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

[Grinkle]

You can't simply associate information transfer with a faster speed without rewriting all the laws of relativity.

I imagine not. I find the concept of time travel so intermingled with the concept of information travel that faster-than-light travel seems like an oxy-moron to me. I acknowledge that my cartoonish sound analogy is not valid even at a superficial level.

(edit spelling)

 

[nitsuj]

Grinkle, the speed of light has more fundamental significance than the speed of sound. You have things like time dilation which occur as you approach the speed of light, but nothing analogous as you approach the speed of sound. You can't simply associate information transfer with a faster speed without rewriting all the laws of relativity.

it was an analogy, and a good one.

 

[Denis]

Faster than light information transfer is unproblematic for causality, except if one assumes that Lorentz invariance holds. Which seems to be a rather strange additional assumption.

If there is, instead, a preferred set of coordinates, so that the faster than light information transfer is information transfer into the future in this preferred time coordinate, nothing problematic for causality happens.

 

[PeterDonis]

Which seems to be a rather strange additional assumption.

Why? Every experimental test we have made says that Lorentz invariance is valid.

 

[Denis]

First, the question is about something we have not observed yet. So, it makes a lot of sense to assume that it can have also not yet observed properties.

Then, the alternatives are, on the one hand, something which is completely in agreement with common sense, no more strange than classical Newtionian gravity, if the maximal speed is larger than c but finite it is even local in any reasonable way, and, on the other hand, a completely counterintuitive thing which violates causality in a quite horrible way, with causal interactions into the past.

 

[Khashishi]

What alternatives are there to Lorentz invariance that haven't been ruled out by experiments?

 

[Denis]

None-Lorentz-invariance. You cannot rule out it by observing that all you observe is Lorentz-invariant. Tomorrow you may observe something which is not.

In fact, there is no possibility to distinguish Lorentz-invariance from a hidden preferred frame. There exist such theories with preferred frame for relativistic gravity too.

 

[PeterDonis]

it makes a lot of sense to assume that it can have also not yet observed properties

That's not what you're hypothesizing. You're hypothesizing that this new thing we haven't observed lacks a key property (Lorentz invariance) that everything we've observed up to now has. That does not make a lot of sense to me. Also, it seems more complicated than the simple assumption that, except for the specific property where it differs (FTL vs. non-FTL), this new thing should have all the same properties as things we've already observed.

if the maximal speed is larger than c but finite

Then we simply have Lorentz invariance with a different maximum speed. It has been shown that any finite "maximum speed" means Lorentz invariance, unless your theory violates translation and rotation invariance. The only other alternative is Galilean invariance

 

[PeterDonis]

there is no possibility to distinguish Lorentz-invariance from a hidden preferred frame

You put this backwards. What you should say is that there is no possibility to detect a "hidden preferred frame" unless it violates Lorentz invariance (which we haven't observed), so by Occam's razor the "hidden preferred frame" doesn't exist--you can drop it from your theory without affecting any predictions at all.

There exist such theories with preferred frame for relativistic gravity too.

Reference, please?

 

[Mister T]

None-Lorentz-invariance. You cannot rule out it by observing that all you observe is Lorentz-invariant. Tomorrow you may observe something which is not.

So what? Science is a process of making generalizations from observation. You can make all the generalizations you want that are not based on observation. It doesn't make them wrong. It just means they are not science.

 

[Denis]

That's not what you're hypothesizing. You're hypothesizing that this new thing we haven't observed lacks a key property (Lorentz invariance) that everything we've observed up to now has.

Yes. Once we start with assuming that it lacks a key property (having speed lower or equal the speed of light) that everything we have observed up to now has, this seems quite naturla. Above properties are very closely related (if you have a wave equation with some charachteristic speed, with or without mass term, the solutions of the equation will have the corresponding Lorentz symmetry).

Also, it seems more complicated than the simple assumption that, except for the specific property where it differs (FTL vs. non-FTL), this new thing should have all the same properties as things we've already observed.

