Physicists Theorize New Method for FTL Travel

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New method would not break Einstein's Theory of Relativity

Virtually all science fiction that involves intergalactic travel or convenient travel between planets in our own solar system revolves around faster than light travel. One problem with many theories for faster than light travel is the proposed methods would violate Einstein's Theory of Relativity.

Two physicists from Baylor University have theorized what they believe to be a method of faster than light travel that would not break the Theory of Relativity. Einstein's Theory of Relativity states that objects accelerating to the speed of light require an infinite amount of energy.

The physicists -- Gerald Cleaver and Richard Obousy -- have theorized a new idea for faster than light travel that involves manipulating dark energy to propel a spacecraft . According to Space.com the universe -- in theory -- moved faster than light for a short time after the Big Bang, propelled by dark energy which represents about 74% of the mass energy budget in the universe. Space.com goes on to say that, 22% of the mass energy budget consists of dark matter and what remains of the mass-energy budget in the universe being made up of stars, planets and other things we see.

. . .
-xCross
Source: http://www.dailytech.com"
 
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Interesting, but any form of FTL also allows for time travel, which suggests to me, anyway, that it is very unlikely.
 
CJames said:
Interesting, but any form of FTL also allows for time travel, which suggests to me, anyway, that it is very unlikely.

Why? I never understood that connection.
 
As I understand it, if you can travel outside of your own future light cone, than from some reference frame you are traveling backward in time. And if you can travel backward in time in one reference frame, you can do it in all of them.
 
K.J.Healey said:
Why? I never understood that connection.
It's kind of obvious if you think about it properly. Imagine looking at a distant star. You see it as it was long ago in the past. Now imagine somebody would leave this star at a certain time in a frame where both you and the distant star are at rest, and travel faster than light towards your planet. He would reach you before the light carrying the image of him leaving even made it. When he would look back, he would see that distant star as it was before he even left ! Therefore, he could also come back to the distant star at another point in space on his planet at the moment he left. Faster than light travel would thus amount to both time travel and also to teleportation. All those are somehow equivalent.
 
Where is their paper? The only source I see is space.com and in a quick search I didn't have a lot of luck with finding any of their actual work. Whatever they're doing I doubt it is the way space.com depicts it, or if it is I doubt that they actually have proposed a mechanism for performing the act they want to perform (i.e. maybe this is just another case of "if you can do N impossible thing, you can travel faster than light". The revelation that if you can do one impossible thing you can do other impossible things also is not surprising...)
 
Coin said:
Where is their paper?

Here is a link to one of their papers: http://arxiv.org/abs/0712.1649. There is also a more popular one, posted to the popular science section of the arxiv.
 
cristo said:
Here is a link to one of their papers: http://arxiv.org/abs/0712.1649. There is also a more popular one, posted to the popular science section of the arxiv.
Thanks!
 
xCross said:
New method would not break Einstein's Theory of Relativity

Dead on arrival, I'm afraid. If it's faster than light it implies closed, or nearly closed, timelike curves in a spacetime. And global hyperbolicity doesn't jive with those curves.
 
  • #10
Rich is floating around these fora, although I haven't seen him lately.

You might send a PM to robousy and see if he will join the discussion :)
 
  • #11
What would happen if I threw in the hypothetical tachyon? any response/explanation from someone far more experienced than me? From what I have heard, it arrives at its destination before departure, but what property would allow it to do that that the massless photon has not? charge?
 
  • #12
Questman said:
What would happen if I threw in the hypothetical tachyon? any response/explanation from someone far more experienced than me? From what I have heard, it arrives at its destination before departure, but what property would allow it to do that that the massless photon has not? charge?

non-zero imaginary-valued mass
 
  • #13
So the tachyon has imaginary mass, and the photon has no mass, ergo no volume. Why isn't it a point particle? and if I i am right (which I most likely am not) if it has no volume, how can it be real?
 
  • #14
I've been thinking that dark energy was "the key" to FTL travel. It seems pretty obvious, since dark energy allows the Universe to expand faster than the speed of light...
 
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  • #15
I understand that in Special Relativity, moving faster than light (that is, traveling out of your light cone, which is tachyonic motion) implies time travel. However, how is this also the case with Warp Drives and Wormholes (which do not need tachyonic motion of the traveller)?
 
