Which by definition is time travel, it's just not all that science fiction has hyped itself up to be.
But you were arguing that you would go back in time. You wouldn´t. You just went ahead in time a bit slower. If we both walk on the sidewalk and I walk 0.05% faster than you you would not go backwards.
The clock in the lattice will not read t+epsilon if your signal travels faster than light for the signal maintaining the lattice time structure is traveling at light speed hence your signal will arrive at the next lattice point at t-epsilon hence going back in time which is why none of the faster than light travel makes sense in an unbent lattice because it is always possible to set the clocks up according to the fastest signal -- and right now the fastest signal and all related calculations suggest the speed of light is the speed limit of the universe.
I'm beginning to feel like it's as if I'm saying "Suppose the Earth were flat, then...", and rather than go along with the idea, just to see what interesting things that might come out of supposing that the Earth were flat, instead you'd rather argue why the Earth isn't flat.
Let me go step by step through what I'm trying to establish here:
1) The clocks in the lattice are assumed to have been synchronized using light-speed signals. I care not one whit that if something faster than light were available, that that method would be used instead. I'm saying light has been used so as to establish the usual relativistic sense of time, and of simultaneity within an inertial frame of reference.
2) I'm not trying to work from within the moving frame of reference of an FTL message itself. I don't care about that frame of reference. The assumption is that some how, some way, you send a message at time t, and it arrives at any given destination at t + epsilon, where epsilon is an arbitrarily small positive value. If the message arrives later than you sent the message in the lattice's frame of reference, the message didn't go backwards in time in the lattice's frame of reference. Later equals forward in time... I don't know how I can make that more clear.
3) I think light speed is probably the ultimate speed limit too, but the whole point is to see what, if anything, breaks if you assume something can go faster, and what rules, fanciful or not, would keep temporal paradoxes in an FTL world at bay.
Oh my god. I failed to understand the confusion until now. By definition if something arrives at a lattice clock at t +epsilon it is traveling slower than the speed of light if it left another lattice point at t. By definition. Otherwise you would need to go back in time arriving at a point t-epsilon when you left at t.
Now that we have gotten to the point that traveling faster than light does (in the rest frame) indicate that you go back in time what is your point?
Oh my god. I failed to understand the confusion until now. By definition if something arrives at a lattice clock at t +epsilon it is traveling slower than the speed of light if it left another lattice point at t. By definition. Otherwise you would need to go back in time arriving at a point t-epsilon when you left at t.
Now that we have gotten to the point that traveling faster than light does (in the rest frame) indicate that you go back in time what is your point?
There's confusion here, but I think the confusion is over what is meant by "synchronized".
Are you assuming that when I say "synchronized by a light speed signal" that I'm saying that each clock sets itself to the same time when the light speed signal arrives?
No, no, no...
What's typically meant by synchronizing clocks in relativity is that you compensate for light travel time. If one clock sets itself to 0:00:00 when a synchronization signal passes by, a clock that's one light second away from that clock sets itself to 0:00:01 when the signal arrives.
Bear in mind that people in the present always feel that the "state of the art" of science represents the absolute truth about reality. Ptolemy's model of the universe was a horrible "kludge", but it did explain astronomical phenomena remarkably well until science moved a step further and brought that whole deck of cards crashing down. Perhaps in a couple hundred years (or maybe much less)...we will look back at early 21st Century science as having been decidely primitive. It's all relative.
As we rant about Clark's imagination and "presidential "lunacy"...does anyone recall that infamous poll taken in 2002, in which 44% (!!!!!!!!!!) of the American public (+/- 2%) believed that the Earth was created ex nihil, less than 10,000 years ago!!!!! I just thought I should add this extraordinary (and sad) statistic, re. the state of awareness of one of the most basic facts about the Earth and/or Universe.
Bear in mind that people in the present always feel that the "state of the art" of science represents the absolute truth about reality.
A good scientist knows that "absolute truth" is something we lack, and probably always will. Even if he isn't astute enough to know that, he or she is probably smart enough to avoid phrases like "absolute truth", because saying something like that would make all of the other scientists point and laugh.
Of course, scientists are human, and get rather strongly attached to their ideas, perhaps too attached at times to adapt as quickly as they should to new ideas and new evidence.