For me, it makes no sense to propose that the symmetry group of a wave equation with speed c is relevant for something which has a higher speed.

Then we simply have Lorentz invariance with a different maximum speed. It has been shown that any finite "maximum speed" means Lorentz invariance, unless your theory violates translation and rotation invariance. The only other alternative is Galilean invariance

First, so what? A Lorentz symmetry with higher speed is also an example where causality remains valid even if the speed is higher than c. And in this case the original Lorentz symmetry with c is violated too.

Then, you can have as well simply Euclidean symmetry, with a preferred rest frame, and without any relativity principle. This would also have translational and rotational invariance.

You put this backwards. What you should say is that there is no possibility to detect a "hidden preferred frame" unless it violates Lorentz invariance (which we haven't observed), so by Occam's razor the "hidden preferred frame" doesn't exist--you can drop it from your theory without affecting any predictions at all.

Your argument is positivistic - what is unobservable does not exist. Then, you have to give up realism as well as causality. Sorry, but I prefer a realistic causal theory in comparison with a symmetric but acausal and un-realistic theory.

Reference, please?

Schmelzer, I., A generalization of the Lorentz ether to gravity with general-relativistic limit, Advances in Applied Clifford Algebras 22, 1 (2012), p. 203-242, arXiv:gr-qc/0205035

So what? Science is a process of making generalizations from observation. You can make all the generalizations you want that are not based on observation. It doesn't make them wrong. It just means they are not science.

No, I would recommend you to read Popper. Physical theories are free inventions of the human mind. They have to make empirical predictions, to be empirical theories. They can be tested, and possibly falsified. The process of creating these theories is in no way a "generalization from observation".

 

[PeterDonis]

For me, it makes no sense to propose that the symmetry group of a wave equation with speed c is relevant for something which has a higher speed.

You are misunderstanding the Lorentz group; it is a valid symmetry group for a wave equation with any finite speed. There is nothing in the Lorentz group that picks out a particular finite speed $c$. We use it with a particular value for $c$ because that's what we empirically observe, not because the math only works with that value.

A Lorentz symmetry with higher speed is also an example where causality remains valid even if the speed is higher than c.

Yes, agreed.

in this case the original Lorentz symmetry with c is violated too

Yes, which is an argument for why such a theory is not consistent with experiment.

you can have as well simply Euclidean symmetry, with a preferred rest frame, and without any relativity principle.

How does "Euclidean symmetry" pick out a preferred rest frame? Also, where is the actual theory of physics that has been constructed using this symmetry?

Your argument is positivistic - what is unobservable does not exist.

No, my argument is Occam's Razor: if we have two theories that both explain the same data, and are identical except that one postulates an extra entity that the other one doesn't, then the extra entity explains nothing and should be discarded. The fact that the extra entity is unobservable is irrelevant to the argument, except in the obvious sense that an entity which is not needed to explain any data must be unobservable, since observations are data.

 

[PeterDonis]

Science is a process of making generalizations from observation.

There is no single settled definition of what "science" is, and we should try to keep the discussion focused on physics, not philosophy.

I would recommend you to read Popper.

Popper is a philosopher, not a physicist. Please keep the discussion focused on physics.

 

[Dale]

Sorry, but I prefer a realistic causal theory in comparison with a symmetric but acausal and un-realistic theory.

Or you can have a theory which is both causal and symmetric but without FTL. It seems silly to argue in favor of giving up either since there is no real reason to do so.

 

[Denis]

You are misunderstanding the Lorentz group; it is a valid symmetry group for a wave equation with any finite speed. There is nothing in the Lorentz group that picks out a particular finite speed $c$.

Fine, but I do not think otherwise, so I cannot see where you have seen a misunderstanding on my side.

Yes, which is an argument for why such a theory is not consistent with experiment.

To argue about this makes no sense, given the OP:

So for the sake of argument, let's assume that you could actually build something like the Alcubierre Drive and go FTL (I know a lot of people say it's not possible, but let's just for now assume it is).

