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sdsperth
2010-Jul-25, 12:38 PM
Can anyone explain to me why people hypothesise that you would travel backward in time if you exceed the speed of light?

I realise that superluminal speeds are impossible, but people speculate on it nonetheless.

Iíve seen the time dilation equations and can understand how a stationary observer may see your personal clock run slower as you speed up, and by extension backwards when you pass light speed, but Iím not sure how that would affect entropy within you spacecraft and whether you would grow younger.

I fail to see however, how you would not find yourself in the past, when you slowed back down.

Be gentle with me Ė I only have high school physics and even that is approaching 30 years old.

Ken G
2010-Jul-25, 08:56 PM
It's actually pretty tricky, so it's no wonder you have questions. First of all, going back in time doesn't mean you'd get younger, it means you could in principle, as an old person, go back and meet yourself as a young person. You have not discovered the fountain of youth, as your own time, called proper time, always behaves completely normally in relativity.

But if you could go faster than c as reckoned by those you leave behind, then turn around and again go faster than c as reckoned by those you leave behind the second time, then it is possible to return to meet your younger self. That's the only sense to which you "went back in time", and note it requires two trips, and your speed is reckoned each time by those you leave behind at each stage. What's more, and this is the real tricky point, the people you leave behind at those two points must also be separating from each other at very high speed. They don't need to be separating from each other faster than c, but the slower they are separating, the more you'll need to exceed c by their reckoning to return to your own past. So it's a complicated situation to really show up in your own past. (If gravity is involved, that's another issue-- this answer is all in special relativity but allowing speeds > c).

grant hutchison
2010-Jul-25, 10:55 PM
to supplement Ken's description with a specific example:

The fundamental issue is with how simultaneity works under Special Relativity: observers in motion relative to each other disagree about which distant events are simultaneous with their own local "now".
As an extreme example of travelling faster than light, we can imagine some sort of instantaneous jump from one location to another. But because of the disagreement about simultaneity, what constitutes "instantaneous" will be observer-dependent: what is instantaneous for one observer will take some time in the coordinates of another observer who is moving relative to the first, and will involve backwards time travel for a third observer in a different state of relative motion. So if we can make an instantaneous jump according to our own coordinates, it's always possible to find an observer, in relative motion to ourselves, who will measure our journey as going backwards in time in their coordinates.
The trick to going "properly" back in time to meet your younger self is to make two journeys (as Ken says). First, jump instantaneously to some distant location, and then come to rest relative to your departure point. Now accelerate to some moderate velocity directed away from your departure point. Under SR, this shifts your concept of simultaneity pastwards down the worldline you departed from. So when you jump back to your departure point, instantaneously in your new reference frame, you find yourself in your own past.
The same thing can be done using any velocity faster than light: you just need to tune the distance you travel and the sublight speed you exploit at your destination in order to adjust your simultaneity appropriately. But if you are constrained to move slower than light, you can never pull this trick within the rules of SR. Hence the anxiety that FTL signalling will allow "causality violations".

Grant Hutchison

baskerbosse
2010-Jul-26, 12:44 AM
I think the question is the wrong way around.

Due to time dilation, your travel time gets shorter and shorter the closer to lightspeed you get.
At lightspeed, travel time is instantaneous. That makes it quite difficult to accelerate further to say the least! ;-)
You would have to arrive before you started. You need to travel in time in order to reach lightspeed.
In my view, that is the tricky bit (-oh and there's the little detail of needing infinite energy to reach lightspeed :-))

/Peter

Ken G
2010-Jul-26, 01:16 AM
Due to time dilation, your travel time gets shorter and shorter the closer to lightspeed you get.
At lightspeed, travel time is instantaneous. That makes it quite difficult to accelerate further to say the least! Yes, this would be a problem for accelerating faster than c. Perhaps a more interesting way to set up the problem is to imagine an information-carrying signal that can be sent faster than c without accelerating any rockets faster than c-- just a particle that can carry a signal and travels faster than c. Than use the above two-jump schemes to send that particle back and forth between rapidly separating observers, and this could send a signal back in time from when it was initiated. But it takes two jumps, each following the same rules for that special particle.


You would have to arrive before you started. You need to travel in time in order to reach lightspeed.In a global sense, yes, but that's just a coordinate choice. It doesn't become anything "real" until you, or your signal, makes the return trip. Traveling faster than c would not go back in time if it was only a fixed speed faster than c in one frame.

astromark
2010-Jul-26, 06:30 AM
It sounds so simple. Accelerate to above c. and for you time has stopped... But only from a point of view.

If you were on the ship your only perception might be that you get were you are going real fast...

But to travel back in time. thats another leap. Lets say five times c. as a velocity.

What of, where you left and where you are going to ?

excepting that some will insist impossible... there is just no energy available... and that might well be the case.

Its still a very interesting thought process... Just treating it as a question.

I like what has been said thus far... and no please do not change the subject. A signal that went back in time is not this question.

What would be the perception of the travelers ?

( Mark does not think this can ever work. )

dgavin
2010-Jul-26, 02:12 PM
In matmatical terms as soon as you hit Light Speed, time (from perspective of thing in motion) irreguardless of distance is always 0. Basically the math breaks down at this point. If you want to compute for velosities FTL then you have to invert the formulas, which changes the math from Space like to time like, and it yeilds results of negative times in all other frames of reference but the thing in motion.

BadTrip
2010-Jul-26, 02:45 PM
In matmatical terms as soon as you hit Light Speed, time (from perspective of thing in motion) irreguardless of distance is always 0. Basically the math breaks down at this point. If you want to compute for velosities FTL then you have to invert the formulas, which changes the math from Space like to time like, and it yeilds results of negative times in all other frames of reference but the thing in motion.

Pardon me while I struggle with this.... not that I'm arguing... just trying to understand.

So then, if you’re traveling at the speed of light it takes you zero time to get to your destination with respect to your own frame of reference. Yes?

Motion is defined as a change in position over time. Yes?

