FTL travel and causality

[Kuroneko]

Some people go to say, Everything2, and read the argument there, which uses the Lorentz transformations but starts them 20 minutes apart. I've never seen one use the Poincare transformation, so if you can come up with one feel free to convince me.

The Poincaré group is formed by Lorentz transformations and spacetime translations. It is possible that your source did perform a proper translation and you simply did not notice it... but it also possible that they are simply wrong. I don't know what some other place does in regards to this question, but there is nothing wrong here. As long as the ship's trajectories intersect and their velocities are constant, there is nothing wrong with using a simple Lorentz transformation with that event as the origin. Incidently, that is exactly the situation in your example and my diagram. I don't see any "bad math" in that.

That's what I was getting across with the three possibilities. Which reference frame gets to define instant.

If that was your intent from the beginning, then all you have shown is that your own scenario is not well-defined due to this ambiguity.

Consider the statement "Jack is the worst player on his team." Depending on the status of the team, this statement might mean that Jack is objectively bad, but it might also mean that he is very good (after all, the worst of a set of great players might would still be great). Those two possibilities are contradictory, but it does not follow that Jack's very existence is somehow contradictory. This is essentially what you are doing--you have posed a scenario in which there is an inherent ambiguity and conclude from it that the whole thing is self-contradictory. All it really means is that more information must be provided before the issue can be decided.

A very natural interpretation of "instantaneous" is "instantaneous in the sender's frame of reference"--after all, it is the sender that initiates the signal. In that case, a genuine transfer of information back in time is possible, as in sending a reply, B would be the sender.

If matter is an extension of the fabric of space, then matter's progress towards entropy is its own perception of time, rather than 'real' time as perceived by the universe itself. This would mean that there is a standard frame of reference, but it would be impossible to perceive using currently known laws of physics.

Great Scott! First, let's not mix our physics too much here. In the general theory relativity, matter and energy are coextensive with Ricci curvature, but GTR can make its own causality paradoxes and superluminal communication; here, we are dealing with the special theory. Second, there no such thing as "time as perceived by the universe itself"; such a thing would need events to be totally ordered with respect to time. There is only a partial order--some events are not temporally comparable to others (i.e., spacelike). In general relativity, it is even worse--there no guarantee of being able to define any sort of global time coordinate at all.

Let's say A just sends an 'instantanious' message to B. Depending on what 'instantanious' means, B might get it at 7.5 seconds (instantanious to A's frame of reference) or at 30 seconds (instantanious to it's own frame of reference).

It's generally quite obvious what kind of "instantaneous" is intended in discussions of this nature, particularly if spacetime diagrams are provided. At best, your critique means that such discussions could use more precision in their wording. I still don't see any examples of "bad math," and your claim that you have never seen a valid example of causal breakdown means that either you are not looking or not understanding--there is one above in this very thread that is quite explicit as to which notion of simultaneity is used at every step.

Now, if we're to accept the Twin Paradox, the particle that does not undergo acceleration does the aging, and not vise versa.

Yes, although more explictly: the particle that does not switch inertial frames ages more. (In general, proper time is maximized along geodesics [maximally straight trajectories]).

Thus, when A sends its 'instantanious' message to B, B's reference frame is what should be considered 'instant' and not A's, because the message is an effective acceleration back to B.

I don't see any change of inertial frames for either A or B, so your claim of "effective acceleration" appears to me to be completely nonsensical.

[Kuroneko]

The thing that really cracks my brain about all this is that A and B are simultaneous, B and C are simultaneous, but C takes place prior to A. ... Is this a personal limitation, or are humans just not wired to understand this stuff any way but mathmatically?

Well, even if it is understood only mathematically, it's not as if mathematics is necessarily disjoint with intuition. A more explicit geometrical analogy might be helpful. Take out a pen, hold it in front of you, and observe its length. Now twirl it in different directions. The pen's apparent length will change depending on your perspective on it. Its proper length is unchanged; all that is different is the orientation at which you are viewing it. The three-dimensional pen is projected onto a two-dimensional field of vision. The relative orientation of the viewer is important. Make note of the fact that differently oriented viewers have a different sense of depth ("away"), and that it is orthogonal to their two-dimensional view. Suppose two differently oriented observers disagree as to what the "true field of vision" is (and consequently which direction is "depth"). Surely that is nonsensical; each observer has their own perspective.

