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Dying Earther
2008-Sep-11, 03:51 AM
Before I begin, may I first apologise for the obvious fact that this discussion will have been rehashed ad nauseum. In my defence, I have trawled through past threads on the matter in an effort to understand this conceptually.

Now my understanding of why FTL implies time travel is that two observers in relative motion with respect to one another do not experience the same present, and any FTL transfer of information between them will thus necessarily go back in time. Doing it twice could allow the information to be received before it is sent, and then what is to stop the sender never sending it in the first place?

So far, so good (or is it, that’s what I’m asking). Let me illustrate my confusion with an example.

Planets A, B and C are at equal distances on a line, stationary with respect to one another.

Starship A is at Planet A. It teleports to Planet B and then accelerates to relativistic speeds and proceeds to Planet C.

Now if it teleports to Planet B, it arrives before it teleported from Planet C (from Planet B’s perspective). By teleporting again, it can meet up with itself on the way to Planet C.

If it teleports to Planet A, though, rather than Planet B, the time travel effect is much the same (what is the difference?). A further teleport to meet up with itself can interrupt its journey to Planet C, but no more. It cannot arrive at Planet B before it first teleported there (or can it?).

I guess what I’m trying to say (abandoning all attempts now at any precision of language), is that time travel occurs because going from rest to motion with respect to another observer allows one to accumulate a difference in nows, which is then exploited by FTL. Yes? Being at rest, I cannot simply power up my thrusters then teleport back to before I was born, I am limited (in hoping from the frame of movement to that of rest, over and over) in time travel back towards the point of departure, and no more.

And now, further apologies and a thank you for your patience.

Sam5
2008-Sep-11, 05:00 AM
It might be a good idea for someone to post Einstein's original "no-FTL" thought experiment of 1907, so we can discuss why he has the "material strip" over which the signaling "effect" propagates at the speed W, which he says can be W>c, and then he moves the "material strip" in the opposite direction of the propagating "effect". It would be interesting, for a change, to discuss the FTL issue from the point of view of actually knowing what Einstein said about it and why he decided to move the “material strip” at all.

thorkil2
2008-Sep-11, 05:55 AM
I don't see where your teleport back to B from C gets you there before you left Planet C. It takes an interval of time even at relativistic speed to reach planet C. The shorter interval is experience only by the traveler in the spacecraft. On Planet B, the craft is observed to arrive at Planet C at a certain time; the return teleport from C to B follows that arrival, so nothing is out of sequence (if I'm understanding what you are trying to say). There is no time travel. You wouldn't arrive before you left. It's moot anyway because FTL is impossible. I've been trying to post remarks about the Arrow of Time on ATM (which is pertinent to this), but the posting link won't work and I'm reluctant to post here lest I incur the wrath of the rules police.

thorkil2
2008-Sep-11, 06:07 AM
One more note. The reason FTL implies travel in time is because the only way to achieve a negative interval (backward movement in time) is to exceed c. Forward time travel is easy (conceptually, if not technically). Let's say you travel a significant distance out and back at a very high average relativistic speed. You arrive at your starting point 10 years after you left (by the local calendar), at a subjective cost of only one year. That equals time travel. The catch: You can't go back.

Dying Earther
2008-Sep-11, 06:14 AM
On Planet B, the craft is observed to arrive at Planet C at a certain time; the return teleport from C to B follows that arrival, so nothing is out of sequence (if I'm understanding what you are trying to say).
I’m ignoring observation, since delay due to the speed of light isn’t what I’m interested in here.

Now as I understand it, from the point of view of Planet B time travels more slowly for the spacecraft moving away at relativistic speeds due to relativistic time dilation. That is why when the spacecraft finishes its journey (from the spacecraft’s perspective) and teleports back, it will be travelling back into the past. I think.


It's moot anyway because FTL is impossible.
I agree it’s impossible, but the point of this exercise is to explore all the implications of its impossibility.


One more note. The reason FTL implies travel in time is because the only way to achieve a negative interval (backward movement in time) is to exceed c.
That seems to be a tautology rather than an explanation.

pzkpfw
2008-Sep-11, 06:39 AM
Now as I understand it, from the point of view of Planet B time travels more slowly for the spacecraft moving away at relativistic speeds due to relativistic time dilation. That is why when the spacecraft finishes its journey (from the spacecraft’s perspective) and teleports back, it will be travelling back into the past. I think.