Within your own frame of reference…. Have you changed position? The answer must be yes, right? You started out at point A and have now arrived at point B, even though, within your own frame of reference no time has elapsed. If no time has elapsed has there been any motion? Or more appropriately I suppose… according to you, within your own frame of reference, have YOU moved? Perhaps you have remained motionless, since no time passed?... has the other coordinate, your destination coordinate, been in motion rather than you?

There was another thread around here that asked the question of “does a photon age?”…or something similar. Perhaps, from the frame of reference of the photon, it is not in motion?, but rather everything else is.

Oh man… I need another cup of coffee.

cosmocrazy
2010-Jul-26, 04:10 PM
Pardon me while I struggle with this.... not that I'm arguing... just trying to understand.

So then, if you’re travelling at the speed of light it takes you zero time to get to your destination with respect to your own frame of reference. Yes?

Motion is defined as a change in position over time. Yes?

Within your own frame of reference…. Have you changed position? The answer must be yes, right? You started out at point A and have now arrived at point B, even though, within your own frame of reference no time has elapsed. If no time has elapsed has there been any motion? Or more appropriately I suppose… according to you, within your own frame of reference, have YOU moved? Perhaps you have remained motionless, since no time passed?... has the other coordinate, your destination coordinate, been in motion rather than you?

There was another thread around here that asked the question of “does a photon age?”…or something similar. Perhaps, from the frame of reference of the photon, it is not in motion?, but rather everything else is.

Oh man… I need another cup of coffee.

There would be motion up until light-speed was achieved at that point the journey would appear to be instantaneous for the traveller, only any other frame of reference would measure the journey differently.

Since for the photon, which is always travelling at C relative to everything else, time and space have no meaning. From its own perspective time and space are 0, from its own point of view it occupies all of space and time or no space and time which ever way you prefer to look at it.

nokton
2010-Jul-26, 04:16 PM
Can anyone explain to me why people hypothesise that you would travel backward in time if you exceed the speed of light?

I realise that superluminal speeds are impossible, but people speculate on it nonetheless.

Iíve seen the time dilation equations and can understand how a stationary observer may see your personal clock run slower as you speed up, and by extension backwards when you pass light speed, but Iím not sure how that would affect entropy within you spacecraft and whether you would grow younger.

I fail to see however, how you would not find yourself in the past, when you slowed back down.

Be gentle with me Ė I only have high school physics and even that is approaching 30 years old.

Thankyou for posing a very difficult question, but one with an answer. High school physics will get you so far, comprehension get you much further. Think on this, you are in a space ship orbiting a black hole at near the event horizon, time slows down for you, ( Albert ), your brother is in stasis on earth, you come back to earth having experienced 6 months of living, 50 years having past on earth, wake up your brother and he will be the same age
he was relative to you. That is not time travel, just a misunderstanding and distortion of Alberts equations.
Your input on this site is appreciated by me,
Nokton

grant hutchison
2010-Jul-26, 04:35 PM
Motion is defined as a change in position over time. Yes?

Within your own frame of reference…. Have you changed position? The answer must be yes, right? You started out at point A and have now arrived at point B, even though, within your own frame of reference no time has elapsed. If no time has elapsed has there been any motion.You never move in your own "frame of reference", since you define its coordinates according to your own instantaneous location. Stuff move relative to you, in that reference frame.
And, if we want to say that zero time passes for a traveller at lightspeed, we also have to note that the Universe spans zero distance for that traveller in the direction of travel: you can get anywhere in zero time. So we begin to get into messy undefined quantities, dividing zero by zero, which makes the lightspeed reference frame a rather suspect one.
At speeds faster than light, as dgavin says, the maths of SR tells us that the traveller's clock ticks off spacelike intervals (which behave like time for the traveller). At the extreme, what one observer sees as an instantaneous jump of eight light years will take eight years on the traveller's clock. Like conventional travellers, FTL travellers minimize their own proper time for a given journey by staying close to lightspeed.

Grant Hutchison

Ken G
2010-Jul-26, 04:41 PM
So then, if you’re traveling at the speed of light it takes you zero time to get to your destination with respect to your own frame of reference. Yes?Yes.


Motion is defined as a change in position over time. Yes?Yes, but motion of what? And whose time? These are no longer absolute issues in relativity. Typically, the observer observes motion in something else, an observer does not observe its own motion. Indeed, relativity allows all observers to imagine they are stationary, since all they can measure is motion relative to themselves.


Within your own frame of reference…. Have you changed position? The answer must be yes, right?Not necessarily-- you may imagine that your position, as an observer, is always the same, you can always be at "the origin" of your coordinate system. Or you can use different coordinates, it's all just the language you are using to talk about what is happening. What is actually happening must be independent of coordinates, that is the deepest principle at the core of relativity.


You started out at point A and have now arrived at point B, even though, within your own frame of reference no time has elapsed. If no time has elapsed has there been any motion? When you consider time dilation, you must also consider length contraction. (What that really means is, if you are using a coordinate system that exhibits time dilation, it will also have to exhibit length contraction, or else the speed of light won't be constant and your coordinates have monkeyed with the laws of physics in ways you do not want to allow.) In particular, if it takes you zero time to get from point A to point B, then the distance between point A and B is zero. If point A and B are not the same point, yet the distance between them is zero, then they are moving at speed c (or if you prefer, you are moving between them at speed c).


Perhaps you have remained motionless, since no time passed?... has the other coordinate, your destination coordinate, been in motion rather than you?You can always think that way, for any kind of translational motion-- not just motion at c. (Spinning motion is a bit trickier, and as far as I know, it remains an open question as to whether or not you are allowed to think that way in regard to spinning motion.)