Now, to carry the analogy to spacetime, the key concept is that spacetime orientation is a velocity--on the (t,x) plane, vector r*[1,0] corresponds with velocity v = 0, r*[1,1] with v = 1 (any scalar r, although it is usually normalized so that the length is 1), etc. This vector forms the basis for the observer's of time, the orthogonal complement of which the observer's space. Just as the pen changes in apparent length in space depending on its orientation, the pen will also change in apparent length in spacetime--this is Lorentz contraction. Here, a four-dimensional pen (it exists in time as well as space) is projected onto a three-dimensional space which is the observer's "now". Disagreements over what is "the real now" (and which spacetime direction is "time") are analogous to the dispute in the previous paragraph, and as before, they are not meaningful.

I'm not certain if this will be helpful to you, but personally I found geometrical thinking invaluable to an intuitive understanding relativity. The caveat is that Minkowski spacetime has a slightly different notion of orthogonality (or dot product in general), which I've already noted previously in this thread.

[Wyrm]

The thing that really cracks my brain about all this is that A and B are simultaneous, B and C are simultaneous, but C takes place prior to A. I accept Kuroneko's model because he's demonstrated numerous times in the past he knows what he's talking about when it comes to this stuff, but I really really can't get my head around that concept the way I can stuff like evolution or electrons. Is this a personal limitation, or are humans just not wired to understand this stuff any way but mathmatically? I suspect the former, and it's a shot to the ego.

Thinking relativistically does take some getting used to. I only came fully to terms with relativity when I was an undergrad, and only when doing some independent study and getting down to the brass tacks.

One of the things you learn is that many concepts we think are invariant are actually very dependent on our frame of reference. Your statement that "A and B are simultaneous, B and C are simultaneous, but C takes place prior to A" shows that you still think simultaneity is an absolute concept. It isn't. It depends on your frame of reference, so the statement should read: "A and B are simultaneous in frame O, B and C are simultaneous in frame O', but C takes place prior to A for all frames." The statement works because the events O considers simultaneous to any given event E is different from the events O' considers simultaneous to that same event E.

Anyway, all you're going to get out of us is the two-cent tour of relativity. In order to really "get it," you'll need to get yourself a good physics text and get cracking.

[Ariphaos]

The Poincaré group is formed by Lorentz transformations and spacetime translations. It is possible that your source did perform a proper translation and you simply did not notice it... but it also possible that they are simply wrong.

Simply moving them apart faster and sending STL signals allowed for causality paradoxes, so that was my problem with it.

I don't know what some other place does in regards to this question, but there is nothing wrong here. As long as the ship's trajectories intersect and their velocities are constant, there is nothing wrong with using a simple Lorentz transformation with that event as the origin. Incidently, that is exactly the situation in your example and my diagram. I don't see any "bad math" in that.

I made an assumption, sorry. The last time I did a google search on this subject several months ago, every single result in the top 20 or so showed a bad graph or used funny math. But your graph gets to the below which I seem to have a hell of a time explaining :-/

Are you talking about a problem with the possible nature of FTL or just my interpretation of it?

Second, there no such thing as "time as perceived by the universe itself"; such a thing would need events to be totally ordered with respect to time.

Or rather the fabric of space itself. If c is a universal constant, and the vibrations that make up individual particles in such a case represent that particle's eventual decay, then that is how that particle will perceive time, not time how it 'really' is.

It's generally quite obvious what kind of "instantaneous" is intended in discussions of this nature, particularly if spacetime diagrams are provided. At best, your critique means that such discussions could use more precision in their wording. I still don't see any examples of "bad math," and your claim that you have never seen a valid example of causal breakdown means that either you are not looking or not understanding--there is one above in this very thread that is quite explicit as to which notion of simultaneity is used at every step.

A bit of both, I think. I looked very hard for awhile and had to extrapolate my own example, because others didn't work.

http://www.orionsarm.com/intro/ftl-paradoxes.html

The graph here is an example of what I generally found - if you rotate it so that Bob and Carol are the 'standard' frame of reference, their ansible line isn't any sort of instantanious communication.

I don't see any change of inertial frames for either A or B, so your claim of "effective acceleration" appears to me to be completely nonsensical.

When A sends a message to B at any speed, there is a switch in reference frames - for the message. If it helps, picture them launching a clock at an arbitrary speed (up to 'infinite'). Or a clone of themselves. Or whatever.

[drachefly]

You will always have some observers for which the cause will follow the effect, but if the usage of an ansible automatically disallows further ansible communication (within some time period), perhaps the more dramatic paradoxes like that above could be avoided (I'm not yet certain of this, however).