We start with the hypothesis that something exists which is not consistent with actual experiment.

How does "Euclidean symmetry" pick out a preferred rest frame? Also, where is the actual theory of physics that has been constructed using this symmetry?

It is not the symmetry which picks a preferred frame. It is the non-existence of a larger symmetry. If the symmetry group of the theory is Euclidean symmetry, together with translations in time, but not greater, that means Galilean or Lorentz symmetry is not a symmetry of the theory. In this case, a frame where the Euclidean symmetry acts as usual on the spatial coordinates and time translational symmetry on the time coordinate defines a preferred frame. The link to such a theory I have already given.

No, my argument is Occam's Razor: if we have two theories that both explain the same data, and are identical except that one postulates an extra entity that the other one doesn't, then the extra entity explains nothing and should be discarded.

This rule makes no sense in this form, given that the meaning of "explain the data" is not specified. Doesn't "God's ways are inexplicable" explain the data? If yes, your criterion would tell us to throw away science. If not, you have to specify the meaning of "explaining the same data". This specification will probably have to contain degrees of explanations, with one theory giving better explanations than the other one. So, we reject ""God's ways are inexplicable" because of its low degree of explanatory power, and would have to add "both explain the same data with the same explanatory power".
One could try to start with Popper's empirical content, not? Then, if the additional entity gives some empirical content, it is preferable despite your version of Occam's razor.

Now, a theory with classical causality makes falsifiable predictions which GR cannot make: Namely that causal loops are impossible. GR allows for solutions with causal loops.

There is no single settled definition of what "science" is, and we should try to keep the discussion focused on physics, not philosophy. Popper is a philosopher, not a physicist. Please keep the discussion focused on physics.

If a clearly wrong scientific methodology is used, this error somehow has to be corrected, not? I would accept that this is not the ideal place to discuss objections against the scientific methodology accepted by the mainstream, which is Popper's critical rationalism. But to clarify that somebody makes an error, being in contradiction with this accepted methodology, should be possible.

Or you can have a theory which is both causal and symmetric but without FTL. It seems silly to argue in favor of giving up either since there is no real reason to do so.

There is. Given that causality (in any sufficiently strong sense to contain Reichenbach's common cause principle) is sufficient to prove, together with Lorentz covariance, Bell's inequality, your theory would be in conflict with the predictions of quantum theory. (Which would have to be discussed in the quantum section or so, if there are doubts about it.)

 

[PAllen]

There is. Given that causality (in any sufficiently strong sense to contain Reichenbach's common cause principle) is sufficient to prove, together with Lorentz covariance, Bell's inequality, your theory would be in conflict with the predictions of quantum theory. (Which would have to be discussed in the quantum section or so, if there are doubts about it.)

The common cause is the preparation of entangled particles, which has timelike relation to either measurement. I thus dispute your contention.

 

[PeterDonis]

We start with the hypothesis that something exists which is not consistent with actual experiment.

That's not quite true. We don't have any experimental data that says FTL is possible, but we don't have any experimental data that says it's impossible either. The reasons for thinking something like the Alcubierre drive is impossible are theoretical, not experimental.

We do, however, have a lot of experimental data showing Lorentz invariance with a particular finite speed. So a theory that has Lorentz invariance with a different finite speed, which is what you were suggesting, is inconsistent with experiment.

If the symmetry group of the theory is Euclidean symmetry

What theory? Is there one?

This rule makes no sense in this form, given that the meaning of "explain the data" is not specified.

"Explain the data" means "predict the data". In other words, the theory has to predict that we will observe the particular data we do in fact observe, and will not observe data that we do not in fact observe. See further comments below.

Doesn't "God's ways are inexplicable" explain the data?

Not unless you can show how that premise makes predictions that explain the data in the sense I just gave above.

If yes, your criterion would tell us to throw away science.