BadTrip
2010-Jul-26, 04:47 PM
You never move in your own "frame of reference", since you define its coordinates according to your own instantaneous location. Stuff move relative to you, in that reference frame.
And, if we want to say that zero time passes for a traveller at lightspeed, we also have to note that the Universe spans zero distance for that traveller in the direction of travel: you can get anywhere in zero time. So we begin to get into messy undefined quantities, dividing zero by zero, which makes the lightspeed reference frame a rather suspect one.
At speeds faster than light, as dgavin says, the maths of SR tells us that the traveller's clock ticks off spacelike intervals (which behave like time for the traveller). At the extreme, what one observer sees as an instantaneous jump of eight light years will take eight years on the traveller's clock. Like conventional travellers, FTL travellers minimize their own proper time for a given journey by staying close to lightspeed.

Grant Hutchison

Thank you Grant. .... I am sufficiently confused now. LOL

The first two portions of your response make a lot of sense to me... alas, I do not yet follow the last portion of your response.


........
At speeds faster than light, as dgavin says, the maths of SR tells us that the traveller's clock ticks off spacelike intervals (which behave like time for the traveller). At the extreme, what one observer sees as an instantaneous jump of eight light years will take eight years on the traveller's clock. Like conventional travellers, FTL travellers minimize their own proper time for a given journey by staying close to lightspeed.

Grant Hutchison

I concede that I do not follow the math at all and am not arguing with you or dgavin's responses... but it sure does seem as if these two statements are at odds with one another:

"And, if we want to say that zero time passes for a traveller at lightspeed, we also have to note that the Universe spans zero distance for that traveller in the direction of travel: you can get anywhere in zero time."

"At the extreme, what one observer sees as an instantaneous jump of eight light years will take eight years on the traveller's clock."

Again...not arguing.. still struggling though. :) Thank you for the response and education!

Jon

BadTrip
2010-Jul-26, 05:15 PM
Yes.
Yes, but motion of what? And whose time? These are no longer absolute issues in relativity. Typically, the observer observes motion in something else, an observer does not observe its own motion. Indeed, relativity allows all observers to imagine they are stationary, since all they can measure is motion relative to themselves.

yes....thank you for resetting my idea on the frames of reference. Those are excellent points. I'm still tripping up on the issue of there not being a "universal clock". Quite odd for me thus far.


Not necessarily-- you may imagine that your position, as an observer, is always the same, you can always be at "the origin" of your coordinate system. Or you can use different coordinates, it's all just the language you are using to talk about what is happening. What is actually happening must be independent of coordinates, that is the deepest principle at the core of relativity.
Excellent!! Very well stated.. thank you.



When you consider time dilation, you must also consider length contraction. ...... In particular, if it takes you zero time to get from point A to point B, then the distance between point A and B is zero. If point A and B are not the same point, yet the distance between them is zero, then they are moving at speed c (or if you prefer, you are moving between them at speed c).
This one is difficult for me. I comprehend what you're saying....almost. heh... All the way up until you state that either both points are moving at c, or I'm moving between them at c. You imply that there is no difference between the two, right? That's what I'm struggling with. Wouldn't this only be the case if they are on the path I'm travelling?...the same vector? (if that's the correct term)

Thaks for the guidance and lessons!

Ken G
2010-Jul-26, 08:10 PM
You imply that there is no difference between the two, right?Right-- whether you are moving, or the objects you visit are moving, depends only on your own chosen coordinate system. I would say that reality itself does not seem to adjudicate the question, because we don't know how to ask reality "which one is really moving?" You might allow that you are the one moving if you are in a spaceship, but it's still just a choice of language, like all coordinates.

That's what I'm struggling with. Wouldn't this only be the case if they are on the path I'm travelling?Yes, the length is only contracted along the path you are traveling. The space between the different objects A and B would appear to be squeezed to nothing along the direction you were traveling, and that direction must link A and B if you are to visit both those objects.

BadTrip
2010-Jul-26, 08:17 PM
Thanks again for the excellent details and explanations Ken G.

grant hutchison
2010-Jul-26, 08:51 PM
I concede that I do not follow the math at all and am not arguing with you or dgavin's responses... but it sure does seem as if these two statements are at odds with one another:

"And, if we want to say that zero time passes for a traveller at lightspeed, we also have to note that the Universe spans zero distance for that traveller in the direction of travel: you can get anywhere in zero time."

"At the extreme, what one observer sees as an instantaneous jump of eight light years will take eight years on the traveller's clock."The statements apply to two different situations. We have to keep track of who is measuring the time and who is measuring the distance.
1) If the traveller moves at light-speed, then he will take eight years to cover eight lightyears, according to all observers but himself. By the dodgy application of SR to the traveller's "lightspeed reference frame" we find that zero time passes for the traveller, but that he measures all distances along his line of travel as zero, too. He can go anywhere in no time by his own clock.
2) But if an FTL traveller moves instantaneously across eight lightyears according to some outside observer, then the traveller's own clock will have ticked off eight years. There will be only one reference frame in which the journey is instantaneous and spans eight lightyears; it will look different to other observers. In fact, for any FTL traveller, we can find an observer who measures the journey to be instantaneous. That observer will always measure the distance travelled in lightyears to be equal to the traveller's own clock time in years.

Or so the equations of SR seem to tell us. :)

Grant Hutchison

Ken G
2010-Jul-26, 09:57 PM
But if an FTL traveller moves instantaneously across eight lightyears according to some outside observer, then the traveller's own clock will have ticked off eight years. There will be only one reference frame in which the journey is instantaneous and spans eight lightyears; it will look different to other observers. In fact, for any FTL traveller, we can find an observer who measures the journey to be instantaneous. That observer will always measure the distance travelled in lightyears to be equal to the traveller's own clock time in years. That's interesting, I hadn't appreciated that. One minor nitpick though that I know you are already aware of-- we can't really say there's an observer who would measure it to be instantaneous, we can say that they could use measurements to reckon it to be instantaneous using the Einstein convention. But that convention relies on light transit to arbitrate the meaning of "simultaneous" and "instantaneous", so it is arguable that if superluminal signals ever became possible, we might have to reconsider our reliance on Al's convention altogether! In fact, we might have to toss the whole concepts of simultaneity and instantaneity as having any physical meaning at all-- I'd argue the only reasons they survived relativity in the first place is because when the speed of light is not exceeded, our pre-relativistic notions of causality still survive as well. Chuck that, and we have no flavor of time except the proper time owned by each individual-- for whom instantaneous means something physical only when applied to events happening at both the same place and time.

publius
2010-Jul-26, 10:14 PM
Yeah, any FTL path, that is a line with a slope > c, will be the spatial axis for some observer. The relation is this:

uv = c^2, or (u/c)(v/c) = 1, where v is the (time-like) velocity, and u is the space-like path.

