Does SR actually forbid FTL travel?

[DrSnarl]

Does SR actually imply that FTL travel would allow for violations of causality? Here is some reasoning to suggest that it does not:

(I would be surprised if there were no holes in the reasoning. My desire to find these holes is what motivated me to post this here.)

Consider the following thought experiment (which demonstrates why FTL travel would violate causality):

1) Observers A and B are in a shared frame of reference at the same location. Let us call this location "the origin".
2) B teleports some distance away from the origin, but does so without accelerating (thus remaining in a shared frame of reference with A).
3) B then accelerates in a direction away from the origin (and A). By doing so, B effectively moves into A's past (to a time when B was still at the origin).
4) Finally, B teleports back to the origin. B has now returned to the origin before it left (and could stop itself from leaving if it so chose).

On the surface, this violation seems to support the idea that FTL travel is forbidden by SR. However, it has a problem. Consider what happens when we add a third observer to the thought experiment:

1) Observer C joins A and B at the origin in their common reference frame.
2) B teleports away as before.
3) B accelerates away from the origin as before. At the same time, C accelerates in the same direction by the same amount, thus remaining in a shared reference frame with B. As before, B believes that it has traveled to A's past, but it remains in C's present. From C's perspective, however, both A (co-located) and B (same reference frame) share its same time.
4) B teleports back to the origin. Is B now in A's past, C's present, or both?

When step 3) occurs, and B accelerates, a paradox arises. From B's perspective, A's time (At) is less than B's time (Bt), but C's time (Ct) is equal to B's time. Here are the perceived time relationships for each observer after step 3:

A) At = Ct, At > Bt
B) Bt = Ct, Bt > At
C) At = Bt = Ct

The solution to this paradox is that all of the above are true. We can go further, however, and say that from B's perspective, it simultaneously exists at every point in time at the origin, depending on an observer at the origin's frame of reference. This explanation works fine if you do not allow FTL travel.

However, if B is able to teleport back to the origin (via entanglement or some undiscovered physics), SR does not actually predict what A's time will be when B arrives. While we could excuse the notion that B was simultaneously in A's past and C's present while B was far away from them, we can no longer do so when it is co-located. According to SR, all co-located observers must agree on the order of events (and time) at their shared location.

I would suggest that this agreed upon time amongst all origin-located observers is, in fact, the "proper" time at the origin. If B were able to teleport back to the origin, this would be B's time as well (from B's step 3 perspective, this would be C's present and not A's past).

If true, that would mean that SR does not forbid FTL travel. (Yes, the speed of light is still the limit to how fast matter can move, but there are other potential methods that get around this, such as entanglement and wormholes).

If you made it this far, thanks for reading! Any thoughts?

 

[fzero]

Your logic is faulty. If you assume that teleportation is possible, then that is already FTL travel. You can't prove what you've already assumed.

 

[DrSnarl]

I am not assuming that teleportation is possible. I am suggesting that SR does not forbid it.

 

[Jonathan Scott]

Does SR actually imply that FTL travel would allow for violations of causality? ...

If it is possible to communicate faster than light by at least a finite amount in every frame (so the laws of physics are the same in every frame, as required by SR) then violations of causality are certainly possible as this makes it possible to send a signal backwards in time.

If there is only some "preferred frame" in which some influence can travel at unlimited speed (which is sometimes suggested as an explanation for quantum entanglement, and is probably the basis for the "subspace" idea in science fiction) this does not create a causality problem, but it violates SR anyway by having a preferred frame.

 

[Vorde]

I am not assuming that teleportation is possible. I am suggesting that SR does not forbid it.

But you are, your thought experiment for proving the FTL is not forbidden requires a method of FTL (teleportation). You can't prove something is possible by using a situation where that things existence is given.

 

[mfb]

3) B accelerates away from the origin as before. At the same time, C accelerates in the same direction by the same amount, thus remaining in a shared reference frame with B.

At the same time in which reference frame?
Think about it, this is the problem in your argument. If they begin to accelerate at the same time (viewed by A, for example), they will have a different time-scale in their inertial frames after the acceleration. Just by accelerating, B gets into C's past.

With FTL travel (and your teleportation is similar to that, with "infinite" speed), you can violate causality. This is not a fundamental problem. But it has a lot of strange consequences.

 

[DrSnarl]

If it is possible to communicate faster than light by at least a finite amount in every frame (so the laws of physics are the same in every frame, as required by SR) then violations of causality are certainly possible as this makes it possible to send a signal backwards in time.

The point I was attempting to illustrate with my thought experiment is that if you could travel faster than light, you would not be traveling an absolute amount into the past. Instead, you would be traveling different amounts into the past depending on the frame of reference of the observer into whose past you were traveling. However, because all observers at a single location all agree on the time regardless of their frame of reference, the idea of simultaneously traveling to multiple points in time at a single location does not make any sense.

 

[DrSnarl]

But you are, your thought experiment for proving the FTL is not forbidden requires a method of FTL (teleportation). You can't prove something is possible by using a situation where that things existence is given.

There is a subtle distinction between proving that something is possible (which I am not doing) and proving that a disproof of something is flawed (which is what I am trying to do). When we say that SR forbids FTL information transfer, we do so because we can set up thought experiments that show it to violate causality if we assume FTL information transfer is possible. I am merely stating that those same thought experiments do not necessarily violate causality and thus cannot be used to prove that SR unequivocally forbids FTL information transfer.

I hope that makes sense.

 

[DrSnarl]

At the same time in which reference frame?
Think about it, this is the problem in your argument. If they begin to accelerate at the same time (viewed by A, for example), they will have a different time-scale in their inertial frames after the acceleration. Just by accelerating, B gets into C's past.

With FTL travel (and your teleportation is similar to that, with "infinite" speed), you can violate causality. This is not a fundamental problem. But it has a lot of strange consequences.

