Trying to understand how FTL would violate causality....

[sawtooth500]

So I'm not a professional scientist, but rather an avid physics fan. This is one question that no matter how much I research I can't find a clear answer...

So for the sake of argument, let's assume that you could actually build something like the Alcubierre Drive and go FTL (I know a lot of people say it's not possible, but let's just for now assume it is). Let's assume that being in your Alcubierre Drive spaceship, since the spacetime your are in itself is moving (vs you moving through spacetime) you do not experience any acceleration (if I'm wrong in this assumption of how an Alcubierre Drive would work in principle, let me know).

Let's take two events that happen simultaneously, say a marble drop, both on Earth and the Sun. The distance is 1 AU, about 8:20 min travel time at velocity C. Now your spaceship can go 2C velocity and you depart for the Sun at the exact time of the marble drop on Earth (we'll call that departure time T=0). You arrive at the Sun at T=4:10, and then pointing a sufficiently powerful telescope back at Earth at T=8:20 (your reference frame) you will see both the marble drop and your departure.

In the above scenario, you could SEE into the past (hence seeing your own departure) but how would you violate causality? I also know that for such scenarios, there are situations where if you had a 3rd party observer looking at your trip it would look to them as if you traveled backwards in time... But is only observing the past equivalent to violating causality? If you only observe the past, then you still can't change it.

A classic paradox here is the grandfather paradox. To me, it's clear that if you could go FTL and have a good enough telescope you could get to a point where you could observe your grandfather being born... but how could you possibly put yourself into a situation where you could change causality and kill your grandfather? YOUR timeline, as the spaceship traveler, would always have to stay positive, would it not? Especially in something like an Alcubierre Drive, as *technically* in such a spaceship you would not be moving FTL within spacetime, but spacetime itself would be moving FTL on which there is no speed limit...

Thoughts?

 

[Mister T]

So for the sake of argument, let's assume that you could actually build something like the Alcubierre Drive and go FTL (I know a lot of people say it's not possible, but let's just for now assume it is).

Then you don't get causality violations!

Let's call this Statement A: FTL travel violates causality.

That statement is a consequence of assuming that light speed is the same for all observers. When you introduce the possibility of FTL travel you violate the assumption upon which Statement A is founded. And so naturally, if you violate the assumption upon which Statement A is founded, you can reach the conclusion that Statement A is false.

All of the evidence we have, though, supports the assertion that light speed is the same for all observers. So therefore all the evidence we have supports the notion that Statement A is valid.

 

[Nugatory]

In the above scenario, you could SEE into the past (hence seeing your own departure) but how would you violate causality? I also know that for such scenarios, there are situations where if you had a 3rd party observer looking at your trip it would look to them as if you traveled backwards in time... But is only observing the past equivalent to violating causality? If you only observe the past, then you still can't change it.

Google for "tachyonic antitelephone". You can arrange for someone to receive a reply to a message that they haven't sent yet, and although you can't kill your grandfather yourself you can send a message to a hitman who will take care of this gruesome chore for you.

 

[Jeronimus]

Because then you could do this

All you would have to do, would be to accelerate to some velocity relative to your grandfather's rest frame. Have someone put you in a box, and then shoot you at higher then C towards the spacetime location i marked with the red line in the right diagram.
To the one shooting you out, it would just look like FTL travel, moving forward in time still within his rest frame.

From within your grandfather's rest frame however, it would look like you just traveled BACK IN TIME 4 second. You traveled 10 lightseconds in MINUS 4 seconds! Quite a feat!

You would de-accelerate then at this point, and have someone reapeat this neat trick, shooting you towards the other direction, back towards your grandfather. You travel again 10 lightseconds within MINUS 4 seconds from your grandfather's reference frame perspective.

RIP Grandfather

 

[Orodruin]

since the spacetime your are in itself is moving (vs you moving through spacetime)

I would start by trying to dispel this misconception. It is a common one and unfortunately one that will haunt you if you try to learn more in the future. Spacetime is not an object that can be moving. It is also not possible to "be at rest relative to spacetime".

