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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Re: Yet another FTL question...

Postby tomandlu » Fri Jan 19, 2018 7:20 pm UTC

gmalivuk wrote:
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...


Thanks for that. I've started doodling light cones - I'm determined to make it something I understand rather than just go along with IYSWIM.
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Re: Yet another FTL question...

Postby lightvector » Sat Jan 20, 2018 5:51 am UTC

Here's a graphical demonstration. In Newtonian physics, the following image shows how your spacetime coordinates transform when you begin at rest and then suddenly accelerate to start moving at a constant velocity to the right.
galilean.png

  • Upward is forward in time.
  • Right and left are forward and backward in space.
  • The thick horizontal black axis is is a line of constant time - the set of all points in spacetime whose time is the current time, i.e. "now".
  • The thick vertical black axis a line of constant position - the set of all points in spacetime that are at the same position as you, in the reference frame where you're at rest, i.e. "here". Or, you can think of it as the set of all points in spacetime that you will visit if you remain at your constant velocity and do not accelerate.
  • Initially, you start at rest relative to the grid. Things at rest relative to you trace out vertical blue lines as time progresses. Every horizontal line marks one unit of time passed.
  • Then, you suddenly accelerated to the right. Now the vertical lines slant to the left - this shows that as you move forward in time at your new constant velocity, things that used to be at rest relative to you are now moving leftward relative to you. But the horizontal lines haven't changed - what used to be 1 second when you were at rest is still 1 second now.

How does special relativity differ?

Go to this site, which has an interactive Minkowsky diagram: http://ibises.org.uk/Minkowski.html. Scroll down to where it says "Grid" and click "Make Grid". Then, go up, and in the "Boost to velocity" field, type in 0.15 and click "Boost".

That is how the grid transforms in special relativity when you accelerate to the right!
minkowsky.png

  • The vertical lines still slant to the left. Things that used to be at rest relative to you are still moving leftward relative to you, that's still true.
  • But the horizontal lines have slanted too! That means that "now" from your current perspective is a different set of points than "now" from the perspective you had before you accelerated to the right. Distant events that used to be in the past or in the future are still distant but are "now" instead of past or future.
  • Notice also that if you were to draw 45-degree lines, they would still perfectly pass through exactly the same corners of all the grid squares that they used to before the transformation. This shows that despite suddenly accelerating to the right, your light cone is actually still the same as before. If a photon initially travels rightward at the speed of light relative to you, tracing a 45 degree line, and you accelerate to the right, afterward it will *still* be travelling rightward at the full speed of light relative to you, still tracing the same fully-slanted 45 degree line, as opposed to the speed of light minus the speed added by your acceleration, which would be a less-slanted line.

Edit:
  • Also, the slanting of time across distance means that any form of instantaneous travel is also a form of time travel. For example, I placed a green and a blue "x" on the grid above.
  • Notice via the red grid how the green 'x" used to be at a point in spacetime at an earlier time from the origin (although distant in space), and the blue "x" at a yet earlier time. However, since we've boosted by 0.15c to the right, now the green "x" is at the same time, so if we were to instantaneously travel to the left, we would now be at the green x.
  • Now, fire your rockets in the other direction until you've gotten to a velocity of -0.15c relative to your original reference frame. Now the grid looks like this.
    minkowsky2.png
  • The blue x is now directly horizontal from the green x. They are at different positions in space, but they are at the same time. So activate your instantaneous travel device again and jump rightward, from the green x to the blue x. Then, fire your rockets until you are back at 0c relative to your original situation, and the grid is all nice and square again. You have now successfully traveled directly to the past from your starting point.

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Re: Yet another FTL question...

Postby tomandlu » Thu Mar 15, 2018 7:38 am UTC

Can I check something? Does the distortion of the light-cone grid arise naturally from what happens to space and time in special relativity? i.e. can those grids be derived from those two aspects of SR alone, or is another factor required?
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Re: Yet another FTL question...