1) Viewed by A, B and C will appear to begin accelerating at the same time (because A, B, and C will all start in the same reference frame and so will agree on simultaneity). However, as B and C continue to accelerate, A will think that C is accelerating faster than B (and that B and C are not traveling at the same speed).

2) From both B's and C's perspective, however, they will be accelerating at the same time and at the same rate (ie. the distance between them will not change). Or another way to put it is that a light signal sent from B to C and bounced back to B will have a constant round trip time throughout the acceleration and afterwards (from both B and C's perspective, but not A's).

The fundamental problem that I am trying to show is that thought experiments that show a violation of causality are nonsensical because they involve simultaneously traveling to an infinite number of points in time (one corresponding to every possible frame of reference), not just a single point in some observer's past.

Now to counter my own argument, you could say that SR forbids FTL information transfer BECAUSE it involves simultaneously traveling to an infinite number of points in time. That is, however, not the same as saying that it would violate causality.

 

[DaveC426913]

DrSnarl's logic is flawless.

If we are able to travel faster than the speed of light to do our experiments then we can do any number of experiments in which we will be able demonstrate that faster-than-light travel is possible.

 

[PAllen]

You can't strictly say SR prohibits FTL. You can say that the following lead to causality violation:

1) FTL travel
2) equivalence of all inertial reference frames, and Lorentz transform being valid between reference frames with relative velocity < c.

All you need to do is:

- pick a reference frame; in the frame suppose there is a rocket going near c.
- travel FTL to the rocket, from some start position in the starting reference frame.
- In the rocket's reference frame, travel FTL back to the start position in the starting reference frame.
- you will arrive there before you left, in the starting reference frame.

 

[DrSnarl]

DrSnarl's logic is flawless.

If we are able to travel faster than the speed of light to do our experiments then we can do any number of experiments in which we will be able demonstrate that faster-than-light travel is possible.

Nice. :)

I am not claiming that FTL transfer of information is possible. It probably is not. I do not how to state that any more strongly. My only point is that you cannot use thought experiments (at least not like the one I presented) to support the claim that SR forbids it.

I should also reiterate that I am not trying to push some "new" theory. I am merely trying to refine my understanding of SR.

In my experience, most people who are educated enough to know something about relativity can tell you that SR forbids FTL information transfer. Those same people will say that a scheme that uses quantum entanglement and interference patterns (or lack thereof) to instantaneously transfer information cannot possibly work BECAUSE it violates SR. My question is, why? What is the basis for such a dismissal? Is it because of thought experiments such as the one I described? My understanding is that it is.

 

[PAllen]

Nice. :)

I am not claiming that FTL transfer of information is possible. It probably is not. I do not how to state that any more strongly. My only point is that you cannot use thought experiments (at least not like the one I presented) to support the claim that SR forbids it.

I should also reiterate that I am not trying to push some "new" theory. I am merely trying to refine my understanding of SR.

In my experience, most people who are educated enough to know something about relativity can tell you that SR forbids FTL information transfer. Those same people will say that a scheme that uses quantum entanglement and interference patterns (or lack thereof) to instantaneously transfer information cannot possibly work BECAUSE it violates SR. My question is, why? What is the basis for such a dismissal? Is it because of thought experiments such as the one I described? My understanding is that it is.

On the last paragraph, nonsense. No one knowledgeable says entanglement can't transfer information FTL because it would violate SR. Instead they say entanglement can't transfer information because the actual mathematics of entanglement says it can't. Period. Note, especially, that you can't even verify that you have successfully produced entanglement without transferring information from one place to another by some other means. Then, (long) after the fact, you can verify you successfully entangled interactions.

 

[Nabeshin]

Nice. :)

I am not claiming that FTL transfer of information is possible. It probably is not. I do not how to state that any more strongly. My only point is that you cannot use thought experiments (at least not like the one I presented) to support the claim that SR forbids it.

I should also reiterate that I am not trying to push some "new" theory. I am merely trying to refine my understanding of SR.

In my experience, most people who are educated enough to know something about relativity can tell you that SR forbids FTL information transfer. Those same people will say that a scheme that uses quantum entanglement and interference patterns (or lack thereof) to instantaneously transfer information cannot possibly work BECAUSE it violates SR. My question is, why? What is the basis for such a dismissal? Is it because of thought experiments such as the one I described? My understanding is that it is.

Hasn't this already been outlined by PAllen? FTL leads to causality violation, which is not something we're willing to give up. Quantum entanglement simply does not transfer information, and anyone who claims that it does is mistaken. It's not like QM predicts FTL information travel but we discard those results because of special relativity. Rather, QM tells us entanglement schemes do not transmit information FTL, in accord with our intuition from SR.

Edit: Ugh! PAllen has bested me!

 

[DrSnarl]

You can't strictly say SR prohibits FTL. You can say that the following lead to causality violation:

1) FTL travel
2) equivalence of all inertial reference frames, and Lorentz transform being valid between reference frames with relative velocity < c.

All you need to do is:

- pick a reference frame; in the frame suppose there is a rocket going near c.
- travel FTL to the rocket, from some start position in the starting reference frame.
- In the rocket's reference frame, travel FTL back to the start position in the starting reference frame.
- you will arrive there before you left, in the starting reference frame.

Thank you. I understand exactly what you are saying, and your thought experiment is very similar to my initial one (with only A and B). I completely agree that you will arrive before you left in the starting reference frame. However, here is the rub: you will arrive even earlier in some reference frames, and you will arrive after you left in yet others. That violates SR in and of itself because all observers must agree on the order of events if the observers and the events are all at the same location.

 

[PAllen]

Thank you. I understand exactly what you are saying, and your thought experiment is very similar to my initial one (with only A and B). I completely agree that you will arrive before you left in the starting reference frame. However, here is the rub: you will arrive even earlier in some reference frames, and you will arrive after you left in yet others. That violates SR in and of itself because all observers must agree on the order of events if the observers and the events are all at the same location.