 

[PAllen]

Please note that if alcubierre drive exists, it is possible to use it to travel back in time and violate causality. The logical principle is that same as the tachyonic anti-telephone. You just need to perform two trips and you can end up in the past of when you started. I believe the first derivation of this fact is in the following paper:

https://www.scribd.com/document/78783695/Allen-E-Everett-Warp-drive-and-causality

Note the generality of what they show:

If a warp drive can be constructed, and if flat spacetime is Lorentz invariant, then a time machine can be constructed by the same methods. This is a strong reason for skepticism of such possibilities.

Also it should be noted that if you could simply produce a blob of negative energy, it could travel on a spacelike path (FTL), directly allowing sending messages to the past via tachyonic anti telephone. This follows from the following (wherein he shows exotic matter of the type needed for drives can directly travel on spacelike paths):

https://arxiv.org/abs/1106.2336

 

[PAllen]

Then you don't get causality violations!

Let's call this Statement A: FTL travel violates causality.

That statement is a consequence of assuming that light speed is the same for all observers. When you introduce the possibility of FTL travel you violate the assumption upon which Statement A is founded. And so naturally, if you violate the assumption upon which Statement A is founded, you can reach the conclusion that Statement A is false.

All of the evidence we have, though, supports the assertion that light speed is the same for all observers. So therefore all the evidence we have supports the notion that Statement A is valid.

Theories of tachyons in SR and alcubierre drive in GR nowhere violate the principle that lightspeed is invariant for all observers. They both allow for causality violations if Lorentz invariance is assumed. Instead, if one additionally discards Lorentz invariance, allowing a detectable preferred frame, then it is possible to have FTL without causality violation. The preferred frame, in its most general form, is simply the frame in which FTL phenomena never move back in time. In other frames they may. However, the existence of a preferred frame where they don't allows the complete elimination of causality issues. How plausible, or palatable, this is, is another question.

 

[Mister T]

Theories of tachyons in SR and alcubierre drive in GR nowhere violate the principle that lightspeed is invariant for all observers. They both allow for causality violations if Lorentz invariance is assumed. Instead, if one additionally discards Lorentz invariance, allowing a detectable preferred frame, then it is possible to have FTL without causality violation. The preferred frame, in its most general form, is simply the frame in which FTL phenomena never move back in time. In other frames they may. However, the existence of a preferred frame where they don't allows the complete elimination of causality issues. How plausible, or palatable, this is, is another question.

Right. I realized that just a couple of hours ago when I reviewed the alcubierre situation. Basically, my comments apply only to the flat spacetime of SR. I realize now that they are in general not valid for the reasons you stated.

 

[sawtooth500]

I would start by trying to dispel this misconception. It is a common one and unfortunately one that will haunt you if you try to learn more in the future. Spacetime is not an object that can be moving. It is also not possible to "be at rest relative to spacetime".

Well let me try to understand this for starters...

1. I understand that you are never considered "at rest" within spacetime in a context of GR due to geodesic motion - correct?

2. "Spacetime is not an object that can be moving." - So I look at the wikipedia article for Alcubierre Drive - https://en.wikipedia.org/wiki/Alcubierre_drive - and this implies that theoretically (assuming such a drive were possible) you would be stationary inside a moving bubble of spacetime, and that is a valid solution to GR... so how is spacetime itself not an object that can be moving? Yes typically spacetime does not move... TYPICALLY. But another example - gravity waves. Is that not spacetime itself moving?

 

[PAllen]

Well let me try to understand this for starters...

1. I understand that you are never considered "at rest" within spacetime in a context of GR due to geodesic motion - correct?