Postby gmalivuk » Thu Mar 15, 2018 11:52 am UTC

More like the other way around. SR says spacetime behaves a certain way and from that you can derive what happens with space and what happens with time.
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Re: Yet another FTL question...

Postby tomandlu » Thu Mar 15, 2018 12:16 pm UTC

gmalivuk wrote:More like the other way around. SR says spacetime behaves a certain way and from that you can derive what happens with space and what happens with time.


So, yes? (i.e. nothing else involved?)
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Re: Yet another FTL question...

Postby doogly » Thu Mar 15, 2018 12:26 pm UTC

The starting point for all SR derivations is just "the speed of light is the same for all observers."
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Re: Yet another FTL question...

Postby Nicias » Thu Mar 15, 2018 1:39 pm UTC

tomandlu wrote:Can I check something? Does the distortion of the light-cone grid arise naturally from what happens to space and time in special relativity? i.e. can those grids be derived from those two aspects of SR alone, or is another factor required?


The light cones don't get distorted. In either grid,they are 45 degree lines. The "now" lines and "here" lines are distorted. Light cones are actually the things that get preserved.

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Re: Yet another FTL question...

Postby tomandlu » Wed Apr 25, 2018 8:29 pm UTC

I'm still trying to turn this into something I understand rather than just accept, and that's led me into something else that's now bugging me.

One of the principals of relativity is that there are no privileged frames of reference, but isn't there one special frame of reference where time, relative to all other frames of reference, moves faster?

I'm assuming I'm wrong, but my logic, ignoring any gravitational effects, is this.

Imagine a universe that only consists of the planet Earth, from which two spaceships leave. It doesn't matter how fast they go relative to each other; inevitably, on returning to Earth, they will find the clocks ahead of theirs. They applied acceleration at some point; the Earth did not.

Extrapolating outwards, mustn't there exist some real reference frame where that condition exists - no any other frame of reference has clocks that run faster? A sort of baseline reference.

I have two theories as to the solution of this personal conundrum:

1. Yeah, that frame exists, so what? It's still not special.
2. I'm wrong.
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Re: Yet another FTL question...

Postby doogly » Wed Apr 25, 2018 8:45 pm UTC

I thinkt he best answer is "it's not that special." There is a sort of important analog for a kind-of-special frame used in cosmology -- if you operate at a scale where the universe is just a homogeneous bulk, then there is a frame in which that bulk is at rest. This frame is pretty special and if you are doing cosmology you are working in this frame because it is maximally convenient. But none of the *laws* of physics find this frame to be special. It is just *most convenient.*
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Re: Yet another FTL question...

Postby DavidSh » Wed Apr 25, 2018 9:23 pm UTC

I think the best answer is "nope". Under special relativity, all inertial frames are equivalent. Sure, in your reference frame you measure the clocks in the other reference frame as running slow, but, in the other reference frame they measure the clocks in your reference frame as running slow. It's tied up (again) in the fact that different reference frames disagree on what distant events are simultaneous.

And also, that two objects moving at constant nonzero velocity relative to each other can meet at most once. Violations of this rule require general relativity to handle.

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Re: Yet another FTL question...

Postby Pfhorrest » Wed Apr 25, 2018 9:26 pm UTC

Also keep in mind that in the specific example you gave, what makes the difference is not the inertial motion of the spaceships and earth, but their acceleration. There's no absolute sense of how fast you're going, but there's an absolute sense of how much faster you're going now than you were a moment ago. The earth and the spaceships on it are all going the same speed to start with, which they all consider "0" but any other frame could just as validly consider as any other speed. Then, from any frame of reference, the spaceships change up their speed a lot as they fly around and then return to earth; what speed they end up going when will differ depending on what frame you measure it from, but how much their speed changed will be agreed up on by all. Meanwhile everyone agrees that the earth kept doing what it was doing before, whatever that was according to their reference frame.

It's that change in speed, acceleration, that results in the spaceships' clocks being behind when then rejoin the earth in its state of motion.
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Re: Yet another FTL question...

