Tachyons travel backward in time?

[CJames]

The time dilation equation:

\Delta t' = \Delta t/\sqrt{1 - v^2/c^2}

Now let's consider a tachyon with v = 2c

\Delta t' = \Delta t/\sqrt{1 - (2c)^2/c^2}
\Delta t' = \Delta t/\sqrt{1 - 4c^2/c^2}
\Delta t' = \Delta t/\sqrt{1 - 4}
\Delta t' = \Delta t/\sqrt{-3}
\Delta t' = \Delta ti/\sqrt{3}

I've always heard that tachyons, if they exist, move backward in time. I would've thought this would be expressed as a negative delta t, but from this it appears to be a complex number. Can somebody explain why a complex delta t describes backward time travel? Or am I going about this the wrong way?

 

[gel]

As tachyons travel faster than light then you can always change to a different inertial coordinate frame so that they travel backwards in time (or instantaneously) according to that frame.

 

[Jorrie]

As tachyons travel faster than light then you can always change to a different inertial coordinate frame so that they travel backwards in time (or instantaneously) according to that frame.

Is it not true that in a specific inertial frame timing the travel of a tachyon between an emitter and detector, the time can never be negative, but limits as instantaneous for infinite speed? It appears to me that the "traveling backwards in time" can only be apparent if you switch coordinates during the measurement.

 

[belliott4488]

Is it not true that in a specific inertial frame timing the travel of a tachyon between an emitter and detector, the time can never be negative, but limits as instantaneous for infinite speed? It appears to me that the "traveling backwards in time" can only be apparent if you switch coordinates during the measurement.

I'm not sure I've understood your question. The identification of an "emitter" and a "detector" depends on the frame of reference. You can think of the tachyon's presence at the emitter as one space-time event and its presence at the detector as another. The key here is that the space-time interval between these events is space-like, not time-like. That means that while one observer sees the "emission" event occurring before the "detection" event, you can easily find other reference frames in which the "detection" event comes first (and so you could claim that the tachyon moved backwards in time in that frame, although that's arbitrary, since its direction in time is not absolute). There will also be a frame in which they are simultaneous. In that frame the tachyon actually exists at all points along its path simultaneously, which is kind of what you'd expect for events that have space-like separations.

 

[Dale]

The identification of an "emitter" and a "detector" depends on the frame of reference.

I would think that energy considerations could unambiguously identify the emitter and detector.

 

[Jorrie]

That means that while one observer sees the "emission" event occurring before the "detection" event, you can easily find other reference frames in which the "detection" event comes first (and so you could claim that the tachyon moved backwards in time in that frame, although that's arbitrary, since its direction in time is not absolute).

Exactly. It is the way different observers in relative motion synchronize their frame's clocks. I still believe that no inertial frame that does an experiment with a hypothetical tachyon and synchronized clocks could find it to have "moved backwards in time" in that frame. If a tachyon moves at 2c in that frame, it will take half the time that light would take to travel from emitter to detector. This fact cannot depend upon who else is watching from some other inertial frame, or can it?

Obviously, other frames timing "my tachyon" may get different answers from their respective synchronized clocks. BTW, how do we add super-luminal speeds relativistically?

 

[Xeinstein]

Feynman diagram of quantum field theory shows antiparticles travel backward in time

 

[malawi_glenn]

Feynman diagram of quantum field theory shows antiparticles travel backward in time

that is true, but does they do so in reality? not what I know..

 

[belliott4488]

I would think that energy considerations could unambiguously identify the emitter and detector.

Yes, but that's an example of what makes tachyons non-physical. They don't obey the basic notion of cause preceding effect.

 

[belliott4488]

Exactly. It is the way different observers in relative motion synchronize their frame's clocks. I still believe that no inertial frame that does an experiment with a hypothetical tachyon and synchronized clocks could find it to have "moved backwards in time" in that frame. If a tachyon moves at 2c in that frame, it will take half the time that light would take to travel from emitter to detector. This fact cannot depend upon who else is watching from some other inertial frame, or can it?

Obviously, other frames timing "my tachyon" may get different answers from their respective synchronized clocks. BTW, how do we add super-luminal speeds relativistically?

