Why does FTL imply causality violation?

[Smokeskin]

I don't understand why FTL should imply causality violation.

 

The only examples I've been able to find of this violation is essentially like the tachyon pistol duel outlined here: http://sheol.org/thr...on-pistols.html.

 

It just seems that the tachyon pistol duel (TPD) has several problems, for example:

 

1) The tachyon bullet from A is assumed to travel along A's "line of simultaneity". Why not along B's, or the referee's? The bullet certainly isn't flying along their line's of simultaneity. Imagine another tachyn gun at the same point in spacetime as where A fires his tachyon bullet, but this gun stationary relative to B. Both A and the stationary gun fire at the same time, but only A's bullet goes back in time!

2) Imagine that instead of a tachyon bullet, we're sending out an omnidirectional tachyon signal. According to the TPD thought experiment, B would of course receive the signal at the same time and place as he would be hit by the bullet. Now imagine an observer stationary relative to A, at the same point in timespace as where B receives the signal. According to A, the stationary observer's clock is running similarly to A's clock, so when the stationary observer immediatedly sends out a tachyon signal to reply, A receives that just after he sent his message. However, B also sends out a message in reply (similar to the return fire in the TPD example), and supposedly A receives that 6 seconds before he sent out his message! The reason for this discrepancy is that the stationary observer did not receive the message when B did, despite the fact that they were at the same point in spacetime. According to the TDP thought experiment, tachyon signals do not follow defined paths through spacetime - it depends entirely on the speed of the receiver relative to the sender, and at the same location observers at different speeds will pick it up at different times, locally. Does relativity theory really predict that FTL signals take an infinite number of spacetime paths, and at which path you can pick up the signal is defined by the speed of the receiver (what mechanism, what property of elementary particles should be responsible for this, and how relativity theory could predict this peculiar and novel interaction from math alone is mindboggling)?

 

It all seems entirely unreasonable to me that a tachyon signal's propagation should require that you look at it from the sender's reference frame, and that it doesn't take a well defined path through spacetime but rather that it depends on the speed of the receivers. A much more reasonable view of an infinite speed signal would be that it would take a path defined such that if it was sent back at any point, it would be received instantly. This would remove all discrepancies - all senders at receivers would agree on local reception times.

 

Have I misunderstood the tachyon pistol duel thought experiment? When it seems that everyone else thinks it is correct, that's what I assume, but I can't see the flaw in my thinking, only lots of what seems like inconsistencies in the TPD.

 

Please help

[swansont]

If FTL is possible you can send a signal and get the response before you sent it.

[Smokeskin]

If FTL is possible you can send a signal and get the response before you sent it.

 

Yes, that is what people say. I want to understand why they think this. The explanation for this is typically that you bounce the signal back and forth with someone moving at relativistic speeds, but as I outlined above, that seems to rely on

 

1) That we cherry pick among reference frames when we decide what "instant" means

2) That observers disagree on even the local timing of the same event (very unlikely, that is way worse than just causality breaking), or that FTL signals take different paths through spacetime depending on the receiver's speed, so two receivers at the same point in spacetime could have one receiver pick up the signal while the other couldn't.

 

That all seems terribly unreasonable to me. Either it is not true that it follows from SR that you can use FTL signals to violate causality, or the explanation is wrong, or I misunderstood the explanation. Either way, I'd love to hear from someone who understands the reasoning behind it.

[swansont]

http://www.theculture.org/rich/sharpblue/archives/000089.html

[Mystery111]

If FTL is possible you can send a signal and get the response before you sent it.

 

That I assume however depends on whether FTL particles can oscillate in time.

 

This reminds me of the Chronological Protection Conjecture which may need to be reformulated to make sense of particles as well.

Edited October 18, 2011 by Mystery111

[Smokeskin]

http://www.thecultur...ves/000089.html

 

That is just a more convoluted version of the tachyon pistol duel.

 

It has all the same problems. In fact it has all the observers in place needed to highlight the problems.

 

1) It cherry picks reference frames when signals are sent. Isn't it strange that every time a signal is sent it is done "in his reference frame"? How would you go about that, sending a signal "in someone's reference frame" and not someone else's (where it would behave wildly different)? Are reference frames really like different tubes you can shoot your bullet down one and not any other? Isn't the answer "of course not"?