Not unless you can show how "God's ways are inexplicable", assuming for the sake of argument that it can in fact explain the data in the sense I gave above, is a simpler theory than the scientific theory that explains the data. Here "simpler" means "makes fewer assumptions", but that is itself somewhat vague; when you make it precise you arrive at something like the Kolmogorov complexity of the axiom system on which the theory is based, or the number of bits in the smallest computer program that generates all of the theory's predictions. It's going to take an awful lot of bits to unpack "God's ways are inexplicable" into detailed predictions of all of our experimental data.

we reject ""God's ways are inexplicable" because of its low degree of explanatory power, and would have to add "both explain the same data with the same explanatory power"

"Explanatory power" here basically means how precisely the data is predicted--in other words, how narrowly is all other possible data that we could have observed, but did not, ruled out. Yes, that's part of how "explain the data" gets unpacked into something more precise.

if the additional entity gives some empirical content, it is preferable despite your version of Occam's razor.

Not unless you can explain what "empirical content" means if it doesn't mean "explain the data" in the sense I gave above (and I don't see anything else that it could usefully mean).

a theory with classical causality

What is "classical causality"? And what theory that has it are you referring to?

the scientific methodology accepted by the mainstream, which is Popper's critical rationalism

I don't think there is a single "scientific methodology accepted by the mainstream". But in any case, that is off topic. We are talking about a specific area of physics and don't need to wander off into generalities about scientific methodology.

 

[Evo]

Denis is no longer allowed to reply to this thread.

 

[zonde]

The common cause is the preparation of entangled particles, which has timelike relation to either measurement. I thus dispute your contention.

In derivation of Bell's inequality it is assumed that the choices of two measurement settings do not have common cause. In experiments this assumption is replaced by usage of QRNG or PRNG (or combination) and assumption of no superdeterminism i.e. any possible common cause would have to affect measurement settings by very complicated relationship that tracks and/or controls very large number of parameters.

 

[PAllen]

In derivation of Bell's inequality it is assumed that the choices of two measurement settings do not have common cause. In experiments this assumption is replaced by usage of QRNG or PRNG (or combination) and assumption of no superdeterminism i.e. any possible common cause would have to affect measurement settings by very complicated relationship that tracks and/or controls very large number of parameters.

There is no common cause for the measurements, but there is for each measurement to be of an entangled state. Thus, IMO, there is no causality issue with the Bell violation that is observed.

 

[zonde]

There is no common cause for the measurements, but there is for each measurement to be of an entangled state. Thus, IMO, there is no causality issue with the Bell violation that is observed.

There is no causality issue in Bell's inequality violations. But there is issue with relativistic (sub-luminal) causality. Take a look at this simple explanation of Bell's inequality.

 

[Battlemage!]

No. You can always consider yourself at rest as long as your pocket accelerometer reads zero (and even when it doesn't, if you aren't afraid of maths). Newton threw out the concept of "at rest" except with respect to some object. We've seen no evidence that he was wrong on that point in 350 years.
That was your first mistake...

No. Incidentally, gravity waves are a type of water wave. You mean gravitational wave.

Think of a flipbook - one of those things with a slightly different picture on each page. As you flip through it the picture seems to move. Imagine each page has a small wrinkle on it in a different place on each page. As you flip through it the wrinkle seems to move. But it's an illusion. The thing you're thinking of as a moving wrinkle in a 2d page is actually your viewing of a static 3d structure.

This is analogous to what's going on in gravitational waves. They only seem to move because you only see a 3d slice of a 4d world. In the 4d world nothing is moving. This is what PAllen is telling you - the part of each page that is wrinkled is different, but the wrinkle is not moving.

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.

 

[Battlemage!]

Another question:

I know this thread kind of went off topic, but for the sake of knowledge enrichment, assuming there was a speed limit greater than c, why would this entail causality violations when we'd still have the Lorentz transformations, just with a different letter instead of c? Sure, you might be able to watch yourself leave after you've arrived at your destination, but you still couldn't travel faster than the maximum speed, so you couldn't get back before you left, right? I mean, being able to travel faster than sound doesn't result in causality violation (although sound requires a medium... not sure if that matters or not).