Yes, that's true - no one observer would conclude that a tachyon moved backward in time (what would that look like, anyway?). What would be the case is that different observers would disagree whether it moved from pt. a to pt. b or from pt. b to pt. a. If one event were clearly defined as the "start", however, like a projectile being launched from a gun, then there would be some observers who would see it move "backwards" from its "destination" back to the gun. I wouldn't call that moving backwards in time; I'd just call it a non-physical sequence of events.

The observer who see the object at all places at once is clearly going to have difficult time describing any kind of "motion" for this object.

 

[belliott4488]

Feynman diagram of quantum field theory shows antiparticles travel backward in time

Not exactly. If you try to interpret the field as the field of a particle, say an electron, then yes, it appears to move in reverse. That's part of the reason why it makes more sense to interpret it as an anti-particle - the positron in this case - that moves forward in time like anything else.

 

[JesseM]

Yes, that's true - no one observer would conclude that a tachyon moved backward in time (what would that look like, anyway?). What would be the case is that different observers would disagree whether it moved from pt. a to pt. b or from pt. b to pt. a. If one event were clearly defined as the "start", however, like a projectile being launched from a gun, then there would be some observers who would see it move "backwards" from its "destination" back to the gun. I wouldn't call that moving backwards in time; I'd just call it a non-physical sequence of events.

But if you accept that tachyons obey the principle of relativity--that they work the same way in all reference frames--then if it is possible for the receiving of a tachyon message to happen before the sending of that message in at least one frame, it must be possible in all frames. So if you are traveling away from me at sublight speeds, and I send you a tachyon signal which goes FTL in my frame but "backwards in time" in your frame (meaning just that in your frame you receive the signal before I sent it), then you immediately send a reply which travels FTL in your frame but backwards in time in mine, then it is possible for me to receive your reply before I sent the original message, a clear physical violation of causality. This is nicely illustrated with a spacetime diagram on this page:

http://www.theculture.org/rich/sharpblue/archives/000089.html

 

[CJames]

Thanks for the diagrams, JesseM.

By the way, it seems to me that this sort of thing would happen regardless of the method for superluminal velocity. Even if the object weren't traveling faster than light locally, as in the Alcubierre drive, it still looks like you could use it to violate causality. Is that correct? Wormholes might get around it, because if you construct one that violates causality vacuum noise causes it to collapse. But then if you can have wormholes why couldn't you have the Alcubierre drive?

Sorry, slightly off topic.

What does complex time mean, anyway?

 

[peter0302]

That's part of the reason why it makes more sense to interpret it as an anti-particle - the positron in this case - that moves forward in time like anything else.

Who says that makes more sense? So in other words all anti-matter could simply be explained by normal matter moving backwards in time? That sounds like a much simpler explanation than doubling the number of fundamental particles just to preserve a forward-only time dimension (for which no one knows _why_ it must always be forward).

 

[JesseM]

Who says that makes more sense? So in other words all anti-matter could simply be explained by normal matter moving backwards in time? That sounds like a much simpler explanation than doubling the number of fundamental particles just to preserve a forward-only time dimension (for which no one knows _why_ it must always be forward).

My understanding is that "moving forwards in time" vs. "moving backwards in time" doesn't really have any clear physical meaning (if you draw a vertical line on a piece of paper, is it 'moving up the page' or 'moving down the page'? Why should a timelike worldline in relativity be any more directional than a line on paper?), and that the idea of antiparticles being like regular particles "moving backwards in time" is more like a mathematical trick that can simplify things when summing feynman diagrams, something like the difference between doing an integral from \int_{t_0}^{t_1} vs. an integral from \int_{t_1}^{t_0}. I could be wrong about this, but this statement from an FAQ on virtual particles seems to be saying something along these lines:

Now, consider a virtual photon that comes from the particle on the right and is absorbed by the particle on the left. Actually calculating the photon's wave function is a little hairy; I have to consider the possibility that the photon was emitted by the other particle at any prior time. (However, I can save myself a little effort later by automatically including the possibility that the photon actually comes from the particle on the left and is absorbed by the particle on the right, with the recoil nudging the left particle: all I have to do is include situations in which the photon is "emitted on the right" in the future and goes "backward in time," and take its momentum to be minus what it really is! As long as I remember what's really going on, this trick is formally OK and saves a lot of trouble; it was introduced by Richard Feynman.)