Postby tomandlu » Thu Apr 26, 2018 7:09 am UTC

doogly wrote:I thinkt he best answer is "it's not that special." There is a sort of important analog for a kind-of-special frame used in cosmology -- if you operate at a scale where the universe is just a homogeneous bulk, then there is a frame in which that bulk is at rest. This frame is pretty special and if you are doing cosmology you are working in this frame because it is maximally convenient. But none of the *laws* of physics find this frame to be special. It is just *most convenient.*


Thanks - that's pretty much what I suspected. As a side note, presumably this frame and the point-source for the birth of the universe are intrinsically linked?
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Re: Yet another FTL question...

Postby tomandlu » Thu Apr 26, 2018 7:13 am UTC

DavidSh wrote:I think the best answer is "nope". Under special relativity, all inertial frames are equivalent. Sure, in your reference frame you measure the clocks in the other reference frame as running slow, but, in the other reference frame they measure the clocks in your reference frame as running slow. It's tied up (again) in the fact that different reference frames disagree on what distant events are simultaneous.

And also, that two objects moving at constant nonzero velocity relative to each other can meet at most once. Violations of this rule require general relativity to handle.


Is the bold bit right? Surely, when the spaceships return to earth, the earth clocks will show a later time than both ship's clocks?

Just to clarify, my scenario is:

1. Both ships accelerate away from Earth (not necessarily the same acceleration, or applied for the same time)
2. Both ships then turn around and return to Earth
3. On reaching Earth, all clocks are compared
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Re: Yet another FTL question...

Postby tomandlu » Thu Apr 26, 2018 7:20 am UTC

Pfhorrest wrote:Also keep in mind that in the specific example you gave, what makes the difference is not the inertial motion of the spaceships and earth, but their acceleration

...

It's that change in speed, acceleration, that results in the spaceships' clocks being behind when then rejoin the earth in its state of motion.


Indeed - hence "They applied acceleration at some point; the Earth did not."

I have to admit that it was fairly recently that I learned this (acceleration not speed* as the significant factor)

* because, duh, that would create a paradox
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Re: Yet another FTL question...

Postby Soupspoon » Thu Apr 26, 2018 10:58 am UTC

If you actually have a wrap-around universe, you could have a spaceship pass the Earth (or the Earth pass the spaceship) at relativistic speeds and either/both travel towards the wrap-around boundary (as defined against any arbitrary stationary FoR) and remeet with neither having accelerated to confound the usual acceleration-based aspect to the problem.

I think that would probably then have to prove an edge-on-edge temporal disjoint (not that you could identify that disjoint 'point', except wrt every non-unique FoR) although the problem arises that two opposite-moving ships, counter-passing Earth, would be assumed to observe each other as moving thus (whenever they meet, at wrap-around, then again as they re-pass Earth, with surely equally shifted chronology wrt Earth, no matter what the disjoint from Earth) if they ought to each think that they are the privilidged frame (the other ship having travelled) they can be seen to be actually equal as they hove past each other, and (more conveniently to observe) again as they hove past Earth.

Which implies something about the nature of the disjoint 'around the wrap'. Or rather about the whole spacetime geometry.


Spoiler:
This includes if we're on the (volumetric) surface of a non-Euclidean high-dimensional curved space. Hypershpherical, say, with two or more constant-direction journeys around setting off from a point, all on great-(hyper)circular paths reconverging at the arbitrary antipode (then back at the origin, assuming they manage to pass without colliding).

(In the hypershperical space-time, with radial time and circumferential space, there seems to remain no need for a priviliged point other than the ultimate central point which is at t=0 and undefined/undefinable spacial location, from all points there on out you can then choose your frame of reference in space (and Lorentzially/Minkowskiishly warp spacetime around that as you see fit based on that) in a way that expanding handles the effectively expanding spacial 'surface'. If it's that simple, and actual observation indicates that it might be further levels of hyperness beyond 4 dimensions, to accommodate the changing observed rate expansion, if we're not misunderstanding another effect. But the more basic version works as an interesting model, IME.)