Maybe I'm going about this wrong, but looking at the Lorentz factor, I have this weird intuition that violating causality requires β ≥ 1, so you can get division by zero or an imaginary value for the Lorentz factor (and of course β = v/ς where ς > c). It has to be connected, or so my lame intuition suggests. Which would mean that if you had a Lorentz invariant universe where the maximum speed is greater than c, you'd still not be able to violate causality.Am I way off on this? Why or why not?

 

[Stephen Tashi]

Physical systems are conventionally described by specifications that give their "state". Is a point in "spacetime" supposed to represent the (complete) state of a physical system? What system would that be? A point particle? The entire universe?

I don't understand how the notion of a physical system being completely described by a state is compatible with the notion of "going back in time". In particular, if you "went back in time" to alter the "state" of a physical system in the remote past, your presence in the description of that physical system would change the description of its state. So you would not actually have arrived in the physical system that lacks your presence, you would have arrived at a physical system with a different state description (because you are present).

It seems to me that to discuss "going back in time" , one must use incomplete descriptions of physical systems. So if a person were to go back in time to kill his grandfather and we wish to say this is a paradox then we must count a past day when the time traveller wasn't present as being the "same" physical system as a past day when the time traveller was present.

If spacetime is a static representation of a state space then one can draw curve in that state space that goes backwards in time, but that does not change the states that are represented by the points on that curve. So how can anything like a kill-you-grandfather paradox be formulated if we use a consistent concept of the state of a physical system?

 

[PAllen]

Another question:

I know this thread kind of went off topic, but for the sake of knowledge enrichment, assuming there was a speed limit greater than c, why would this entail causality violations when we'd still have the Lorentz transformations, just with a different letter instead of c? Sure, you might be able to watch yourself leave after you've arrived at your destination, but you still couldn't travel faster than the maximum speed, so you couldn't get back before you left, right? I mean, being able to travel faster than sound doesn't result in causality violation (although sound requires a medium... not sure if that matters or not).

Maybe I'm going about this wrong, but looking at the Lorentz factor, I have this weird intuition that violating causality requires β ≥ 1, so you can get division by zero or an imaginary value for the Lorentz factor (and of course β = v/ς where ς > c). It has to be connected, or so my lame intuition suggests. Which would mean that if you had a Lorentz invariant universe where the maximum speed is greater than c, you'd still not be able to violate causality.Am I way off on this? Why or why not?

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.

 

[PAllen]

Physical systems are conventionally described by specifications that give their "state". Is a point in "spacetime" supposed to represent the (complete) state of a physical system? What system would that be? A point particle? The entire universe?

I don't understand how the notion of a physical system being completely described by a state is compatible with the notion of "going back in time". In particular, if you "went back in time" to alter the "state" of a physical system in the remote past, your presence in the description of that physical system would change the description of its state. So you would not actually have arrived in the physical system that lacks your presence, you would have arrived at a physical system with a different state description (because you are present).

It seems to me that to discuss "going back in time" , one must use incomplete descriptions of physical systems. So if a person were to go back in time to kill his grandfather and we wish to say this is a paradox then we must count a past day when the time traveller wasn't present as being the "same" physical system as a past day when the time traveller was present.

If spacetime is a static representation of a state space then one can draw curve in that state space that goes backwards in time, but that does not change the states that are represented by the points on that curve. So how can anything like a kill-you-grandfather paradox be formulated if we use a consistent concept of the state of a physical system?

If you take a block view of spacetime, there are no paradoxes like killing your grandfather. Either you were or weren't present before you were born, you did what you did if you were present in your past, etc. But what you have instead are information paradoxes. For example you have accept possibilities like plays without authors: I go back in time hand Shakespeare a copy of Julius Caesar, he then writes it out, it becomes famous, I go back in time with a copy, etc. There is only one version of any spatial slice of spacetime, but the play has no author.