Quote:
Ptolemy's model of the universe was a horrible "kludge", but it did explain astronomical phenomena remarkably well until science moved a step further and brought that whole deck of cards crashing down. Perhaps in a couple hundred years (or maybe much less)...we will look back at early 21st Century science as having been decidely primitive. It's all relative.
Newton's Principia Mathematica is over 300 years old, and it's hardly looked at as primitive today. His work holds up so well that his equations are still used routinely today... not Absolute Truth™ for sure, but close enough to reality to get the job done.
I do not foresee Relativity or Quantum Mechanics as appearing quaint or primitive in the foreseeable future. They may not be, and probably aren't, the last word, but they work so well over such large practical domains that they will likely remain useful even when superseded by something else.
While it's important to understand that science changes over time, some people make the mistake of going a bit too far with that notion, acting dismissively towards today's science as if it were ephemeral, just a bit of fashionable intellectual fluff waiting to be blown away by the next thing that comes along.
Such is not typically the case. I believe we've set down some solid foundations in many areas of science that are more likely to be built upon and enhanced, rather than swept aside and utterly replaced.
What's typically meant by synchronizing clocks in relativity is that you compensate for light travel time. If one clock sets itself to 0:00:00 when a synchronization signal passes by, a clock that's one light second away from that clock sets itself to 0:00:01 when the signal arrives.
Nope thats not what is meant in the conventional sense. Think about traveling with that light wave if you took into account how fast the signal was moving then it would appear to you that time is passing, but it is not since you are moving at the speed of light.
I am sorry for calling you on this but without these basic concepts SR thought experiments have no uniformity.
Nope thats not what is meant in the conventional sense.
Of course that's what's typically meant by synchronizing clocks... think about a basic two dimensional space-time diagram, with position x being the horizontal axis, and time t being the vertical axis.
A horizontal line across such a diagram represents simultaneity in the frame of reference of any body with zero motion along the x axis. Light obviously can't travel straight across such a diagram (it's typically shown at a 45 degree angle, with each axis in like units, such as seconds and light seconds), yet despite the fact that light can't cut straight across, all of those points in a straight horizontal line are said to represent simultaneous events in the rest frame of the diagram.
A row of clocks set to the same time would be plotted horizontally across a space-time diagram, not arbitrarily along a left-leaning or right-leaning light line. If you think clocks are synchronized along a light line, how would you choose which one?
You are wrong, the clocks are synchronized at the reception of a light signal sent out from any clock it doesnt matter which -- think about it, if you had one clock on which all were based you would have to know the distance you are from all clocks, in einstein's construction all clocks are equivalent and measure a signal of light passing by at the same time.
You are wrong, the clocks are synchronized at the reception of a light signal sent out from any clock it doesnt matter which -- think about it, if you had one clock on which all were based you would have to know the distance you are from all clocks, in einstein's construction all clocks are equivalent and measure a signal of light passing by at the same time.
My iChat is [email protected] if you want to hash this out... it's getting hard to do with posts back and forth.
When you synchronize clocks, you're supposed to know the distance between them. Yes, you can't synchronize until a light-speed signal arrives, but once it does, you compensate for light-travel time.
Suppose we want to synchronize two clocks that are some distance apart.
We could stand beside one of them and look at the other through a telescope, but we'd have to remember in that case that we are seeing the clock as it was when the light left it, and correct accordingly.
We can't get anywhere unless we agree on the very basics of what it means to synchronize clocks.
I hate to make this sort of appeal, but at least consider this: I was the sole software developer for an award-winning piece of software for teaching Special Relativity. The software won two awards in the 1992 EDUCOM national educational software competition: one for Best Natural Science Software (Physics), the other for Best Design.
The software would have utterly failed if I did not understand the concept of clock synchronization. My math would have utterly failed. The clock synchronization demo written using the software would have failed. I could not have slipped such gross errors past either the reviewers or the physicists I worked with as advisors to the project.
At least give me a little benefit of the doubt, and look a little harder for what you might be misunderstanding that I'm saying.
I cant say whether what you did in your program matters really because presumably you only used the lattice of clocks as a teaching tool and the math from there on out had been worked out.
The software was a free-from thought experiment constructor. When you start up the program, a blank document consists of a single default object at rest at 0, 0 in an x/y coordinate system.