Without wrap-around/sufficient non-Euclideanness, though, the necessary accelerative aspects matter most.

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Re: Yet another FTL question...

Postby gmalivuk » Thu Apr 26, 2018 11:53 am UTC

tomandlu wrote:
doogly wrote:I thinkt he best answer is "it's not that special." There is a sort of important analog for a kind-of-special frame used in cosmology -- if you operate at a scale where the universe is just a homogeneous bulk, then there is a frame in which that bulk is at rest. This frame is pretty special and if you are doing cosmology you are working in this frame because it is maximally convenient. But none of the *laws* of physics find this frame to be special. It is just *most convenient.*


Thanks - that's pretty much what I suspected. As a side note, presumably this frame and the point-source for the birth of the universe are intrinsically linked?

There is no point source for the beginning of the universe. It began everywhere, but everywhere was closer together back then.

tomandlu wrote:
DavidSh wrote:I think the best answer is "nope". Under special relativity, all inertial frames are equivalent. Sure, in your reference frame you measure the clocks in the other reference frame as running slow, but, in the other reference frame they measure the clocks in your reference frame as running slow. It's tied up (again) in the fact that different reference frames disagree on what distant events are simultaneous.

And also, that two objects moving at constant nonzero velocity relative to each other can meet at most once. Violations of this rule require general relativity to handle.


Is the bold bit right? Surely, when the spaceships return to earth, the earth clocks will show a later time than both ship's clocks?

Just to clarify, my scenario is:

1. Both ships accelerate away from Earth (not necessarily the same acceleration, or applied for the same time)
2. Both ships then turn around and return to Earth
3. On reaching Earth, all clocks are compared
Yes, the bold bit is correct and true as long as the ships are moving. The one-sided dilation happens because the ships don't stay in the same inertial reference frame (because they couldn't turn back to Earth if they did.

Soupspoon wrote:If you actually have a wrap-around universe, you could have a spaceship pass the Earth (or the Earth pass the spaceship) at relativistic speeds and either/both travel towards the wrap-around boundary (as defined against any arbitrary stationary FoR) and remeet with neither having accelerated to confound the usual acceleration-based aspect to the problem.

I think that would probably then have to prove an edge-on-edge temporal disjoint (not that you could identify that disjoint 'point', except wrt every non-unique FoR) although the problem arises that two opposite-moving ships, counter-passing Earth, would be assumed to observe each other as moving thus (whenever they meet, at wrap-around, then again as they re-pass Earth, with surely equally shifted chronology wrt Earth, no matter what the disjoint from Earth) if they ought to each think that they are the privilidged frame (the other ship having travelled) they can be seen to be actually equal as they hove past each other, and (more conveniently to observe) again as they hove past Earth.

Which implies something about the nature of the disjoint 'around the wrap'. Or rather about the whole spacetime geometry.


Spoiler:
This includes if we're on the (volumetric) surface of a non-Euclidean high-dimensional curved space. Hypershpherical, say, with two or more constant-direction journeys around setting off from a point, all on great-(hyper)circular paths reconverging at the arbitrary antipode (then back at the origin, assuming they manage to pass without colliding).

(In the hypershperical space-time, with radial time and circumferential space, there seems to remain no need for a priviliged point other than the ultimate central point which is at t=0 and undefined/undefinable spacial location, from all points there on out you can then choose your frame of reference in space (and Lorentzially/Minkowskiishly warp spacetime around that as you see fit based on that) in a way that expanding handles the effectively expanding spacial 'surface'. If it's that simple, and actual observation indicates that it might be further levels of hyperness beyond 4 dimensions, to accommodate the changing observed rate expansion, if we're not misunderstanding another effect. But the more basic version works as an interesting model, IME.)