Thus, for u = 2c, that is instantaneous for v = 1/2 c.

grant hutchison
2010-Jul-26, 10:16 PM
One minor nitpick though that I know you are already aware of-- we can't really say there's an observer who would measure it to be instantaneous, we can say that they could use measurements to reckon it to be instantaneous using the Einstein convention.
...Hence my little disclaimer at the end: "Or so the equations of SR seem to tell us." :)

Grant Hutchison

Ken G
2010-Jul-26, 10:40 PM
Hence my little disclaimer at the end: "Or so the equations of SR seem to tell us." :)
Oh but I'm not contradicting any of those equations, I, like you, am taking them at face value. Those equations don't require the Einstein simultaneity convention, they can be interpreted in entirely coordinate-free ways (i.e., each observer can be left to bear witness to their own local environment, with no effort to "export" their concept of time elsewhere). I'm saying that the day we discover a superluminal particle, we might still have all the equations of special relativity, but any idea that Einstein's simultaneity convention admits a physical interpretation that two distant events can be "simultaneous" at all will be kaput. It's arguable that it is already kaput, but there remains the general causality connections that it supports, so it has some value. Take those away, and the Lorentz transformations (which embody the Einstein simultaneity convention and the global constancy of the speed of light) have nothing whatever to recommend them, beyond being the way to translate within an arbitrary coordinatization scheme that will get the invariants right, along with all the other arbitrary coordinatizations that do the same (like Tangherlini coordinates, for example).

grant hutchison
2010-Jul-26, 11:06 PM
Oh but I'm not contradicting any of those equations, I, like you, am taking them at face value.So you're separating the solution to the equations from how we interpret the solution?

Grant Hutchison

BadTrip
2010-Jul-27, 12:11 AM
I REALLY appreciate you guys taking the time with me... and I am also enjoying, and am most appreciative and impressed, to see you debate and discuss topics such as this with respect and courtesy for one another.

Thanks!

Ken G
2010-Jul-27, 02:01 AM
So you're separating the solution to the equations from how we interpret the solution?
Yes. A solution requires that a particular set of coordinates be chosen, that's true even in regular Newtonian mechanics (gravity points in the z direction, here is z(t), and so on). So that's like choosing what language, English or Spanish or French, that you are going to use to talk about what is happening, except that these different languages also lend themselves to different interpretations of concepts like simultaneity. The language, and its interpretations, can be separated from the actual physics of the predictions you are making, and that's important to do because only the latter benefits from the evidence of successful testing. Language about global simultaneity connections, or what counts as instantaneous travel, are of the English/Spanish/French type, they are our own choices that are not arbitrated by the physics or the predictions.

I think this is an important distinction to make, because special relativity conventionally chooses a particular language (Einstein simultaneity), yet no part of the theory of special relativity and its predictions requires that global coordinate choice. If every physics book in the world was written in English, we might fall under a false sense that physics is an English description of reality, and that's what is to be avoided when understanding special relativity (I would argue). All the same, in this case it really is as though every textbook was written in English, so some would say, what's the harm in imagining that it's a theory that is expressly English? The harm is that it suffers the ironic fate of being untrue to the core principle of relativity itself.

As with all the theories of physics, special relativity is a local theory, tested by local observations. It's key goals are limited to translating between observers who are at the same event but in relative motion, making observations with standard clocks and rulers. And you can span event space with observers in arbitrary states of motion, and still obtain a complete picture of the testable physical predictions. So that is the first key point-- cobbling together global pictures manifestly involves making arbitrary choices about what observers you are using to bear witness to the events they experience, and that's what making an arbitrary coordinate choice is all about.

But then there is also the issue of what freedom you have for translating among the local observers in relative motion, and there we take the Lorentz transformation (locally) if our goal is to codify certain symmetry principles (isotropic speed of light, laws of physics in the same form for all). That this works was viewed by Einstein as a core philosophical pillar of relativity, so to break from that local description does border on leaving the realm of relativity theory. However, in terms of just the physical predictions, one can instead choose to drop the symmetry principles in favor of other philosophical priorities, like maintaining a fixed set of local spacetime axes (that's what Tangherlini does, everyone uses the same time and space axes used in one arbitrarily chosen "aether frame", but sets clocks differently so that the speed of light is only isotropic in the aether frame). Or one can take the perspective that clocks and rulers only work properly in one frame, again an aether frame, as originally imagined by Poincare and Lorentz himself). So even in the purely local physics, we still have to arbitrarily navigate between Einsteinian relativity, and that of Lorentz and Poincare, and that of Tangherlini (now but footnotes to history-- Einstein's symmetry principles are preferred). All the testable predictions are the same-- the differences are purely philosophical. Shall this be a part of our understanding of special relativity, or shall we all just agree to use the same language, and risk losing sight of what is physical demonstrable, and what is just convention?

undidly
2010-Jul-27, 03:17 AM
Can anyone explain to me why people hypothesise that you would travel backward in time if you exceed the speed of light?

I realise that superluminal speeds are impossible, but people speculate on it nonetheless.

I’ve seen the time dilation equations and can understand how a stationary observer may see your personal clock run slower as you speed up, and by extension backwards when you pass light speed, but I’m not sure how that would affect entropy within you spacecraft and whether you would grow younger.

I fail to see however, how you would not find yourself in the past, when you slowed back down.

Be gentle with me – I only have high school physics and even that is approaching 30 years old.

No one can explain it because it is not true.
Those who say it is true do not understand the math.