  • #16
Emanresu56 said:
I've been thinking that dark energy was "the key" to FTL travel. It seems pretty obvious, since dark energy allows the Universe to expand faster than the speed of light...
Isn't it actually space-time itself that's expanding? So things aren't actually moving away from each other, but the space between them is getting bigger.
 
  • #17
Not that I am a fan of FTL travel but
Emanuel said:
Isn't it actually space-time itself that's expanding? So things aren't actually moving away from each other, but the space between them is getting bigger.
is it not exactly the best hope for FTL travel ?!
 
  • #18
Questman said:
the photon has no mass, ergo no volume.

The electron has a non-zero mass, but it also has no volume in our current theories (it is described by a point-like particle). It turns out that there is no meaningful quantum analogue to volume.

Why isn't it a point particle? and if I i am right (which I most likely am not) if it has no volume, how can it be real?

The photon is a point particle. It has no volume and it is real, and as I have explained this is because quantum mechanics. Before going "beyond the standard model", I think you would enjoy learning about quantum mechanics.
 
  • #19
Just noticed you guys talking about a paper we brought out in 07. Nice to see some interest.

I thought I'd jump in and address some issues that seem to be cropping up.

We avoid issues of CTC's and the grandfather paradox by placing the hypothetical spacecraft inside a bubble of asymmetric expanding and contracting spacetime analogous to the Alcubierre bubble. This link should help in visualizing the concept. A stationary spacecraft with the ability to create such a bubble would always move inside its own light-cone, thus avoiding said problems.

Our approach was similar in spirit to the Morris-Thorne-Yurtsever wormhole paper (Phys.Rev.Lett.61:1446-1449,1988) in the sense that our starting point was the question: "What limitations the laws of physics places an arbitrarily advanced civilization?" i.e imagine a technology that could achieve 'anything' as long as it did not defy the known laws of physics. What could it do?

What makes this work unique and original is the fact that we adopt an approach that is fundamentally quantum field theoretic in nature, which contrasts to the traditional GR approach taken by previous warp drives papers. Casimir energy, extra dimensions and dark energy play a critical role in our model, and the combination of ideas has never been explored in this context.

Another important aspect of this work was the fact that many young people feel that physics is 'boring', 'difficult' and 'irrelevant', and thus an unattractive career option. We believe that the exploration of novel ideas in interstellar propulsion, using advanced physics, encourages new minds to enter our subject. Indeed, this was our main reason for writing the 'laymans version you can find here.' The aim being to make these ideas accessible to a wider audience. We also felt that for those already studying physics, that this work would encourage them to tackle the subjects traditionally considered to be more challenging, i.e. GR, QFT and string theory.

Rich
 
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  • #20
CJames said:
Interesting, but any form of FTL also allows for time travel, which suggests to me, anyway, that it is very unlikely.
Why do you think that time travel is unlikely? Because of the causal paradoxes? I don't think that time travel leads to any causal paradoxes:
http://xxx.lanl.gov/abs/gr-qc/0403121 [Found.Phys.Lett. 19 (2006) 259-267]

I fact, I think that "causal paradoxes" are an artefact of a failure to distinguish two very different notions of "time", where only one of them is really physical:
http://fqxi.org/community/forum/topic/259
(see PDF)
 
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  • #21
I distinguish between movement and connection over a static field. A static field connects, but doesn't move. Light passes through space and can't be faster than c in the frame of reference of the sender. In respect to itself it stands still. Now think, that the space we observe isn't 'reality', but spacetime itself. In that 'space' we have infinity as speed of a connection and c as speed of observed movement of light in the reference frame of the observer.
So we can't move faster than c in the FoR of earth, but once in movement, we don't move at all (in respect to ourselfs), since than we would be the ones, that measure time.
So in this spacetime view, we have a universal simultinaity with infinite speed over static fields and c is only a limit for light in vacuum in respect to any observer.
 
  • #22
Demystifier said:
Why do you think that time travel is unlikely? Because of the causal paradoxes? I don't think that time travel leads to any causal paradoxes:
http://xxx.lanl.gov/abs/gr-qc/0403121 [Found.Phys.Lett. 19 (2006) 259-267]

I fact, I think that "causal paradoxes" are an artefact of a failure to distinguish two very different notions of "time", where only one of them is really physical:
http://fqxi.org/community/forum/topic/259
(see PDF)

This is correct, I've also recommend this: http://en.wikipedia.org/wiki/Novikov_self-consistency_principle

However, Novikov speculates about billard balls, but what happens to entropy in the closed time-like loops?