2) The same signals is not received by both receivers even though they are at the same point in spacetime. When Carol sends her signal to Dave and Dave receives it, Alice is in the same time and place as Dave - yet she doesn't see it. If she stopped (relative to Dave/Carol) at that same spot she would receive the signal later. So the same signal goes through point P at time t and is received by Dave but not Alice, and then the same signal goes through point P again at time t+x where Alice picks it up. x is determined by the speed of Alice relative to Carol (when Carol sent the signal it seems) - we could have plenty of Alice's moving at different velocities, meaning that Carol's single signal is able to take an infinite number of paths through spacetime!

 

Again, the thought experiment seem to be based on cherry picking and doesn't even attempt to adress the inconsistencies that pop up.

[swansont]

Isn't it strange that every time a signal is sent it is done "in his reference frame"? How would you go about that, sending a signal "in someone's reference frame" and not someone else's (where it would behave wildly different)?

No, it's not strange at all. It's what is meant by a reference frame. You cannot be "in" (i.e at rest in) anyone else's reference frame if you are moving with respect to them.

[baric]

To be perfectly honest, FTL thought experiments always confuse because they are impossible situations. Everything breaks down for matter at c, so trying to conjecture what happens above c doesn't really compute.

 

What happens to matter as it approaches c? Time slows and it lengthens in space.

 

At c, time has stopped completely for an object with mass and it exists everywhere simultaneously.

 

How exactly are you going to possibly conjecture past those infinities? Asking what happens at FTL is like asking why raising the volume of the color blue to avocado doesn't make mathematical sense.

[Smokeskin]

No, it's not strange at all. It's what is meant by a reference frame. You cannot be "in" (i.e at rest in) anyone else's reference frame if you are moving with respect to them.

 

Absolutely not. The thought experiment has different events happening in different reference frames. That is not how reference frames normally work. We may disagree on some things like timing and length, but we don't disagree on the events. In the thought experiment, what is basically happening is that I shoot a basketball and in my reference frame it goes through the hoop, but in your reference frame it misses - which makes absolutely no sense and is certainly not consistent with anything else in SR or even the basic premises.

 

Please try to go through the thought experiment - it has pairs of observers at the same spacetime coordinate, but only one of them able to receive the signal. The way the author achieves that is by saying "I send the signal in this reference frame but not this one". If you go through it and check the signals in the other reference frames, you get different events, which is not consistent with SR.

[swansont]

Absolutely not. The thought experiment has different events happening in different reference frames. That is not how reference frames normally work. We may disagree on some things like timing and length, but we don't disagree on the events. In the thought experiment, what is basically happening is that I shoot a basketball and in my reference frame it goes through the hoop, but in your reference frame it misses - which makes absolutely no sense and is certainly not consistent with anything else in SR or even the basic premises.

 

Please try to go through the thought experiment - it has pairs of observers at the same spacetime coordinate, but only one of them able to receive the signal. The way the author achieves that is by saying "I send the signal in this reference frame but not this one". If you go through it and check the signals in the other reference frames, you get different events, which is not consistent with SR.

 

The sending in one reference frame but not another is the contradiction that shows the impossibility of FTL communication. The events have to happen in all frames, as you say. But since you can send an answer that arrives before the question, you can get this contradiction. Contradictions mean that one of your assumptions is false. In this case, FTL travel is the assumption.

[Smokeskin]

The sending in one reference frame but not another is the contradiction that shows the impossibility of FTL communication. The events have to happen in all frames, as you say. But since you can send an answer that arrives before the question, you can get this contradiction. Contradictions mean that one of your assumptions is false. In this case, FTL travel is the assumption.

 

I'm not sure I've made my point clear yet.

 

The contradiction does not arise from allowing you to send and answer that arrives before the question. That is just what the authors claim the thought experiment demonstrates.

 

My issue is that the way signals/tachyon bullets are sent in the thought experiments contain a contradiction.

 

Imagine you are standing on a field, and someone flashes their flashlight at you. At the exact moment you see it, I whizz by at the exact same spot - yet I don't see the light! We are at the same point in spacetime but the photons from the flashlight hit you but not me. Even if I was moving at relativistic speeds, that is definetely not in accordance with SR, and we would reject such a scenario outright..

 

In the thought experiment however, the authors are quite happy that this happens, or for some reason they ignore it. In your link, Dave and Alice are at the same spot, and Dave can pick up the FTL signal and tell Alice the contents - no one stops to wonder why Alice couldn't just have picked up the signal? The answer, that in her reference frame the signal (the exact same signal, the same particles) takes an entirely different path through spacetime or only travel in certain reference frames, which is even more ludicrous and breaks down concepts FAR more central to our understanding than mere causality.