2. "Spacetime is not an object that can be moving." - So I look at the wikipedia article for Alcubierre Drive - https://en.wikipedia.org/wiki/Alcubierre_drive - and this implies that theoretically (assuming such a drive were possible) you would be stationary inside a moving bubble of spacetime, and that is a valid solution to GR... so how is spacetime itself not an object that can be moving? Yes typically spacetime does not move... TYPICALLY. But another example - gravity waves. Is that not spacetime itself moving?

curvature of spacetime can be considered to move (though this is a coordinate dependent statement), but this does not mean spacetime can move, nor that there is any notion of at rest relative to spacetime. May I suggest that wikipedia is not as reliable a source as Orodruin?

 

[sawtooth500]

curvature of spacetime can be considered to move (though this is a coordinate dependent statement), but this does not mean spacetime can move, nor that there is any notion of at rest relative to spacetime. May I suggest that wikipedia is not as reliable a source as Orodruin?

Well yes I agree that wikipedia isn't as reliable a source, but please bear with me I'm just a layman trying to understand this :) But if spacetime doesn't move, what about gravity waves, since they've been described as "ripples in spacetime" and look just like ripples in water in every picture of them I've seen (which to me implies movement...)

 

[PAllen]

Well yes I agree that wikipedia isn't as reliable a source, but please bear with me I'm just a layman trying to understand this :) But if spacetime doesn't move, what about gravity waves, since they've been described as "ripples in spacetime" and look just like ripples in water in every picture of them I've seen (which to me implies movement...)

curvature of spacetime moves; spacetime does not move.

 

[Orodruin]

Is that not spacetime itself moving?

No. Nothing is moving. A gravitational wave is a distortion of the metric.

"A bubble of space-time that moves" is not an accurate description of the Alcubierre drive. You cannot take "a piece of space-time" (or a piece of space) and move it to a different location. Space-time is the union of all positions at all times. A (finite) part of space time is a finite volume during some finite time interval.

 

[PAllen]

Well yes I agree that wikipedia isn't as reliable a source, but please bear with me I'm just a layman trying to understand this :) But if spacetime doesn't move, what about gravity waves, since they've been described as "ripples in spacetime" and look just like ripples in water in every picture of them I've seen (which to me implies movement...)

I suggest this semantic discussion is irrelevant to your main questions. I have provided links demonstrating that if GR is correct (the theory on which Alcubierre drive is based) is correct, then if Alcubierre drive can be realized, so can time travel by material bodies. This answers your question fully (in the way you didn't want).

 

[Ibix]

1. I understand that you are never considered "at rest" within spacetime in a context of GR due to geodesic motion - correct?

No. You can always consider yourself at rest as long as your pocket accelerometer reads zero (and even when it doesn't, if you aren't afraid of maths). Newton threw out the concept of "at rest" except with respect to some object. We've seen no evidence that he was wrong on that point in 350 years.

2. "Spacetime is not an object that can be moving." - So I look at the wikipedia article for Alcubierre Drive - https://en.wikipedia.org/wiki/Alcubierre_drive -

That was your first mistake...

and this implies that theoretically (assuming such a drive were possible) you would be stationary inside a moving bubble of spacetime, and that is a valid solution to GR... so how is spacetime itself not an object that can be moving? Yes typically spacetime does not move... TYPICALLY. But another example - gravity waves. Is that not spacetime itself moving?

No. Incidentally, gravity waves are a type of water wave. You mean gravitational wave.

Think of a flipbook - one of those things with a slightly different picture on each page. As you flip through it the picture seems to move. Imagine each page has a small wrinkle on it in a different place on each page. As you flip through it the wrinkle seems to move. But it's an illusion. The thing you're thinking of as a moving wrinkle in a 2d page is actually your viewing of a static 3d structure.

This is analogous to what's going on in gravitational waves. They only seem to move because you only see a 3d slice of a 4d world. In the 4d world nothing is moving. This is what PAllen is telling you - the part of each page that is wrinkled is different, but the wrinkle is not moving.

 

[Orodruin]

May I suggest that wikipedia is not as reliable a source as Orodruin?

Aaaaaw ... now you made me blush.

