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

[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"

 

[Herman Trivilino]

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"

Right. Or that if we were to discover that light has a speed relative to its source that's less than the maximum possible speed.

 

[Battlemage!]

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.

What I mean in this make believe universe is that there is an invariant speed, but light isn't it. It's just much closer to it than anything else.

 

[PeterDonis]

It's just much closer to it than anything else.

And Nugatory's point is that, if light does not travel at the invariant speed, then how "close" the speed of light (meaning, the actual speed at which light is measured to travel) is to the invariant speed is frame-dependent; there will be frames in which the speed of light is not closer to the invariant speed than the speed of anything else. In fact, there will be frames in which the speed of light is zero--in which light is at rest.

 

[Battlemage!]

And Nugatory's point is that, if light does not travel at the invariant speed, then how "close" the speed of light (meaning, the actual speed at which light is measured to travel) is to the invariant speed is frame-dependent; there will be frames in which the speed of light is not closer to the invariant speed than the speed of anything else. In fact, there will be frames in which the speed of light is zero--in which light is at rest.

But shouldn't that only be a problem if the speed of light is the invariant speed?

 

[Nugatory]

But shouldn't that only be a problem if the speed of light is the invariant speed?

It is a problem for your description of that world: "The speed of light is really close to the invariant velocity". That's why Dale suggested that you think in terms of the photon rest mass instead.

 

[Battlemage!]

It is a problem for your description of that world: "The speed of light is really close to the invariant velocity". That's why Dale suggested that you think in terms of the photon rest mass instead.

Well let me ask another question, if you don't mind, so I can better grasp the situation:

Let's go back to actual special relativity. Say I am traveling parallel to the direction of a beam of light, and I try to look at a photon moving along the direction of the beam. Could I ever see that photon, as opposed to photons radiating perpendicularly to the beams which are (I'm assuming) the ones I normally see in such scenarios?

 

[Ibix]

You can only see a photon that hits a sensor such as your eye. If you see a laser beam, for example, what you are actually seeing is light scattered from the beam because it's passing through a scattering medium. This is why nightclubs pump in smoke before shining lasers through them. Also why it's always cloudy above Gotham. Batman wouldn't be able to see the bat signal on a clear starry night.

 

[Battlemage!]

You can only see a photon that hits a sensor such as your eye. If you see a laser beam, for example, what you are actually seeing is light scattered from the beam because it's passing through a scattering medium. This is why nightclubs pump in smoke before shining lasers through them. Also why it's always cloudy above Gotham. Batman wouldn't be able to see the bat signal on a clear starry night.

I thought as much.

So, if light isn't the maximum speed and I'm moving away from a photon at the same speed as the photon, I'd never see it, correct? I'm not seeing the logical inconsistency if the universe is Lorentz invariant but the speed of light isn't the maximum speed (aside from the fact that Maxwell's equations obviously suggest light as the speed limit). Since this isn't a homework thread, could someone spell it out for a dummy like myself? :)

 

[Ibix]

There isn't one. There is a logical inconsistency if there are two invariant speeds, which tells you that if light does not travel at the invariant speed then it does not have a single defined speed. There is no "speed of the neutron" and there would be no "speed of the photon". That's the point being made here - talking about "the speed of light not being the same as the invariant speed" is slightly wrong because in that case light doesn't have "a" speed, it has many. Better to talk about the photon having zero mass (and traveling at a well defined invariant speed) or non-zero masd (and acting like any other particle).

 

[Nugatory]

I'm not seeing the logical inconsistency if the universe is Lorentz invariant but the speed of light isn't the maximum speed (aside from the fact that Maxwell's equations obviously suggest light as the speed limit). Since this isn't a homework thread, could someone spell it out for a dummy like myself? :)

If the universe is Lorentz invariant, then it would be impossible for the speed of light to be "really, really close to the invariant speed", as you were trying to specify. Either it would be exactly the invariant speed or light would work like everything else from snails to bullets to cosmic muons and any number between zero and the invariant speed would be "the speed of light" depending on the frame we choose. The underlying problem is that the phrase "the speed of X" is undefined for all X not moving at the invariant speed; the invariant speed is unique in that you don't have to say what it is relative to.