Well actually, this last argument is not compelling. There is no frame dependence of the order of events on along a timelike world line. There is frame dependence of the order of a sequence events on a spacelike path (the FTL away and back). Frame dependence of the order of events on spacelike paths is a given in SR, not an anomaly. It is only a causality problem if you propose the matter or information can follow these spacelike paths.

 

[DrSnarl]

Hasn't this already been outlined by PAllen? FTL leads to causality violation, which is not something we're willing to give up. Quantum entanglement simply does not transfer information, and anyone who claims that it does is mistaken. It's not like QM predicts FTL information travel but we discard those results because of special relativity. Rather, QM tells us entanglement schemes do not transmit information FTL, in accord with our intuition from SR.

Edit: Ugh! PAllen has bested me!

Thank you (and PAllen as well) for your time in thinking about this. I would like to discuss quantum entanglement further (including experiments that people have done), but as that is really a detour from this discussion, I will refrain. Just to head that off for now, I will accept that you are correct in your assertion about QM and the FTL transmission of information.

However, you said "FTL leads to causality violation, which is not something we're willing to give up." Many people much smarter than I have been studying this since before I was born, and they agree with you, so there must be a clear explanation as to why we are not willing to give it up. I am looking for that explanation.

Again, I will accept that the reason SR forbids FTL transmission of information is that it leads to the nonsensical traveling through time to an infinite number of points in time at a given location. That, however, is not a "violation of causality". Rather, it is merely because you logically cannot be at two different points in time within your own frame of reference (ie. your clock cannot simultaneously have more than one value when you observe it.)

 

[DrSnarl]

Well actually, this last argument is not compelling. There is no frame dependence of the order of events on along a timelike world line. There is frame dependence of the order of a sequence events on a spacelike path (the FTL away and back). Frame dependence of the order of events on spacelike paths is a given in SR, not an anomaly. It is only a causality problem if you propose the matter or information can follow these spacelike paths.

The fact that there is "no frame dependence of the order of events along a timelike world line" is central to my entire point. That is the reason why all observers must agree on the sequence of events if the observers and the events are all at the same location - the sequence of events does not depend on the observers' frames if the observers are all co-located with the events. Or did I misunderstand what you are saying?

 

[PAllen]

However, you said "FTL leads to causality violation, which is not something we're willing to give up." Many people much smarter than I have been studying this since before I was born, and they agree with you, so there must be a clear explanation as to why we are not willing to give it up. I am looking for that explanation.

The only reason fundamental reason to reject causality violation is paradoxes. Some physicists have explored how far we can go to admitting FTL travel in limited ways (e.g. by tachyons; alcubierre drive; wormholes). One technique for limiting the impact of paradoxes is to propose, e.g. the Novikov Consistency conjecture (see, for example http://en.wikipedia.org/wiki/Novikov_self-consistency_principle ). However, even this principle fails to prevent the following type of paradox:

I transmit (via tachyon round trip) the content of a current edition of a Shakespere play to Shakespere before he wrote it. He looks at it, likes it, and publishes it as his own. None of this violates Novikov. So who wrote it? If you are fine with the answer that nobody wrote it, it just 'is', then you can happily pursue FTL theory.

Again, I will accept that the reason SR forbids FTL transmission of information is that it leads to the nonsensical traveling through time to an infinite number of points in time at a given location. That, however, is not a "violation of causality". Rather, it is merely because you logically cannot be at two different points in time within your own frame of reference (ie. your clock cannot simultaneously have more than one value when you observe it.)

Again, I disagree with this summary. SR per se, only says FTL information transfer or travel produces causality violations, it does not say the things you claim above. SR also says various other things: even infinite energy would allow ordinary matter to exceed the speed of light. But you can develop mathematically consistent theories of tachyons.

 

[PAllen]

The fact that there is "no frame dependence of the order of events along a timelike world line" is central to my entire point. That is the reason why all observers must agree on the sequence of events if the observers and the events are all at the same location - the sequence of events does not depend on the observers' frames if the observers are all co-located with the events. Or did I misunderstand what you are saying?

I think you misunderstand that the existence of a spacelike round trip path between two events on a timelike world line has no effect whatsoever on the order of those events for any observer. Actually, perhaps there is something I failed to question earlier in your various analyses. For a round trip FTL path that connects two points on a given timelike world line, there is no frame dependence at all on the order of the events it connect (say e1 and e2). Let us call the turnaround event et. There is only disagreement on the relative ordering of e1, and et, and on e2 and et. Despite this disagreement between frames, all agree on the ordering of e1 and e2 irrespective of the existence or nature of the proposed FTL path between them.

[edit: For example, frame 1 thinks e2->et is forward in time, and et->e1 is back in time more, and e1->e2 is forward in time. Meanwhile, frame 2 thinks e2->et is back in time more, et->e1 is forward in time less, and e1->e2 is forward in time. ]

 

[DrSnarl]

Again, I disagree with this summary. SR per se, only says FTL information transfer or travel produces causality violations, it does not say the things you claim above.

Now I think we have arrived at the heart of the matter. I think that SR does say the following (and if one of these is wrong, then that will expose my premise):

1) When an observer A is separated by observer B in space, any acceleration by B relative to A will cause B to travel through time relative to A.

2) The amount and direction of time travel by B relative to A depends on a) the distance between A and B, and b) the difference in velocity between A and B.

3) Consider an infinite continuum of observers co-located with A (let's call this the point of interest, or POI, and define it as A's location) across every frame of reference (with each observer having a different velocity relative to B). Because of 1) and 2), when B accelerates, it will be traveling a different amount of time relative to each of those observers.

So far, there is no problem. Sure, after B accelerates, it is simultaneously (when considered from its own reference frame) at different points in time for each of the observers at the POI, but because we cannot transmit information faster than light, we cannot turn this into a logical problem. If B then travels towards the POI at any velocity, it will perceive each observer on the continuum having a different degree of time dilation, so by the time B arrives at the POI, B will think that all clocks are in agreement. By agreement, I mean that B will be able to correctly predict to value of any observer's clock and vice versa.