Well yes I agree that wikipedia isn't as reliable a source, but please bear with me I'm just a layman trying to understand this :) But if spacetime doesn't move, what about gravity waves, since they've been described as "ripples in spacetime" and look just like ripples in water in every picture of them I've seen (which to me implies movement...)

Water does not move due to a wave passing either. Well, the wave is a distortion in the position of the water, but when the wave has passed it goes back to where it was.

 

[nitsuj]

Well let me try to understand this for starters...

1. I understand that you are never considered "at rest" within spacetime in a context of GR due to geodesic motion - correct?

2. "Spacetime is not an object that can be moving." - So I look at the wikipedia article for Alcubierre Drive - https://en.wikipedia.org/wiki/Alcubierre_drive - and this implies that theoretically (assuming such a drive were possible) you would be stationary inside a moving bubble of spacetime, and that is a valid solution to GR... so how is spacetime itself not an object that can be moving? Yes typically spacetime does not move... TYPICALLY. But another example - gravity waves. Is that not spacetime itself moving?

Err, the wiki article used the term "region" multiple times, as well as "bubble"...in physics region is better understood than "bubble". Should've interpreted region, instead of bubble...(wth is a spacetime "bubble") ..But either way, most understand bubbles to be things, and regions to be defined. With a wave the state of the area changed, the cause propagates, the effect doesn't "move"...the cause does.

Slightly different than a flip book...consider this "propagation" the same as a domino line tipping over...one domino falls and pushes the next so on and so forth. Do you then consider the state of a domino to be "moving" from the start of the domino line to the end? The area of currently in motion dominos could be called a region, and the region propagates...but is anything moving?

so whether considering the rate the pages flip in a flip book or the rate at which energy is transferred from one domino to the next at some point you'll have to consider just what the heck the limit is on this "propagation" of cause and effect. I got one...posit that c is invariant...beyond that rate..what are we even talking about? Lastly before riding on "spacetime waves" we should at least test this gravitational manipulation at sea...a surf board from the dreams of surfers everywhere!

 

[sawtooth500]

So in layman's terms (sorry I don't understand the math of this) - let's say if I were to go to the sun and back at speed 2C (if that were possible), from MY reference frame I would still be going forward in time but to the reference frame of an observer standing on Earth I would be arriving before I left (go back in time) because that's how the math of GR works, correct?

If that's so, I can accept that.

 

[nitsuj]

So in layman's terms (sorry I don't understand the math of this) - let's say if I were to go to the sun and back at speed 2C (if that were possible), from MY reference frame I would still be going forward in time but to the reference frame of an observer standing on Earth I would be arriving before I left (go back in time) because that's how the math of GR works, correct?

If that's so, I can accept that.

The line "if that were possible" means the discussion is outside the realm of physics...even beyond a moon made of green cheese underneath the crust. There is lots of neat info on the far away galaxies receding at greater than c. in a way effectively similar to the Alcubierre Drive, via geometry.
of course the Earth observer would measure your trip took 4 minutes'ish instead of 8 minutes...

Don't need to know GR math to read a clock :D

Lastly time, like space has no "direction" to it, or more properly all directions are the same.

 

[Ibix]

So in layman's terms (sorry I don't understand the math of this) - let's say if I were to go to the sun and back at speed 2C (if that were possible), from MY reference frame I would still be going forward in time but to the reference frame of an observer standing on Earth I would be arriving before I left (go back in time) because that's how the math of GR works, correct?

If that's so, I can accept that.

Not exactly. Any faster than light travel is only exceeding the speed of light by a modest amount in some frames and backwards in time in others. You can exploit this to create a negative round trip time if any faster than light travel is allowed. Also, no GR is required - it's demonstrable in flat spacetime too.

It's not entirely clear what one would mean by "time" when traveling faster than light.

 

[PAllen]

So in layman's terms (sorry I don't understand the math of this) - let's say if I were to go to the sun and back at speed 2C (if that were possible), from MY reference frame I would still be going forward in time but to the reference frame of an observer standing on Earth I would be arriving before I left (go back in time) because that's how the math of GR works, correct?