Also: during the travel, from the point of view of the spacecraft, time on Planet B is going more slowly.

It doesn't matter which one is "moving"*; that's relativity.

That's why "instant" teleportation ends up causing issues - time for both of them is slower than the other, by their point of view. Any instant (or FTL) something (communication or travel) between things invokes an inconsistency.

(* This is not the case in something like the "twins paradox" or the actual "two clocks flying around the Earth" experiment; the first involves changing frames, the second is similar but also involves rotating frames [and note that the Earth-bound clock is not stationary].)

grant hutchison
2008-Sep-11, 08:07 AM
If it teleports to Planet A, though, rather than Planet B, the time travel effect is much the same (what is the difference?). A further teleport to meet up with itself can interrupt its journey to Planet C, but no more. It cannot arrive at Planet B before it first teleported there (or can it?).I think your constraint is just coming from the "equal spacing" rule you've imposed.
Place A and B much farther apart than the distance between B and C. Teleport from A to B. Accelerate conventionally from B to C. Teleport back to A. Decelerate at A.
You can reach any arbitrary point in the past of A's worldline by this method, using arbitrarily small velocity changes between B and C, simply by increasing the distance A-B. Having thereby established yourself at rest in the deep past of the reference frame containing A and B, you can teleport back from A to B and arrive before your previous departure.

Grant Hutchison

grant hutchison
2008-Sep-11, 08:16 AM
Now as I understand it, from the point of view of Planet B time travels more slowly for the spacecraft moving away at relativistic speeds due to relativistic time dilation. That is why when the spacecraft finishes its journey (from the spacecraft’s perspective) and teleports back, it will be travelling back into the past. I think.Ah, I see now why you think you can't get back to a time before you started accelerating: you're invoking a difference in the elapsed time between traveller and rest frame.
But there are actually two effects going on with relativistic acceleration: a time dilation and a simultaneity shift. (It's those two effects working together which resolve the "twin paradox" for instance.)
For the time travel associated with instantaneous teleportation, you just exploit large distances, causing large simultaneity shifts with even small velocities. So you can do it without any sort of relativistic acceleration or noticeable time dilation.

Don spacesuit. Teleport many millions of light years into intergalactic space. Fire small manoeuvring jet to start drifting away from the Earth. Teleport back to starting point, stumbling slightly because of the velocity difference caused by your manoeuvre. Prepare to kill own grandfather.

Grant Hutchison

Dying Earther
2008-Sep-11, 08:43 AM
Ah, I see now why you think you can't get back to a time before you started accelerating: you're invoking a difference in the elapsed time between traveller and rest frame.
But there are actually two effects going on with relativistic acceleration: a time dilation and a simultaneity shift.
Thank you so much for bearing with me! So it’s the combination of velocity difference and distance that yields a seperate “now” in different frames? I don’t think I gave any thought before to distance at all.

It would certainly be much easier to think of this as a function of distance and velocity difference rather than accumulated relativistic effects. I hope I’m right in how I’m understanding you.

Hmm, okay. Is there a formula for what the difference in “now” between two points is given values for distance and relative velocity?

grant hutchison
2008-Sep-11, 09:09 AM
Hmm, okay. Is there a formula for what the difference in “now” between two points is given values for distance and relative velocity?The important velocity is the vector component directed towards or away from "home" (the place you've teleported from and will teleport back to, after having made the velocity change).
Express that velocity as a fraction of light speed. That's the number of years of time travel you get per light-year of separation. Velocities away from home will displace you into the past of your home worldline when you return; velocities towards home will displace you into the future.

The remote simultaneity shift is actually just the inverse of your velocity: velocity in metres per second gives you a simultaneity shift in seconds per metre (of separation). If you're travelling at relativistic speeds then time dilation gets involved as well; if your FTL transport is not instant, then journey time must be allowed for, too.

Grant Hutchison

Dying Earther
2008-Sep-11, 10:07 AM
Excellent; that’s cleared things up nicely. Thank you again for helping me out.