Without wrap-around/sufficient non-Euclideanness, though, the necessary accelerative aspects matter most.
There doesn't have to be any disjoint or wrap-around point or non-Minkowskiness. A cylinder is Euclidean

The difference is that a universe like that *does* have a privileged rest frame: the frame where the "circumference" is maximal.
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Re: Yet another FTL question...

Postby Soupspoon » Thu Apr 26, 2018 12:50 pm UTC

gmalivuk wrote:A cylinder is Euclidean.
But a 'straight cylinder' has an axis that does not wrap around, either falling off the un-wrapping edges or continuing along its infinite extent. (It could be Euclideanally toroidal, as per the Asteroids universe, of course.)

Yet upon the surface of the cylinder (featureless, frictionless, and you blind to any landmarks inwards and outwards of the sheet you are sitting upon) your movement 'sideways' around the cylinder alters your perception of other inhabitants on their own sideways paths (and vice versa) if the cylinder axis direction is 'time' then your relative movements sideways repersent an angled 'now plane' that does disjoint, like taking lined paper and making it into an imperfectly wrapped cylinder where a line on the overlap touches a different other-end-of-line than itself.

Because you're (mis)aligning each ruled line over the opposite line the next line (or several) 'up' the paper, it's still strictly cylindrical. Though you could also add a rotation at the overlap to form a conic structure, with or without the offset, giving parallel straight lines that cross themselves (and other lines) at an angle upon the overlap, but the formed cone has no real reason to restrict a brand new drawn 'straight' line coming from any other point around that surface (locally perpendicular to the cone-point axis) crossing itself at an angle at the antipode side of the conic. The sheet overlap as you wrapped the sheet is purely on view to yoir own (Godlike) perspective. Without deliberately maintaining the seam as a delinerste feature, an observer trapped upon the continuous surface of cylinder or conic forms could perhaps discover the geometry but not the precise orientation of its construction.

Back especially to the cylinder, locally Euclidean, you can have two differently inclined non-parallel lines cross each other multiple times. The size of the (out-of-surface) wrap dictates how trivially visible that would be to a surface-explorer. A basic circumference at least as great as the visible size of the universe (vision curving around the meta-curve in our existence being totally confined the 'flat' surface) would not make itself easily known.

The difference is that a universe like that *does* have a privileged rest frame: the frame where the "circumference" is maximal.
According to external metrics, and probably helped by there being that priviliged axial direction. But I usually look at it by taking it up a level.

Standing on a featureless frictionless sphere (with effectivelt non-descript sky, etc) sliding around 'at rest' you are on a totally non-unique spot of reference, and if you are actually moving then you are on a totally non-unique great-circular path that could have been based upon an one of realistically infinite 'start' (and antipode) positions and oriented in any one of.the ininitesimally differentiable angles of departure. (It takes work to describe the relationship between the apparent paths of two arbitrarily great-circling observers, wrt to each other, but the sphere surfsce itself is curved out of the Euclidean plane and you may assume that there is nothing intrinsically special about any points like a 'pole' and thus no equatorial great circle or lines of longitude.) Exstensive-enough experimentation would reveal the curvature of space, but (as per Flat Earthers) a sufficiently limited amount of observation upon a laege enough sphere allows for assumption of flatness, or dismissal of borderline signs of non-flatness as being mere optical illusions to the limits of localised understanding

Maybe, though, consider that surface as 'co-nows' to your here-and-now (out of your light-cone) as time progresses radially the surface travelling outwards (or inwards, making time's arrow ultimately differentiable as you've headed from an infinite past to a definite singularity future destination) the actual great-circles you follow are 'great-'spirals through the expanding universe.


Which is almost certainly not how the Real World is (if it bears any artful resemblence, there'll be other twists to the actual story) but makes for an interesting thought model all the same.


It also doesn't help with the OP's question (any more than already helped, which I thought was sufficient) but I thought that perhaps it'd be interesting to consider the extended problem, without realising I would inadvertently start a discussion more existential than theoretical. :oops:

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Re: Yet another FTL question...

Postby doogly » Thu Apr 26, 2018 1:28 pm UTC

I don't follow what you are talking about with cylinders but it sounds suspicious.

