FTL thought experiment

[md65536]

3 hours ago, swansont said:

C should not know this for 5 years.

But that's not a paradox. I think that a one-way teleporting of information would not break causality (not sure though). To make the situation into a paradox you'd have to add something to it. You could assume generalization and 2-way travel, but I think you could also add restrictions to make a paradox impossible (use one-way wormholes or black holes).

3 hours ago, swansont said:

No specific information was listed, but that's because of the vague description of the scenario. It certainly exists.

Yes, I think without more specifics, we can't conclude that there's for sure a paradox, or no possibility of a paradox.

 

1 hour ago, jajrussel said:

If at point C you are 5 years in star A's past and you are presumably between Point A and point B it is seemingly a paradox. But if you are seeing light five ly's in A's past and B is five years in A's future it seems more like an equal radius than a paradox. 

What does it mean for B to be five years in A's future? Can you explain in terms of events or coordinates?

My reading of the description is that A and B can be assumed to be at rest, 10 ly apart. Say they have clocks sync'd to year 2020. The events are the ship leaves A when A's clock reads 2020, and arrives at B when B's clock reads 2020.

5 years in A's future is 2025? And B is in 2025? I'm obviously not getting that right but I don't see any meaning of an object being in another object's future. An event can be in another event's future, but I don't see any events here that can be described like that.

 

Edited November 2, 2020 by md65536

[Janus]

17 minutes ago, md65536 said:

But that's not a paradox. I think that a one-way teleporting of information would not break causality (not sure though). To make the situation into a paradox you'd have to add something to it. You could assume generalization and 2-way travel, but I think you could also add restrictions to make a paradox impossible (use one-way wormholes or black holes).

 

Generally to create a paradox you would have two inertial frames in relative motion, each capable of instantaneous information transfer within themselves.

Example:  You are in a spacecraft which passes Earth at 0.8c as both your and the Earth clock reads the same. Trailing 1 ly behind you ( as measured by you) is another spacecraft.

1.25 yrs later, by your clock, you are 1 ly from Earth and the trailing craft is next to Earth.  The time on earth is just 0.75 years later than when you passed it. (An Earth observer would also agree that the trailing craft passed the Earth 0.75 years after you passed.  At that moment, you transmit an instantaneous message to the trailing craft, and that craft hands it off to the Earth as it passes.

The Earth, in turn, send this message to a buoy floating in space which is 0.6 ly away and long your path.  Because,  in 0.75 yrs at 0.8 c, that is how far you have traveled from the Earth. So you will be right next to that buoy.  Your clock will read 0.45 yrs past what it read when you passed Earth.

You will also agree that you passed the buoy when you clock reads 0.45 yrs, As the 0.6 ly distance ( as measured by the Earth) is 0.36 ly as measured by you, and it take 0.45 yrs to travel that distance at 0.8 c.

The buoy hands the message off to you as you pass it.  Thus a message you sent 1.25 yrs after leaving Earth is received by you 0.8 yrs before you sent it!

 

[jajrussel]

22 minutes ago, md65536 said:

What does it mean for B to be five years in A's future? Can you explain in terms of events or coordinates?

In terms of events I was trying to paraphrase a section of the OP, but personally I don't think we can see the future, we can only assume it, so in a sense I was making an assumption based on my best understanding of the OP under the conditions it allowed. Even then, my thought was wrong because I assumed angular positions possibly less than or possibly greater than 180 degrees.

 

35 minutes ago, md65536 said:

Can you explain in terms of events or coordinates?

I assume, not even if my life depended on it. However, if there is an emoji for it I can grovel. 🙂

Personally, I think we can only assume past, present, and future.

This is a great thread, but some of the post are more confusing than the OP, no offense intended Moontanman.🙂

[md65536]

2 hours ago, jajrussel said:

This is a great thread, but some of the post are more confusing than the OP, no offense intended Moontanman.🙂

Yes, it's not a problem as long as everyone understands a statement consistently. Even "traveling to someone's future" could be discussed without confusion if someone defined what that meant and everyone agreed on it.

2 hours ago, Janus said:

Thus a message you sent 1.25 yrs after leaving Earth is received by you 0.8 yrs before you sent it!

Combining this and OP's example: Say there are 2 events, A-2020 ("now" at A) and B-2020 ("now" at B). A ship (or message) travels FTL from A-2020 to B-2020. It travels from "the present" at A to "the present" at B (that is the present relative to the two events, in A & B's shared frame of reference).

Then say B immediately accelerates away from A. In the new frame of reference, A's clock could "now" (according to B) read 2019. The event A-2020 is in the future of B-2020 in this frame. It's not in its future light cone, but in its elsewhere, and in the future relative to B's plane of simultaneity at B-2020.

Then if B immediately sent a message instantly to A-2019 say, A in 2019 could receive information from A-2020, an event in A-2019's own future.

In this example there's no mention of relative past or future until there's relative motion. Also, B receiving a message, accelerating, and sending a message, if done all at once, could be considered a single event.