 

[Dale]

Why should a timelike worldline in relativity be any more directional than a line on paper?

That is a very interesting point. Since there is only one time dimension (dimension with opposite sign in spacetime interval) timelike lines have a definite before-end and after-end which cannot be swapped. On the other hand with three spatial dimensions spacelike lines don't have a definite left-end and right-end since you can always rotate things around.

I have no idea what the implications are for something like that, but it makes a clear difference between a tachyon and a positron-is-an-electron-running-backwards-in-time. In the case of the positron the worldline is still timelike, just running in reverse. That seems to be a much more clear "backwards in time" than the spacelike worldline of a tachyon.

 

[JesseM]

That is a very interesting point. Since there is only one time dimension (dimension with opposite sign in spacetime interval) timelike lines have a definite before-end and after-end which cannot be swapped.

What do you mean "cannot be swapped"? The laws of physics are time-symmetric (or in quantum field theory, charge-parity-time-reversal invariant) so you're free to reverse the labels of which direction in time you call the "future" and which you call "the past", and for any physical process you can find another physically allowable process which looks like a backwards version of the first (though you may need to flip the charges and parity of the system of particles in the second as well).

I have no idea what the implications are for something like that, but it makes a clear difference between a tachyon and a positron-is-an-electron-running-backwards-in-time. In the case of the positron the worldline is still timelike, just running in reverse.

What do you mean "running in reverse"? What physical statement are you making here? Again, as far as I know the concept of treating a positron like an electron "going back in time" is just a mathematical trick for summing feynman diagrams.

 

[Dale]

What do you mean "cannot be swapped"?

I mean that you cannot rotate in a single dimension.

I am not talking physics here, just geometry. In a single dimension you cannot rotate an object so there is a clear directionality to the two ends of a line. In two or more dimensions there is no longer a clear directionality to the two ends of a line. You can always approach the line from the other side and then the sense of the direction of the line is reversed.

I thought that was the point you were making with your "Why should a timelike worldline in relativity be any more directional than a line on paper?" comment.

 

[peter0302]

I've just never heard an explanation as to why a "normal particle backwards in time" model is any less "real" and more of simply a "trick" than a "anti-particle forwards in time" model. Seems to me like people use the latter view just to comfort themselves into believing in the absolute nature of linear time.

I also find it incredibly interesting that a 4-dimensional Euclidean view of Relativity has particles moving faster than the speed of light as moving backwards in time as well. These particles would be indistinguishable from anti-particles. But, again, we don't use that model, and instead use the Minkowski model, simply to keep our minds at ease that time always moves forward.

[Edit] Just wanted to add, in that model,whether the particle is a "real" particle or "anti" particle is frame-dependent. In other words, _all_ of the quantum numbers, not just mass, become frame dependent. Doesn't this make for a simpler unified theory?

 

[JesseM]

I've just never heard an explanation as to why a "normal particle backwards in time" model is any less "real" and more of simply a "trick" than a "anti-particle forwards in time" model. Seems to me like people use the latter view just to comfort themselves into believing in the absolute nature of linear time.

But what do you mean by "forwards in time" or "backwards in time"? As far as I know particles don't "move" in time in either direction in any meaningful physical sense, they just have worldlines in spacetime. Like I said, maybe in the course of certain mathematical procedures you would integrate along the worldline from one end to the other or something like that, but I don't think there's any reason to take this too literally as some sort of physical reality (and note that even as a mathematical procedure, I don't think you're forced to treat antiparticles as normal particles moving backwards, it just simplifies the calculation, and I imagine you could equally well say antiparticles are moving forwards and normal particles are antiparticles moving backwards.)

I also find it incredibly interesting that a 4-dimensional Euclidean view of Relativity has particles moving faster than the speed of light as moving backwards in time as well. These particles would be indistinguishable from anti-particles. But, again, we don't use that model, and instead use the Minkowski model, simply to keep our minds at ease that time always moves forward.