NOTE: I realize that all but one of the observers at the POI will no longer be there by the time B arrives - if this is a problem for you, then assume that each "observer" is actually a stream of observers with a shared frame of reference (ie. velocity) moving through the POI.

4) SR does state that if B could travel fast enough to get out of the light cone (while preserving a reference frame with a velocity < c relative to A, such as via a wormhole), then the time dilation experienced by the observers at the POI relative to B WOULD NOT be sufficient to bring the clocks into agreement by the time B arrived. Hence time travel.

5) The amount of time travel experienced by B relative to an observer at the POI would depend on that observer's frame of reference.

6) All observers at the POI should agree on the value of each other's clocks at the exact time when they are all at the POI.

5) and 6) conflict with each other, yet both are supported by SR. That is my premise. What gives? Is 5) wrong or is 6) wrong?

Thanks again for taking the time to have this discussion. I very much appreciate your insights, and I know it takes effort to try to figure out what someone else is saying, particularly if there is a faulty assumption underlying their argument somewhere.

 

[DrSnarl]

I think you misunderstand that the existence of a spacelike round trip path between two events on a timelike world line has no effect whatsoever on the order of those events for any observer. Actually, perhaps there is something I failed to question earlier in your various analyses. For a round trip FTL path that connects two points on a given timelike world line, there is no frame dependence at all on the order of the events it connect (say e1 and e2). Let us call the turnaround event et. There is only disagreement on the relative ordering of e1, and et, and on e2 and et. Despite this disagreement between frames, all agree on the ordering of e1 and e2 irrespective of the existence or nature of the proposed FTL path between them.

[edit: For example, frame 1 thinks e2->et is forward in time, and et->e1 is back in time more, and e1->e2 is forward in time. Meanwhile, frame 2 thinks e2->et is back in time more, et->e1 is forward in time less, and e1->e2 is forward in time. ]

What you are saying seems like it has to be true, but that also would imply that the existence of an FTL spacelike round trip path between ANY two events on a timelike world line cannot be used to violate causality. This is precisely the point I set out to make, though you did it in a much more concise fashion.

So that said, how can FTL travel violate causality?

 

[PAllen]

What you are saying seems like it has to be true, but that also would imply that the existence of an FTL spacelike round trip path between ANY two events on a timelike world line cannot be used to violate causality. This is precisely the point I set out to make, though you did it in a much more concise fashion.

So that said, how can FTL travel violate causality?

No, my example shows the round trip violates causality by a frame independent amount. All observers agree that the path (e2,et,e1) violates causality by connecting e2 on given timelike world line to earlier e1 on the timelike worldline. They all agree on the proper time interval between e1 and e2, and that e1 occurs before e2. The only thing they disagree on is which part(s) of the path (e2,et,e1) go backwards in time, and by how much - but the total violation along the (e1,e2) world line is invariant.

[edit: what makes it impossible to prevent this type of thing is the assumptions I gave a number of posts ago. In frame of e1,e2 being stationary, e2->et is a forward in time FTL path. Then in rapidly moving frame (which should have all the same capabilities), et->e1 is forward in time FTL. So two actions that must be allowed if you have both FTL and the principle of relativity produce causality violation. The key is the in frame of (e1,e2), the path et->e1 is the one that shoots back in time; while in the rocket frame, it is the path e2-et that shoots back in time.]

[edit2: If you add to SR the axiom that no possible FTL path can appear to go back in time to any inertial observer, then you conclude that no FTL path is possible at all. But this would be an additional assumption to the normal axioms of SR.]

 

[mfb]

2) From both B's and C's perspective, however, they will be accelerating at the same time and at the same rate (ie. the distance between them will not change).

This is not possible, unless B accelerates really slowly, as "at the same time" shifts with increasing speed. But in that case, he wastes the time he wanted to go into the past. Of course, if you wait long enough, you won't come into the past.

 

[Demystifier]

I transmit (via tachyon round trip) the content of a current edition of a Shakespere play to Shakespere before he wrote it. He looks at it, likes it, and publishes it as his own. None of this violates Novikov. So who wrote it? If you are fine with the answer that nobody wrote it, it just 'is', then you can happily pursue FTL theory.

To some extent, asking who wrote it is like asking where the circle begins, suggesting that the best answer is that that nobody wrote it. But actually, there is even a better answer. One can compare entropies at two times and say that the "earlier" one is the one with lower entropy. For more details on such type of reasoning see
http://xxx.lanl.gov/abs/gr-qc/0403121 [Found.Phys.Lett. 19 (2006) 259-267]

 

[PAllen]

To some extent, asking who wrote it is like asking where the circle begins, suggesting that the best answer is that that nobody wrote it. But actually, there is even a better answer. One can compare entropies at two times and say that the "earlier" one is the one with lower entropy. For more details on such type of reasoning see
http://xxx.lanl.gov/abs/gr-qc/0403121 [Found.Phys.Lett. 19 (2006) 259-267]

From a quick read of this paper, I see no way the entropic time definition helps with this paradox. It doesn't matter how you order time, you still have information with no cause, because there is no event anywhere of someone writing the play.

However, another line of argument in the paper helps to somewhat ameliorate the paradox. That is, the paradox has effectively built the existence of the play into the boundary conditions of the universe. It is analogous, in this respect, to the complete SC geometry as a GR solution - there is a causeless, eternal, white hole / black hole. Thus, your answer is: if the play is provided as a boundary condition, then the solution may contain it without cause.

Then you get into what classes of solutions are physically plausible, and you can presumably come up with arguments to suggest that WH/BH solutions, and 'causeless information' solutions, are not plausible.

 

[merp]

The arguments are based off of our third dimension... What about FTL travel possabilities in other dimensions?