Also, it could be an interesting way to test different interpretations experimantally. For example, I suspect that transactional interpretation should give different results in such conditions. Also, as noted in the article, it is not known if Novikovs principle is consistent with MWI.
 
  • #23
robousy said:
We avoid issues of CTC's and the grandfather paradox by placing the hypothetical spacecraft inside a bubble of asymmetric expanding and contracting spacetime analogous to the Alcubierre bubble. This link should help in visualizing the concept. A stationary spacecraft with the ability to create such a bubble would always move inside its own light-cone, thus avoiding said problems.

Careful, this, by itself, is not sufficient to prevent Closed Timelike Curves. In fact, the whole point behind CTCs is that it's possible for an observer to travel into the observer's past while staying within the observer's future light-cone. In other words, there is an event p on the observer's worldline such that the intersection of the past and future light-cones at p is non-empty.
 
  • #24
Dmitry67 said:
but what happens to entropy in the closed time-like loops?
For an outside observer, at some point entropy reaches its maximum, after which it starts to decrease. But this is not how it will be perceived by an observer whose brain entropy also behaves in that way. Instead, it will be perceived as TWO observers that eventually meet and die at the point of maximum entropy.

Dmitry67 said:
Also, as noted in the article, it is not known if Novikovs principle is consistent with MWI.
It is consistent with MWI. In this case, the Novikov principle is to be applied to the wave function.
 
  • #25
Demystifier said:
For an outside observer, at some point entropy reaches its maximum, after which it starts to decrease. But this is not how it will be perceived by an observer whose brain entropy also behaves in that way. Instead, it will be perceived as TWO observers that eventually meet and die at the point of maximum entropy.

WOW, what I marked BOLD was unexpected to me - I did not think about it - but it must be true as our perception of time just point in the direction where entropy increases.

So 1 of the split-observers is a unique conditions - his personal time is another direction as physical time. He would see the whole universe (outside the loop) rolling back in time...

But it would be really interesting to trace light rays to understand, what would observers actually see. It is especially interesting how he would see his 'twin'.

What can you say about the splitting event, when 1 observer is 'split' into 2? Did you think about drawing some diagrams to better understand it? What can you say about the memories of these observers?
 
  • #26
Dmitry67 said:
What can you say about the memories of these observers?
At each time, they remember the stuff that occurs when entropy is lower than the entropy at that time. Unfortunately, for obvious reasons I cannot draw it here.
 
  • #27
Dmitry67 said:
What can you say about the splitting event, when 1 observer is 'split' into 2?
At that time, one can say that they become 2 independent persons.

(By the way, something similar happens in real life, for humans whose connections between the two halves of the brain are cut in a surgery. They also show some behavior of two independent persons.)
 
  • #28
No, they can not be 2 independent persons

Lets call these 2 observers F (forward) - normal observer and B (backward)
F experience 3 events X,Y,Z and he remembers these events.
He collides with B and the point with max entropy. B and F must be consistent there, hence, before they meet B also remembers events X,Y,Z!

So observer B should get the same experiences as F, otherwise he would not be identical to F when they meet. At the same time, B can witness other events P,Q,T. Do you see the problem here?
 
  • #29
Dmitry67 said:
No, they can not be 2 independent persons

Lets call these 2 observers F (forward) - normal observer and B (backward)
F experience 3 events X,Y,Z and he remembers these events.
He collides with B and the point with max entropy. B and F must be consistent there, hence, before they meet B also remembers events X,Y,Z!

So observer B should get the same experiences as F, otherwise he would not be identical to F when they meet. At the same time, B can witness other events P,Q,T. Do you see the problem here?
Yes, I do see a mistake in your reasoning. Just before the collision, B remembers P,Q,T, while F remembers X,Y,Z. There is nothing inconsistent with it. But at the point of collision, they merge and become one person that remembers both X,Y,Z and P,Q,T. After that, they die. (In fact, taking into account a finite extension of their bodies, they probably die slightly before their brains get chance to become one person, which makes the whole scheme even more intuitive.)
 
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  • #30
Well, I have to completely rethink what we were talking about.

