## Time-compressed but non-FTL interstellar travel.

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Crane
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### Time-compressed but non-FTL interstellar travel.

Okay, so I've been reading about the causality violation of FTL travel, and wondering if this would serve as a way around it within the context of fiction.

We have a standard 4D spacetime.
We have an additional dimension/set of dimensions which we'll call M-space.
Any given position in 4D spacetime maps to a specific point in M-space.

Travel through M-space is constrained such that if you go from 1,1,1:t' to 1,1,5:t" then t" must be t' + 4. That is to say, any distance you travel in "space" requires a corresponding shift in "time".
The differentials are such that if you leave Earth at 1NC and travel to Elswyr 5 light years away, you will arrive at Earth-time 6NC, but your subjective travel time will be negligible. Then, if you wish to travel back, going from 1,1,5:t' to 1,1,1:t", then t" must be t' - 4.

So you could never, for example, fire a laser from Earth to Elswyr and beat the beam there, and while technically you're travelling 'backwards' from Earth 6NC to 1NC on your return journey, you'll be arriving later than you left by exactly the amount of time you spent at Elswyr.

I feel sure there must be some big logical flaws here, and I'm quite certain there are some assumptions I'm making without noticing: so, what are they?

Edit: Ah, shit. I've just realised that of course you could travel to Elswyr, fire a laser back at Earth, then arrive back on Earth before the laser was fired. But would that be a problem if there's then no possible way for you (or anyone else) to change the fact of its being fired, since you couldn't travel to the time and LOCATION at which it was fired?

Xanthir
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### Re: Time-compressed but non-FTL interstellar travel.

The first part is just using M-space to effectively get near-c travel in the real world. That's totally fine.

The second part (being able to travel back and only having the time pass that you spent at the destination) is time-travel and violates causality, at least if deployed generally. Dunno the rigor of it, but there's an old essay on traversable wormholes exploring how you could set up instantaneous travel without causality violations. Basically, you can't create a wormhole, or wormhole network, whose time-skip is larger than its space-skip. So once you've put in the "10 lightyears, takes you to the destination 1y later in the comoving frame" Earth-to-Elswyr pair (10 space, 9 time, good), you can't then produce a wormhole pair with more than a year of timeskip in the Elswyr-to-Earth direction, as it would create a circuit (by traversing both) that would bring you back to your destination earlier than you left. Virtual-particle production takes advantage of that and ramps up asymptotically to infinity as the reverse-direction pair's timeskip approaches 1y, flooding the wormhole with energy and collapsing it.
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ijuin
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### Re: Time-compressed but non-FTL interstellar travel.

Stuff like this is why physicists speak of "closed timelike curves". Basically, causality is only broken if an object can intersect its own past--i.e. If you could hypothetically send an object or a bit of data to your younger self. As long as you cannot contact your own past (even through intermediaries), then it does not matter if an external observer sees your events out-of-order any more than it matters if someone hears a gun firing after the bullet has whizzed past due to supersonic motion.

Crane
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### Re: Time-compressed but non-FTL interstellar travel.

Ahhh, thank you.
It sounds then like the really handwavy part is how M-space knows you're going "backwards" in time when you make your return voyage from Elswyr to Earth, so you come out back at 1NC (+layover time) rather than just having you emerge on Earth at 11NC.
"Waffle-waffle Alderson matrix mumble directions in space dictate a time vector in M-space murmur mumble slopes, hills and valleys tachyon pulse."

But I don't really have to explain that aspect to a reader anyway. It's sufficient to note that you're not actually travelling faster than light and you can never return to a location at a local time before you left it. You can send a message faster than light in some circumstances, but never to your own past, because whoever sends the message will arrive at a local time after the message was sent.

The most you could do is go somewhere else and send a message back to your origin point, then arrive back before it was sent according to the reference frame in your point of origin. But that doesn't matter, because it's impossible to travel to any point in the origin reference frame before you originally left to send the message, so you can't cancel it out that way. You can't get to the other reference frame at a point before the message was sent, so you can't stop it that way. The message itself is still limited by c, so it can't reach any point in your past. In effect, "what happens, stays happened".

Xanthir
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### Re: Time-compressed but non-FTL interstellar travel.

No, time-travel message-passing is still possible.

Person A starts at Earth at time 1, heads to Elswyr and arrives at time 6. Picks up a message from person B, an Elswyr native, then heads back to Earth, arriving at time 1+ε.

Meanwhile, Person B is on Elswyr at time 1, heads to Earth and arrives at time 6. Finds person A and asks them for the message future-B gave them, then heads back to Elswyr, arriving at time 1+ε.