Another approach is to introduce a medium which determines the rest frame of your FTL communication. Note that this medium can be inhomogeneous in space and time, and one can devise field equations for that medium that prevent causality breaches. So, even if B tries to communicate to C, he can't -- he sees the medium is projecting his message back toward A. Doesn't matter how fast B is moving.

I used this method in a hard fantasy setting - And beyond the in-principle requirements, I also restricted their actual ability to use FTL to flat (or curved in a specific, simple fashion) regions of this medium, the 'ether'. The ether follows matter in a manner analogous to the 'frame dragging' ideas concerning the 'luminiferous ether' before relativity. Since the Earth is spinning at a different rate than the moon, the flat region of this ether doesn't go far beyond the radius of geosynchronous orbit.

In addition to preventing time travel, this was very useful for letting people have FTL communication and teleportation on earth without having to worry about them teleporting off the planet, or communicating with distant aliens. And it also smoothed out the classic problem of "... but you're in motion all the time with the rotation of the Earth!" by having the local ether more or less fixed to the Earth.

If however, they had managed to get into interplanetary space, the local ether might have permitted teleportation much further... and if they got out of the solar system they might have been able to teleport across the galaxy or something... Note how this neatly incorporates within itself the old 'no FTL straight from interstellar space into your living room' idea without using the usual 'gravity well' argument.

[Wyrm]

The Poincaré group is formed by Lorentz transformations and spacetime translations. It is possible that your source did perform a proper translation and you simply did not notice it... but it also possible that they are simply wrong.

Simply moving them apart faster and sending STL signals allowed for causality paradoxes, so that was my problem with it.

No, they don't. STL signals remain within the future light cone of the transmitter for all reference frames, and so there will be no causality violations unless a genuine time machine is used.

If your sources claim otherwise, then they are wrong, wrong, wrong!

there no such thing as "time as perceived by the universe itself"; such a thing would need events to be totally ordered with respect to time.

Or rather the fabric of space itself.

Meaningless. Read again what kuroneko said: "time as perceived by the universe itself" would need events to be totally ordered with respect to time. But even in SR, events are only partially ordered wrt time, and in GR in many cases (some of them astrophysically meaninful) a global time coordinate cannote be defined for even one observer!

If c is a universal constant, and the vibrations that make up individual particles in such a case represent that particle's eventual decay, then that is how that particle will perceive time, not time how it 'really' is.

Again, the phrase "time how it 'really' is" is meaningless. All physically meaningful examples of time passing involve physical processes. A nice summary is this: "Time is what clocks measure."

...your claim that you have never seen a valid example of causal breakdown means that either you are not looking or not understanding--there is one above in this very thread that is quite explicit as to which notion of simultaneity is used at every step.

A bit of both, I think. I looked very hard for awhile and had to extrapolate my own example, because others didn't work.

http://www.orionsarm.com/intro/ftl-paradoxes.html

The graph here is an example of what I generally found - if you rotate it so that Bob and Carol are the 'standard' frame of reference, their ansible line isn't any sort of instantanious communication.

You do not rotate the graph to make Bob and Carol the 'standard' frame of reference (which we will call O'). Notice that when you rotate the graph, the x-axis of O' --a line of simultaneity in frame O'-- is not horizontal; it does NOT have constant time, which by definition it should. To make frame O' the 'standard', you perform a Lorentz transformation, which is a different beast from a rotation.

I don't see any change of inertial frames for either A or B, so your claim of "effective acceleration" appears to me to be completely nonsensical.

When A sends a message to B at any speed, there is a switch in reference frames - for the message.

Where did you get that silly idea? A's reference frame remains the frame in which A is not moving. In special relativity, the only time you change reference frames is when considering measurements made by an observer moving relative to you. The message makes no measurements, so there's no need to consider its reference frame.

The only place you may need to switch reference frames is when figuring out which event on A's world-line is simultaneous to event B from O' reference frame, but that's easy enough to find in O by drawing a few lines.

[RedImperator]

Anyway, all you're going to get out of us is the two-cent tour of relativity. In order to really "get it," you'll need to get yourself a good physics text and get cracking.

I'll put that on my to-do list.

One interesting side effect of this thread has been to put myself in the same position a lot of my students are in--trying to grasp something that's totally alien to them, and, on the surface, makes no damn sense whatsoever. They had the same "wha?" look on their faces today when I was trying to explain how the Electoral College makes votes from small states count for more.