So we have a time loop. How a spaceship appeared there in a first place? It came from the outside. If you draw his world line, can it end with a circle, like in a character "P" ? No, because in the point where his 'entry" worldline is 'attached' to the circle the law of conservation of energy is violatated: 2 objects become one.

So, for the sake of consistency and Novikov's principle after a full circle spaceship *must* appear at the same time, but in some other place. Time flows normally inside a spaceship and entropy always increases. So even there are timelike loops, matter can not make a full loop, it always spirals... Oly matter which originally was inside the loop can form a loop.

Pilot will be able to see another copies of 'his' spaceship(s) and communicate with them in a consistent manner. If he tries to violate the consistency, he would see that it is preserved (something must happen, like radio becomes dead suddenly, a cloud blocks light for sometime etc).

If pilot decides to go away from a loop then the number of copies inside the loop is limited. If not, then energy diverges, and there are 2 options: 'extra' matter leaks outside the loop because of the heat or degeneracy pressure, or a loop collapses and becomes a black hole.
 
  • #31
robousy said:
Another important aspect of this work was the fact that many young people feel that physics is 'boring', 'difficult' and 'irrelevant', and thus an unattractive career option. We believe that the exploration of novel ideas in interstellar propulsion, using advanced physics, encourages new minds to enter our subject.
Don't write checks you can't cash. Any FTL craft is a time machine in an appropriate frame OR you are breaking Lorentz covariance. Invoking entropic time doesn't change this unless you are asserting that the entropy of the entire region across which the flight occurs is being affected (i.e. the attempt causes a BIG Bang.) Two "jumps" (with an intermediate boost) puts you into your own past (and the boost can be replaced with a communication to a second craft.) It doesn't matter if your craft is locally STL due to some funny warp bubble effect.

The Nikolic entropic time paper cited is IMNSHO being misinterpreted. It doesn't provide an "out" for FTL causality paradoxes. It rather seems to impose more restrictions on causal ordering which would imply an impossibility of globally FTL paths being causal even if they are locally STL. (I think the Nikolic paper may relate to the 2nd horizon in certain black-hole/worm-hole solutions where you hit an infinite temperature though you avoid the singularity.)

The basic idea of FTL travel is that you jump in a ship at point A and arrive at point B faster than light could travel by a direct path. Specifically you get ahead of the sphere of light emitted by the television coverage of your departure.

Saying one travels there via some modification of local space-time around the craft doesn't matter. If the arrival event at B is outside the future light cone of the departure event at point A then you can boost the whole mechanism of travel (assuming local Lorentz covariance) so that the arrival event is prior to the departure event and then reverse the boost and reverse the trip so as to arrive at A prior to the original departure.

If this is avoided it must be due to an additional restriction, one which breaks Lorentz covariance and thus you are working with a new theory of physics. Give the rules and empirical predictions so it can be tested. But don't claim FTL is consistent with current tested physics AND avoids causality paradoxes. (Maybe current tested physics is wrong. Maybe causality paradoxes are resolvable some other way...Maybe the universe ceases to exist when someone tries this...or maybe FTL travel is just plain impossible) but the paradox must be resolved in any talk of FTL travel. You can't wish it away by finding a unique mechanism of propulsion.

As to the "Warp Drive" paper by Obousy and Cleaver note that the picture of Alcubierre metric is via the Kaluza-Klein model equivalent to putting a gauge field (say electromagnetic for analogy) around the ship. There will necessarily be a charge distribution effecting this field and affected by it. It seems to me equivalent of the old cartoon lifting oneself by one's own suspenders approach (i.e. ignoring a reaction force). Put a positive charge on a boom in front of the ship, a negative charge on a boom behind the ship, and a negative charge on the ship...ignore the force of the booms and the ship is "pulled forward" but account for the reaction force necessary to maintain the configuration and the ship just sits there.

This might be avoided by allowing the ship to surf a wave but it will also dissipate this wave and cannot accelerate past the wave which will have a fixed speed <= c w.r.t. any outside observer. This is no different than the idea of pushing a light-sail with lasers or microwave transmitters stationed at home. (Now that is an interesting bit of physics!)

The paper is a lot of "gee wizzery" when you look at it with half an eye but it is just plain bad physics no matter how esoteric a theory it invokes.

