Trying to understand how FTL would violate causality....

[OCR]

They agree with me, not you...

Perfectly fine... but I agree with me.

Lol... they seem to have an affect, though...

Emojis don't strengthen your argument.

 

[PAllen]

I don't understand whether the assumption of a "block universe" is being made in these time transportations of documents. If a copy of the play exists today and we were to travel "back in time" then would we not pass through the states the involve how the copy of the play was created in reverse order? So when we arrived in the remote past, our copy of the play would no longer exist - nor would we, for that matter.

By that line of thinking, a time traveler cannot arbitrarily decide to create an information paradox because when he "goes back in time", he may go back in a path that "un-creates" the information he wishes to transmit as well as un-creates himself. That still leaves open the possibility that a "lucky" time traveler might find a way to go back to a state where he exists - e.g. go back to a day in Shakespear's life that never existed in any other way except being a day when the time traveller was present. However, this only shows that time travel does not rule-out certain paradoxes. It doesn't show show such paradoxes would definitely exist. Such paradoxes might be prevented by other physical laws.

I am making the assumption of block universe. This means, ipso facto, that there is only one version of any spatial hypersurface. However, it does not mean there is any undoing if CTCs are present. They are simply paths in the manifold the are timelike everywhere but can end up at or near an earlier event on the same world line. There is forward aging all along such world line. In this sense you don't really decide to create an information paradox; instead the universe simply contains one. At some level, information paradoxes are unavoidable if CTCs really exist.

 

[puzzled fish]

No, that's not what I'm saying. Look at the timeline again. That is the timeline of copy #313 (or whichever copy you took with you). Look at the calendar years: in every year from 1620 through 2020, copy #313's timeline intersects that year twice, not once. There is only one timeline, but that timeline crosses those years two times. Each of those crossings is part of copy #313's timeline. From the standpoint of any of those years, considered as a spacelike surface, there are two copy #313's. One of them is the one labeled by some proper time year from 0 to 400, in other words, the "original" one that was printed and which you are going to take back in time with you. The other is the one labeled by some proper time year from 430 to 830 (I just realized I originally labeled those years wrong, I've gone back and fixed them), which is in the vault and stays in the vault indefinitely.

Please re-write your list. I do not understand. There is a contradiction in it. How do I travel back with a book labelled 0 years when I bought it from a bookstore with 380 years on it (second line)?
To cut a long story short, the only way out of this paradox that I am aware of, is only when there is not a considerable amount of infrormation to be transmitted. Eg. you find an equation in a book, learn it by heart, travel in the past, write it down on a blackboard, it's a wave equation, Maxwell is becoming aware of it, end of the story. No books, no media, no press. I think this is the essence of what PAllen is trying to say, but his example was very complicated.

 

[PeterDonis]

How do I travel back with a book labelled 0 years when I bought it from a bookstore with 380 years on it (second line)?

You aren't reading the timeline. Read it again. When you step into the time machine, the book is labeled 400 years, not 0.

 

[PeterDonis]

I think this is the essence of what PAllen is trying to say

No, it isn't. There is no need to limit the complexity of the information.

 

[Stephen Tashi]

They are simply paths in the manifold the are timelike everywhere but can end up at or near an earlier event on the same world line.

It's the "at" a earlier event that's the problem for perspective time travellers. They have to gamble that there is an earlier state of the universe where they were present.

At some level, information paradoxes are unavoidable if CTCs really exist.

I see that information paradoxes aren't prevented if CTCs exist. I don't see any proof that information paradoxes must exist. I don't see any demonstration that a paradox can be created at will by a time traveller. To suppose that a time traveller goes "back in time" is one thing. To suppose he goes back in time and takes things with him and continues to exist himself is assuming more.

 

[PAllen]

It's the "at" a earlier event that's the problem for perspective time travellers. They have to gamble that there is an earlier state of the universe where they were present.



I see that information paradoxes aren't prevented if CTCs exist. I don't see any proof that information paradoxes must exist. I don't see any demonstration that a paradox can be created at will by a time traveller. To suppose that a time traveller goes "back in time" is one thing. To suppose he goes back in time and takes things with him and continues to exist himself is assuming more.

They don't need to gamble. If there are CTCs they can access, and they feel like doing so, then they must 'have' done so.

If any substantial body goes back in time and interacts with things, you have events that are influenced by their future an also influence their future. This is tantamount to an information pradox.

 

[Stephen Tashi]

They don't need to gamble. If there are CTCs they can access, and they feel like doing so, then they must 'have' done so.

If any substantial body goes back in time an interacts with things, you have events that are influenced by their future an also influence their future. This is tantamount to an information pradox.