If a some imaginary pink unicorn travels at 2C to the nearest star (4 light years away) and back at the same speed ,when will
it arrive here or when did it arrive here.

I never get an answer to this simple question because they cannot do the math.

Ken G
2010-Jul-27, 03:35 AM
No one can explain it because it is not true.
Those who say it is true do not understand the math.

If a some imaginary pink unicorn travels at 2C to the nearest star (4 light years away) and back at the same speed ,when will
it arrive here or when did it arrive here.

I never get an answer to this simple question because they cannot do the math.Actually, I'm quite certain that any of the previous posters who described the time travel scenario above would be happy to answer your question, because the math is quite easy. Nor is it the scenario we described above-- indeed, if you actually read what we said more carefully, you will find all kinds of differences between our scenario and yours. Those differences are there because your scenario does not lead to time travel (and time travel does not mean the traveler undergoes reverse aging, we already corrected that part).

Thus I will answer your question. If a pink unicorn traveled at 2c, as reckoned by an observer left behind, to a star 4 LY away, the observer left behind would reckon that the trip takes two years. Then if the pink unicorn returned at 2c that same distance, it would take another 2 years. The pink unicorn returns 4 years after leaving, as measured by the observer left behind. In particular, as 4 years has passed at the departure point, there is no "younger version" of the pink unicorn there to meet his older self. That scenario does not produce time travel.

Now go back and read the actual scenarios that do yield time travel. I will give you a hint-- the key element in the scenarios that lead to time travel is that the superluminal speed of the pink unicorn, called u above, is reckoned from two different reference frames, separating at relative speed v from each other. I'm sorry it had to be that complicated, but it did-- the simple scenario you describe (where v = 0) simply doesn't work to give time travel-- that much you got right.

The complication I refer to does bring up an important point, however-- to get time travel requires more than superluminal speed. It also requires a symmetry principle that allows that superluminal speed to be achieved from two different reference frames-- there cannot be anything different about the return trip as seen from the distant departure point than there was on the outbound trip as seen from the origin. If it instead turned out that superluminal speeds could be achieved, but not in a symmetric way in different reference frames, it would usher in the return of absolute motion through an aether-- and superluminal motion would not necessarily allow time travel. My point with Grant is that all of this could be accomplished while still being described by the equations of special relativity, but not within the spirit and philosophical postulates of special relativity that provide a path to deriving those equations-- which invoke a symmetry principle that would be violated unless superluminal travel could yield time travel.

Drunk Vegan
2010-Jul-27, 04:00 AM
Out of curiosity, how does the answer to this question change if you consider the possibilities of FTL in a quantum universe?

I am far from an expert, but it strikes me that including quantum mechanics should vastly change what is said concerning the effects of hypothetical FTL. In particular I'm thinking of quantum entanglement, which from what I understand makes it difficult not to come to the conclusion that some events * can * happen simultaneously, even when the two events are not local with respect to one another.

undidly
2010-Jul-27, 04:16 AM
Actually, I'm quite certain that any of the previous posters who described the time travel scenario above would be happy to answer your question, because the math is quite easy. Nor is it the scenario we described above-- indeed, if you actually read what we said more carefully, you will find all kinds of differences between our scenario and yours. Those differences are there because your scenario does not lead to time travel (and time travel does not mean the traveler undergoes reverse aging, we already corrected that part).

Thus I will answer your question. If a pink unicorn traveled at 2c, as reckoned by an observer left behind, to a star 4 LY away, the observer left behind would reckon that the trip takes two years. Then if the pink unicorn returned at 2c that same distance, it would take another 2 years. The pink unicorn returns 4 years after leaving, as measured by the observer left behind. In particular, as 4 years has passed at the departure point, there is no "younger version" of the pink unicorn there to meet his older self. That scenario does not produce time travel.

Now go back and read the actual scenarios that do yield time travel. I will give you a hint-- the key element in the scenarios that lead to time travel is that the superluminal speed of the pink unicorn, called u above, is reckoned from two different reference frames, separating at relative speed v from each other. I'm sorry it had to be that complicated, but it did-- the simple scenario you describe (where v = 0) simply doesn't work to give time travel-- that much you got right.

The complication I refer to does bring up an important point, however-- to get time travel requires more than superluminal speed. It also requires a symmetry principle that allows that superluminal speed to be achieved from two different reference frames-- there cannot be anything different about the return trip as seen from the distant departure point than there was on the outbound trip as seen from the origin. If it instead turned out that superluminal speeds could be achieved, but not in a symmetric way in different reference frames, it would usher in the return of absolute motion through an aether-- and superluminal motion would not necessarily allow time travel. My point with Grant is that all of this could be accomplished while still being described by the equations of special relativity, but not within the spirit and philosophical postulates of special relativity that provide a path to deriving those equations-- which invoke a symmetry principle that would be violated unless superluminal travel could yield time travel.

""The pink unicorn returns 4 years after leaving,""

I agree .
How is that backward time travel?.

Ken G
2010-Jul-27, 05:05 AM
Out of curiosity, how does the answer to this question change if you consider the possibilities of FTL in a quantum universe?

I am far from an expert, but it strikes me that including quantum mechanics should vastly change what is said concerning the effects of hypothetical FTL. In particular I'm thinking of quantum entanglement, which from what I understand makes it difficult not to come to the conclusion that some events * can * happen simultaneously, even when the two events are not local with respect to one another.That's probably a whole different thread, but I will say that quantum entanglement does not actually require that distant events happen simultaneously. Quantum mechanics forces us to track the difference between reality and information about reality, and information about reality can always change instantaneously, because that information resides in the brain that is noticing the information. It's really only a little more complicated than a perfectly classical analog, where you can imagine a grenade blows up into two pieces that fly away from each other for thousands of years in deep space. Then if you catch up to one piece, and look at it carefully, by inference of what is missing from the whole grenade, you can determine the attributes of the distant piece. That piece may be outside your past light cone, yet you know something about it. That's no violation because the explosion itself happened within your past light cone.