As to physics being "difficult" it is very hard to be rigorous and careful of bias. As to being boring... well anything is boring unless you develop a passion for it. You can't tempt them in with candy which they'll later find is made of wax. You'll turn them off in the long term. What is worse you'll possibly turn them against science convincing them it has no substance.
 
  • #32
Dmitry67 said:
So we have a time loop. How a spaceship appeared there in a first place? It came from the outside. If you draw his world line, can it end with a circle, like in a character "P" ? No, because in the point where his 'entry" worldline is 'attached' to the circle the law of conservation of energy is violatated: 2 objects become one.
The world line has the shape of "O", not "P". The local energy-momentum conservation is not violated; you can interpret it as circulating.

Dmitry67 said:
So, for the sake of consistency and Novikov's principle after a full circle spaceship *must* appear at the same time, but in some other place. Time flows normally inside a spaceship and entropy always increases. So even there are timelike loops, matter can not make a full loop, it always spirals... Oly matter which originally was inside the loop can form a loop.
The consistency can be achieved even with true matter loops. The second law of thermodynamics cannot be globally valid and initial conditions cannot be chosen at will, but there is nothing inconsistent with it.
 
  • #33
jambaugh said:
The Nikolic entropic time paper cited is IMNSHO being misinterpreted. It doesn't provide an "out" for FTL causality paradoxes. It rather seems to impose more restrictions on causal ordering which would imply an impossibility of globally FTL paths being causal even if they are locally STL.
I certainly agree with the last sentence above. But it also does something more. It explains why exactly self-consistent solutions (required by the Novikov's principle) look as paradoxes to us. They look so because we are used to think on time as something fundamentally different from space. Instead, if you think of time merely as a fourth spatial coordinate, and if you think of Universe as a static 4-dimensional object, then no paradox with self-consistent solutions remains. Further, the paper argues that the ONLY reason why we are used to think on time as something fundamentally different from space is the fact that there is a thermodynamic time arrow, while there is no thermodynamic space arrow. Since the thermodynamic time arrow is not fundamental at all (but only corresponds to a property of the specific solution in which we live), it means that there is no fundamental reason to think on time as something different from space (except for the irrelevant opposite sign in the metric signature), implying that there are no true paradoxes with self-consistent solutions.
 
  • #34
Demystifier said:
The world line has the shape of "O", not "P". The local energy-momentum conservation is not violated; you can interpret it as circulating.

No
If it is "O" then spacehip had never entered this area from outside, it always existed there.
 
  • #35
Dmitry67 said:
No
If it is "O" then spacehip had never entered this area from outside, it always existed there.
Exactly. But such a solution is self-consistent, which is the only requirement.
Of course, your spiralling solutions are also self-consistent. Moreover, your spiralling solutions may be more interesting from the physical point of view. Still, O-solutions are possible as well.
 
  • #36
Demystifier said:
Exactly. But such a solution is self-consistent, which is the only requirement.
Of course, your spiralling solutions are also self-consistent. Moreover, your spiralling solutions may be more interesting from the physical point of view. Still, O-solutions are possible as well.

How exactly would it be possible?
 
  • #37
jambaugh said:
... Any FTL craft is a time machine in an appropriate frame OR you are breaking Lorentz covariance...

The basic idea of FTL travel is that you jump in a ship at point A and arrive at point B faster than light could travel by a direct path. Specifically you get ahead of the sphere of light emitted by the television coverage of your departure.

Saying one travels there via some modification of local space-time around the craft doesn't matter. If the arrival event at B is outside the future light cone of the departure event at point A then you can boost the whole mechanism of travel (assuming local Lorentz covariance) so that the arrival event is prior to the departure event and then reverse the boost and reverse the trip so as to arrive at A prior to the original departure.

Does anybody know if wormholes suffer from similar problems?
 
  • #38
Mr. Paradox said:
How exactly would it be possible?
You mean in practice, by acts of an advanced civilization? I am not saying that it is possible in that sense. All I'm saying is that such solutions of the equations of motion exist, so nature may (or may not) realize such solutions in reality. If you want, I can write such solutions explicitly. But if you are familiar with Fourier expansions of periodic functions, you can also do it by yourself.
 
  • #39
I add Dmitry67 conjecture :)
I state: There are no macroscopic objects without a history

An object without a history is an object, which exists exclusively inside a time loop. So it had been never created and its entropy does not always increase.