If that's so, I can accept that.

Basically that is correct. Technically, you need to interpose one step to arrive before you left.: you launch your return trip at FTL while having a substantial (less than c) velocity relative to your initial starting point. Note that a sense of time while traveling is what requires GR. In SR there is no FTL approach for which time is defined for the traveling body or signal (e.g. tachyons). However, in GR, the alcubierre traveler is timelike, and can be normal matter. Using two such trips with the right conditions, they arrive before they left. The result is called a 'closed timelike curve'. These are only possible in GR. Many physicists think they are not actually possible due to limitations on the existence exotic matter.

 

[nitsuj]

Basically that is correct. Technically, you need to interpose one step to arrive before you left.: you launch your return trip at FTL while having a substantial (less than c) velocity relative to your initial starting point.

So I am on Earth with my clock and time that return trip at 2c would be 8 minutes...where or how could it possibly AND reasonably be calculated the trip took negative time to complete...only with that assumption applied to the FTL traveler would I determine that the traveler "experienced" negative time compared to me on Earth. But as discussed the traveler is in a inertial FOR and measures proper time. These two regions (Earth and spaceship) are exactly the same and not in relative motion in the kinetic sense. Much like the receding galaxies. Said differently those two regions would continue to be "synchronized". What kind of FTL are we talking here? Kinetic, or geometry?

 

[PAllen]

So I am on Earth with my clock and time that return trip at 2c would be 8 minutes...where or how could it possibly AND reasonably be calculated the trip took negative time to complete...only with that assumption applied to the FTL traveler would I determine that the traveler "experienced" negative time compared to me on Earth. But as discussed the traveler is in a inertial FOR and measures proper time. These two regions (Earth and spaceship) are exactly the same and not in relative motion in the kinetic sense. Much like the receding galaxies. Said differently those two regions would continue to be "synchronized". What kind of FTL are we talking here? Kinetic, or geometry?

Alcubierre drive. If you want the math, see the paper I linked in post #6.

 

[nitsuj]

I read the paper and it's tough for me to follow...is this "merely" a phenomenon of coordinate time and choices of metrics...would this calculated negative coordinate time match anyone's clock? The statement that someone can arrive before leaving makes no sense to me...as if the travelers clock would regress at some point. despite always being inertial to the comparative clock.

 

[Ibix]

The statement that someone can arrive before leaving makes no sense to me.

That's kind of the point...

 

[nitsuj]

That's kind of the point...

?? That a physical body can...or that the coordinate time can...this is my point.

 

[Ibix]

Travelling backwards in time doesn't really make sense. It allows all sorts of paradoxes. Fortunately, you're protected from having to think about it by the fact that you can't do it without exceeding the speed of light, which you can't do. That's all I meant.

 

[PAllen]

I read the paper and it's tough for me to follow...is this "merely" a phenomenon of coordinate time and choices of metrics...would this calculated negative coordinate time match anyone's clock? The statement that someone can arrive before leaving makes no sense to me...as if the travelers clock would regress at some point. despite always being inertial to the comparative clock.

If you believe the warp drive is possible, you must accept that time travel is possible. That is why many physicists are convinced the warp drive is not realizable. The main way to get this result is that negative energy is only realizable I very special contexts, in very small amounts. Quite genarally, if negative energy is macroscopically achievable, and GR is true, you must accept causality paradoxes.

Note, what the paper shows is that if warp drive is possible, you can use it to construct a closed timeline curve.

 

[Mister T]

Note, what the paper shows is that if warp drive is possible, you can use it to construct a closed timeline curve.

I take it that a closed timelike curve is equivalent to a closed worldline?

 

[PAllen]

I take it that a closed timelike curve is equivalent to a closed worldline?

Yes.