The point is, you can learn about a whole system by looking at part of it, even if only the part you are looking at is within your past light cone when you look at it. The only thing quantum entanglement adds is the weirdness of correlations that don't allow you to imagine the other piece of the grenade was "always like that, even before you observed its other half"-- but quantum mechanics is always like that, you often cannot say that a system had a given attribute before you measure it.

Ken G
2010-Jul-27, 05:08 AM
""The pink unicorn returns 4 years after leaving,""

I agree .
How is that backward time travel?.
It isn't.

baskerbosse
2010-Jul-27, 06:24 AM
It isn't.

Ah! -But what does the pink unicorn experience at 2c!? ;-)

/Peter

Ken G
2010-Jul-27, 08:10 AM
Ah! -But what does the pink unicorn experience at 2c!? The life of a pink unicorn. After all, to it, is it you who are moving at 2c, not it.

undidly
2010-Jul-27, 08:27 AM
Quote Originally Posted by undidly View Post
""The pink unicorn returns 4 years after leaving,""

I agree .
How is that backward time travel?.

Ken G "" It isn't.""

So why do so many say that anything traveling faster that light goes back in time?.
That is what this topic is about.

Ken G
2010-Jul-27, 09:20 AM
So why do so many say that anything traveling faster that light goes back in time?.
That is what this topic is about.
Well, I'd say the topic is about under what circumstances could you unambiguously claim to have traveled back in time, and how superluminal travel could accomplish that. Time travel is unambiguous if you meet up with a younger version of yourself, or visit Earth's early history, or some such thing-- merely occupying an earlier time at some distant location in some particular global coordinate system is not convincing evidence of time travel (but is the one used by those who claim that all superluminal motion implies time travel). The circumstances required for the unambiguous version of time travel are described early in the thread, and constitute more than just superluminal travel-- which is exactly why the OPer asked the question, and why you might have asked a similar question.

grant hutchison
2010-Jul-27, 10:18 AM
So you're separating the solution to the equations from how we interpret the solution?Yes. A solution requires that a particular set of coordinates be chosen, that's true even in regular Newtonian mechanics (gravity points in the z direction, here is z(t), and so on). So that's like choosing what language, English or Spanish or French, that you are going to use to talk about what is happening, except that these different languages also lend themselves to different interpretations of concepts like simultaneity. The language, and its interpretations, can be separated from the actual physics of the predictions you are making, and that's important to do because only the latter benefits from the evidence of successful testing. Language about global simultaneity connections, or what counts as instantaneous travel, are of the English/Spanish/French type, they are our own choices that are not arbitrated by the physics or the predictions..
...That's the same separation I was acknowledging, by writing about what "the equations of SR seem to tell us" (as contrasted with what they straighforwardly tell us). It was a rather opaque was of expressing it, though.

Grant Hutchison

grant hutchison
2010-Jul-27, 10:33 AM
No one can explain it because it is not true.
Those who say it is true do not understand the math.

If a some imaginary pink unicorn travels at 2C to the nearest star (4 light years away) and back at the same speed ,when will
it arrive here or when did it arrive here.

I never get an answer to this simple question because they cannot do the math.As Ken points out, that's not the way to use FTL for time travel into your own past.
Your pink unicorn needs to change reference frames at its destination before beginning its journey back to Earth. I explained how to do that, earlier in the thread. I can even offer a spacetime diagram (http://www.ghutchison.pwp.blueyonder.co.uk/relativity/instajump.jpg) of a round trip into one's own past, using two instantaneous "jumps" and two reference frames in relative motion.
Time in the Earth frame is vertical, space horizontal. Live life from A to B on Earth. Jump instantaneously to a nearby star along BC. Live for a while at that star along CD. Accelerate away from Earth to a sublight velocity at D, and coast between DE. Your new standard of simultaneity now slopes relative to the simultaneity standard of the reference frame: so an instantaneous jump in your new reference frame takes you along EF. Arriving in the vicinity of Earth with your residual sublight velocity, you coast home along FA, and decelerate to rest in Earth's reference frame at A, ready to kill your own grandfather.
The maths is relatively straightforward: if your sublight velocity (along DE and FA) is x lightyears per year, then your simultaneity line for the instantaneous jump slopes at x years per lightyear. The rest is conventional geometry.

Grant Hutchison

Ken G
2010-Jul-27, 02:25 PM
That's the same separation I was acknowledging, by writing about what "the equations of SR seem to tell us" (as contrasted with what they straighforwardly tell us). It was a rather opaque was of expressing it, though.
OK, then our mini-disagreement centered on what we should take as the message that special relativity seems to tell us. To me, what relativity tells us is the elevation of observers as the supreme arbiters of reality (like measurements on rulers and clocks), equipped with a kind of democratic principle that we can use the testimony of any of them, in contrast with approaches that speak about a reality independent of those observers (like absolute space and time). Since observer measurements are purely local, expressions of the existence of global attributes like simultaneity between distant events is a bit of a backslide into language suggesting that reality adjudicates in favor of some observer sets over others. I realize such language is quite standard in applying special relativity, but I argue it is a throwback to Einstein's original formulation-- and one that he later corrected but we basically weren't listening! Hence, all special relativity seems to tell us is that we still cling too tightly to pre-relativistic notions about global space and time. If superluminal signaling were possible, then even the boundaries enforced by causality would be taken down, and there would remain no vestige of any physical notion of global simultaneity.

grant hutchison
2010-Jul-27, 02:38 PM
OK, then our mini-disagreement centered on what we should take as the message that special relativity seems to tell us. To me, what relativity tells us is the elevation of observers as the supreme arbiters of reality (like measurements on rulers and clocks), equipped with a kind of democratic principle that we can use the testimony of any of them, in contrast with approaches that speak about a reality independent of those observers (like absolute space and time). Since observer measurements are purely local, expressions of the existence of global attributes like simultaneity between distant events is a bit of a backslide into language suggesting that reality adjudicates in favor of some observer sets over others. I realize such language is quite standard in applying special relativity, but I argue it is a throwback to Einstein's original formulation-- and one that he later corrected but we basically weren't listening! Hence, all special relativity seems to tell us is that we still cling too tightly to pre-relativistic notions about global space and time.Again, no disagreement here.