 

So when they're saying "this is why you can have at most two of SR, FTL, causality", haven't they misunderstood it and are understating the implications wildly?

 

I see four options:

 

 

a) Everyone is right, I just haven't understood the thought experiments.

b) SR actually predicts that FTL implies causality violation, but the thought experiments presented show something else because they use the wrong math. But a good reasoning does exist, somewhere.

c) SR predicts that FTL implies not only causality violation but that but FTL particles don't follow defined spacetime paths but rather take an infinite number of paths based on the reference frames of those hit by the particles, we have to throw out a lot of basic assumptions about physics in case FTL is possible, and no one noticed so far.

d) The thought experiments are wrong, the idea that FTL implies causality violation is based on them, and so everyone was wrong.

 

For obvious reasons (chief of them being that many people much smarter than me have thought about this far more than me) c and d seems highly unlikely. I probably haven't overturned a concept in speculative physics.

 

Most likely it is option a - it could be b, but again lots of smart people looked at that.

 

But am I understanding you right, that as you see it those thought experiments are cherry picking what reference frames to signal in to reach the conclusion they do, and that if we follow their logic the particles that make up FTL signal would take different spacetime paths "in different reference frames"?

[swansont]

I'm not sure I've made my point clear yet.

 

The contradiction does not arise from allowing you to send and answer that arrives before the question. That is just what the authors claim the thought experiment demonstrates.

 

My issue is that the way signals/tachyon bullets are sent in the thought experiments contain a contradiction.

 

Imagine you are standing on a field, and someone flashes their flashlight at you. At the exact moment you see it, I whizz by at the exact same spot - yet I don't see the light! We are at the same point in spacetime but the photons from the flashlight hit you but not me. Even if I was moving at relativistic speeds, that is definetely not in accordance with SR, and we would reject such a scenario outright..

 

In the thought experiment however, the authors are quite happy that this happens, or for some reason they ignore it. In your link, Dave and Alice are at the same spot, and Dave can pick up the FTL signal and tell Alice the contents - no one stops to wonder why Alice couldn't just have picked up the signal? The answer, that in her reference frame the signal (the exact same signal, the same particles) takes an entirely different path through spacetime or only travel in certain reference frames, which is even more ludicrous and breaks down concepts FAR more central to our understanding than mere causality.

 

If one of you is moving, you are not at the same point in spacetime. You agree on your position, but not on the time.

 

In the example, the author chose to use four observers, probably to preserve some symmetry in the problem and perhaps simplify it somewhat, since each pair are co-located. That removes a variable from the problem. I don't see where he says that Alice cannot see the signal.

[Smokeskin]

If one of you is moving, you are not at the same point in spacetime. You agree on your position, but not on the time.

 

That is not correct. Just because our clocks have run differently and we don't agree on the time, we still agree on points in spacetime. As we meet, even if one of us is moving, we agree on both being right here, right now.

 

In the example, the author chose to use four observers, probably to preserve some symmetry in the problem and perhaps simplify it somewhat, since each pair are co-located. That removes a variable from the problem. I don't see where he says that Alice cannot see the signal.

 

 

If Alice could see the signal at the same time as Dave, she would see it, rather than Carol having to signal Dave first who then sends a lightspeed signal to Alice. If Alice could see the signal, Dave wasn't needed at all, Carol could just signal Alice.

 

It isn't said outright, but it is implied, and the thought experiment's peculiar use of reference frames doesn't work out to a causality violation if the signal was "sent at" Alice. Again this strange idea that instead of sending a signal in a certain direction (maybe aimed at someone), you send signals "to" someone and the signal behaves in different ways according to the receivers speed.

[swansont]

That is not correct. Just because our clocks have run differently and we don't agree on the time, we still agree on points in spacetime. As we meet, even if one of us is moving, we agree on both being right here, right now.

The concept here ties in with the relativity of simultaneity. You can have two people at the same point, one stationary and one moving, and while one observes two events as simultaneous, the other will not. "right here, right now" is ambiguous. In science we tend to quantify things.

[Mystery111]

The concept here ties in with the relativity of simultaneity. You can have two people at the same point, one stationary and one moving, and while one observes two events as simultaneous, the other will not. "right here, right now" is ambiguous. In science we tend to quantify things.

 

This is true.