The minkowski model doesn't say time moves forward or backward, any more than it says space moves left or right, at least not as far as I can tell. And what do you mean by "4-dimensional Euclidean view"?

 

[JesseM]

I mean that you cannot rotate in a single dimension.

I am not talking physics here, just geometry. In a single dimension you cannot rotate an object so there is a clear directionality to the two ends of a line. In two or more dimensions there is no longer a clear directionality to the two ends of a line. You can always approach the line from the other side and then the sense of the direction of the line is reversed.

I thought that was the point you were making with your "Why should a timelike worldline in relativity be any more directional than a line on paper?" comment.

No, my point was about physics, that there isn't any physical meaning to the notion of something actually physically "moving" in a particular direction in time. And the fact that a line isn't "moving up the page" or "moving down the page" doesn't have any relation to the question of whether or not you can rotate the paper, as far as I can tell--why do you think it would?

 

[peter0302]

The minkowski model doesn't say time moves forward or backward, any more than it says space moves left or right, at least not as far as I can tell. And what do you mean by "4-dimensional Euclidean view"?

https://www.physicsforums.com/showthread.php?t=103977

And, as far as the Minkowski model, if you draw the worldlines of various particles moving at relativistic speeds, none are ever moving in the -t direction for any observer. In a 4-dimensional Euclidean relativity, with time on equal footing with space, if you continue to accelerate "past" 'c' relative to an observer you wind up moving backwards in time relative to that observer. By extension, that observer would believe you to be made of "antimatter".

 

[JesseM]

https://www.physicsforums.com/showthread.php?t=103977

That's a lot to look over, but I'll try to get to it sometime.

And, as far as the Minkowski model, if you draw the worldlines of various particles moving at relativistic speeds, none are ever moving in the -t direction for any observer.

I still don't know what you're talking about here. What does it mean for a worldline to "move" at all, given that spacetime is completely static? Do you claim that worldlines are "moving in the +t direction" for any observer? If so, in what sense? Can you give a numerical example or something? Perhaps you're talking about the "arrow of time" for macroscopic objects (including the psychological arrow) rather than something that can be applied to individual particles?

 

[peter0302]

Do you claim that worldlines are "moving in the +t direction" for any observer? If so, in what sense? Can you give a numerical example or something?

I really think I'm being obvious, but nonetheless:

Take a two-dimensional Minkowski diagram for any particle, one axis being "x", one being "T", where T=ict. dT/dx is always >= 1 and, obviously, is always greater than 0. That's what I mean by "forward" in time.

 

[JesseM]

I really think I'm being obvious, but nonetheless:

Take a two-dimensional Minkowski diagram for any particle, one axis being "x", one being "T", where T=ict.

Why are you multiplying by i here?

dT/dx is always >= 1 and, obviously, is always greater than 0.

Given your definition of T, won't dT/dx be imaginary? Consider the worldline of a particle moving at 0.5c (we can use units of 0.5 light-seconds per second) in the +x direction. Then we'd have x(t) = 0.5 l.s./s * t, meaning that t(x) = 2 s/l.s. * x. In this case if T(t)=ict = it*(1 l.s./s) then T(x) = 2i * x. So, dT/dx = 2i.

 

[peter0302]

Why are you multiplying by i here?

I thought "ict" was the conversion used in SR for time to space. Maybe there's no 'i'. Either way, same point.

 

[JesseM]

I thought "ict" was the conversion used in SR for time to space. Maybe there's no 'i'. Either way, same point.

But the point doesn't work if you remove the i either. Before I imagined an object moving in the +x direction at 0.5c, now just imagine one moving in the -x direction at 0.5c; if dT/dx (with T = ct) was 2 in the first case, it's -2 in the second case.

 

[Dale]

And the fact that a line isn't "moving up the page" or "moving down the page" doesn't have any relation to the question of whether or not you can rotate the paper, as far as I can tell--why do you think it would?

Sure it does. This is pretty basic topology. If you have a line segment in one dimension, and you consider arbitrary smooth transformations (homeomorphisms), the only way to swap the positive end and the negative end is through a degenerate state (a point or an infinitely long segment). In other words, topologically the positive end is always the positive end and the negative end is always the negative end. On the other hand, if you have a line segment in two dimensions, and you consider arbitrary smooth transformations, you can easily swap the positive end and the negative end without passing through a degenerate state.