By the way, would it be possible to avoid the causality problem by saying the trip is instantaneous for the message/ship/crew, but the trip's duration in real space depends on causality? Most of the time, trips take reasonable lengths of time, but if you try to jump at the wrong moment, you may spend years, decades, or even longer in transit.

[Ariphaos]

No, they don't. STL signals remain within the future light cone of the transmitter for all reference frames, and so there will be no causality violations unless a genuine time machine is used.

If your sources claim otherwise, then they are wrong, wrong, wrong!

Err, that's not what *I* said, so much as it is an effect of using Lorentz equations improperly, like here:
http://everything2.com/index.pl?node_id=1527132

Meaningless. Read again what kuroneko said: "time as perceived by the universe itself" would need events to be totally ordered with respect to time. But even in SR, events are only partially ordered wrt time, and in GR in many cases (some of them astrophysically meaninful) a global time coordinate cannote be defined for even one observer!

Is there a mathematical difference between a particle's progress towards entropy and its perception of time? I don't think I'm quite getting why you're repeating that.

I'm assuming that by 'ordered wrt time' you are talking about the fact that we can't rightly pick out what happenned first between event A and B when they are in separate light-cones, correct?

If matter/energy consists of ripples or holes/singularities stretching the fabric of space, and those ripples all move at c, whether via internal harmonics (defining the particle and its path to entropy) or raw movement (thus limiting the former) then no such order will be observable by any particle within the Universe, unless some event occured that either changed the nature of the fabric or some external force played on it.

You do not rotate the graph to make Bob and Carol the 'standard' frame of reference (which we will call O'). Notice that when you rotate the graph, the x-axis of O' --a line of simultaneity in frame O'-- is not horizontal; it does NOT have constant time, which by definition it should. To make frame O' the 'standard', you perform a Lorentz transformation, which is a different beast from a rotation.

Okay.

Where did you get that silly idea? A's reference frame remains the frame in which A is not moving. In special relativity, the only time you change reference frames is when considering measurements made by an observer moving relative to you. The message makes no measurements, so there's no need to consider its reference frame.

A's reference frame no longer matters once the message has been sent. The ship may as well be teleporting back, firing a clock back, turning back instantly a la the Twin Paradox or whatever. That's where I got the silly idea.

In the case of firing a clock back, it's clear that the clock's hands will tick back in time assuming it's not rendered into plasma or some strange form of matter.

[Kuroneko]

Overall, I agree with Wyrm's reply, but there is one point I'd like to comment on.

You do not rotate the graph to make Bob and Carol the 'standard' frame of reference (which we will call O'). Notice that when you rotate the graph, the x-axis of O' --a line of simultaneity in frame O'-- is not horizontal; it does NOT have constant time, which by definition it should. To make frame O' the 'standard', you perform a Lorentz transformation, which is a different beast from a rotation.

You're right--if Bob and Carol are considered stationary, one would apply a Lorentz transformation, which is not the same thing as simply rotating the graph that is drawn on an essentially Euclidean surface (e.g., paper). However, a Lorentz boost can quite naturally be characterized as a rotation. Any velocity |v|<1 can be identified with a unit vector V = [cosh T; sinh T] (ds² = dt²-dx², so |V|² = cosh²T - sinh²T = 1), which is a point on the hyperbola (1 = t²-x²) with T determined by tanh T = v being a direct analogue of angular measure [1]. An advantage of this view is that the composition of two Lorentz boosts with angles T and S is simply the Lorentz boost of angle T+S (observe that tanh(T+S) = [tanh T+tanh S]/[1+ tanh T tanh S]). This hyperbolic angle is commonly called "rapidity" in relativistic contexts.

[1] The Euclidean unit-circle definition based on 1² = t²+x², mirroring the Euclidean metric ds² = t²+x², which would have V = [cos T; sin T] if the angle ismeasured from t-axis. The Minkowski metric is ds² = dt²-dx², hence it is natural to base angular measures on the hyperbola 1² = t²-x². Moreover, the Lorentz transformation is derivable from the Euclidean rotation by a simple substitution of imaginary values either the time or spatial axes (e.g., x->ix).

By the way, would it be possible to avoid the causality problem by saying the trip is instantaneous for the message/ship/crew, but the trip's duration in real space depends on causality? Most of the time, trips take reasonable lengths of time, but if you try to jump at the wrong moment, you may spend years, decades, or even longer in transit.