 

[Stephen Tashi]

But what you have instead are information paradoxes. For example you have accept possibilities like plays without authors: I go back in time hand Shakespeare a copy of Julius Caesar, he then writes it out, it becomes famous, I go back in time with a copy, etc. There is only one version of any spatial slice of spacetime, but the play has no author.

I can see that such a scenario is an information paradox if we assume that there are deterministic physical laws that determine how states change into other states - in such a manner that a given state must have only one set of states that preceede it. If the state of the universe whose description includes "I have a copy of Shakespear's Julius Caesar" can only follow from the state whose description includes "Shakespear was given a copy of Julius Caesar by a time traveller from the future" then the play indeed has no author. However, if the state of "I have a copy of Shakepspear's Julius Caesar" could have followed from several different prior states, one of which includes "Shakespear writes Julius Caesar" and one of which includes "Francis Bacon writes Julius Caesar" then the authorship of the play becomes ambiguous, but do we have an information paradox?

 

[PAllen]

I can see that such a scenario is an information paradox if we assume that there are deterministic physical laws that determine how states change into other states - in such a manner that a given state must have only one set of states that preceede it. If the state of the universe whose description includes "I have a copy of Shakespear's Julius Caesar" can only follow from the state whose description includes "Shakespear was given a copy of Julius Caesar by a time traveller from the future" then the play indeed has no author. However, if the state of "I have a copy of Shakepspear's Julius Caesar" could have followed from several different prior states, one of which includes "Shakespear writes Julius Caesar" and one of which includes "Francis Bacon writes Julius Caesar" then the authorship of the play becomes ambiguous, but do we have an information paradox?

Determinism is irrelevant. All you need assume for an information paradox is that closed timelike curves are possible and that there is only one version of any interaction.You need not assume that any future state can be predicted from past states. That is, a quantum block universe model simply assumes all history is played out. Whatever interactions that are unpredictable from their past have already happened. Add to this closed timelike curves, and you have the possibility of information paradoxes.

 

[puzzled fish]

If you take a block view of spacetime, there are no paradoxes like killing your grandfather. Either you were or weren't present before you were born, you did what you did if you were present in your past, etc. But what you have instead are information paradoxes. For example you have accept possibilities like plays without authors: I go back in time hand Shakespeare a copy of Julius Caesar, he then writes it out, it becomes famous, I go back in time with a copy, etc. There is only one version of any spatial slice of spacetime, but the play has no author.

Is the aging copy of Julius Caesar a member of the same set of information paradoxes? For suppose you have in your hands a 400 year old copy. You travel back in time and hand it to Shakespeare. For the time Shakespeare reads and copies the book, time passes as normal. Suppose this procedure ( for Shakespeare to copy the book) takes more than a year. In the meantime, the copy ages more. Now, regardless if you take your book back to the time you began your trip at, or you leave it with Shakespeare for another 400 years, in both cases you end up ( or begin with) with a book > 400 years. Paradox.

 

[PeterDonis]

Now, regardless if you take your book back to the time you began your trip at, or you leave it with Shakespeare for another 400 years, in both cases you end up ( or begin with) with a book > 400 years.

No. The 400 year old book you take back to hand to Shakespeare is the one that was printed by Shakespeare himself (or someone who took his manuscript and printed it) 400 years before you stepped into your time machine. Shakespeare takes the book you hand him and writes his own manuscript, which then gets printed, and 400 years later you take it and step into your time machine...

As for what happens to the book you handed Shakespeare after he uses it to write his manuscript, that's not specified in the scenario.

 

[PAllen]

No. The 400 year old book you take back to hand to Shakespeare is the one that was printed by Shakespeare himself (or someone who took his manuscript and printed it) 400 years before you stepped into your time machine. Shakespeare takes the book you hand him and writes his own manuscript, which then gets printed, and 400 years later you take it and step into your time machine...

As for what happens to the book you handed Shakespeare after he uses it to write his manuscript, that's not specified in the scenario.

Actually, I was thinking of the simple possibility the time traveler hands Shakespeare a modern book, which he then copies in his own hand and destroys. A brutal follow on possibility is to kill the traveler so there is no record of the play's absence of authorship.