If you want to describe a universe in which light does not travel at the invariant speed yet is close to the "speed of light is $c$" universe we think we live in, you would say "a universe in which photons have a very small rest mass".

 

[Battlemage!]

There isn't one. There is a logical inconsistency if there are two invariant speeds, which tells you that if light does not travel at the invariant speed then it does not have a single defined speed. There is no "speed of the neutron" and there would be no "speed of the photon". That's the point being made here - talking about "the speed of light not being the same as the invariant speed" is slightly wrong because in that case light doesn't have "a" speed, it has many. Better to talk about the photon having zero mass (and traveling at a well defined invariant speed) or non-zero masd (and acting like any other particle).

If the universe is Lorentz invariant, then it would be impossible for the speed of light to be "really, really close to the invariant speed", as you were trying to specify. Either it would be exactly the invariant speed or light would work like everything else from snails to bullets to cosmic muons and any number between zero and the invariant speed would be "the speed of light" depending on the frame we choose. The underlying problem is that the phrase "the speed of X" is undefined for all X not moving at the invariant speed; the invariant speed is unique in that you don't have to say what it is relative to.

If you want to describe a universe in which light does not travel at the invariant speed yet is close to the "speed of light is $c$" universe we think we live in, you would say "a universe in which photons have a very small rest mass".

Ah. When I said light might be really close to the maximum speed in this hypothetical universe, I meant just according to our current measuring devices sitting here at rest in our own frame.

Just like when we accerate particles "close to the speed of light" here in the real universe. Obviously in the frame of the hypervelocity particles, pulses of light still move away from them at c, but yet we can measure them to achieve near light speed.What I'm wondering is the following: IF light wasn't the speed limit, is there a logical scenario where our experiments might not be sensitive enough to tell? For example, in real life I imagine the first attempts to measure the speed of light might have ended with people believing it was infinite.

 

[Nugatory]

What I'm wondering is the following: IF light wasn't the speed limit, is there a logical scenario where our experiments might not be sensitive enough to tell

Sure. Google for "photon mass upper bound" and you'll find some discussion of different ways of calculating the maximum photon mass that would be consistent with current experiments.

For example, in real life I imagine the first attempts to measure the speed of light might have ended with people believing it was infinite.

The first recorded measurement of the speed of light was made by Galileo in 1638, and he carefully avoided going beyond what his experimental results (at least ten times the speed of sound) supported: "If not instantaneous, it is extraordinarily rapid".

 

[timmdeeg]

What I'm wondering is the following: IF light wasn't the speed limit, is there a logical scenario where our experiments might not be sensitive enough to tell?

In a practical sense this would mean that the speed of light emitted by a lamp which you measure in your frame depends on the relative motion between you and the lamp. If you adjust your speed closer and close to that of the lamp, then the speed of the light of this lamp will slower and slower measured in you frame.

 

[Battlemage!]

In a practical sense this would mean that the speed of light emitted by a lamp which you measure in your frame depends on the relative motion between you and the lamp. If you adjust your speed closer and close to that of the lamp, then the speed of the light of this lamp will slower and slower measured in you frame.

Yes but in practice we wouldn't be able to do that for a long while, which would mean in this hypothetical universe we might not be able to know that light wasn't the maximum speed.

After all, the speed transformstion equation is asymptotic (it can always approach bit never reach c), right?
On a slightly off topic note, here's an experiment verifying the Lorentz invariance of the kinetic energy of electrons, if I didn't miss read the anstract.

http://www.nature.com/nature/journal/v517/n7536/full/nature14091.html

 

[ArmChairPhysicist]

Now I could be wrong, but in the study I've done and thinking about the issue of "Time travel" and causality, neither exist. They are fantasy. If you went faster than light you will arrive at a destination faster, but not at a date that has not occurred. Due to dilation your physical system will have only experienced a short travel time, where as real time continued on. To paraphrase, a for every minute realtime, you and your area only experienced a few seconds. Everyone else observing experienced a minute and observed you experiencing a minute, but in your bubble that minute was only a few seconds. Note that these aren't real measurements, simply describing how I see this to work.
Logically and from what we have seen in science, time travel as we see in popular culture is impossible. That which has happened has already passed, that which has not happened doesn't exist, there is only now. You can adjust the relative "frame rate" of your time by attaining high speeds, but you aren't jumping forward or backward.