I'm sorry that I misunderstood your point. The way I misunderstood it was pretty interesting though. I haven't thought about it enough to attach to it any physical significance yet, but I think that there may be something geometrically or topologically different between the two ends of a timelike line and that there is not such a difference between the two ends of a spacelike line. I could easily be wrong on that point, and even if I am right I haven't thought it through to a physical conclusion, but I find it interesting.

 

[JesseM]

Sure it does. This is pretty basic topology. If you have a line segment in one dimension, and you consider arbitrary smooth transformations (homeomorphisms), the only way to swap the positive end and the negative end is through a degenerate state (a point or an infinitely long segment). In other words, topologically the positive end is always the positive end and the negative end is always the negative end.

Yes, obviously if a line comes pre-labeled with a "positive end" and a "negative end", you can distinguish between lines with the positive end up and lines with the negative end up, and in one dimension you can't smoothly rotate one into the other. But if I just draw a line on a piece of paper without any labeling, how are you going to decide whether it's "moving up the page" or "moving down the page"? Likewise, what physical features (not arbitrary decisions about how we humans choose to label things) do you think distinguish a worldline that's "moving forward in time" from one that's "moving backwards in time"?

 

[Magic Man]

The fact that diagrams and equations show that something could travel back in time doesn't mean it's a fact, it just shows the maths can go both ways - we developed the maths to explain observed results. Time doesn't exist, it's simply what we measure as the passing of one moment to the next.

Light doesn't govern the passage of time, we base the measurment of time on the speed of light but something traveling ftl doesn't mean it travels back in time. What we observe in experiments involving such particles is not neccessarily what is actually happening - our observations are limited by the speed of light afterall.

 

[peter0302]

But the point doesn't work if you remove the i either. Before I imagined an object moving in the +x direction at 0.5c, now just imagine one moving in the -x direction at 0.5c; if dT/dx (with T = ct) was 2 in the first case, it's -2 in the second case.

Ok, then why don't you tell me the mathematical way of saying what you know I'm trying to say?

 

[JesseM]

Ok, then why don't you tell me the mathematical way of saying what you know I'm trying to say?

I don't know what you're trying to say, because I don't think there's any physical meaning to the notion of "moving forward in time" vs. "moving backwards in time".

 

[peter0302]

I don't know what you're trying to say, because I don't think there's any physical meaning to the notion of "moving forward in time" vs. "moving backwards in time".

Ah, then why don't you go change the past for us?

 

[JesseM]

Ah, then why don't you go change the past for us?

Physicists talk about the notion of time travel without any need for a notion of "moving" in time--they just talk about "closed timelike curves", analogous to a line on a piece of paper which bends around into a loop so two different parts of the line can cross. As long as there are no timelike curves, time travel isn't possible.

 

[peter0302]

Ok I finally figured out how to say what I mean mathematically.

Nothing goes backwards in time because for every "t" coordinate, there can be one and only one observed value of "x,y,z".

 

[heskam]

So in an imaginary negative energy "anti"world a signal would go backwardtime to the sender of the photon that came here. That would make a "real time" loop.?

 

[JesseM]

Ok I finally figured out how to say what I mean mathematically.

Nothing goes backwards in time because for every "t" coordinate, there can be one and only one observed value of "x,y,z".

What does that have to do with "moving backwards in time" or "moving forwards in time"? If I hang a string from my ceiling and then use an x-y-z grid to plot spatial coordinates of things in my room, it may be that for ever "z" coordinate, there is only one observed value of "x,y"...does that tell me whether the string is "ascending from the floor to the ceiling" or "descending from the ceiling to the floor"?

 

[A.T.]

Nothing goes backwards in time because for every "t" coordinate, there can be one and only one observed value of "x,y,z".

This is not preventing anything from going back in time. It just prevents from changing the direction in time. Move forward and then back in time doesn't work.