 

[puzzled fish]

No. The 400 year old book you take back to hand to Shakespeare is the one that was printed by Shakespeare himself (or someone who took his manuscript and printed it) 400 years before you stepped into your time machine. Shakespeare takes the book you hand him and writes his own manuscript, which then gets printed, and 400 years later you take it and step into your time machine...

As for what happens to the book you handed Shakespeare after he uses it to write his manuscript, that's not specified in the scenario.

Ok. Suppose that the book the traveller handed to Shakespeare, gets destroyed. And further suppose that Shakespeare was in the habit of carefully numbering the copies that were printed by himself. What you are saying is that I began my journey back in time with one of those copies that somehow was found in my possession.
Let's say copy 313. But history records show that copy 313 has been destroyed. ( Suppose that the book the traveller handed to Shakespeare, gets destroyed: is what we began with.)
Paradox.

 

[PAllen]

Ok. Suppose that the book the traveller handed to Shakespeare, gets destroyed. And further suppose that Shakespeare was in the habit of carefully numbering the copies that were printed by himself. What you are saying is that I began my journey back in time with one of those copies that somehow was found in my possession.
Let's say copy 313. But history records show that copy 313 has been destroyed. ( Suppose that the book the traveller handed to Shakespeare, gets destroyed: is what we began with.)
Paradox.

No paradox at all, though not the scenario I intended. Copy 313 was written by Shakespeare say January 10, 1590. Its world line continues to 2121 when it travels to January 5, 1590. Shakespeare copies it and destroys the duplicate on January 11, 1590 (soon after he finishes copying it). There are 6 days when the very old state and the developing new state of the book coexist; but that feature goes without saying if closed timelike curves are possible (in this case, we rely on an 'almost closed' timeilike curve). It is no paradox at all, just weird. What is paradoxical is the information generation issue: who wrote the play? No one - it just exists without authorship.

 

[puzzled fish]

Actually, I was thinking of the simple possibility the time traveler hands Shakespeare a modern book, which he then copies in his own hand and destroys. A brutal follow on possibility is to kill the traveler so there is no record of the play's absence of authorship.

Which leaves us with the strange possibility a 400 years old copy of Julius Caesar to co-exist somewhere together with the brand new modern facsimile copies of itself, in the unfortunate circumstance that it doesn't get destroyed. A most curious find indeed!

 

[puzzled fish]

No paradox at all, though not the scenario I intended. Copy 313 was written by Shakespeare say January 10, 1590. Its world line continues to 2121 when it travels to January 5, 1590. Shakespeare copies it and destroys the duplicate on January 11, 1590 (soon after he finishes copying it). There are 6 days when the very old state and the developing new state of the book coexist; but that feature goes without saying if closed timelike curves are possible (in this case, we rely on an 'almost closed' timeilike curve). It is no paradox at all, just weird. What is paradoxical is the information generation issue: who wrote the play? No one - it just exists without authorship.

I am not arguing who wrote copy 313 ( I do not mean the play itself ). It goes without saying that Shakespeare did. And surely he must have had more time than 6 days if he were to print 313 copies. Now, suppose, as you say, that copy 313 co-existed side by side with an older copy of itself, for as long as Shakespeare was on the task. What is the possibility of making a copy exactly similar to itself? Same amount of ink in each printed letter, same fabric and grain of pages down to molecular level, everything should be the same. Almost nil.
But suppose that this is not the same copy (as the one presented by traveller), and we are back to the original scenario you intended. How do you explain the fact that, right before our traveller begins his backward journey ( if the book he presents Shakespeare with survives through time ) there must co-exist two facsimile copies down to the minutest grain: one old and one new somewhere? As above, what are the possibilities of such a terrible coincidence? Almost nil.
Please allow me to be very skeptical on this, and stick to the impossibility of such a preposterous scenario and to my old aging copy paradox. But I have to admit that your scenario was a very successful one and got me to thinking.