 

[DrSnarl]

No, my example shows the round trip violates causality by a frame independent amount. All observers agree that the path (e2,et,e1) violates causality by connecting e2 on given timelike world line to earlier e1 on the timelike worldline. They all agree on the proper time interval between e1 and e2, and that e1 occurs before e2. The only thing they disagree on is which part(s) of the path (e2,et,e1) go backwards in time, and by how much - but the total violation along the (e1,e2) world line is invariant.

I think I understand what you are saying. If an observer is truly moving FTL (ie. not taking a shortcut of some kind that preserves a sub-c velocity), such as would be the case with a tachyon, then all observers will agree that the FTL observer traveled backwards in time. There does not appear to be a paradox there.

It seems to me then that SR makes no claim about shortcuts (where an observer is actually moving < c but still is able to change its location in space by an amount greater than what light can do in that interval - ie. wormhole or teleportation).

Actually, the wormhole case is illustrative. If a flash of light causes some photons to travel through a wormhole and other photons to take a conventional route, then an observer at the end of the wormhole will see those photons arrive at different times. If that observer accelerates relative to the source of the light flash, then it would travel backwards (or forwards, depending on the direction of acceleration) in time relative to that source, but which distance will govern the amount of time travel that occurs? The distance along the geodesic that passes through the wormhole, or the distance along the geodesic that does not?

If the answer is "both", then we can cause trouble by having the observer travel through the wormhole after it receives the first photon, arrive at the source before the light flash occurred according to non-wormhole geodesic but after the flash occurred according to the wormhole geodesic. Does this mean that wormholes are impossible?

 

[DrSnarl]

The arguments are based off of our third dimension... What about FTL travel possabilities in other dimensions?

That would be similar to wormhole travel or teleportation in the sense that your velocity would be sub-c in a relativistic sense (that sub-c velocity would define your frame of reference), and yet you would manage to change your spatial coordinates by a greater amount than what light can do in the same interval.

I am trying to figure out whether or not SR forbids precisely this kind of travel by predicting causality violations if it occurs.

 

[Demystifier]

From a quick read of this paper, I see no way the entropic time definition helps with this paradox. It doesn't matter how you order time, you still have information with no cause, because there is no event anywhere of someone writing the play.

If two events are causally connected, the idea is that the event with smaller entropy is naturally interpreted as "cause" of the event with larger entropy.

 

[PAllen]

If two events are causally connected, the idea is that the event with smaller entropy is naturally interpreted as "cause" of the event with larger entropy.

So how does that say anything at all about my information paradox? There is no event of its being written anywhere in the 4-manifold, and that is the paradox, not any issue of ordering of events.

I think my answer is appropriate: causeless entities of many types are possible in GR solutions. If one is bothered by this, you must look outside of (or beyond) GR to rule these out.

[Edit: Let me note that my scenario has an event of writing down the play, but no event of authoring the play. The physiology of copying or recalling are considered to be distinguishable from authoring/creating. Thus the crux of the problem is the absence of an authoring event anywhere in the spacetime.]

 

[Demystifier]

So how does that say anything at all about my information paradox?

Here is how. Shakespeare lived at time t1, while you sent him the text of the book at time t2>t1. The second law of thermodynamics implies that entropy S satisfies S(t2)>S(t1). Therefore, my resolution of the paradox is based on the claim that Shakespeare's writing is the "cause", while your sending of the book is the "consequence". In other words, you sent him the book at t2 BECAUSE he wrote it at t1, and not vice versa. So it was Shakespeare who wrote the book first, not you. Not because it seems intuitive to me, but because I know that at his time the entropy was lower.

A natural question is the following. But what if you decided to send him a distorted book? The answer, consistent with the Novikov self-consistency principle, is that you could NOT do that. This, of course, contradicts the assumption that you have free will, but the known laws of physics contradict free will even without FTL travel. If nature is deterministic, there is no free will. If nature is probabilistic, there is no free will again.

In other words, free will is only an illusion. You do what the laws of physics tell you to do, but then your consciousness, unable to see the real cause of your actions, interpret the actions as being "chosen freely".

 

[Goodison_Lad]

In other words, free will is only an illusion. You do what the laws of physics tell you to do, but then your consciousness, unable to see the real cause of your actions, interpret the actions as being "chosen freely".

Just in case anybody's interested: there's an interesting debate on this running in the Philosophy area:

https://www.physicsforums.com/showthread.php?t=568146&highlight=free+will

 

[PAllen]

Here is how. Shakespeare lived at time t1, while you sent him the text of the book at time t2>t1. The second law of thermodynamics implies that entropy S satisfies S(t2)>S(t1). Therefore, my resolution of the paradox is based on the claim that Shakespeare's writing is the "cause", while your sending of the book is the "consequence". In other words, you sent him the book at t2 BECAUSE he wrote it at t1, and not vice versa. So it was Shakespeare who wrote the book first, not you. Not because it seems intuitive to me, but because I know that at his time the entropy was lower.

That was all obvious to me, and irrelevant. You don't seem to get my point. I am comparing two consistent worlds:

1) Shakespeare created the play at t1. Our world.

2) Shakespeare received the play at t0, wrote it in his hand at t1, I sent it at t2 back to t0.

My issue with (2) has nothing to do with free will or the order of events. It doesn't matter whether you say t1 was the first of these events. The act of writing something from memory and creating it are physically distinguishable neurological processes. In (2), the act of creating the play no where exists. No ordering of events can change this. Further, since Shakespeare physically aged between t0 and t1, I do not buy the argument that t1 was the first of these events, but that is irrelevant to my main issue.

So, my claim remains, neither Novikov nor thermodynamic arguments do anything at all to resolve the problem of causeless information paradoxes. My partial resolution is to note that GR also perfectly allows causeless objects (like eternal WH/BH), so there is really nothing more unexpected about causeless information.

[Edit: also, please note, from my first post on this, I propose that only an image or modern copy is sent from t2 to t0. Shakespeare might choose to burn it after writing it out in his hand.]