You are allowed to add objects at any point in space, assign those objects velocities, assign actions which occur at given moments of time, such as sending out pulses of light or changing speed and direction.
You can select any object in the simulation and switch into that object's frame of reference. On the fly, all space and time coordinates are updated using the appropriate relativistic transforms.
If you'd been thinking the software was just a dumb playback tool showing canned scenarios that were pre-computed for me by someone else, you'd have the wrong picture. The simulations had to be based on a proper understanding of special relativity, including how time is defined, or the simulations would fail.
My simulation worked so well, I even rediscovered a phenomenon that the physicists I was working with hadn't known about themselves ahead of time.
Rather than putting all motion in a straight line, as is typical in many discussions of SR and related thought experiments, I decided to give the user a playing field with two spacial dimensions. I set up a square course to travel around at high speed... starting at rest wrt to the square, moving around the square, then returning to rest wrt to the square.
When I came to rest at the end of the course, the square course was rotated slightly, tipped on its side. I thought I had a bug in my software. My physicist colleagues were intrigued -- they thought maybe it was a bug too, but worth looking into. One of them came up with the answer after a little research: I'd rediscovered something called "Wigner rotation".
If the software was good enough to rediscover phenomena that we, the writers of the software, didn't even explicitly put into the code, I'd say that's a pretty good sign the math I was using and my understanding of SR that I applied to the code was solid.
Quote:
We agree that if you are traveling at the speed of light that time does not change according to you in some inertial frame (any inertial frame in fact).
Actually, I don't think we can agree on this, because it's a mistake to talk about an observer traveling at the speed of light. Near c is okay -- at c is verboten.
The procedure of synchronizing clocks has nothing to do with trying to put yourself into the frame of reference of photons flying between one clock and the next. You start by assuming the clocks you wish to synchronize are at rest with one another (in the same inertial frame), that you know the distance between the clocks, and that you know the speed of light.
Quote:
That means that the clocks you see in the inertial frame (lets say in this case a lattice of clocks) always seem to read the same time when you pass them.
If you were truly at the speed of light, the universe would be crunched down to zero length in your direction of travel... or, to be more mathematically precise about something you can't really do, length l would approach 0 as velocity v approached c.
Let's see if there is something else we can find to agree on, and work from there...
I think we can both agree that it makes no sense to try to synchronize clocks that are in motion relative to each other, that we are talking about synchronization of clocks within a shared inertial reference frame.
Now, can you agree to this: If two clocks are very accurate, then after an initial synchronization, later synchronization should simply confirm the initial synchronization, altering it very little, if at all. Can you agree to that?
Can you also agree that once two clocks are synchronized, it shouldn't matter which clock you choose to use for a later confirmation of synchronization?
Now consider this: Two clocks at rest wrt to each other, exactly one light second (aproximately 300,000 km) apart.
Your clock is not yet set. The distant clock has been set, and you can read what that clock says through a very powerful telescope. What do you do when you see the distant clock strike midnight?
Unless I'm totally misreading you, what I'm getting out of what you're saying is that the moment you see midnight on the distant clock, you set your own clock to midnight too.
What I'm saying is that as soon as you see midnight on the distant clock, you should set your own clock to one second after midnight.
Before I go on, do you agree with what I've said so far, and my evaluation of what you are saying?
You want to ignore the real/imaginary space transition made at v=c?
Yes... because the exercise simply starts with the assumption that FTL messages can get from one place to another with a preferred reference frame with an arbitrarily small, positive delay. The way the message system would work -- tachyons, quantum gnomes, wishful thinking -- is immaterial.
One thing than can be said... these FTL messages would never travel at the speed of light. Like tachyons, their timelines would also lie outside of the light cone, and no transformation to any inertial frame would change that.
Although I don't know exactly how to bring full mathematical rigor to bear on this, I think I can go this far in explaining what a preferred frame of reference buys you for FTL...
By definition, all of my FTL cause-and-effect relationships will move forward in time within the preferred FTL frame -- a cause at t, an effect at t + epsilon. Since this direction is always forward, a chain of causality linked to these messages will always be forward.
Add normal, light-speed or slower interactions to the mix, and still, everything must move forward in time, because all normal cause-and-effect time lines, in any frame of reference, occur within the light cone, and move forward in time in all frames of reference, including the preferred FTL frame.