Your earlier idea of travel at the speed of light is causally unproblematic in flat spacetime as well as being instantaneous for the crew, but going faster will cause problems. In curved spacetime, you could exploit warp bubbles, although they have their own caveats.

[Kuroneko]

Another approach is to introduce a medium which determines the rest frame of your FTL communication. Note that this medium can be inhomogeneous in space and time, and one can devise field equations for that medium that prevent causality breaches. So, even if B tries to communicate to C, he can't -- he sees the medium is projecting his message back toward A. Doesn't matter how fast B is moving. ... The ether follows matter in a manner analogous to the 'frame dragging' ideas concerning the 'luminiferous ether' before relativity. Since the Earth is spinning at a different rate than the moon, the flat region of this ether doesn't go far beyond the radius of geosynchronous orbit.

I was thinking of a kind of field (or ether) created (or drawn by) the ansibles only, but either one should work. Which one is more appropriate depends on what exactly ansibles really are, which is story-dependent anyway. It's an interesting mathematical problem as well.

Is there a mathematical difference between a particle's progress towards entropy and its perception of time? I don't think I'm quite getting why you're repeating that.

Absolutely. Decreases of entropy are observable, if subject to strict probabilistic conditions (cf. fluctuation theorem, although for individual particles it is not all that forbidding), whereas time flowing backwards is not only unobservable but logically meaningless.

If matter/energy consists of ripples or holes/singularities stretching the fabric of space, and those ripples all move at c, whether via internal harmonics (defining the particle and its path to entropy) or raw movement (thus limiting the former) then no such order will be observable by any particle within the Universe, unless some event occured that either changed the nature of the fabric or some external force played on it.

You keep bringing this up, but it is still not relevant to the conclusion. No such order will be observable by anyone even in STR, where particles are not pieces of spacetime geometry in any sense. More strongly, the existence of such an order is logically impossible under the assumption of causes preceding effects for all observers. It's not just unobservable, it's just plain incoherent.

A's reference frame no longer matters once the message has been sent. The ship may as well be teleporting back, firing a clock back, turning back instantly a la the Twin Paradox or whatever. That's where I got the silly idea.

Don't confuse A with A's reference frame. The ship could indeed do whatever by that point, but it does not change the fact that information was sent backwards in time in that frame (i.e., for any observer sharing that frame).

In the case of firing a clock back, it's clear that the clock's hands will tick back in time assuming it's not rendered into plasma or some strange form of matter.

I'm afraid that I don't share your clarity of vision. If the "ansible signal" is a physical clock, then proper time along that path is imaginary. I don't see how a clock going along an imaginary time interval would be ticking bacwards, or doing anything physically meaningful at all. Now, it is possible that the clock would simply experience spacetime as Euclidean (t->ix turns the Minkowski metric into an essentially Euclidean one), and it may even be possible to interpret this as a kind of "virtual clock" (ala "virtual particle"), but characterizing this experience from the point of view of the clock seems very dubious.

[Ariphaos]

Absolutely. Decreases of entropy are observable, if subject to strict probabilistic conditions (cf. fluctuation theorem, although for individual particles it is not all that forbidding), whereas time flowing backwards is not only unobservable but logically meaningless.

At the expense of surrounding entropy. Restoring something to an exact previous state (or something that effectively qualifies as one) is the idea behind going back in time. In the case of most time travel scenarios, the goal seems to be to restore the Universe to a previous state.

You keep bringing this up, but it is still not relevant to the conclusion. No such order will be observable by anyone even in STR, where particles are not pieces of spacetime geometry in any sense. More strongly, the existence of such an order is logically impossible under the assumption of causes preceding effects for all observers. It's not just unobservable, it's just plain incoherent.

I'm not sure what you mean. As far as I can understand it, that only applies to a universal frame of reference that is not extremely close to c (from us) for all involved -and- is within our 4D spacetime manifold. If it's outside that, everything is moving at near c, or both, then I don't see how your point applies.

Don't confuse A with A's reference frame. The ship could indeed do whatever by that point, but it does not change the fact that information was sent backwards in time in that frame (i.e., for any observer sharing that frame).

Err, you mean B's or something?

A would calculate B to be 13 light-seconds away at tA=15, if it fires a light pulse, B will get it at tB=28. From A's frame of reference, though, they fired it at tB = 7.5, correct? So by this 'senders frame counts', they would calculate B to receive the message at tB=21.5 instead of tB=28.