[Smokeskin]

The concept here ties in with the relativity of simultaneity. You can have two people at the same point, one stationary and one moving, and while one observes two events as simultaneous, the other will not.

 

It feels like you're just replying with snippets of relativity theory instead of actually working your way through the scenario, and because of that your snippets don't apply to the situation.

 

I am standing still. A ship moves by me at relativistic speed. When distance is effectively zero and we're at the same position, I signal (standard lightspeed) to the ship. The ship does the same - when distance is effectively zero, it signals (standard lightspeed) me.

 

So, does this signalling happen simultaneously or not? Do I and the ship think it happens simultaneously? Does any observer, anywhere moving at any speed, think that this happens simultaneously or not?

 

I don't know if you want to call this scenario one or two events, but when they both happen at the same point in spacetime, all observers agree on the simultaneity. Points in spacetime are points in spacetime, the same to all observers. Observers have different coordinate systems and such and might label and time the points differently, but that doesn't change anything. If one observer thinks that two events happen at the same point in spacetime, all observers will see those two events happen at the same point in spacetime also.

 

You could also imagine the ship crashing into me. Do you really believe that some observers will see the ship hit me before they see me hit by the ship?

 

 

"right here, right now" is ambiguous. In science we tend to quantify things.

 

"Right here, right now" is the quantification. Alice is at the same position as Dave while Dave receives the signal. As above, imagine them crashing instead and ask yourself if there's any ambiguity about the simultaneity of the event.

 

 

Have you gone through the trouble of working through the scenario (you know, science-like, where you try to understand the issues and maybe even (!) use pen and paper) so you can participate in a meaningful manner? I don't need basic SR common knowledge replies, and I certainly don't need the glib commentary.

[swansont]

It feels like you're just replying with snippets of relativity theory instead of actually working your way through the scenario, and because of that your snippets don't apply to the situation.

 

…

 

Have you gone through the trouble of working through the scenario (you know, science-like, where you try to understand the issues and maybe even (!) use pen and paper) so you can participate in a meaningful manner? I don't need basic SR common knowledge replies, and I certainly don't need the glib commentary.

 

The link I provided runs through the scenario. I thought it was presented well. I was trying to avoid duplication of that effort.

[Smokeskin]

The link I provided runs through the scenario. I thought it was presented well. I was trying to avoid duplication of that effort.

 

 

I have not once asked for a presentation of the scenario. I have put forth 2 issues/questions I have regarding it that are not adressed in the text. This requires that you put effort into understanding those questions, which you appear unwilling to do. Frankly, I'm not sure you're that much into the scenario either, when you don't realize that Alice and Dave are at the same point in spacetime upon signal reception.

 

Since you're not adressing anything from my last post, I assume you've lost interest in the matter. Thanks for your time though.

[swansont]

I have not once asked for a presentation of the scenario. I have put forth 2 issues/questions I have regarding it that are not adressed in the text. This requires that you put effort into understanding those questions, which you appear unwilling to do. Frankly, I'm not sure you're that much into the scenario either, when you don't realize that Alice and Dave are at the same point in spacetime upon signal reception.

As I've already mentioned, they are not at the same point in spacetime, the understanding of which may or may not be the crux of the matter, and if it is, clearing up this misconception is required before you can move on and analyze the FTL scenario.

[Smokeskin]

As I've already mentioned, they are not at the same point in spacetime, the understanding of which may or may not be the crux of the matter, and if it is, clearing up this misconception is required before you can move on and analyze the FTL scenario.

 

To quote http://www.thecultur...ves/000089.html (last paragraph before the comments):

 

Notice that we've arranged for Dave to receive the signal from Carol as he's flying past Alice

Using D for Dave and A for Alice, their coordinates at the time of Dave's reception is, in any reference frame:

(x_A, y_A, z_A, t_A) = (x_D, y_D, z_D, t_D)

The same point in spacetime. Every observer agrees on this. That each observer use their own coordinate system and so the coordinates between observers are different doesn't change the fact that each and every observer find them at the same point in spacetime.

If this doesn't convince you, imagine that instead of Dave flying past Alice, he crashes into her. Would any observer believe that the impact did not happen at a single point in spacetime?

Edited October 20, 2011 by Smokeskin

[swansont]

If this doesn't convince you, imagine that instead of Dave flying past Alice, he crashes into her. Would any observer believe that the impact did not happen at a single point in spacetime?