 

[PeterDonis]

for every minute realtime

There is no "realtime" in relativity; time is not absolute.

That which has happened has already passed, that which has not happened doesn't exist, there is only now.

There is no "now" in relativity; simultaneity is not absolute.

you aren't jumping forward or backward

If I rephrase this as "your path through spacetime must be continuous; it can't have jumps in it", then it is true. But it doesn't follow from the rest of the things you have said.

 

[timmdeeg]

Yes but in practice we wouldn't be able to do that for a long while, which would mean in this hypothetical universe we might not be able to know that light wasn't the maximum speed.

We would know that the speed of the light isn't invariant, because we have proofed that it depends on relative motion.

 

[Battlemage!]

We would know that the speed of the light isn't invariant, because we have proofed that it depends on relative motion.

What if, in this strange new universe, the difference is too small to detect? That is, what if the fringe shift in a newer Michaelson-Morley experiment is just too small to detect?

 

[Ibix]

It's still possible that photons do have a very very small mass. The upper bound consistent with experiment is absurdly low (because photons with mass have broader implications for electromagnetism than just slower speeds), but it is not and never will be zero.

In terms of relativity, we would just have to stop calling c the speed of light. And come up with a substitute for the light clock experiment.

 

[timmdeeg]

It's still possible that photons do have a very very small mass.

Is there a theoretical reason to assume the same propagation velocity of electromagnetic- and gravitational waves?

 

[Nugatory]

Is there a theoretical reason to assume the same propagation velocity of electromagnetic- and gravitational waves?

If you assume that these speeds are invariant, yes - there can be only one invariant speed, so they have to be the same. And there are fairly convincing theoretical reasons to expect both speeds to be invariant.

 

[timmdeeg]

If you assume that these speeds are invariant, yes- there can be only one invariant speed, so they have to be the same.

Yes, in this case.
The similarity is that in both cases oscillating charges and oscillating masses as well are emitting waves which propagate through empty space and can be detected elsewhere. So, naively one could suspect here a connection on a deeper level with the effect that both are either invariant (necessarily the same invariant speed then) or not. I'm not sure if this makes sense.

 

[Ibix]

If you assume that these speeds are invariant, yes - there can be only one invariant speed, so they have to be the same. And there are fairly convincing theoretical reasons to expect both speeds to be invariant.

I understand that the speed of gravitational waves drops out of the Einstein field equations, so more or less has to be the invariant speed unless we're chucking GR out of the window. But I thought it was possible to construct massive photons in a coherent way - Proca's work, further developed by Yukawa, I gather (e.g. https://galileospendulum.org/2013/07/26/what-if-photons-actually-have-mass/).

 

[Nugatory]

I understand that the speed of gravitational waves drops out of the Einstein field equations, so more or less has to be the invariant speed unless we're chucking GR out of the window. But I thought it was possible to construct massive photons in a coherent way - Proca's work, further developed by Yukawa, I gather (e.g. https://galileospendulum.org/2013/07/26/what-if-photons-actually-have-mass/).

That's what the hedge about "fairly convincing" was for.

 

[PAllen]

Is there a theoretical reason to assume the same propagation velocity of electromagnetic- and gravitational waves?

In classical GR there is a theoretical reason for GW to travel at the invariant speed. This is independent of whether you include EM in the matter energy sector of your GR model.

 

[timmdeeg]

In classical,GR there is a theoretical reason for GW to travel at the invariant speed. This is independent of whether you include EM in the matter energy sector of your GR model.

Okay, thanks.