I think it's fair to say that if your timeline always moves forward, you can't have a loop, a troubling paradox where an effect turns back on it's own chain of causality.
Now, when you observe a causality timeline that has both FTL and normal components from any other frame of reference, it is possible that some of the steps in that timeline will go backward in time. However, geometrically speaking, such transformations are simple matters of skew and rotation -- they can't put a loop into something that doesn't start with a loop.
As artificial as this construction might be, I feel fairly confident that it allows for FTL without causality paradoxes.
The moment you introduce another inertial frame in which messages can be sent at arbitrarily fast FTL speeds, however, you're in trouble. Some of those timelines will be seen to go backward in time in the orginal FTL frame, and suddenly, you now have a way to make a closed loop out of a chain of events, and thus possibly create a violation of causality.
There is a range of FTL speeds/distances that will always be allowed without paradox since they will never be able to arrive back at the original emission point "before" they were emitted in one frame. FTL occurs -- locally, for instance, in the faster than light travel of beta particles from nuclear decays ( the local speed of light is slower than the speed of the electron, hence the blue glow of light from the pools under which they store nuclear fuel). However, avoiding the paradox in one frame doesn't solve the problem in all frames, in some frame (in a lot of frames) the signal may arrive at the next clock at t+epsilon, but if the signal was traveling faster than light in at least one frame there would be a backwards in time problem. Defining that in all frames you have the signal arriving at some t+epsilon(1,2,3,4...), I think will force you to reach a mathematical paradox in which the assumption that the t+epsilon(1,2,3,4...) cannot be true.
sorry
You should know that GR doesn't have a real way of defining a universal speed of light, ie it the local speed that matters...
but if the signal was traveling faster than light in at least one frame there would be a backwards in time problem. Defining that in all frames you have the signal arriving at some t+epsilon(1,2,3,4...), I think will force you to reach a mathematical paradox in which the assumption that the t+epsilon(1,2,3,4...) cannot be true.
I'm not trying to hide the fact that an FTL signal will appear to move backwards in time in some frames of reference. I plainly admitted to that.
My point was about loops is causality -- does the backward-through-time timeline of an FTL effect ever result in a loop such as sending yourself a message telling yourself not to send the message. What I believe is that the artificial constraint of a preferred frame for FTL signals prevents such loops from being formed.
causality will be broken in at least one frame -- time moving backwards is inherently reversing the properties of the event.
i don't have issues conceiving of things moving faster than light locally. but the things that do cannot carry info (for instance entanglement of quantum particles).
Comments
Originally posted by Argento
Which by definition is time travel, it's just not all that science fiction has hyped itself up to be.
But you were arguing that you would go back in time. You wouldn´t. You just went ahead in time a bit slower. If we both walk on the sidewalk and I walk 0.05% faster than you you would not go backwards.
Originally posted by billybobsky
The clock in the lattice will not read t+epsilon if your signal travels faster than light for the signal maintaining the lattice time structure is traveling at light speed hence your signal will arrive at the next lattice point at t-epsilon hence going back in time which is why none of the faster than light travel makes sense in an unbent lattice because it is always possible to set the clocks up according to the fastest signal -- and right now the fastest signal and all related calculations suggest the speed of light is the speed limit of the universe.
I'm beginning to feel like it's as if I'm saying "Suppose the Earth were flat, then...", and rather than go along with the idea, just to see what interesting things that might come out of supposing that the Earth were flat, instead you'd rather argue why the Earth isn't flat.
Let me go step by step through what I'm trying to establish here:
1) The clocks in the lattice are assumed to have been synchronized using light-speed signals. I care not one whit that if something faster than light were available, that that method would be used instead. I'm saying light has been used so as to establish the usual relativistic sense of time, and of simultaneity within an inertial frame of reference.
2) I'm not trying to work from within the moving frame of reference of an FTL message itself. I don't care about that frame of reference. The assumption is that some how, some way, you send a message at time t, and it arrives at any given destination at t + epsilon, where epsilon is an arbitrarily small positive value. If the message arrives later than you sent the message in the lattice's frame of reference, the message didn't go backwards in time in the lattice's frame of reference. Later equals forward in time... I don't know how I can make that more clear.