 

[Demystifier]

2) Shakespeare received the play at t0, wrote it in his hand at t1, I sent it at t2 back to t0.

Ah, so I misunderstood you. Now it is clear that t0 is the earliest moment of time at which the text of the book exists. So, I think your paradox is - who is the true author of the book? I would say, and I think you would agree, that the answer is: Nobody - it just appeared spontaneously at t0. Shakespeare is only the first guy who discovered it, but it existed even before his discovery.

 

[PAllen]

Ah, so I misunderstood you. Now it is clear that t0 is the earliest moment of time at which the text of the book exists. So, I think your paradox is - who is the true author of the book? I would say, and I think you would agree, that the answer is: Nobody - it just appeared spontaneously at t0. Shakespeare is only the first guy who discovered it, but it existed even before his discovery.

Exactly.

 

[Whovian]

Ah, so I misunderstood you. Now it is clear that t0 is the earliest moment of time at which the text of the book exists. So, I think your paradox is - who is the true author of the book? I would say, and I think you would agree, that the answer is: Nobody - it just appeared spontaneously at t0. Shakespeare is only the first guy who discovered it, but it existed even before his discovery.

This raises another question. Say someone's capable of time travel. They have a device which they give to their friend to free themselves in their own past. Their friend then frees the first person and gives the device to the first person ... and the first person accidentally gives the one their friend received from themselves to their friend, instead of the one they had all along which they were planning to give to their friend. How old is that device? Shouldn't it have crumbled to dust by now?

 

[DrSnarl]

This raises another question. Say someone's capable of time travel. They have a device which they give to their friend to free themselves in their own past. Their friend then frees the first person and gives the device to the first person ... and the first person accidentally gives the one their friend received from themselves to their friend, instead of the one they had all along which they were planning to give to their friend. How old is that device? Shouldn't it have crumbled to dust by now?

I think this and other questions of time travel do not have to be paradoxes. It is reasonable to state that any time loop will result in multiple, overlapping spaces that are related only in that they share the same time. There is no reason why such a loop could not be infinite, resulting in an infinite number of overlapping spaces.

Causality is thus preserved. In your scenario, the device will eventually crumble, and there will be no more time loops (at least not at that point in space-time).

In the Shakespeare play scenario, Shakespeare wrote the play. However, in one set of space coordinates, he essentially received the play from the overlapping version of himself (the one located in the overlapping space).

I suppose you could call these spaces "multiple dimensions", but that is kind of misleading, as they do not have to be global. There is also no reason (philosophically speaking, at least) why these overlapping spaces could not re-merge in the future. In other words, there is no issue with the Shakespeare who received the play via time travel meeting up with the Shakespeare who wrote it.

 

[DrSnarl]

One technique for limiting the impact of paradoxes is to propose, e.g. the Novikov Consistency conjecture (see, for example http://en.wikipedia.org/wiki/Novikov_self-consistency_principle ).

Novikov Self-Consistency seems like a bit of a stretch to me. What would happen in the Shakespeare scenario? Would it be like the movie "Final Destination", where "fate" just seems to have your number, foiling you at every turn as you try to send the play back in time? It may be logically consistent, but it seems pretty fanciful.

 

[Whovian]

Yea, I don't like Novikov. I've thought of sort of the general concept of what could become a theory that sort of brings Novikov and the multiple universe theory together, or, at least, gives a reason for Novikov, but if all my previous modifiers haven't notified you, it's highly speculative and actually yields no testable predictions that aren't yielded by Novikov.

 

[DaveC426913]

In the Shakespeare play scenario, Shakespeare wrote the play. However, in one set of space coordinates, he essentially received the play from the overlapping version of himself (the one located in the overlapping space).

Yes, I've heard of this hypothesis. Essentially, traveling into the past is not traveling into your own past, it is traveling into a past that was identical to yours, but that no longer will be. I guess that's tantamount to splitting off a whole universe when you time travel into the past.

 

[PAllen]

In the context of SR with tachyons (and my author-less Hamlet scenario can readily be constructed this way), the problem with universe splitting as a solution (rather than Novikov + you must accept causeless information), is that every event of tachyon creation or absorption must split the universe, because any such event represents time travel for some class of inertial observers. Also, there is no model of universe splitting in either SR or GR, so you must add the phenomenology of this. So, pick your poison if you want FTL in SR or GR. To me, the more parsimonious theory is clearly Novikov + acceptance of causeless entitities. However, my honest opinion is that I don't accept author-less plays, and therefore I believe:

- tachyons will never be observed
- a successor to GR will avoid CTC's, singularities (note: I don't believe GR as a physical theory, even its current form, really allows wormholes or alcubierre drive because of the negative energy requirement; but CTC's and singularities occur without negative energy).
- no form of FTL (=time travel) will ever exist.

 

[DrSnarl]

In the context of SR with tachyons (and my author-less Hamlet scenario can readily be constructed this way), the problem with universe splitting as a solution (rather than Novikov + you must accept causeless information), is that every event of tachyon creation or absorption must split the universe, because any such event represents time travel for some class of inertial observers. Also, there is no model of universe splitting in either SR or GR, so you must add the phenomenology of this. So, pick your poison if you want FTL in SR or GR. To me, the more parsimonious theory is clearly Novikov + acceptance of causeless entitities. However, my honest opinion is that I don't accept author-less plays, and therefore I believe:

- tachyons will never be observed
- a successor to GR will avoid CTC's, singularities (note: I don't believe GR as a physical theory, even its current form, really allows wormholes or alcubierre drive because of the negative energy requirement; but CTC's and singularities occur without negative energy).
- no form of FTL (=time travel) will ever exist.

Everything you said makes sense. I agree completely regarding tachyons (along with the prediction that they will never be observed). However, your third assertion (that any form of FTL = time travel in some inertial frame) brings us full circle.