I'm not sure if this extended exercise in agreement about matters deep to the OP is in violation of Q&A rules. Maybe we should stop before we find out. :)

Grant Hutchison

Ken G
2010-Jul-27, 02:48 PM
Yes, to keep it germane to the OP, all I'm saying is that whether or not superluminal travel always leads to time travel, or whether it only leads to time travel in more complicated scenarios (relevant also to the discussion with undidly), depends on how seriously one takes the standard special-relativistic language on the topic of global simultaneity. The (u/c)*(v/c) > 1 requirement that came up in regard to time travel applies to the unambiguous (invariant) version of time travel (where you go back and meet your younger self), whereas only u/c > 1 is required to have time travel in the context of the Einstein global simultaneity convention.

Moose
2010-Jul-27, 04:24 PM
You don't need to wait for us if you want to start a new thread in Astronomy for supplemental discussion. Have fun.

Swift
2010-Jul-27, 04:24 PM
I have split Cosmocrazy's question about reality into this thread (http://www.bautforum.com/showthread.php/106299-What-really-are-time-space-and-reality). If other posts also need to get moved, please let me know.

Cougar
2010-Jul-28, 02:08 AM
Can anyone explain to me why people hypothesise that you would travel backward in time if you exceed the speed of light?

Well, you could travel to your own past without exceeding the speed of light if you could find a region of spacetime defined by a closed timelike curve (http://en.wikipedia.org/wiki/Closed_timelike_curve). But you can't get there using special relativity, only general relativity.







In extreme examples, in spacetimes with suitably high-curvature metrics, the light cone can be tilted beyond 45 degrees. That means there are potential "future" positions, from the object's frame of reference, that are spacelike separated to observers in an external rest frame. From this outside viewpoint, the object can move instantaneously through space. In these situations the object would have to move, since its present spatial location would not be in its own future light cone. Additionally, with enough of a tilt, there are event locations that lie in the "past" as seen from the outside. With a suitable movement of what appears to it its own space axis, the object appears to travel though time as seen externally.

A closed timelike curve can be created if a series of such light cones are set up so as to loop back on themselves, so it would be possible for an object to move around this loop and return to the same place and time that it started. An object in such an orbit would repeatedly return to the same point in spacetime if it stays in free fall. Returning to the original spacetime location would be only one possibility; the object's future light cone would include spacetime points both forwards and backwards in time, and so it should be possible for the object to engage in time travel under these conditions. [Thanks to wiki contributors. (http://en.wikipedia.org/wiki/Closed_timelike_curve)]

nokton
2010-Jul-28, 05:26 PM
No one can explain it because it is not true.
Those who say it is true do not understand the math.

If a some imaginary pink unicorn travels at 2C to the nearest star (4 light years away) and back at the same speed ,when will
it arrive here or when did it arrive here.

I never get an answer to this simple question because they cannot do the math.

Hi undidly, The math is not important here, concept is. The original question that created this thread has not
been answered. Just a forum for sophisticated rhetorticians to promulgate their esoteric ideas in the interest
of self worth, and to achieve brownie points at the expence of their opponents.
undidy, in the search for truth, language is suspect.
Nokton

grant hutchison
2010-Jul-28, 06:16 PM
Hi undidly, The math is not important here, concept is. The original question that created this thread has not
been answered.Was something unclear about the answer I provided? Do you have any specific questions?

Grant Hutchison

Ken G
2010-Jul-28, 07:08 PM
Just a forum for sophisticated rhetorticians to promulgate their esoteric ideas in the interest
of self worth, and to achieve brownie points at the expence of their opponents.

I can see how someone who does not understand what is being said could imagine that to be true, perhaps as a kind of coping mechanism, but it is still a stance that essentially represents giving up. More constructive would be to identify where something is being said that you do not understand, and try to form a specific question relating to it. That there are very subtle issues here is no secret, and we can all find ourselves vacillating between periods when we think we understand, and periods where we find our understanding lacking. But we have to be willing to try to understand, and not simply discount the only hope we will ever have of actually understanding. (That's also what Grant said, but characteristically, you have to read between the lines more.)

publius
2010-Jul-28, 11:54 PM
For the record, if one wants to "see the math", it's very simple. All we need if the t equation from the Lorentz transform:

T = y(t - vx/c^2), where y is "gamma" and I use T for t-prime.

In the x-t frame, consider some straight line path x = ut. For clarity we'll paramertize that path by 's', and thus we have x = us, and t = s (trivial, but it helps to keep coordinate times and invariant intervals along paths separate). Plug that into the T transform and we have an expression for the coordinate time of that path in a frame moving at 'v' vs the interval s:

T = y(s - vus/c^2) = y(1 - uv/c^2)s

Now, if uv/c^2 >1, which means u > c^2/v, then T runs backwards with s. Consider negative v as well as positive, and you'll see that condition for T to always run foward is |u| <= c^2/|v|. Since we can have frames with any v up to c, that condition becomes
|u| <= c. Causal influences must travel no faster than c to preserve the chronological order in all frames. That's the famous "light cone", and what we might call "strong causality", ie all frames much see a causal chain occur in proper order.

Mere "weak causality" might just say "no closed loops", but, as discussed above by Ken and Grant, that is equivalent to a preferred frame, and that frame is just the one where all such chains run in proper order, which could easily be discovered by all observers by doing appropriate "FTL signal" experiments.

-Richard

Ken G
2010-Jul-29, 02:15 AM
Good point-- if FTL signals were really possible, we could quickly discover if there was an "aether" or not. If there was, the FTL signals would experience a strange limit that depended on the v of the frame. If instead, the FTL signals behaved symmetrically in all frames, then not only would we not need an aether (as is the current situation without FTL), we would finally know for sure there wasn't one-- and we wouldn't have weak causality either (which would be bizarre indeed). So assuming a break in weak causality is unthinkable, it means that FTL requires an aether rather than the observer symmetries of relativity.