Or am I wrong in thinking that B would get the message at tB=28?

I'm afraid that I don't share your clarity of vision. If the "ansible signal" is a physical clock, then proper time along that path is imaginary. I don't see how a clock going along an imaginary time interval would be ticking bacwards, or doing anything physically meaningful at all. Now, it is possible that the clock would simply experience spacetime as Euclidean (t->ix turns the Minkowski metric into an essentially Euclidean one), and it may even be possible to interpret this as a kind of "virtual clock" (ala "virtual particle"), but characterizing this experience from the point of view of the clock seems very dubious.

I'm not thinking along your train of thought, no. :-/

You're right, though we won't figure that out until we manage to shove something along imaginary time or space, though I think it'd have meaning, though in what terms I have no idea. The only fiction I know of that touches on that is Xenosaga.

[Kuroneko]

At the expense of surrounding entropy. Restoring something to an exact previous state (or something that effectively qualifies as one) is the idea behind going back in time. In the case of most time travel scenarios, the goal seems to be to restore the Universe to a previous state.

Incorrect. It can, does, and must happen for isolated systems as well. Once again, I refer you to the fluctuation theorem.

I'm not sure what you mean. As far as I can understand it, that only applies to a universal frame of reference that is not extremely close to c (from us) for all involved -and- is within our 4D spacetime manifold. If it's outside that, everything is moving at near c, or both, then I don't see how your point applies.

If the events are completely ordered for some reference frame, which would consist of forcibly defining some order to spacelike events in that reference frame with origin O, then picking two events C and E both spacelike to O and C<O<E, there is always a Lorentz boost that reverses the order to, say, C<E<O or O<C<E. The total order then becomes physically meaningless, since all intertial frames are observationally equivalent. This has absolutely nothing to do with the relationship of particles to spacetime curvature, which was my main point. As for logical inconsistency, I was thinking of the past in terms of causality (the past causes the future).

Err, you mean B's or something?

No. I meant exactly what I stated.

A would calculate B to be 13 light-seconds away at tA=15, if it fires a light pulse, B will get it at tB=28. From A's frame of reference, though, they fired it at tB = 7.5, correct? So by this 'senders frame counts', they would calculate B to receive the message at tB=21.5 instead of tB=28. Or am I wrong in thinking that B would get the message at tB=28?

Don't bring this "sender's frame counts" into this; it only counts as to what is considered simultaneous. If the Lorentz factor is . = 2, then the velocity v is v = sqrt(3)/2. At t = 15.0, B is indeed at x = 13.0. If A fires a light-pulse to B at t = a, then its trajectory in the (t,x)-plane is given by the line x = t-a, while B's trajectory is x = vt; they intersect at t = a/(1-v). Here, a = 15.0 and v = sqrt(3)/2, so B receives the signal at t = 112, at which time B is at x = 97.0. A then calculuates that B receives the signal at t' = 56 and x' = 48.5 due to time dilation and length contraction.

Is this consistent? Based on the (t',x') axes on the (t,x) plane, absolutely, but let's consider how B would describe it with B's own frame as stationary. In the (t',x')-plane, A's trajectory is given by x' = -vt'. If B receives light a signal at t' = a' from A's direction, then the light signal's trajectory must be x' = t'-a'. Obviously, the trajectories intersect at t'=a'/(1+v), so if the light signal is received at a' = 56.0 (meanwhile, x' = 56.0v = 48.5), it must have been sent at t' = 30.0, at which time A is at x' = 26.0. B then calculates that A's time would be t = 15.0 and x = 13.0, again due to time dilation and length contraction.

Note that both observers agree that A sent the light at t = 15 (A-time) and B received the signal as t' = 56 (B-time). Additionally, both observers agree that A measured their distance as x = 13.0 when their signal was sent and that B measured their distance as x' = 48.5 when the signal was received. What they don't agree on is whose time is dilated or whose length is contracted--but this is not problematic. This disagreement is exactly analogous to the case of two differently persons standing in the same room having a different visual experience because they have different orientation or position. What's important is that those two people, if they have enough information about the other's position, orientation, and objects in this room, can in principle reconstruct the other's view exactly. (See the second post on this page for a more in-depth analogy along these lines.)

[lazerus]

Arrgh. This thread makes my brain hurt and I've taken this physics course allready. I can see the mathmatics of it just fine (the charts, etc) but conceptually I think I need some help.