I still do not understand how SR equates teleportation to time travel. Set aside for the moment that there is no known mechanism for teleportation; I am trying to figure out why SR says that (unless you allow for time travel) such a mechanism CANNOT exist.

Just so we are discussing the same thing, by "teleportation", I mean an instantaneous coordinate shift in space while preserving a sub-c frame of reference. This is an important distinction. I completely understand why tachyons would result in time travel.

It seems to me that SR does not allow for teleportation, not because it violates causality, but because the result would create the unresolvable paradox described in the thought experiment with which I started this thread. Another way of looking at it is that SR does not tell us anything about what would happen if we teleported.

Personally, I think the idea of teleportation is far fetched. However, if a science fiction author were to postulate undiscovered physical laws that allowed for teleportation, would those laws conflict with SR by very definition, regardless of what they were? I am picking on teleportation, but the same argument applies to any FTL coordinate shift while in a sub-c reference frame.

 

[PAllen]

Teleportation trivially leads to time travel in SR as follows (again, also assuming principle of relativity - same laws in all inertial frame):

1) Teleport to a rocket traveling at .9c. Pure coordinate shift in the home frame.

2) Teleport back home from the rocket. Pure coordinate shift in the rocket frame.

You arrive home before you left. Teleportation is pure FTL. How can it be different from tachyons in the phenomena it allows?

However, teleportation is really much more absurd than tachyons. There is no plausible theoretical framework for it that I've seen for it (while there are, up to a point, consistent theoretical frameworks for tachyons and GR time travel options). Note that so called quantum teleportation does not involve transmission of matter, nor does it even allow sending FTL messages.

In any case, my position is that neither SR per se, and certainly not GR, preclude certain fanciful FTL/time travel(or message) scenarios. What they do say is that FTL + relativity principle => time travel, with the concomitant choices (and I don't distinguish between time travel by messages versus matter; the choices for dealing with the results are the same).

I don't see any unresolvable paradoxes with teleportation=FTL=time travel - just choices I find implausible.

 

[DrSnarl]

1) Teleport to a rocket traveling at .9c. Pure coordinate shift in the home frame.

2) Teleport back home from the rocket. Pure coordinate shift in the rocket frame.

You arrive home before you left. Teleportation is pure FTL. How can it be different from tachyons in the phenomena it allows?

I think that thought experiment does not appear to create a paradox because we are only considering one frame of reference. Add a rocket at home that is also traveling at .9c, and now you have a problem. Consider the following additions to your experiment:

1) You have three clocks. One you keep with you (your clock). One you leave at home (home stationary clock). One you put on your home rocket (home rocket clock - not the distant rocket that we will teleport to).
2) Synchronize all these clocks so that they read 0.
3) Accelerate the home rocket to 0.9c (towards the away rocket). All clocks still read 0.

4) Teleport to the away rocket. Let's go ahead and accelerate the away rocket after you get there so that you don't instantly accelerate to 0.9c by splattering on the back of the spaceship. (I know, all of our accelerations are instantaneous, so why should this bother us now?)
- After teleporting (but before accelerating), here is what the clocks will read:
From "home stationary perspective":
----home stationary clock = 0
----home rocket clock = 0
----your clock = 0
From "home rocket perspective":
----home stationary clock=0
----home rocket clock=0
----your clock=FUTURE
From "your perspective":
----home stationary clock=0
----home rocket clock=FUTURE
----your clock=0

5) Now, accelerate in the "away rocket" to 0.9c away from home. Here are the new clocks:
From "home stationary perspective":
----home stationary clock = 0
----home rocket clock = 0
----your clock = PAST
From "home rocket perspective":
----home stationary clock = 0
----home rocket clock = 0
----your clock = 0
From "your perspective":
----home stationary clock = PAST
----home rocket clock = 0
----your clock = 0

6) Finally, teleport back home. Here are the new clocks:
From "home stationary perspective":
----home stationary clock = 0
----home rocket clock = 0
----your clock = PAST
From "home rocket perspective":
----home stationary clock = 0
----home rocket clock = 0
----your clock = 0
From "your perspective":
----home stationary clock = PAST
----home rocket clock = 0
----your clock = 0

If you only look at the "home stationary clock", then it would appear that you traveled back into the past. However, the home clock also thinks that it traveled into your past. Additionally, the home rocket thinks that nobody traveled into anybody's past.

According to SR, once you are back home, everyone should agree on the value of everyone else's clocks (they don't have to be the same values, but they should agree on what those values are).

Which clock values are incorrect?

 

[PAllen]

I think that thought experiment does not appear to create a paradox because we are only considering one frame of reference. Add a rocket at home that is also traveling at .9c, and now you have a problem. Consider the following additions to your experiment:

1) You have three clocks. One you keep with you (your clock). One you leave at home (home stationary clock). One you put on your home rocket (home rocket clock - not the distant rocket that we will teleport to).
2) Synchronize all these clocks so that they read 0.
3) Accelerate the home rocket to 0.9c (towards the away rocket). All clocks still read 0.

4) Teleport to the away rocket. Let's go ahead and accelerate the away rocket after you get there so that you don't instantly accelerate to 0.9c by splattering on the back of the spaceship. (I know, all of our accelerations are instantaneous, so why should this bother us now?)
- After teleporting (but before accelerating), here is what the clocks will read:
From "home stationary perspective":
----home stationary clock = 0
----home rocket clock = 0
----your clock = 0
From "home rocket perspective":
----home stationary clock=0
----home rocket clock=0
----your clock=FUTURE
From "your perspective":
----home stationary clock=0
----home rocket clock=FUTURE
----your clock=0

5) Now, accelerate in the "away rocket" to 0.9c away from home. Here are the new clocks:
From "home stationary perspective":
----home stationary clock = 0
----home rocket clock = 0
----your clock = PAST
From "home rocket perspective":
----home stationary clock = 0
----home rocket clock = 0
----your clock = 0
From "your perspective":
----home stationary clock = PAST
----home rocket clock = 0
----your clock = 0

6) Finally, teleport back home. Here are the new clocks:
From "home stationary perspective":
----home stationary clock = 0
----home rocket clock = 0
----your clock = PAST
From "home rocket perspective":
----home stationary clock = 0
----home rocket clock = 0
----your clock = 0
From "your perspective":
----home stationary clock = PAST
----home rocket clock = 0
----your clock = 0

If you only look at the "home stationary clock", then it would appear that you traveled back into the past. However, the home clock also thinks that it traveled into your past. Additionally, the home rocket thinks that nobody traveled into anybody's past.