You resorted to "if" to give those examples. I agree that if a time traveller did find a path to go back in time to a day when he, Shakespeare, and the time traveller's copy of Julius Caesar did exist then an information paradox could exist. However, I don't see the proof that such a path must exist if FTL travel is possible.

I return to the question of what state space is being discussed in the notion of time travel. Does going back in time mean going to a previous state of the universe, where "state" means a complete physical description of the universe? - including the detail of whether the time traveller is present in that state?

 

[Ibix]

Why isn't this possible? I inherit a note saying: Dear Mr Shakespeare, Please duplicate this note and give the copy to Mr John Ibix (my great-great-whatever grandfather). However, in the copy please add 1 to this number: 1. Then please destroy this original. Then I put the note in a time machine and send it back to Shakespeare.

If Shakespeare follows the instructions the result seems genuinely paradoxical. What would an observer outside the CTC see on the note?

 

[Ibix]

Doesn't this also apply to say, waves on a rope? The rope isn't getting any closer even though the waves seem to be moving toward you.

I don't see the analogy. The flipbook with wrinkled pages represents spacetime and has a concept of time built into itself. We see the gravitational wave passing us because we see one page of the book[1] at a time and compare it to our memories of previous pages. GR just describes the whole book, with the wrinkle, in one go.

[1]Our past light cone, more precisely.

 

[PeterDonis]

I return to the question of what state space is being discussed in the notion of time travel.

Remember that we're discussing this in the context of GR, where spacetime is a single 4-dimensional manifold. We're discussing the case where this manifold happens to have timelike paths that loop back around so that they intersect the same spacelike hypersurface more than once. But each spacelike hypersurface, which is the closest thing to a "state of the universe" in this model, is what it is: a given timelike curve intersects it a well-defined number of times, and that is an invariant fact about the spacetime.

Does going back in time mean going to a previous state of the universe, where "state" means a complete physical description of the universe? - including the detail of whether the time traveller is present in that state?

It should be evident from the above that the answer to this is "yes" (reading "state" to mean "spacelike hypersurface").

 

[GTOM]

Well, not according to this one.

https://arxiv.org/abs/1407.2528

If that is crackpottery, at least i'd like to know why is it, because i only saw mathetmaics and implications.

Otherwise does relativity truly show that time is more than the changing of things? Yes time slows down at big speeds, near a black hole, but is it really more than electromagnetic based interactions slow down under theese conditions? Our measurement of time and everything else depends on electromagnetic based interactions.

 

[PAllen]

You resorted to "if" to give those examples. I agree that if a time traveller did find a path to go back in time to a day when he, Shakespeare, and the time traveller's copy of Julius Caesar did exist then an information paradox could exist. However, I don't see the proof that such a path must exist if FTL travel is possible.

"Must" is too strong a claim. Sorry if I implied that. However any material object occupying an exact CTC is itself an information paradox. You have a structured odbject without origin. You can, of course, add rules that say this can't happen. However most physicists believe it is CTCs themselves that are prevented in the real world. For example, if the dominant energy condition is mostly true, and the perturbatively stable variants of Kerr interior avoid CTCs, all cases are prevented. Personally, that is what I would bet on.

 

[PAllen]

Why isn't this possible? I inherit a note saying: Dear Mr Shakespeare, Please duplicate this note and give the copy to Mr John Ibix (my great-great-whatever grandfather). However, in the copy please add 1 to this number: 1. Then please destroy this original. Then I put the note in a time machine and send it back to Shakespeare.

If Shakespeare follows the instructions the result seems genuinely paradoxical. What would an observer outside the CTC see on the note?

This is where the block universe comes in. If there is one note whose world line begins in 1590, is then passed to your ancestor, then sent back in time, and destroyed in 1590, then it can have only one thing written on it. Shakespeare wrote one thing on it, and that is the only state it has. Whatever Shakespeare's internal perception is, he would effectively ignore the instruction, simply because that is what he did. Block universe erases true free will, which is certainly related to how it implements the chronology protection conjecture.

 

[puzzled fish]

You aren't reading the timeline. Read it again. When you step into the time machine, the book is labeled 400 years, not 0.

Yes, I've read the timeline again and it seems to me exactly identical to Pallen's answer.
I've explained myself before that a near CTC allows two objects to co-exist, I have no objection to that. My objections is to the making of the copy itself. Copying is a procedure that requires a tremendous amount of interactions with the original object. And suppose that a block-universe is constructed in such a way that past-present is inter-woven in a way as to account for those interactions. I find, macroscopically, the probability that I might be able to reproduce an exact identical copy of a complex object like a book, to be 0 (almost.. very).
By the way, I like post #99 very much. It is like my aging copy example. What do you have to say about this?

