Yet another FTL question...

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Yet another FTL question...

Postby tomandlu » Sat Dec 30, 2017 5:40 pm UTC

If you could teleport instantly to any point in the universe, but didn't have any magical way to change your relative momentum, which you'd still have to handle conventionally, could you still potentially break causality?
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Re: Yet another FTL question...

Postby doogly » Sat Dec 30, 2017 5:50 pm UTC

Changing relative momentum doesn't require magic to do, just teleporting instantly. That breaks causality.
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Re: Yet another FTL question...

Postby eSOANEM » Sun Dec 31, 2017 12:21 am UTC

With enough time beforehand, any FTL travel can always be combined with prepared sublight systems to create the standard ansible paradoxes.
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Re: Yet another FTL question...

Postby ucim » Sun Jan 07, 2018 3:42 am UTC

jewish_scientist wrote:What does 'breaking causality' actually mean?
Causality: For two events A and B, "A can cause B" implies that "B cannot cause A".

Generally, A can cause B if B is in the light cone of A. They have a timelike separation. In such a case, if A is before B in one reference frame, it must be before B in all reference frames. ("There's not enough space between A and B to turn into enough time to change the ordering."). B could not cause A because B happens after A in all reference frames.

If A and B are separated by a spacelike interval, then there are reference frames in which A happens before B, and reference frames in which B happens before A. A and B are outside each other's light cone. A could not cause B, and B could not cause A, because in either case, A and B are too far apart for a message to pass between them, even at the speed of light.

But what if a message could get from A to B faster than light? Then the light cone "no longer matters". In one reference frame (where A happens before B), the message goes from A to B, (so A could cause B), but in another reference frame (where B happens before A) the message is seen to go from B to A. So B could cause A. And these two statements are both true at the same time, because there is no "preferred" reference frame. The "causality implication" (in blue, above) is no longer true. It is "broken".

Your dying of a bullet wound could conceivably cause somebody to shoot the gun that fires the bullet that already hit you. That seems nonsensical.

Of course, "seeming nonsensical" is not the same as "being false". Exhibit A: Quantum mechanics. :)

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Re: Yet another FTL question...

Postby doogly » Mon Jan 08, 2018 3:21 am UTC

Very precisely, it means [A(x_1),B(x_2)] = 0 if x_1 and x_2 are space-like separated. A and B are any observable operator. [ , ] is the commutator. Quantum mechanics obeys this condition, which is why the "spooky" action at a distance should not actually be considered spooky.
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Re: Yet another FTL question...

Postby ucim » Mon Jan 08, 2018 3:48 am UTC

I must be flying over Redmond. :)

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Re: Yet another FTL question...

Postby jewish_scientist » Thu Jan 11, 2018 11:36 pm UTC

Okay. I understand all of that. I had a different question though.

On a Penrose Diagram light travels at 45o, so anything moving FTL would be at >45o. Drawing these lines would create a FTL cone. Since an object's FTL cone is larger than its light cone, then two objects not in each others light cones still be in each other's FTL cones. Basically take all of the research done on causality and substitute 'light cone' with 'FTL cone'. Wouldn't causality not break now even though messages can travel FTL.

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Re: Yet another FTL question...

Postby DavidSh » Fri Jan 12, 2018 12:49 am UTC

I'm probably repeating what a previous poster has said, but I'll continue anyway.

If the path from one event A in spacetime to another event B is faster-than-light, then they have "space-like" separation. From some inertial frames, A occurs before B. From other inertial frames, B occurs before A. We can even find, for any faster-than-light speed S we like, an inertial frame from which the speed of travel from A to B is S, and another inertial frame from which the speed of travel from B to A is S. If the functioning of your FTL drive is the same in any inertial reference frame (principal of relativity), then you can use it to travel a loop in time from A to B back to A.

The general conclusion is (FTL, relativity, causality), pick at most two.

Not to say you couldn't create interesting fictional science with preferred reference frames that are hard to detect, just like the breaking of apparent symmetries in particle physics.

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Re: Yet another FTL question...

Postby gmalivuk » Fri Jan 12, 2018 1:45 am UTC

Yeah, there's no single agreed-upon "FTL cone" unless there's a single privileged rest frame for the universe. Otherwise any path that looks goes at all faster than light from one frame (even if only by 1% or something) will go back in time from another frame moving sufficiently fast relative to the first one.