According to SR, once you are back home, everyone should agree on the value of everyone else's clocks (they don't have to be the same values, but they should agree on what those values are).

Which clock values are incorrect?

I am not going analyze all your verbiage above. It's all unnecessary distraction. This repeats stuff others have commented on. I don't need to deal in clocks at all. The space time path for the the teleportation round trip connects one event on a timelike world line to an earlier event on a timelike world line. Different frames will have different views on which teleportation went back in time and by how much, but all will agree on the order of events on a timelike worldline, and all will agree that your two teleportations have you arrive at an event your world line before you left. All will agree with the amount you have gone back along your initial timelike world line.

[edit: taking a quick look at your write, the thing that is just plain wrong is that there is never frame dependence on what any actual clock reads, however overly complex you make your scenario. There is disagreement only on the order teleportation end point events and coordinate time differences between these endpoints. By construction, no clock time passes for a teleported clock. I would have to correct most of what you wrote, and I am not willing to bother.]

 

[DrSnarl]

I am not going analyze all your verbiage above. It's all unnecessary distraction. This repeats stuff others have commented on. I don't need to deal in clocks at all. The space time path for the the teleportation round trip connects one event on a timelike world line to an earlier event on a timelike world line. Different frames will have different views on which teleportation went back in time and by how much, but all will agree on the order of events on a timelike worldline, and all will agree that your two teleportations have you arrive at an event your world line before you left. All will agree with the amount you have gone back along your initial timelike world line.

I certainly don't fault you for not wanting to analyze my "verbiage"; in fact, at admire your willingness to continue in this thread at all.

I'll try to be as concise as possible: observers in all frames must agree not only on the order of events, but also exactly on how far back in time you went, if all observers are co-located with you. Your thought experiment shows that they do not. I merely took your thought experiment and listed out clock values to illustrate this.

Perhaps the extra rocket was a distraction. Here is the basic problem: when you teleport home, you travel into your home's past, but your home also travels into your past. That is obviously bogus.

 

[PAllen]

I certainly don't fault you for not wanting to analyze my "verbiage"; in fact, at admire your willingness to continue in this thread at all.

I'll try to be as concise as possible: observers in all frames must agree not only on the order of events, but also exactly on how far back in time you went, if all observers are co-located with you. Your thought experiment shows that they do not. I merely took your thought experiment and listed out clock values to illustrate this.

Perhaps the extra rocket was a distraction. Here is the basic problem: when you teleport home, you travel into your home's past, but your home also travels into your past. That is obviously bogus.

1) All observers need not and do not agree on the order of events with spacelike separation (e.g. the endpoints of a teleportation). Observers need not agree on the amount of coordinate time difference between these spacelike separated events (could be 0, -5, + 10 depending on observer). All of this is fine and normal for SR.

2) All observes do agree on order and amount of proper time between events on a timelike world line. Thus all agree (despite different interpretations of what each teleport represented), that e.g. you left with your clock reading 5:00 pm, and arrived at a point on your world line where your past copy has 4:00 pm. You and your past self are next to each other. You have 5:00, they have 4:00. All frames agree on this.

 

[Austin0]

On the last paragraph, nonsense. No one knowledgeable says entanglement can't transfer information FTL because it would violate SR. Instead they say entanglement can't transfer information because the actual mathematics of entanglement says it can't. Period. Note, especially, that you can't even verify that you have successfully produced entanglement without transferring information from one place to another by some other means. Then, (long) after the fact, you can verify you successfully entangled interactions.

Although everything you have said here is true , isn't it also true that:
if the findings developed after the fact, that entangled interactions have occurred, are accurate, then this seems to infer non-local instantaneous transfer of information.
Not at all useful for human communication of information , for the reason you pointed out, but information just the same . On the particle level a transmission of a change of state of some kind from one location to another.
Am I missing or misinterpreting some aspect of the experiments?.

 

[PAllen]

Ok, I had some time to fool with this. Taking your scenario, clarifying that rocket movement is in +x direction and teleportation is in +x direction. I will use 'your' exactly where you did. Then my disagreement starts at your (4): (4) All clocks read zero. This is frame independent. According to home rocket,'your clock' is now in its PAST, but still reads zero. According to "your perspective", all clocks are still zero and in the PRESENT - "your clock" is still in same frame as home stationary clock, just teleported.

(5) All clocks still read zero for everyone (we are assuming effectively instant accelerations and effectively zero time betweein (4) and (5)). "your clock" is in past compared to "home rocket", and "home clock" is now in future compared to "away clock" (and also according to "your clock"). But they all stil read zero. Note, home rocket thinks teleport was into past from its 'present', away rocket (now that it is going .9c) thinks teleport was to its present from its future.

(6) Teleport back, in away rocket's frame, to away rocket's now simultaneous point on home world line. This will bring you to, say, -1 on this world line. What everyone agrees: your orginal world line ended at its reading of zero. Your 0 time self is now located at -1 on the home world line. Your past self clock reads -1, your coincident present self clock reads 0. All agree on this. Home rocket and away rocket both think the second teleport was a simultaneous teleport (in (5), they both considered the first teleport to be in the past direction). Home stationary observer thinks the second teleport was into the past.

There are no discrepancies about what clocks read, or about sequence and time differences on the home, timelike world line. There are only SR typical differences on the interpretation of events with spacelike relation.