentz invariance") holds that all frames are equal, period. There is no wiggle room. What "FTL travel is possible" means, in SR terms, is "spacelike separated events can be causally connected". And all the stuff I have been describing is just showing how letting spacelike separated events be causally connected leads to physically unreasonable results. That's really all there is to it; there's no point in squirming around trying to find an "interpretation" that will somehow make FTL consistent with SR by jiggering with stuff. "Spacelike separated events can be causally connected" is a simple, well-defined proposition, and it has unreasonable consequences. That's it.

 

[Saw]

PeterDonis, I appreciate your patience in maintaining this conversation. I see that none of us is going to persuade the other, because we both circle, as you say, around our respective conceptions (or misconceptions). So it will be understandable if any of us drops out at any moment. In the meantime, I am pleased to make some responses.

I would say this: Lorentz invariance requires that the "views" of a given scenario from all inertial frames must be valid--i.e., they must be physically reasonable and consistent with the laws of physics. In this case, we have at least one inertial frame whose "view" of the scenario is *not* physically reasonable and/or not consistent with the laws of physics.

So Lorentz invariance, as you understand it, means that the two views should be ok, but in fact only one is and the other is not.

So Lorentz invariance says that this scenario is not possible. This seems pretty straightforward to me.

That is a non sequitur. At leat there is another possibility: Lorentz invariance, as you understand it, is wrong.

We are dealing with the typical reductio ad absurdum. The absurdum is that there are two physically inconsistent elements. On this we agree, but we differ in calling those elements “situations” or “explanations”. You are assuming that relativity, when stressed under the tension of FTL, brings about two contradictory situations; hence you kill the messenger, you rule out FTL travel. Instead I assume that relativity, in face of FTL travel, only seems to offer contradictory explanations; hence I infer that those explanations are not really contradictory, so I reinterpret them.

So far, so good. The two approaches could be valid. Which one is more straightforward? I tend to think that mine.

Please consider this example. I had two friends, a Spaniard and an Englishman, who had a common girlfriend and they went on and on like this because the girl rejected marriage. However, one day the English guy found her marrying the Spaniard. He said: our respective claims on the girl are both legitimate, none of them should be privileged, but the girl cannot have more than a husband in our legal system. So I must be dreaming: this scenario is impossible. Well, think this if you wish, but nine times out of ten you will be wrong and simply lose the girl.

In any case, leaving jokes aside, the key for choosing one approach or the other is scrutinizing the concept of Lorentz invariance. For this purpose, my epistemological approach is quite a down-to-earth one, apparently not clashing with scientific method. I am saying that the meaning of our concepts (in our discussions, the spacetime coordinates associated to events) is determined by why and how they are in practice set up, that is to say, for which practical purpose and on the basis of which empirical measurement activities.

if you don't believe that the coordinates are "views" about what happens to rockets and muons and so forth, why would you care about coordinates at all?

What? I did not say that at all. I clearly said that coordinates have a practical purpose, not other than precisely predicting what happens with rockets and muons. And I also said that the coordinates contribute to this goal by constituting a “mirror” or at least a “clue” about what happens with muons and rockets. But one thing is being a clue about an object and the other is being the object itself. I tend to use a simile to explain this. The slipper helps you find Cinderella, but the latter is not the former. Conflating the two is intellectual fetishism. Therefore, if you apparently have two conflicting clues, what you do is not assuming that both clues should be at any rate valid (and thus infer that you are dreaming); instead you simply behave like a good detective and reinterpret such clues.

SR (I assume here that "SR" includes "Lorentz invariance") holds that all frames are equal, period.

Why period? You mean, “for no reason and hence without any domain of applicability”? If it were so, it would not be a scientific theory, but a sort of ideology.

Finally, I have to reject your last remark, for the same reasons:

What "FTL travel is possible" means, in SR terms, is "spacelike separated events can be causally connected".

"Spacelike separated events can be causally connected" is a simple, well-defined proposition, and it has unreasonable consequences. That's it.

Right, but insisting that this…

leads to physically unreasonable results.

… is patently wrong. In my thought experiment, I did not include any unreasonable result, did I? If I did, please mentally wipe it out because that was not my intention. I explained that a very judicious person took a rocket and flew from the Earth to Mars. What is unreasonable in that? Of course, the problem is that there is a certain observer whose coordinates or clocks reading show a lower value for event M than for event E. What does that mean? Under a dirty and realistic interpretation, it means that this guy carried out some measurement operations that give out such outcome. Nothing more. So what this guy should be told to do is deducting that his measurements are not the best account of the story, probably because they are faced with a tough challenge (FTL travel) for which those data are no valid clue. That is all.