Here's a nice writeup with some diagrams:
https://arxiv.org/pdf/gr-qc/0503070.pdf
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Re: Yet another FTL question...

Postby Soupspoon » Thu Apr 26, 2018 2:13 pm UTC

Just (so far) having read the Introductory summary, and not gotten to the diagrams, I would have to say that I agree with the precis. (Not that I claim authority to bunk/debunk that kind of thing! It just meshes well with my own ideas.)
Spoiler:
I hadn't gotten quite so far as to think about establishing an absolute frame in the axial direction by comparing the actual timings of wrapped-around light, but the establishment of the perpendicular 'true stationary' (and the orientation of that wrap) does indeed arise if you have a wrap circumference small enough to send signals round. Both directions being space.

If the axial direction is time, it's a different issue but it seems to also establish radial stationaryness even during axial temporal inevitability (I'm warping the equivalent Minkowski diagrams in my head, probably need to graph them to be sure). If the circumference is time, to axial space, then that's interesting, too.


I will read further, later.

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Re: Yet another FTL question...

Postby gmalivuk » Thu Apr 26, 2018 3:37 pm UTC

doogly wrote:I don't follow what you are talking about with cylinders but it sounds suspicious.
Yeah it's a lot of words that mostly seem to miss the point.

Soupspoon wrote:Yet upon the surface of the cylinder (featureless, frictionless, and you blind to any landmarks inwards and outwards of the sheet you are sitting upon) your movement 'sideways' around the cylinder alters your perception of other inhabitants on their own sideways paths (and vice versa) if the cylinder axis direction is 'time' then your relative movements sideways repersent an angled 'now plane' that does disjoint, like taking lined paper and making it into an imperfectly wrapped cylinder where a line on the overlap touches a different other-end-of-line than itself.
Yes, but that's a thing that happens to your own worldline and surface of simultaneity. It's not a feature of the universe itself. There is no "wrap-around point" in the universe.

Without deliberately maintaining the seam as a delinerste feature, an observer trapped upon the continuous surface of cylinder or conic forms could perhaps discover the geometry but not the precise orientation of its construction.
And this is because there is no precise orientation of its construction, if by that you mean some objective reality to the seam you're envisioning because you're imagining making this universe out of flat paper instead of just envisioning the universe as it now is, regardless of how your minds-eye created it.

Back especially to the cylinder, locally Euclidean, you can have two differently inclined non-parallel lines cross each other multiple times. The size of the (out-of-surface) wrap dictates how trivially visible that would be to a surface-explorer. A basic circumference at least as great as the visible size of the universe (vision curving around the meta-curve in our existence being totally confined the 'flat' surface) would not make itself easily known.
Whether or not it would be easy to discover, such a universe would still have a privileged "rest" in the direction of the curve, and thus also privileged directions (angles to the direction of curvature).

The difference is that a universe like that *does* have a privileged rest frame: the frame where the "circumference" is maximal.
According to external metrics, and probably helped by there being that priviliged axial direction. But I usually look at it by taking it up a level.
What external metrics? There's nothing external to the universe, but envisioning it as a curled up piece of paper in front of you makes that difficult to intuit.

Standing on a featureless frictionless sphere (with effectivelt non-descript sky, etc) sliding around 'at rest' you are on a totally non-unique spot of reference, and if you are actually moving then you are on a totally non-unique great-circular path that could have been based upon an one of realistically infinite 'start' (and antipode) positions and oriented in any one of.the ininitesimally differentiable angles of departure. (It takes work to describe the relationship between the apparent paths of two arbitrarily great-circling observers, wrt to each other, but the sphere surfsce itself is curved out of the Euclidean plane and you may assume that there is nothing intrinsically special about any points like a 'pole' and thus no equatorial great circle or lines of longitude.) Exstensive-enough experimentation would reveal the curvature of space, but (as per Flat Earthers) a sufficiently limited amount of observation upon a laege enough sphere allows for assumption of flatness, or dismissal of borderline signs of non-flatness as being mere optical illusions to the limits of localised understanding
I was talking about uniqueness of rest frames, why are you talking about uniqueness of points?