The thing all inertial observers agree on is the spacetime interval between two events. This is the difference between the square of the spatial separation and the square of the (speed of light times) temporal separation.

If we measure time and distance in units where the speed of light is 1 (e.g. we use years and light-years), then we can say
Δs2 = Δt2 - Δx2, where Δt is the temporal separation between events and Δx is the spatial separation in one dimension.
(With this sign convention, Δs is the proper time experienced by an inertial observer that moves from the first event to the second.)

If I observe/calculate that event B happened 3 light-years from A, 5 years after A, then I calculate Δs2 to be 16. You must agree that Δs2 = 16, but maybe you see B as happening in the same location as A, 4 years after it (This happens if you move from where A happens to where B happens and experience 4 years while doing so). For you, a message sent at A and received at B would appear to have zero velocity. For someone else moving very fast relative to both of us, the message could appear to have any sublight speed, but they'd still calculate Δs2 = 16.

If I calculate that B happens 5 light-years from A, 5 years after A, then Δs2 = 0 and I conclude that if A caused B it did so at the speed of light. You must agree with this conclusion, but depending on your own motion relative to me, you could see B happening 1 light-year from A, 1 year later, or 100 light-years from A, 100 years later.

If I calculate that B happens 5 light-years from A, 3 years after A, then Δs2 = -16.
Depending on your motion, you might calculate that B happens 4 light-years from A at exactly the same time as A, or that B happens 5 light-years from A, 3 years before A. We (should) agree that neither A nor B could have caused the other, because to do so would have required moving faster than light, but we don't agree about which one happened first.
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Re: Yet another FTL question...

Postby Pfhorrest » Fri Jan 12, 2018 1:57 am UTC

To maybe simplify things for jewish_scientist: it's only the speed of light that has a constant angle on the Penrose diagram, because it's only the speed of light that's constant for all observers. You can't have an "FTL cone" for the same reason you can't have a "100mph cone" (of all events you could reach by traveling 100mph from a given event): because there's no such thing as absolute speed, for any speed other than c, either slower or faster.
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Re: Yet another FTL question...

Postby ucim » Fri Jan 12, 2018 5:45 am UTC

To simplify things even further ("as simple as possible, but no simpler"), there is something special about the light cone, and only the light cone. It is that it separates spacetime into two regions: one in which the temporal order of A and B is preserved in all reference frames, and another in which it is not. That's the key to the whole thing.

It's not whether something can travel (FTL) between the two... but rather, whether an observer can see A before B while a different observer sees B before A. Only when this is impossible can causality both exist and be preserved. And that only happens within the light cone, and if FTL travel is impossible. The light cone (and only the light cone) is related to the impossibility of temporal reversal, and FTL is related to the impossibility of A causing B if they are outside the light cone.

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Re: Yet another FTL question...

Postby tomandlu » Sun Jan 14, 2018 8:51 pm UTC

Okay, and in all honesty, although I believe in the principle that FTL breaks causality, I never get it.

So, given my original specification, how would I, for instance, arrange to give myself the combination of a safe when the only record of the combination was inside the safe?
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Re: Yet another FTL question...

Postby Eebster the Great » Sun Jan 14, 2018 10:08 pm UTC

But what if we increase the speed of light in 2208?

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Re: Yet another FTL question...

Postby gmalivuk » Mon Jan 15, 2018 1:29 pm UTC

tomandlu wrote:Okay, and in all honesty, although I believe in the principle that FTL breaks causality, I never get it.

So, given my original specification, how would I, for instance, arrange to give myself the combination of a safe when the only record of the combination was inside the safe?

When you receive the combination in a message from your friend, you open the safe and teleport to a distant location just as your friend passes by at a significant fraction of light speed (he left Earth some time ago under sublight propulsion). You send him a message with the combination and he instantly teleports to Earth, where he arrives before you left and sends your past self the password as he flies past at a significant fraction of light speed.

The trick lies in the fact that "instantaneous" means different things in different reference frames, and changing your own momentum isn't the only way to transfer information between frames.

(Of course, you also can't ban momentum changes. You yourself could gradually accelerate away from Earth when you arrive at the distant location, through conventional means, and eventually you'd be going fast enough that your "instantaneous" return hits Earth before you opened the safe.)

Edit: If you jump significantly far away, it only takes a walking speed. Jump a hundred million light-minutes away and then jump back when you're going a hundred millionth of the speed of light, and you'll arrive a minute earlier.
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