Person B has now received a message from their future self, approximately 5 years in the future. Or maybe the "message" is actually a passenger - Person C, who's on Elswyr at time 6, can hitch a ride with Person A back to Earth at time 1, wait 5 years, then hitch a ride with Person B back to Elswyr at time 1, thus time-travelling. Or if they're lucky, find someone else doing the Elswyr->Earth->Elswyr round trip that started at time -4 (just arriving on Earth at time 1), so they can just transfer over immediately and go *10 years* into their own past.

FTL travel always results in time-travel. You can't avoid it. It's part of how physics works - the only way to avoid it is to have different physics, or a privileged rest frame. (And this "two people traveling in opposite directions" scenario is almost always the simplest way to demonstrate it. The amount of time-travel is relative to the amount you exceed c by; since your system is effectively infinite speed, it allows "pure" time-travel like this.)

That's how the Traversable Wormholes essay gets around the issue - the wormhole network establishes a privileged rest frame, and so you can't ever send information into your own past. If Earth and Elswyr are connected via the wormhole network, with Elswyr five years "in the future" according to Earth, then Person A gets the same experience as in your system - leave Earth at time 1, arrive at Elswyr at time 6, then return to Earth at time 1+ε. But the difference is that Person B gets the *same* time diffs - if they leave Elswyr at time 1, they'll arrive at Earth at time -4, then return to Elswyr at time 1+ε. No message-passing can occur; the locations are just shifted in comoving time from each other, and physics prevents you from "doubling up" a shift on the same location, like what you can do in your system.
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speising
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### Re: Time-compressed but non-FTL interstellar travel.

Yeah, actually, when the earth traveller picks up someome at elswyr and takes them back to earth, will they arrive at different times, since it would be a different kind of trip for the two? What's the physical property that differentiates between an outbound (into the future) and a homebound (into the past) trip?

Crane
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### Re: Time-compressed but non-FTL interstellar travel.

Xanthir wrote:No, time-travel message-passing is still possible.

Person A starts at Earth at time 1, heads to Elswyr and arrives at time 6. Picks up a message from person B, an Elswyr native, then heads back to Earth, arriving at time 1+ε.

Meanwhile, Person B is on Elswyr at time 1, heads to Earth and arrives at time 6. Finds person A and asks them for the message future-B gave them, then heads back to Elswyr, arriving at time 1+ε.

Person B has now received a message from their future self, approximately 5 years in the future.

Shit.

Xanthir wrote:If Earth and Elswyr are connected via the wormhole network, with Elswyr five years "in the future" according to Earth, then Person A gets the same experience as in your system - leave Earth at time 1, arrive at Elswyr at time 6, then return to Earth at time 1+ε. But the difference is that Person B gets the *same* time diffs - if they leave Elswyr at time 1, they'll arrive at Earth at time -4, then return to Elswyr at time 1+ε. No message-passing can occur; the locations are just shifted in comoving time from each other, and physics prevents you from "doubling up" a shift on the same location, like what you can do in your system.

No wait, that's exactly what I intended. My thought was that M-space is configured (by magic) in such a way that the vector you take through space dictates a specific time shift.

Like I said: going from 1,1,5:t' to 1,1,1:t", then t" must be t' - 4
I didn't mean that to be a special case for going back to your original location. Does that make sense?

ijuin
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### Re: Time-compressed but non-FTL interstellar travel.

The above argument hinges heavily upon the definitions of the relativity of simultaneity. Under the definitions used in the arguments above, it seems that "now" corresponds to the outer edge of the observer's light cone--i.e. everything that you can see happening "now" is regarded as happening "now". But why do we not regard an event taking place one light-year away as happening one year ago? Consider the following thought experiment:

Say that you have a very slow starship--one that travels so slowly that time dilation relative to the stars that it travels between can be ignored as being smaller than your measurement error. Synchronize your onboard atomic clock with Earth and depart for Alpha Centauri. It will take you "t" years to get there, both in Earth's frame of reference and the starship's frame of reference (negligible time dilation, remember?). Once at Alpha Centauri, the ship will transmit a message back to Earth, and then immediately begin its journey back to Earth. According both to Earth clocks and the shipboard clock, a total of 2t will have passed.

As for the transmitted message, it was transmitted at time t, but received on Earth at time t + 4.2 years. The question is, why do we treat the transmission time and the reception time as being equivalent? Yes, for an observer comoving with the signal, zero time passes during transit of the signal (time dilation is infinite at "c"), but we have already established that the Earth and Starship reference frames remain approximately synchronized throughout the entire journey. In short, why do we look at the signal arriving at Earth "now", and treat it mathematically as having been transmitted "now" with no time-of-transit, instead of backtracking along its path and saying "well, it traveled X light years in our frame of reference, so we should treat it as having been transmitted X years ago"?

Xanthir
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### Re: Time-compressed but non-FTL interstellar travel.