 

[Arkalius]

The worldline for any object with mass must be time-like. Events that are time-like are separated by a non-zero amount of time in all reference frames, but there exists a reference frame where their spatial separation is 0. Example, you get in your car to leave your home, and 15 minutes later you arrive at your place of work. These are time-like events. For you, they occurred in the same distance from yourself (0). For an observer moving relative to you, the relative distances of the events are different. They may even record a different amount of time passing, but it will always be positive, and they will always see you arrive after you depart.

Space-like events, on the other hand, always have a non-zero amount of space separating them, but there exists a frame of reference where they are simultaneous, and there will be sets of reference frames that disagree on which event preceded the other. You leave work as before, and 5 minutes later (relative to you), the sun emits a solar flare. The sun is more than 8 light minutes away, so these events are space-like. There exist frames of reference that will observe the solar flare happen before you leave work, and one that will see them happen at the same time. There is also no way possible for you to reach the location of the solar flare when it happens from your position at home on Earth, meaning the events always have a positive separation in distance.

So what does this mean for FTL travel? Well, the departure and arrival of an FTL traveler will necessarily be space-like events. That means there exist frames of reference that will see the arrival happen before the departure. All you would have to do, then, is ensure you end up in such a frame of reference when you arrive, so that you observe your departure happening after your arrival by enough of a time margin such that you can then make the return trip with the same FTL velocity, now relative to your new rest frame, and you'll arrive before you left.

There's a formula for determining the critical subluminal velocity for this scenario. If you can travel at some multiple $n$ (greater than 1) of the speed of light, then this velocity is given by $v = \frac {2n} {1+n^2}$. As long as the frame of reference at your arrival exceeds this velocity (relative to, and away from your departure location), then it will be possible to travel at $n$ relative to this frame back to your origin and arrive before you left. You'll see that the faster your superluminal velocity is, the slower the subluminal velocity has to be to enable this time travel.

 

[Dale]

So I look at the wikipedia article for Alcubierre Drive - https://en.wikipedia.org/wiki/Alcubierre_drive - and this implies that theoretically (assuming such a drive were possible) you would be stationary inside a moving bubble of spacetime

This is why Wikipedia is an unreliable source. Often it is good, but common errors can be propagated simply because they are common.

Experimentally, tests designed to measure the motion of spacetime are tests of local Lorentz violation. Solutions to GR guarantee that there is no local Lorentz violation.

 

[Grinkle]

Very interesting thread.

I have a hard time getting my head around the concept of time travel.

c is the speed of information travel. In the land of the blind, perhaps we can imagine that sound is the speed of information travel. So in this land, I shout 'I am leaving', then I board my supersonic jet and land next to an observer and I say 'boo'. A few minutes later, my shout 'I am leaving' arrives, and the blind observer says I arrived before I left.

For time travel to mean anything, there would have to be some way that information can travel faster than c, and if that is possible, then the concept of time is then tied to that faster travel mechanism, not to c.

 

[PAllen]

Very interesting thread.

I have a hard time getting my head around the concept of time travel.

c is the speed of information travel. In the land of the blind, perhaps we can imagine that sound is the speed of information travel. So in this land, I shout 'I am leaving', then I board my supersonic jet and land next to an observer and I say 'boo'. A few minutes later, my shout 'I am leaving' arrives, and the blind observer says I arrived before I left.

For time travel to mean anything, there would have to be some way that information can travel faster than c, and if that is possible, then the concept of time is then tied to that faster travel mechanism, not to c.

In relativistic models of FTL (e.g. tachyons in SR; traversable worm holes, alcubierre drive, krasnikov tues etc. in GR), there remains one invariant speed c. Whether you find such models plausible, is a different question. In the GR models mentioned, there is never even any locally FTL travel; the FTL is only relative to different light paths from source to target (e.g. without going through the wormhole).

 

[Khashishi]

Grinkle, the speed of light has more fundamental significance than the speed of sound. You have things like time dilation which occur as you approach the speed of light, but nothing analogous as you approach the speed of sound. You can't simply associate information transfer with a faster speed without rewriting all the laws of relativity.