3) I think light speed is probably the ultimate speed limit too, but the whole point is to see what, if anything, breaks if you assume something can go faster, and what rules, fanciful or not, would keep temporal paradoxes in an FTL world at bay.
Oh my god. I failed to understand the confusion until now. By definition if something arrives at a lattice clock at t +epsilon it is traveling slower than the speed of light if it left another lattice point at t. By definition. Otherwise you would need to go back in time arriving at a point t-epsilon when you left at t.
Now that we have gotten to the point that traveling faster than light does (in the rest frame) indicate that you go back in time what is your point?
Originally posted by billybobsky
WRONG!
Oh my god. I failed to understand the confusion until now. By definition if something arrives at a lattice clock at t +epsilon it is traveling slower than the speed of light if it left another lattice point at t. By definition. Otherwise you would need to go back in time arriving at a point t-epsilon when you left at t.
Now that we have gotten to the point that traveling faster than light does (in the rest frame) indicate that you go back in time what is your point?
There's confusion here, but I think the confusion is over what is meant by "synchronized".
Are you assuming that when I say "synchronized by a light speed signal" that I'm saying that each clock sets itself to the same time when the light speed signal arrives?
No, no, no...
What's typically meant by synchronizing clocks in relativity is that you compensate for light travel time. If one clock sets itself to 0:00:00 when a synchronization signal passes by, a clock that's one light second away from that clock sets itself to 0:00:01 when the signal arrives.
As we rant about Clark's imagination and "presidential "lunacy"...does anyone recall that infamous poll taken in 2002, in which 44% (!!!!!!!!!!) of the American public (+/- 2%) believed that the Earth was created ex nihil, less than 10,000 years ago!!!!! I just thought I should add this extraordinary (and sad) statistic, re. the state of awareness of one of the most basic facts about the Earth and/or Universe.
Originally posted by sammi jo
Bear in mind that people in the present always feel that the "state of the art" of science represents the absolute truth about reality.
A good scientist knows that "absolute truth" is something we lack, and probably always will. Even if he isn't astute enough to know that, he or she is probably smart enough to avoid phrases like "absolute truth", because saying something like that would make all of the other scientists point and laugh.
Of course, scientists are human, and get rather strongly attached to their ideas, perhaps too attached at times to adapt as quickly as they should to new ideas and new evidence.
Ptolemy's model of the universe was a horrible "kludge", but it did explain astronomical phenomena remarkably well until science moved a step further and brought that whole deck of cards crashing down. Perhaps in a couple hundred years (or maybe much less)...we will look back at early 21st Century science as having been decidely primitive. It's all relative.
Newton's Principia Mathematica is over 300 years old, and it's hardly looked at as primitive today. His work holds up so well that his equations are still used routinely today... not Absolute Truth™ for sure, but close enough to reality to get the job done.
I do not foresee Relativity or Quantum Mechanics as appearing quaint or primitive in the foreseeable future. They may not be, and probably aren't, the last word, but they work so well over such large practical domains that they will likely remain useful even when superseded by something else.
While it's important to understand that science changes over time, some people make the mistake of going a bit too far with that notion, acting dismissively towards today's science as if it were ephemeral, just a bit of fashionable intellectual fluff waiting to be blown away by the next thing that comes along.
Such is not typically the case. I believe we've set down some solid foundations in many areas of science that are more likely to be built upon and enhanced, rather than swept aside and utterly replaced.
Originally posted by shetline
What's typically meant by synchronizing clocks in relativity is that you compensate for light travel time. If one clock sets itself to 0:00:00 when a synchronization signal passes by, a clock that's one light second away from that clock sets itself to 0:00:01 when the signal arrives.
Nope thats not what is meant in the conventional sense. Think about traveling with that light wave if you took into account how fast the signal was moving then it would appear to you that time is passing, but it is not since you are moving at the speed of light.
I am sorry for calling you on this but without these basic concepts SR thought experiments have no uniformity.
Originally posted by billybobsky
Nope thats not what is meant in the conventional sense.
Of course that's what's typically meant by synchronizing clocks... think about a basic two dimensional space-time diagram, with position x being the horizontal axis, and time t being the vertical axis.