Okay, lets say we have two observers in our hypothetical example, A and B. We'll call A our reference point, and B is moving at reletavistic speed compared to A. Both A and B have STL and FTL communication devices.

The event in question is somebody at A getting hit by a car.

If that information is FTL relayed to B the instant it happens, then B can relay it back, but A will just get the information as soon as it recived it. No paradox there.

If that information is relayed STL to B the instant it happens and B sends a FTL signal as soon as it gets the information, then A gets the information with a certian lag after it happened. Again, no paradox there.

And if both methods of communication are STL then once again, there is no paradox.

So........where does the paradox come from?

[Ariphaos]

Incorrect. It can, does, and must happen for isolated systems as well. Once again, I refer you to the fluctuation theorem.

Learn something new every day O_o

If the events are completely ordered for some reference frame, which would consist of forcibly defining some order to spacelike events in that reference frame with origin O, then picking two events C and E both spacelike to O and C<O<E, there is always a Lorentz boost that reverses the order to, say, C<E<O or O<C<E. The total order then becomes physically meaningless, since all intertial frames are observationally equivalent. This has absolutely nothing to do with the relationship of particles to spacetime curvature, which was my main point. As for logical inconsistency, I was thinking of the past in terms of causality (the past causes the future).

Right, I'm aware of that.

If you have a wire, and it's stretched tout, it will have a certain vibrational frequency. A wave moving along it can either vibrate around the wire (lateral motion), or along it (linear), or some combination of both, but the effective total must always be exactly equal to that vibrational frequency.

If the wave pulse perceives time based on its lateral motion, then while the wire has a specific frame of reference, the wave packets moving along it do not, and reversals like you described above are possible from the point of view of the wave packets.

snip

'doh! :-/

[Ariphaos]

So........where does the paradox come from?

The paradox comes from time dilation based on the relative velocities of two senders.

At relativistic speed, A experiences time at a different rate then B. If B is moving at .84 of the speed of light away from A, B experiences 2 seconds for every 1 it sees A experience. Likewise, A experiences 2 seconds for every second it sees B experience.

The paradox occurs when one of them sends an instantanious message to another. Unless there is a universal frame of reference (and despite my argument above, it is generally believed that their can't be), then there is no universal definition of instantanious. The term is meaningless for any single observer.

In the example Kunoneko just mathed out, A and B were 13 light-seconds apart after moving apart for 15 seconds. If A sends a message to B instantly, then B appears to get it at tB=7.5. If B sends a response, A will get it at 3.75, before A sent the original message.

The basic gist is that either relativity, causality, or both break down at speeds faster than light. Lorentz and other equations start giving imaginary numbers and other weird results past c.

[Wyrm]

If your sources claim otherwise, then they are wrong, wrong, wrong!

Err, that's not what *I* said, so much as it is an effect of using Lorentz equations improperly, like here:
http://everything2.com/index.pl?node_id=1527132

This site doesn't actually claim that an STL signal goes backward in time. It does claim that for any FTL signal with v > c, that there exists a speed at which B receeds from A, u, such that an FTL signal sent by A will appear to travel back in time in B's reference frame (ie, he will assign an earlier time coordinate to his receiving the FTL signal than the time coordinate that he observes A transmitting it). But that's a different statement.

Is there a mathematical difference between a particle's progress towards entropy and its perception of time?

For any talk of a thing's "perception of time" to be meaningful, then something has to vary with the time coordinate. You can't tell how fast things are not happening in empty space.

I'm assuming that by 'ordered wrt time' you are talking about the fact that we can't rightly pick out what happenned first between event A and B when they are in separate light-cones, correct?

It means that observers A and B can both assign physically consistent time coordinates to events E and F, and they will agree on what happened (Alderaan gets destroyed by the DS I and the Millennium Falcon leaving Tatooine, for instance), but they may not agree on which event happened first! (A might see Alderaan being destroyed first, whereas B may see the Falcon leaving Tatooine first).

If matter/energy consists of ripples or holes/singularities stretching the fabric of space, and those ripples all move at c, whether via internal harmonics (defining the particle and its path to entropy) or raw movement (thus limiting the former) then no such order will be observable by any particle within the Universe, unless some event occured that either changed the nature of the fabric or some external force played on it.