In both examples, the time travel requires two different inertial frames, with the corresponding two different ways that "now" or "instant" apply to the distant events. You send a message "instantly" using one frame's definition of an instant across space, and send another in a different definition of an instant.

 

Also! in this example, B doesn't need to accelerate at all. If it were inertial and moving relative to A, the only change is that it doesn't agree with A about "now". In this case, the original ship or signal from A-2020 arriving at B-2020 (with B moving away from A and B saying that it is "now" 2019 at A), B can say that it originated from an event that has not yet happened in its frame of reference. However since that event's still outside of its future light cone, that alone doesn't violate causality yet.

Edited November 2, 2020 by md65536

[Moontanman]

Is the instantaneous of the movement causing a problem here? A warp drive could get you the same effect and not be impossible, it would depend on some improbable things like negative mass. if it took you one year to span that distance instead on no time at all would that make a difference? 

[dimreepr]

19 minutes ago, Moontanman said:

Is the instantaneous of the movement causing a problem here? A warp drive could get you the same effect and not be impossible, it would depend on some improbable things like negative mass.

Or impossible things like, star trek/wars

[Soulicit7]

im no learned astrophysicist but my thoughts would be that there could be a percieved visual distance, but there could be a tesseract or fold in time-space, or even gaseous obscurance ..or "scalable ambient obscurance" might apply.. 
furthermore, triangulation is intentional based, and (heres where i derail-) transcendent of reality, i humbly believe. though time, space, locality are relative as experience may afford.
chances are, youd be empirically aware of what you could anticpate before en route to point c.
fascinating subject, man!! cheers.

[md65536]

On 11/3/2020 at 7:50 AM, Moontanman said:

Is the instantaneous of the movement causing a problem here? A warp drive could get you the same effect and not be impossible, it would depend on some improbable things like negative mass. if it took you one year to span that distance instead on no time at all would that make a difference? 

If you could travel at all faster than light, multiple times in different directions, you could create paradoxes.

I don't think the instantaneousness of it matters at all, unless you can apply it arbitrarily in different frames of reference. For a counter example without paradoxes (I think), if spacetime is multiply connected between A and B, where one connection is flat spacetime with a proper distance of 10 LY between A and B, and another connection is a stable wormhole between A and B, allowing instantaneous travel in either direction at any time t in one given inertial frame of reference---or in other words, you could instantly travel from A to B and back, and you could even have B earlier than A (or vice versa) in your frame of reference, but not so early that it's in A's past light cone, AND you can travel back from B to A, but never to an earlier time than you left A---then I think no causality paradoxes are possible without something more. Even though you can transmit information in 2 directions faster than light, and try to exploit the 2 different-length connections between A and B, there's no frame of reference in which information from an event at A can be sent to an earlier event at A. (Same with B and everywhere else.) The parameter t of the events never decreases.

The difference here is, arbitrary travel at faster than light over great distances allows traveling to earlier times in both directions.

HOWEVER, traveling through the wormhole I described is not traveling a great distance, and it can be done at low speed. So it's instantaneous travel, but not technically "moving faster than light". Just getting there faster via a shortcut. The difference is important because it's the changes in relative simultaneity across great distances that are exploited in (impossible) FTL time travel, and that doesn't apply to the wormhole here. I suspect it might not apply to the Alcubierre "warp" drive either.

 

 

(Just a further thought on the example above. Say you tried to cause a paradox by switching between different frames of reference. You could start in one frame F such that a traveler leaves A in 2020, travels through the wormhole, and arrives at B "earlier" in your frame of reference. Then you could switch to another frame F' so that if the traveler leaves B just after it arrived, back through the wormhole, it can now arrive in a time at A that is "earlier" again than it left B, but in this other frame F'. However, you'll also find that in this new frame F', the first event where the traveler left A for B, is earlier (by the same amount) than the event of it arriving at B, and in this frame (like in any) you find that the traveler still arrives back at A after it left, without paradox.)

 

Edited November 7, 2020 by md65536

[md65536]

... continued from previous post.

1 hour ago, md65536 said:

if spacetime is multiply connected between A and B, where one connection is flat spacetime with a proper distance of 10 LY between A and B, and another connection is a stable wormhole between A and B, allowing instantaneous travel in either direction at any time t in one given inertial frame of reference

But why stop there?! From here, I think you could add any number of wormholes from anywhere to anywhere, as long as they each linked two events using the same t parameter as all the other wormholes, ie. they each connected two events that were the same instant according to a single common frame of reference, and you wouldn't create any causality paradoxes. But then!, I think you could also add any number of wormholes, each with a different time parameter (so, some wormhole entrances link an event in your frame's present to an event in your frame's past and at a great distance, others to an event in your frame's future at a distance), without causality paradoxes, as long as you kept sufficient distance between the multiple wormholes' endpoints. For any worldline that goes through multiple wormholes, as long as you keep its events far apart enough to stay outside of earlier events' past light cones, there's no causality paradox. I think!)

Edited November 7, 2020 by md65536