 

[puzzled fish]

This is where the block universe comes in. If there is one note whose world line begins in 1590, is then passed to your ancestor, then sent back in time, and destroyed in 1590, then it can have only one thing written on it. Shakespeare wrote one thing on it, and that is the only state it has. Whatever Shakespeare's internal perception is, he would effectively ignore the instruction, simply because that is what he did. Block universe erases true free will, which is certainly related to how it implements the chronology protection conjecture.

What if it's not destroyed? What if it's the same object coming back and forth in a perfectly closed CTC? How old must it be at a given point on its own CTC? 400? 800? 1200?

 

[PAllen]

Yes, I've read the timeline again and it seems to me exactly identical to Pallen's answer.
I've explained myself before that a near CTC allows two objects to co-exist, I have no objection to that. My objections is to the making of the copy itself. Copying is a procedure that requires a tremendous amount of interactions with the original object. And suppose that a block-universe is constructed in such a way that past-present is inter-woven in a way as to account for those interactions. I find, macroscopically, the probability that I might be able to reproduce an exact identical copy of a complex object like a book, to be 0 (almost.. very).
By the way, I like post #99 very much. It is like my aging copy example. What do you have to say about this?

But yet again, there is no copying. Is there some physical copying going on as you age 1 second? In a CTC, it just happens that two points of the history of an object (which is all forward moving in proper time for the object) are accessible simultaneously for some other frame. THERE IS NO COPYING AT ALL!

 

[Stephen Tashi]

What if it's not destroyed? What if it's the same object coming back and forth in a perfectly closed CTC? How old must it be at a given point on its own CTC? 400? 800? 1200?

How are you defining "age"? If the "age" of an object is defined by its physical condition, then at each point on the curve, the object has one-and-only-one physical condition.

 

[PAllen]

What if it's not destroyed? What if it's the same object coming back and forth in a perfectly closed CTC? How old must it be at a given point on its own CTC? 400? 800? 1200?

If it's not destroyed, and it is an exact CTC, rather than a near CTC loop back in time for relevant observers, then a thermodynamic anomaly is inherently present. The object achieves an exact microstate it had before. This Is a feature of an exact CTC, and a good reason to be skeptical, but it does not entail any paradox or violation of fundamental laws - the anomly is statistically bizarre, but no micro-laws of physics are violated.

 

[puzzled fish]

If it's not destroyed, and it is an exact CTC, rather than a near CTC loop back in time for relevant observers, then a thermodynamic anomaly is inherently present. The object achieves an exact microstate it had before. This Is a feature of an exact CTC, and a good reason to be skeptical, but it does not entail any paradox or violation of fundamental laws - the anomly is statistically bizarre, but no micro-laws of physics are violated.

Now, we thoroughly agree. As hard as it is for me, to understand how such things can happen for complex objects, I have to admit that there is always a possibility, although like I said, it's almost nil.

 

[PeterDonis]

My objections is to the making of the copy itself.

I don't understand why, since the making of all the copies in this scenario, as I've already pointed out, is a perfectly mundane process that goes on all the time in our actual world. If you disagree, please point out specifically which copying operation in my timeline you think requires something that is extremely unlikely.

 

[PeterDonis]

What if it's the same object coming back and forth in a perfectly closed CTC?

Then you are talking about a different scenario, in which Shakespeare never writes the book at all, nor does anybody else; it never gets created or destroyed, it just loops around in an exact CTC. In this scenario there is still no copying, but it becomes very difficult to explain the book's existence, because of the thermodynamic issue that PAllen described. The timeline I gave does not apply to this scenario at all; it applies to the original scenario you described.

How old must it be at a given point on its own CTC? 400? 800? 1200?

In this scenario (which, as above, is not the one I described in my timeline), there is no well-defined "age" of the book at any point on its CTC. You can label points on the CTC with "time" values (from 0 to 430), but they are not "ages" in any useful sense, because, as I noted above, the book never gets created in this scenario at all, so there is no point that is picked out as "zero age". The CTC is just a loop, and you can start your "time" coordinate labeling at any point on the loop.

 

[puzzled fish]

I don't understand why, since the making of all the copies in this scenario, as I've already pointed out, is a perfectly mundane process that goes on all the time in our actual world. If you disagree, please point out specifically which copying operation in my timeline you think requires something that is extremely unlikely.

380 / 2000: You find the printed book in a used book store and buy it.
...
810 / 2000: The printed book is in the vault.