Yep. Right now, my left shoulder is (strictly speaking) in the absolute elsewhere of my right shoulder. However, my left shoulder two nanoseconds from now is in the absolute future of my right shoulder right now. If a pulse of light is sent from a flea on my right shoulder to a flea on my left shoulder, who then jumps in response (and only in response) to the right flea's signal, everyone agrees that the left flea received a signal and jumped. To put a finer point on it, the right flea created a photon, which traveled to and was received by the left flea. The right flea was in contact with the photon now, and the left flea will be in contact with the photon somewhere more than one nanosecond from now. The interactions all happen when the interacting things are in contact with each other!

A's reference frame no longer matters once the message has been sent.

The hell it doesn't. The FTL message is "instantaneous", or more properly, is along a line of simultaneity between the transmitter and the receiver in the transmitter's frame of reference. To A, the transfer of information is instantaneous, so it is in A's frame that we must determine at which event B received the message. Notice that the message's frame of reference is not involved, because this is a determination made within A's frame of reference only.

Indeed, since most messages in relativity are sent via light, your statement is obviously incorrect. Try to define a frame of reference for light signals, a coordinate system where a photon knows where and when every event in the universe occured. You will fail, because there is only one line of simultaneity, which is the photon's worldline.

The ship may as well be teleporting back, firing a clock back, turning back instantly a la the Twin Paradox or whatever. That's where I got the silly idea.

It is a silly idea, because you seem to think that when a certain physical phenomenon occurs, the frame of reference automatically switches. There is no "the" frame of reference. A measures physical phenomena from her frame of reference, B measures those same physical phenomena from his frame of reference. In both frames of reference, C is in the absolute past as A.

[Wyrm]

Overall, I agree with Wyrm's reply, but there is one point I'd like to comment on.

<snip long-ass discussion>

In other words, I should've amended that the Lorentz transformation is a different beast from a "rotation in a Euclidean space"?

[lazerus]

In the example Kunoneko just mathed out, A and B were 13 light-seconds apart after moving apart for 15 seconds. If A sends a message to B instantly, then B appears to get it at tB=7.5. If B sends a response, A will get it at 3.75, before A sent the original message.

The basic gist is that either relativity, causality, or both break down at speeds faster than light. Lorentz and other equations start giving imaginary numbers and other weird results past c.

So basicly what your saying is, when I see an event occur one light year away, I am seeing the event occur now. Not seeing it occur one year ago because there is no such thing as an absolute frame of reference?

[Kuroneko]

If you have a wire, and it's stretched tout, it will have a certain vibrational frequency. A wave moving along it can either vibrate around the wire (lateral motion), or along it (linear), or some combination of both, but the effective total must always be exactly equal to that vibrational frequency. If the wave pulse perceives time based on its lateral motion, then while the wire has a specific frame of reference, the wave packets moving along it do not, and reversals like you described above are possible from the point of view of the wave packets.

There is no superluminal motion for any physical medium. If that's not your point, than I'm afraid I don't see the reason for your preoccupation with wave motion, as it simply does not matter how the relative motion is obtained--the reversal of causality is present in all attemps at totally ordering events regardless of how it is obtained.

In other words, I should've amended that the Lorentz transformation is a different beast from a "rotation in a Euclidean space"?

Yes. Although different from Euclidean rotations, Lorentz boosts are spacetime rotations in a very literal sense.

So basicly what your saying is, when I see an event occur one light year away, I am seeing the event occur now. Not seeing it occur one year ago because there is no such thing as an absolute frame of reference?

No, the event was one year ago for you. The superluminal (here, instantaneous) communication paradox comes in from the fact that what each observer counts as simultaneous is radically different.

[Wyrm]

If you have a wire, and it's stretched tout, it will have a certain vibrational frequency. A wave moving along it can either vibrate around the wire (lateral motion), or along it (linear), or some combination of both, but the effective total must always be exactly equal to that vibrational frequency. If the wave pulse perceives time based on its lateral motion, then while the wire has a specific frame of reference, the wave packets moving along it do not, and reversals like you described above are possible from the point of view of the wave packets.

<snip Kuroneko smacking down this wacky idea>

Um, Kuroneko-san, Xeriar wrote that, not me.

In other words, I should've amended that the Lorentz transformation is a different beast from a "rotation in a Euclidean space"?

Yes. Although different from Euclidean rotations, Lorentz boosts are spacetime rotations in a very literal sense.

Lorentz boosts = rotations in spacetime. Gotcha.

[Kuroneko]

Um, Kuroneko-san, Xeriar wrote that, not me.

Aa... I apologize. I knew it was him since it was his argument, but it seems I've been a bit too hasty with the copy and paste.