WayneFrancis
2010-Jul-29, 02:26 AM
Pardon me while I struggle with this.... not that I'm arguing... just trying to understand.

So then, if you’re traveling at the speed of light it takes you zero time to get to your destination with respect to your own frame of reference. Yes?

Motion is defined as a change in position over time. Yes?

Within your own frame of reference…. Have you changed position? The answer must be yes, right? You started out at point A and have now arrived at point B, even though, within your own frame of reference no time has elapsed. If no time has elapsed has there been any motion? Or more appropriately I suppose… according to you, within your own frame of reference, have YOU moved? Perhaps you have remained motionless, since no time passed?... has the other coordinate, your destination coordinate, been in motion rather than you?

There was another thread around here that asked the question of “does a photon age?”…or something similar. Perhaps, from the frame of reference of the photon, it is not in motion?, but rather everything else is.

Oh man… I need another cup of coffee.

If you could, some how, get your velocity of c then in the direction of travel the universe would collapse in front of you to zero length and behind you...nothing as since you are travelling at c no light could catch up with you.

But you can't so the oddities really don't matter.

undidly
2010-Aug-02, 02:36 AM
For the record, if one wants to "see the math", it's very simple. All we need if the t equation from the Lorentz transform:

T = y(t - vx/c^2), where y is "gamma" and I use T for t-prime.

In the x-t frame, consider some straight line path x = ut. For clarity we'll paramertize that path by 's', and thus we have x = us, and t = s (trivial, but it helps to keep coordinate times and invariant intervals along paths separate). Plug that into the T transform and we have an expression for the coordinate time of that path in a frame moving at 'v' vs the interval s:

T = y(s - vus/c^2) = y(1 - uv/c^2)s

Now, if uv/c^2 >1, which means u > c^2/v, then T runs backwards with s. Consider negative v as well as positive, and you'll see that condition for T to always run foward is |u| <= c^2/|v|. Since we can have frames with any v up to c, that condition becomes
|u| <= c. Causal influences must travel no faster than c to preserve the chronological order in all frames. That's the famous "light cone", and what we might call "strong causality", ie all frames much see a causal chain occur in proper order.

Mere "weak causality" might just say "no closed loops", but, as discussed above by Ken and Grant, that is equivalent to a preferred frame, and that frame is just the one where all such chains run in proper order, which could easily be discovered by all observers by doing appropriate "FTL signal" experiments.

-Richard

""Causal influences must travel no faster than c to preserve the chronological order in all frames.""

The chronological order is not affected by any observer in any frame.
The observer (can be a machine) may "see" the chronological order is different but so what?.
Observers in different frames see different rates of time is OK but different sequence is not OK?.
Why is that?.

Ken G
2010-Aug-02, 05:57 AM
The observer (can be a machine) may "see" the chronological order is different but so what?.
Observers in different frames see different rates of time is OK but different sequence is not OK?.
Why is that?.Here I think we encounter the difference between a time coordinate and doing physics using a time coordinate. If we want to do physics, then our own time coordinate should be our proper time, which is the time that our clock reads (and physics, being an empirical science, must be able to connect with our clock). But sometimes we want to do physics in a way that refers to events we are not present at, and more importantly, our clock is not present at. Whenever that is true, we must adopt a coordinate system, which in the context of doing physics, is exactly the same thing as a prescription of establishing which of the various (often hypothetical) clocks that are present at the events we are interested in we are going to use to establish the time intervals along the "world line" of the continuous series of events we are doing physics on.

The prescription for choosing observers can be completely arbitrary, as can be their clock settings, since we will still end up with a faithful witness to the local durations that connect the events we are interested in (but were not present at ourselves). So there is no requirement on these lists of observers that their clock readings must increase along a causal chain that we are interested in talking about. Indeed, we have no interest at all in how those observers would time order the events along the causal chain, as we are only using them for individual segments along that chain (the ones they are local to). What "time orders" the events along that causal chain is the proper time along the world line that connects them, which we can infer from the measurements of these observers, i.e., from our own chosen coordinate system. The sole physical constraint is that the proper time must increase if the world line is inside the forward light cone, stay the same if it is on the light cone, and decrease if it is in the backward light cone, along that world line. Also, if we don't allow time travel, the proper time must be single-valued along that world line (the forward light cones cannot loop back to an earlier place on the world line).

Now, the only way other observers, or other coordinate choices, come into play is that the proper time along the world line is an invariant-- it must come out the same in any coordinate, including those where the events correspond to time readings that are not in order. We already experience that phenomenon right here on Earth, when we drive back and forth across a time zone boundary! The events are not correctly time ordered by the time coordinate, but they are by the invariant proper time. So that's the "so what" you are asking-- the coordinate time is indeed "so what", but the invariant proper time is what all the physics gets done on. So that answers "why is that"-- we need invariants to have a concept of objective science, and it must correctly describe the causal links. To compare with observations that test the physics, we can always convert back to the measurements of the local observers with their clocks and rulers, because we know how to map back and forth from a proper time interval to these kinds of local coordinates. Global coordinates are entirely superfluous, we never needed the concept and I feel it should be completely struck from relativity pedagogy, even that of special relativity.

sdsperth
2010-Aug-10, 02:51 PM
Hi Ken G.
I donít understand why, but I am at least glad to hear that an extra element is required for time travel.
I am heartened to hear that the pink unicorn returns 4 years after leaving where v = 0.

sdsperth
2010-Aug-10, 02:53 PM
Thanks dgavin. How does time pass for the thing in motion? Forwards? Backwards? Frozen?

dgavin
2010-Aug-11, 12:25 AM
Thanks dgavin. How does time pass for the thing in motion? Forwards? Backwards? Frozen?

Thats an unknown as our current physics only describe time for outside ovservers in this case. The following wiki might give some hints of what might happen though.

http://en.wikipedia.org/wiki/Tachyon