On a sphere, unlike a cylinder, every direction has a unique rest frame in which the "circumference" in that direction is maximal. Moving relative to this rest frame makes the circumference seem smaller, thanks to length contraction. The privileged rest frame of the universe is then the one that is at rest in every direction

Maybe, though, consider that surface as 'co-nows' to your here-and-now (out of your light-cone) as time progresses radially the surface travelling outwards (or inwards, making time's arrow ultimately differentiable as you've headed from an infinite past to a definite singularity future destination) the actual great-circles you follow are 'great-'spirals through the expanding universe.
The problem with this is that it doesn't account for relativity in any way. Sure, that's what it looks like from the perspective of the global rest frame (which at least in this case exists, unlike if the universe is flat or open), but it doesn't capture the details of how such a universe would look to anyone moving around one of those "spirals".

Which is almost certainly not how the Real World is (if it bears any artful resemblence, there'll be other twists to the actual story) but makes for an interesting thought model all the same.
Are we at the "almost certainly" level of confidence with regard to whether the universe is or is not closed?
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Re: Yet another FTL question...

Postby Soupspoon » Thu Apr 26, 2018 6:36 pm UTC

I'm seeing you argue against things I didn't say, again. I'm deciding it's definitely my fault. Again.

(Also took ages to find the post giving me the "Notifications [1]", didn't appear under the relevant Quick links linking, perhaps as I'm sure I read your message before it may layer have been invisibly edited to include my quote and activate the Notification. As it originally stood, it seemed fair enough to say it was "a lot of words", it was a lot of concept trying to to be conveyed. And not well enough at that. I'd nothing worth saying in rebuttal to that.)

That there's no seam/wrap-around point(/line/boundary) is part of it. I was trying to say that even from the PoV of the Creator (who knew precisely where the substrate is melded, by Their own hand) that junction ends up becoming arbitrary and inconsequential when drawing lines and the like around the curve. And does the privilige from the curvature matter when there is no reasonable possibility of communications passing all around that wrap? (IRL, see the theories surrounding the structure of the CBR, as to whether, or how much, it was possible for the newly transparent universe to equalise itself enough to exhibit what we see. Or in an equal matter/anti-matter universe whether we can possibly be in the midst of a matter-dominated region far enough away from the boundary to antimatter-dominated region(s) to not see the evidence of the continuing annihilation.)


But I risk confounding things, just for the sake of trying to put right my own sloppy and hastily constructed descriptions, in a manner risking further sloppiness and over-hasty construction. It requires wrapping spacetime for this thought experiment, which is theoretical at best. And don't mistake my description of a radial-time hypersphere for a closed universe (there's a latitudinal-time version of the hypersphere that is truly closed, singularities at both poles for big bang and big crunch, but if expansion is as observed it might be better modelled as a bell-like shape, lacking the end-closure as it splays out and then effectively ends due to the Big Rip effects, maybe).

Depicting it as a sheet (in whatever form) in the next dimension out capable of handling the various dimensions in the sheet is just the mathematical trick necessary to encompass the various models being discussed in a visualisable form. I'm not crediting the 'off sheet' space, surrounding it, with existence outwith the universe. It's just easier to imagine looking down upon an endless Escheresque tiled plane entirely of interlocking dragon-shapes than the equivalent task of an entire volumetric dimension of nothing-but-dragons all squished together with no 'outer dragons' at all.


But, if I may repeat myself, before abandoning any further long-winded defence of my drawn-out attempted explanation of my expanded description of my original interesting (or so I thought) aside…:
Soupspoon wrote:It also doesn't help with the OP's question (any more than already helped, which I thought was sufficient) but I thought that perhaps it'd be interesting to consider the extended problem, without realising I would inadvertently start a discussion more existential than theoretical. :oops:


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