Remember my exaple with spiraling inside the time loop? I arrive inside a time loop and see a future copy of my ship. We fly close to each other, and someone arrives to my ship from a future ship. It is a guy called John Doe. he says "Hi, it is really cool here! I will never die, I am immortal! But don't forget to let me go after a full cycle, otherwise we create a causality paradox!"

I drink beer with him, and then I see my own ship - now it is a "past" copy of my ship. I let John Doe jump into that ship, saying farewell to him, then I hit a pedal to the metal and leave the time loop.

So who was that John Doe? He had no mother, father... How could he appear there in a first place? While it might be consistent with the Novikov's principle it sounds impossible.

So while world line of individual particles can be short cut, world lines of macroscopic objects never intersect and never form loops.
 
  • #40
i read this article somewhere too but its application will be unlikely as to travel FTL for 1 meter you need to have a size or mass (can't remember which one) the size of jupiter. obviously not feasible
 
  • #41
Dmitry67 said:
While it might be consistent with the Novikov's principle it sounds impossible.
If something sounds impossible, it doesn't mean that it IS impossible.
It sounds impossible to you because you are used to think that all events have their cause in the past. But this is only an illusion, caused by the fact that we live in a very UNTYPICAL universe in which entropy increases with time. In reality, there are no causes and consequences. There are only solutions of the equations of motion.
 
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  • #42
Demystifier said:
It sounds impossible to you because you are used to think that all events have their cause in the past. But this is only an illusion, caused by the fact that we live in a very UNTYPICAL universe in which entropy increases with time. In reality, there are no causes and consequences. There are only solutions of the equations of motion.

I agree with you regarding the nature of time.
However, I still don't believe in that John Doe.

The solution where during my spiraling I meet John Doe is mathematically possible, but the probability of it is not higher then the probability that a human being condense from atoms somehwere due to very lucky coincidence.
 
  • #43
Dmitry67 said:
I agree with you regarding the nature of time.
However, I still don't believe in that John Doe.

The solution where during my spiraling I meet John Doe is mathematically possible, but the probability of it is not higher then the probability that a human being condense from atoms somehwere due to very lucky coincidence.
But humans DO exist due to a lucky coincidence (irrespective of the time-travel issue), don't they? Unless God created them, in which case She can also create them in a loop.
So, in a loop, either there will be no humans at all (neither John Doe nor yourself), which indeed is the most probable option, or there will be many "copies" of them.
 
  • #44
Demystifier said:
But humans DO exist due to a lucky coincidence (irrespective of the time-travel issue), don't they?

Correct, but there was 13 billions years to filter out 'useful' coincidences
Time loops (around Kerr singularities) are very short.

P.S.
I've just realized, what if the Big Bang is actually an END of the Universe - we live in the epoque when the entropy decreases? :)
 
  • #45
Dmitry67 said:
Correct, but there was 13 billions years to filter out 'useful' coincidences
Time loops (around Kerr singularities) are very short.
Correct! So probably the loop will not contain any humans at all.
 
  • #46
Demystifier said:
Correct! So probably the loop will not contain any humans at all.

Except the ones coming there from outside
You CAN enter the time loop, even it is a loop.
 
  • #47
Dmitry67 said:
You CAN enter the time loop, even it is a loop.
How? :confused:
Can you describe the topology of such a universe?
 
  • #48
Demystifier said:
How? :confused:
Can you describe the topology of such a universe?

Sure. Check the image attached. yes, I know, my drawings are really bad.
But I did it in Paint using a mouse...

So, you see a naked ring singularity. When you approach it due to frame dragging the 'hourglass' rotate finally forming a closed timelike loop (red). Still, you can enter it approaching to it from outside (green line)

In other words, the timelike loop region can be absolutely "naked", there is no horizon preventing from going inside or outside from it.
 

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  • #49
Hm!
If I understood you correctly, the trajectory of a traveller is described by both the green and the red curve. However, there is something inconsistent with it. The problematic point is the point at which the two lines (green and red) meet. At that point, the traveller has TWO different 4-velocities, which means that this "solution" is not self-consistent. How do you comment on this?
 
  • #50
No, red line just shows 1 example of a timelike loop. Timelike loop region contains infinitely many different timelike loop trajectories, including intersecting trajectories.

So red like is just an example of one of them.

Green line shows that he entered that area, then it depends on his decision what to do (so it did not show what happened next to him).
 
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