A horizontal line across such a diagram represents simultaneity in the frame of reference of any body with zero motion along the x axis. Light obviously can't travel straight across such a diagram (it's typically shown at a 45 degree angle, with each axis in like units, such as seconds and light seconds), yet despite the fact that light can't cut straight across, all of those points in a straight horizontal line are said to represent simultaneous events in the rest frame of the diagram.
A row of clocks set to the same time would be plotted horizontally across a space-time diagram, not arbitrarily along a left-leaning or right-leaning light line. If you think clocks are synchronized along a light line, how would you choose which one?
Originally posted by billybobsky
You are wrong, the clocks are synchronized at the reception of a light signal sent out from any clock it doesnt matter which -- think about it, if you had one clock on which all were based you would have to know the distance you are from all clocks, in einstein's construction all clocks are equivalent and measure a signal of light passing by at the same time.
My iChat is [email protected] if you want to hash this out... it's getting hard to do with posts back and forth.
When you synchronize clocks, you're supposed to know the distance between them. Yes, you can't synchronize until a light-speed signal arrives, but once it does, you compensate for light-travel time.
From Special Relativity: Synchronizing Clocks -- Michael Fowler:
Suppose we want to synchronize two clocks that are some distance apart.
We could stand beside one of them and look at the other through a telescope, but we'd have to remember in that case that we are seeing the clock as it was when the light left it, and correct accordingly.
We can't get anywhere unless we agree on the very basics of what it means to synchronize clocks.
I hate to make this sort of appeal, but at least consider this: I was the sole software developer for an award-winning piece of software for teaching Special Relativity. The software won two awards in the 1992 EDUCOM national educational software competition: one for Best Natural Science Software (Physics), the other for Best Design.
The software would have utterly failed if I did not understand the concept of clock synchronization. My math would have utterly failed. The clock synchronization demo written using the software would have failed. I could not have slipped such gross errors past either the reviewers or the physicists I worked with as advisors to the project.
At least give me a little benefit of the doubt, and look a little harder for what you might be misunderstanding that I'm saying.
Shetline. You have my apologies...
Originally posted by billybobsky
I cant say whether what you did in your program matters really because presumably you only used the lattice of clocks as a teaching tool and the math from there on out had been worked out.
The software was a free-from thought experiment constructor. When you start up the program, a blank document consists of a single default object at rest at 0, 0 in an x/y coordinate system.
You are allowed to add objects at any point in space, assign those objects velocities, assign actions which occur at given moments of time, such as sending out pulses of light or changing speed and direction.
You can select any object in the simulation and switch into that object's frame of reference. On the fly, all space and time coordinates are updated using the appropriate relativistic transforms.
If you'd been thinking the software was just a dumb playback tool showing canned scenarios that were pre-computed for me by someone else, you'd have the wrong picture. The simulations had to be based on a proper understanding of special relativity, including how time is defined, or the simulations would fail.
My simulation worked so well, I even rediscovered a phenomenon that the physicists I was working with hadn't known about themselves ahead of time.
Rather than putting all motion in a straight line, as is typical in many discussions of SR and related thought experiments, I decided to give the user a playing field with two spacial dimensions. I set up a square course to travel around at high speed... starting at rest wrt to the square, moving around the square, then returning to rest wrt to the square.
When I came to rest at the end of the course, the square course was rotated slightly, tipped on its side. I thought I had a bug in my software. My physicist colleagues were intrigued -- they thought maybe it was a bug too, but worth looking into. One of them came up with the answer after a little research: I'd rediscovered something called "Wigner rotation".
If the software was good enough to rediscover phenomena that we, the writers of the software, didn't even explicitly put into the code, I'd say that's a pretty good sign the math I was using and my understanding of SR that I applied to the code was solid.
We agree that if you are traveling at the speed of light that time does not change according to you in some inertial frame (any inertial frame in fact).
Actually, I don't think we can agree on this, because it's a mistake to talk about an observer traveling at the speed of light. Near c is okay -- at c is verboten.
The procedure of synchronizing clocks has nothing to do with trying to put yourself into the frame of reference of photons flying between one clock and the next. You start by assuming the clocks you wish to synchronize are at rest with one another (in the same inertial frame), that you know the distance between the clocks, and that you know the speed of light.
That means that the clocks you see in the inertial frame (lets say in this case a lattice of clocks) always seem to read the same time when you pass them.