Dying Earther
2008-Sep-12, 10:43 AM
Some follow up questions (I hope you don’t mind!). I’ll adapt your example because it’s quite elegant.

Following teleportation to a galaxy one billion light-years away, a rocket blasts off from Earth away from my direction. Unlike in your example, I decide not to fire my manoeuvring thrusters, and teleport back.

Given ordinary escape velocity and the tremendous distances involved, the displacement in time would be something less than forty thousand years in the past. But being stationary with respect to Earth would suggest returning to the present. I’m having difficulty reconciling the two. So what does FTL imply?

grant hutchison
2008-Sep-12, 10:56 AM
Following teleportation to a galaxy one billion light-years away, a rocket blasts off from Earth away from my direction. Unlike in your example, I decide not to fire my manoeuvring thrusters, and teleport back.

Given ordinary escape velocity and the tremendous distances involved, the displacement in time would be something less than forty thousand years in the past. But being stationary with respect to Earth would suggest returning to the present. I’m having difficulty reconciling the two. So what does FTL imply?I'm hoping I understand your set-up: you're talking about the simultaneity shift between the accelerated rocket and your (very distant) "stationary" self?
The core of this is that observers in relative motion disagree about the simultaneity of distant events. If someone teleported from the spaceship to your location, the "instantaneous" transition in their moving reference frame would deposit them in what you consider your past. But if you were to teleport from your distant "at rest" position back to Earth, you'd arrive just after the rocket took off, because that's your present.

Grant Hutchison

Dying Earther
2008-Sep-12, 11:02 AM
I'm hoping I understand your set-up: you're talking about the simultaneity shift between the accelerated rocket and your (very distant) "stationary" self?
Yep.


If someone teleported from the spaceship to your location, the "instantaneous" transition in their moving reference frame would deposit them in what you consider your past. But if you were to teleport from your distant "at rest" position back to Earth, you'd arrive just after the rocket took off, because that's your present.
I think I understand these two outcomes, but say that instead of teleporting to my “at rest” position on Earth, I teleported onto the lifting rocket. The rocket isn’t at rest, so shouldn’t I go back into the past? If I do, where does that leave the stationary Earth, observing from virtually the same location?

grant hutchison
2008-Sep-12, 12:02 PM
I think I understand these two outcomes, but say that instead of teleporting to my “at rest” position on Earth, I teleported onto the lifting rocket. The rocket isn’t at rest, so shouldn’t I go back into the past? If I do, where does that leave the stationary Earth, observing from virtually the same location?You and the Earth agree about what the "present moment" is, because you're at rest relative to each other. And you agree about what time aboard the moving ship matches your present moment. So if you make some instanteous teleport to the ship, you'll arrive in that "present moment".
Let's say that during your travels from Earth, to a very distant stationary point, to the moving ship, you carry a watch and use it to synchronize clocks at the three locations. At the moment you set the ship's clock, all three are showing 12 noon. Anyone on Earth, or at your distant stationary point, would agree to that synchronization.
But aboard the moving ship, they disagree: they think you've set the Earth's clock a microsecond or so slow, and that the very distant clock hasn't even been made or positioned, because it's thousands of years in the future. So they see your arrival as coming from their future.
If they make an instantaneous teleport jump, they'll follow their own definition of simultaneity, and so from your point of view they'll drop back in time by a microsecond at the Earth, and thousands of years at your remote station.

Grant Hutchison

Delvo
2008-Sep-12, 12:33 PM
There is a logical way out of the time-travel trap with teleportation: instead of the relativistic concept of simultaneity, which allows different parts of the universe to be different ages at what seems to be the same time to some observers, simply consider the "instantaneous" teleportation to be taking you to another point in the universe at the time when its age is the same as the age of the part you just departed from.

In other words...

I've read elsewhere that, in empty places of the universe where there's a lot less gravity, the universe would seem to be 18 billion years old instead of 14. Using the relativistic definition of simultaneity, that's the present to us. But in terms of the age of the universe, it's still 4 billion years in the future. Most of the time, when people discuss the problems relativity creates for teleportation, they presume we'd be jumping to what we NOW think of as the present over there in relativistic simultaneity, which would be the 18-billion-year point on the destination's timeline. But what if the way teleportation "really" works is that it always takes you to the destination at the equivalent point on its timeline?