When I hear "single point in spacetime" to me it implies that there is some universal frame of reference. Points are always referenced to a coordinate system.

[Smokeskin]

When I hear "single point in spacetime" to me it implies that there is some universal frame of reference. Points are always referenced to a coordinate system.

 

I don't know why you'd think that, there is no universal frame of reference and from the context it was certainly obvious that that was not the case.

 

Anyways, if two objects are at the same point in spacetime in one reference frame/coordinate system, they will be at the same point in spacetime in any reference frame/coordinate system.

 

Back on topic?

[Iggy]

It just seems that the tachyon pistol duel (TPD) has several problems, for example:

 

1) The tachyon bullet from A is assumed to travel along A's "line of simultaneity". Why not along B's, or the referee's? The bullet certainly isn't flying along their line's of simultaneity. Imagine another tachyn gun at the same point in spacetime as where A fires his tachyon bullet, but this gun stationary relative to B. Both A and the stationary gun fire at the same time, but only A's bullet goes back in time!

If the two tachyons are sent from A's location -- one from A's gun and another from a gun at rest relative to B -- only one of the tachyons goes back in time in B's frame.

 

The one from A's gun reaches B when B's clock is at 4 seconds. The one from the other gun reaches B when B's clock is at 16 seconds. It isn't clear to me why you think this is a problem, but it might be that you're assuming that the speed of the tachyon should not depend on the speed of the source. It does depend on that.

 

2) Imagine that instead of a tachyon bullet, we're sending out an omnidirectional tachyon signal. According to the TPD thought experiment, B would of course receive the signal at the same time and place as he would be hit by the bullet. Now imagine an observer stationary relative to A, at the same point in timespace as where B receives the signal. According to A, the stationary observer's clock is running similarly to A's clock, so when the stationary observer immediatedly sends out a tachyon signal to reply, A receives that just after he sent his message.

Agreed.

 

However, B also sends out a message in reply (similar to the return fire in the TPD example), and supposedly A receives that 6 seconds before he sent out his message!

Agreed.

 

The reason for this discrepancy is that the stationary observer did not receive the message when B did, despite the fact that they were at the same point in spacetime.

No, they both received the signals when they were at the same location -- the reason is that the two return signals go different speeds. Looking at the diagram I'd estimate that the return tachyon coming from the ship at rest relative to A goes about 20% faster than light (1.2c) in B's frame. The other return signal travels much faster.

 

According to the TDP thought experiment, tachyon signals do not follow defined paths through spacetime - it depends entirely on the speed of the receiver relative to the sender, and at the same location observers at different speeds will pick it up at different times, locally.

I agree that they don't follow defined paths... tachyons aren't like light which is always 45 degrees on the diagram. But, it shouldn't depend on the speed of the receiver. It depends on the speed of the sender. Observers at different speeds in the same location would both detect a tachyon signal at that location.

 

Does relativity theory really predict that FTL signals take an infinite number of spacetime paths

Different tachyons take different paths through spacetime (they travel at different angles on a spacetime diagram) depending on the speed of their source.

 

C is the only invariant speed. Anything going faster than c or slower than c will travel different speeds in different frames.

Edited October 23, 2011 by Iggy

[Mystery111]

It turns out you can avoid causality problems for tachyons if you model them spacelike instead of timelike, which is possible.

[Smokeskin]

I agree that they don't follow defined paths... tachyons aren't like light which is always 45 degrees on the diagram. But, it shouldn't depend on the speed of the receiver. It depends on the speed of the sender. Observers at different speeds in the same location would both detect a tachyon signal at that location.

 

Different tachyons take different paths through spacetime (they travel at different angles on a spacetime diagram) depending on the speed of their source.

 

 

While you may be correct in actuality, that is not how it works in either of the two thought experiments linked above. The speed of the sender isn't an objective measurement. The sender's speed is in fact the sender's speed relative to the receiver, so the path the tachyons take through spacetime is different for different receivers, and observers at different speed but in the same location will indeed find that they don't receive the tachyon signal at the same time.

 

I personally can't get the SR math to work out to anything else either. It seems you need to drop the relativity of motion to get FTL signals to not cause such contradictions. And the idea of an objective frame of reference is a pretty big leap to make.

 

Can you make a light cone diagram or similar where what you describe (tachyon signal speed depending on the sender) pans out?

 

It turns out you can avoid causality problems for tachyons if you model them spacelike instead of timelike, which is possible.

 

Sounds interesting. How does that work?