Crane wrote:
Xanthir wrote:If Earth and Elswyr are connected via the wormhole network, with Elswyr five years "in the future" according to Earth, then Person A gets the same experience as in your system - leave Earth at time 1, arrive at Elswyr at time 6, then return to Earth at time 1+ε. But the difference is that Person B gets the *same* time diffs - if they leave Elswyr at time 1, they'll arrive at Earth at time -4, then return to Elswyr at time 1+ε. No message-passing can occur; the locations are just shifted in comoving time from each other, and physics prevents you from "doubling up" a shift on the same location, like what you can do in your system.

No wait, that's exactly what I intended. My thought was that M-space is configured (by magic) in such a way that the vector you take through space dictates a specific time shift.

Like I said: going from 1,1,5:t' to 1,1,1:t", then t" must be t' - 4
I didn't mean that to be a special case for going back to your original location. Does that make sense?

Oh! Okay then, that theoretically works, as long as any path through M-space still only lets you travel timelike intervals in real space. You still have to avoid circuits that result in time-travel. Wormholes (seeded by ships heading out at near lightspeed, as the essay posits) do that fairly naturally, but you can come up with your own mechanism.
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Hypnosifl
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### Re: Time-compressed but non-FTL interstellar travel.

ijuin wrote:The above argument hinges heavily upon the definitions of the relativity of simultaneity. Under the definitions used in the arguments above, it seems that "now" corresponds to the outer edge of the observer's light cone--i.e. everything that you can see happening "now" is regarded as happening "now".

That's not how it works in inertial frames in relativity. If in 2020 I see a light signal from an event that occurred 10 light-years away in my inertial rest frame, then in my frame I retroactively say that event happened simultaneously with my calendar showing a date of 2010.

Hypnosifl
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### Re: Time-compressed but non-FTL interstellar travel.

Crane wrote:No wait, that's exactly what I intended. My thought was that M-space is configured (by magic) in such a way that the vector you take through space dictates a specific time shift.

Like I said: going from 1,1,5:t' to 1,1,1:t", then t" must be t' - 4
I didn't mean that to be a special case for going back to your original location. Does that make sense?

That works OK, but what about at other angles? i.e. say if I have my x-y-z coordinate axes oriented in a particular way, then traveling in the +x direction will take me N years into the future for every N light years I travel, while traveling in the -x direction will take me N years into the past for every N light years I travel. What if I travel in the +y direction, or the +z direction, or along a vector in the x-y plane at a 45-degree angle from both x and y axes? Is there a direction I can go where I will travel into neither the future nor the past, but will arrive at the same time I left, in my rest frame? If so, what happens to some other observer who is moving at some slower-than-light speed relative to me, then does an FTL jump in that direction? Will the arrive simultaneously with their departure in my frame, or in their frame, or neither? Whatever rules you pick, I suspect you're going to end up implicitly having selected a preferred reference frame, violating the first of the two postulates of special relativity.
Last edited by Hypnosifl on Mon Apr 25, 2016 9:39 pm UTC, edited 1 time in total.

Xanthir
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### Re: Time-compressed but non-FTL interstellar travel.

Afaik, tho, picking out a preferred reference frame isn't *bad*. Our universe doesn't appear to have one, but it's fine theoretically for one to exist.
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Hypnosifl
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### Re: Time-compressed but non-FTL interstellar travel.

Xanthir wrote:Afaik, tho, picking out a preferred reference frame isn't *bad*. Our universe doesn't appear to have one, but it's fine theoretically for one to exist.

Yes I agree, but I figured there was a good chance the OP realized that one way of getting around the "FTL -> causality violations" problem is just to discard relativity, and so the point of their question may have been to try to find a version that doesn't clearly violate any of the basic principles of relativity (though it's worth noting you could in theory have a set of laws where all the laws of physics pertaining to objects moving at ≤ c would be Lorentz-symmetric, and the violation of relativity's Lorentz-symmetry only happens with the laws of physics governing FTL). As you mentioned in an earlier post, probably the only version of this that might make sense in terms of known physics is the "traversable wormholes + chronology protection conjecture" idea, where wormholes allow you to take trips that would otherwise be FTL if you had to travel outside the wormhole, but any time you try to move the two wormhole mouths around in a way that would allow you to exit one mouth in the past light cone of the point where you entered the other mouth, there's some kind of pileup of vacuum fluctuations that destroys them.

Crane
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### Re: Time-compressed but non-FTL interstellar travel.

I wasn't specifically trying to avoid a preferred reference frame (since at least that doesn't just immediately open the time-travel issue) but I have to admit I wasn't certain if what I had did actually amount to that. But yes, I can see that's basically what I have.
Ah, well. Ce sont les étoiles.

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