Then you'd be going from here, where the universe is 14 billion years old, to there, at the time when it's 14 billion years old (instead of 18), even though that doesn't seem to be the present from here. It looks like you've just traveled back 4 billion years, right? But over there, when the universe there was 14 billion years old, this part of it was only 10 or 11, not 14 yet. So when you come back, based on your departure point "over there" being 14 billion years old, you still arrive back here when the universe is still 14 billion years old (instead of something like 10 or 11), which then looks like you're traveling a few billion years into the future from where you were. Your travels into what could relativistically be called the past and future cancel out and you arrive back here soon after leaving (whatever time it takes to make two jumps), having never been anyplace that the universe was anything other than 14 billion years old while you were there. So you can never use this trick to reach your own past or future. (The two points we're talking about are well over 4 billion light-years apart.)

Ken G
2008-Sep-12, 01:02 PM
Is there a formula for what the difference in “now” between two points is given values for distance and relative velocity?
If it hasn't come up yet, google "Lorentz transformation" to get that formula.

Ken G
2008-Sep-12, 01:09 PM
There is a logical way out of the time-travel trap with teleportation: instead of the relativistic concept of simultaneity, which allows different parts of the universe to be different ages at what seems to be the same time to some observers, simply consider the "instantaneous" teleportation to be taking you to another point in the universe at the time when its age is the same as the age of the part you just departed from.Yes, that would work to fix the causality issue, as would any specification of a preferred reference frame in regard to instantaneous teleportation. But that requires equipping teleportation with an additional quality absent in all known physics-- an ability to refer to an absolute time. Perhaps that's not so bad, given that teleportation itself already requires elements that are absent in all known physics!

thorkil2
2008-Sep-12, 02:27 PM
That seems to be a tautology rather than an explanation.

Not at all. See the post on the arrow of time in ATM: "Motion, Duration, and Gravity." The latter two parts are speculative, but the math relating to the arrow of time is tough to get around. v/c cannot be greater than 1.

Dying Earther
2008-Sep-14, 04:21 AM
Let's say that during your travels from Earth, to a very distant stationary point, to the moving ship, you carry a watch and use it to synchronize clocks at the three locations. At the moment you set the ship's clock, all three are showing 12 noon. Anyone on Earth, or at your distant stationary point, would agree to that synchronization.
But aboard the moving ship, they disagree: they think you've set the Earth's clock a microsecond or so slow, and that the very distant clock hasn't even been made or positioned, because it's thousands of years in the future. So they see your arrival as coming from their future.
Okay, I think I get it. I’ve collapsed a further inquiry into my reply below.


If it hasn't come up yet, google "Lorentz transformation" to get that formula.
Hi. Yes, that seems to be exactly what thorkil2 is talking about, and it’s also what I thought I was talking about, in my earlier posts. That is, FTL implying time travel due to time dilation effects alone. But, according to grant hutchison, I’ve been neglecting the simultaneity shift. What might be useful is combining the two.

Ship A speeds away from Ship B at 0.9c for ten years and nine light-years. For the crew of Ship A, 4.35 years elapse. From Ship A’s perspective, though, it is Ship B that’s been moving and only 1.9 years have elapsed for them. At this point, Ship A teleports instantaneously back to Ship B.

Do we take away the simultaneity shift (0.9*9, 8.1 years) from the time elapsed due to time dilation (1.9 years) to come up with travel back in time to 6.2 years before Ship B began to speed away?


Not at all. See the post on the arrow of time in ATM: "Motion, Duration, and Gravity." The latter two parts are speculative, but the math relating to the arrow of time is tough to get around. v/c cannot be greater than 1.
Oh, my apologies. I think I understand what you were getting at now.

Ken G
2008-Sep-14, 05:39 AM
That is, FTL implying time travel due to time dilation effects alone. But, according to grant hutchison, I’ve been neglecting the simultaneity shift. What might be useful is combining the two.
Look at the Lorentz transformation again-- it does have the combination of the two effects you are talking about! Note how there is a time shift due to a velocity difference across a separation, right in the transformation.