You just have to add #313 next to "the printed book" to see what I mean : the printed book #313.
Furthermore, you can open the vault in 2000, and corroborate that any differences are owed only due to aging. How likely is that, given that Shakespeare copied the book from his own manuscript that he copied from book #313?
I thoroughly agree with your post #112 as with PAllen's answer. See #110.
By the way, thank you both for your answers.

 

[PeterDonis]

380 / 2000: You find the printed book in a used book store and buy it.
...
810 / 2000: The printed book is in the vault.

Neither of these are copying operations. The two copying operations in my timeline are:

0 / 1620: The printed book containing Shakespeare's play is created, using his manuscript of the play as a source.
...
401 / 1591: You show Shakespeare the printed book, and he copies out his manuscript of the play from it.

you can open the vault in 2000, and corroborate that any differences are owed only due to aging. How likely is that, given that Shakespeare copied the book from his own manuscript that he copied from book #313?

Ah, I see; you are talking, not about how accurate either copying process--book #313 to Shakespeare's manuscript, then Shakespeare's manuscript back to book #313--is in itself, but how accurate their combined result has to be, since it has to be equivalent to a copying operation composed with its exact inverse (because the content of book #313 itself must be unchanged). Yes, I agree this is very unlikely; it's basically a somewhat weakened form of the thermodynamic objection in the exact CTC case. But, as has been pointed out, this doesn't violate any physical laws; it's just statistically very unlikely.

 

[puzzled fish]

Neither of these are copying operations. The two copying operations in my timeline are:

0 / 1620: The printed book containing Shakespeare's play is created, using his manuscript of the play as a source.
...
401 / 1591: You show Shakespeare the printed book, and he copies out his manuscript of the play from it.
Ah, I see; you are talking, not about how accurate either copying process--book #313 to Shakespeare's manuscript, then Shakespeare's manuscript back to book #313--is in itself, but how accurate their combined result has to be, since it has to be equivalent to a copying operation composed with its exact inverse (because the content of book #313 itself must be unchanged). Yes, I agree this is very unlikely; it's basically a somewhat weakened form of the thermodynamic objection in the exact CTC case. But, as has been pointed out, this doesn't violate any physical laws; it's just statistically very unlikely.

Thank you very much Peter. We are both in agreement now. It can happen... Just very unlikely!

 

[Battlemage!]

If the invariant speed were something different from c, then light would have to have varying speed, in general, either like neutrons or like sound (it would only be c and isotropic in the medium rest frame). Such a universe is conceivable, but it is radically different from ours. The derivations of the Lorentz transform (including the limiting case of Galilean for infinite invariant speed) assuming only isotropy, homogeneity and POR, establish that there can only be one invariant speed.

In this imaginary universe I am assuming the speed of light is really, really close to maximum speed, to the point that we couldn't tell the difference with our current technology. Would/could that happen (that is, is such an imaginary universe self-consistent)?

In any event, would such a world have casualty violations?

 

[Herman Trivilino]

In this imaginary universe I am assuming the speed of light is really, really close to maximum speed, to the point that we couldn't tell the difference with our current technology. Would/could that happen (that is, is such an imaginary universe self-consistent)?

In any event, would such a world have casualty violations?

If we were to discover that light travels at some speed that's a bit less than the maximum possible speed nothing in the theory of relativity would change. The speed $c$ that appears in the formulas would simply be the maximum speed instead of the speed of light.

 

[Nugatory]

In this imaginary universe I am assuming the speed of light is really, really close to maximum speed, to the point that we couldn't tell the difference with our current technology. Would/could that happen (that is, is such an imaginary universe self-consistent)?

As phrased, your question is inconsistent because if the speed of light is not exactly equal to the invariant maximum speed $c$, then its value is necessarily frame-dependent (as are all speeds less than $c$). Thus, there will exist frames in which light travels at speeds arbitrarily close to zero, and the hypothesis "the speed of light is really, really close to the maximum speed" is ill-formed.

 

[nitsuj]

who wrote the play? No one - it just exists without authorship.

I imagine that comment could apply to things seen in particle physics. for the play to have no author it MUST have once had one...buried in the physics there seems to be causation.

This all seems so similar to what I envision black hole surface physics to be...if Earth fell onto a black hole and humpty dumpty tried to piece it all back together again it would be all like "it just exists without authorship" for every worldline traced back.

This thread illustrates that telling of spacetime coordinated events can make a confusing story. This sounds like the story telling of a photon or something.

 

[Dale]

If we were to discover that light travels at some speed that's a bit less than the maximum possible speed

As @Nugatory mentioned, this is not exactly the way to say it, but it is pretty close. The way to say what you want to say "If we were to discover that the photon has some extremely small but non zero mass"