If you were truly at the speed of light, the universe would be crunched down to zero length in your direction of travel... or, to be more mathematically precise about something you can't really do, length l would approach 0 as velocity v approached c.
Let's see if there is something else we can find to agree on, and work from there...
I think we can both agree that it makes no sense to try to synchronize clocks that are in motion relative to each other, that we are talking about synchronization of clocks within a shared inertial reference frame.
Now, can you agree to this: If two clocks are very accurate, then after an initial synchronization, later synchronization should simply confirm the initial synchronization, altering it very little, if at all. Can you agree to that?
Can you also agree that once two clocks are synchronized, it shouldn't matter which clock you choose to use for a later confirmation of synchronization?
Now consider this: Two clocks at rest wrt to each other, exactly one light second (aproximately 300,000 km) apart.
Your clock is not yet set. The distant clock has been set, and you can read what that clock says through a very powerful telescope. What do you do when you see the distant clock strike midnight?
Unless I'm totally misreading you, what I'm getting out of what you're saying is that the moment you see midnight on the distant clock, you set your own clock to midnight too.
What I'm saying is that as soon as you see midnight on the distant clock, you should set your own clock to one second after midnight.
Before I go on, do you agree with what I've said so far, and my evaluation of what you are saying?
Originally posted by billybobsky
You are fine shetline -- i was using a construction that i had forgotten to forget...
Well, shall we take things back to the hypothetical "hyper-aether" and FTL, now that this other horse has been beaten to death?
You want to ignore the real/imaginary space transition made at v=c?
Originally posted by billybobsky
sure...
You want to ignore the real/imaginary space transition made at v=c?
Yes... because the exercise simply starts with the assumption that FTL messages can get from one place to another with a preferred reference frame with an arbitrarily small, positive delay. The way the message system would work -- tachyons, quantum gnomes, wishful thinking -- is immaterial.
One thing than can be said... these FTL messages would never travel at the speed of light. Like tachyons, their timelines would also lie outside of the light cone, and no transformation to any inertial frame would change that.
Although I don't know exactly how to bring full mathematical rigor to bear on this, I think I can go this far in explaining what a preferred frame of reference buys you for FTL...
By definition, all of my FTL cause-and-effect relationships will move forward in time within the preferred FTL frame -- a cause at t, an effect at t + epsilon. Since this direction is always forward, a chain of causality linked to these messages will always be forward.
Add normal, light-speed or slower interactions to the mix, and still, everything must move forward in time, because all normal cause-and-effect time lines, in any frame of reference, occur within the light cone, and move forward in time in all frames of reference, including the preferred FTL frame.
I think it's fair to say that if your timeline always moves forward, you can't have a loop, a troubling paradox where an effect turns back on it's own chain of causality.
Now, when you observe a causality timeline that has both FTL and normal components from any other frame of reference, it is possible that some of the steps in that timeline will go backward in time. However, geometrically speaking, such transformations are simple matters of skew and rotation -- they can't put a loop into something that doesn't start with a loop.
As artificial as this construction might be, I feel fairly confident that it allows for FTL without causality paradoxes.
The moment you introduce another inertial frame in which messages can be sent at arbitrarily fast FTL speeds, however, you're in trouble. Some of those timelines will be seen to go backward in time in the orginal FTL frame, and suddenly, you now have a way to make a closed loop out of a chain of events, and thus possibly create a violation of causality.
sorry
You should know that GR doesn't have a real way of defining a universal speed of light, ie it the local speed that matters...
Originally posted by billybobsky
but if the signal was traveling faster than light in at least one frame there would be a backwards in time problem. Defining that in all frames you have the signal arriving at some t+epsilon(1,2,3,4...), I think will force you to reach a mathematical paradox in which the assumption that the t+epsilon(1,2,3,4...) cannot be true.
I'm not trying to hide the fact that an FTL signal will appear to move backwards in time in some frames of reference. I plainly admitted to that.
My point was about loops is causality -- does the backward-through-time timeline of an FTL effect ever result in a loop such as sending yourself a message telling yourself not to send the message. What I believe is that the artificial constraint of a preferred frame for FTL signals prevents such loops from being formed.
i don't have issues conceiving of things moving faster than light locally. but the things that do cannot carry info (for instance entanglement of quantum particles).