See my thoughts about distinguishing objects moving in different directions in time:
https://www.physicsforums.com/showthread.php?t=211332

 

[peter0302]

A.T. is right. There may be no true distinction between "forwards" and "backwards" but the point is that everything is either moving in the same direction in time or not.

JesseM, you're clearly going to argue with me regardless of what I say, but my point has been made.

 

[JesseM]

A.T. is right. There may be no true distinction between "forwards" and "backwards" but the point is that everything is either moving in the same direction in time or not.

If can't even define "moving" then the statement "everything is either moving in the same direction in time or not" makes no sense.

JesseM, you're clearly going to argue with me regardless of what I say, but my point has been made.

I'm only going to argue with statements that seem to depend on poorly-thought out intuitions and fuzzily-defined verbal terms, if you can translate your statements into something that has a clear meaning in terms of mathematical theories of physics I won't have a problem with it. For example, the notion of "closed timelike curves" in relativity is certainly a well-defined one, if that's all you mean by "moving backwards in time" I have no objection, but in this case you should stop claiming that antiparticles move back in time, because their worldlines are not closed timelike curves.

 

[peter0302]

I'm only going to argue with statements that seem to depend on poorly-thought out intuitions and fuzzily-defined verbal terms, if you can translate your statements into something that has a clear meaning in terms of mathematical theories of physics

I just did. Going in a single direction in time means that for all observers, for any value of t there is exactly one (x,y,z) where a particle will be observed. If antiparticles moved "backwards in time" then this statement would not be true. That is my definition, very well defined mathematically.

And I am not claiming anything. I'm trying to have a conversation that's getting derailed because you are claiming ignorance of virtually every word in the English language.

 

[JesseM]

I just did. Going in a single direction in time means that for all observers, for any value of t there is exactly one (x,y,z) where a particle will be observed. If antiparticles moved "backwards in time" then this statement would not be true. That is my definition, very well defined mathematically.

This isn't well-defined unless you give a physical procedure for determining if an antiparticle and a particle which exist at different positions at a single time are "really" the same particle or two different particles.

And I am not claiming anything. I'm trying to have a conversation that's getting derailed because you are claiming ignorance of virtually every word in the English language.

English is not the language of physics--ordinary-language statements about physics are only meaningful if there is a transparent way to translate them into precise mathematical ones.

 

[matheinste]

Good morning Peter0302.

Just to clarify things for me, i take it that for a particle to be at a certain spacetime coordinate (event) more than once it must "travel back in time". If we were to alllow the possibility of a particle's ability to "travel back in time" surely it would have to be one and the same particle to satisfy this requirement of being at the same spacetime coordinate more than once. If it were an anti particle "travelling backwards in time" it would not be the SAME particle at the same spacetime coordinate more than once.

Matheinste.

 

[peter0302]

Good morning Peter0302.

Just to clarify things for me, i take it that for a particle to be at a certain spacetime coordinate (event) more than once it must "travel back in time". If we were to alllow the possibility of a particle's ability to "travel back in time" surely it would have to be one and the same particle to satisfy this requirement of being at the same spacetime coordinate more than once. If it were an anti particle "travelling backwards in time" it would not be the SAME particle at the same spacetime coordinate more than once.

Matheinste.

I don't know if that's true. Perhaps when a particle and antiparticle seem to collide, in fact the "antiparticle" is the original particle knocked backwards in time.

Another way to tell if antiparticles move forward in time or not would be if they were gravitationally repelled by normal matter. Anyone know if this has been tested or can be tested?

 

[JesseM]

I don't know if that's true. Perhaps when a particle and antiparticle seem to collide, in fact the "antiparticle" is the original particle knocked backwards in time.

But unless these two hypotheses lead to different predictions, this is not a question that can be addressed by physics, any more than the question of which "interpretation" of quantum mechanics is correct.

Another way to tell if antiparticles move forward in time or not would be if they were gravitationally repelled by normal matter. Anyone know if this has been tested or can be tested?

What theoretical argument leads you to believe that something "moving backward in time" would be gravitationally repelled by normal matter? In any case, see here and here for some info on the gravitational properties of antimatter.

 

[Xantos]

Time dilation and tachyon speed are two different things. That negative time may in reality just mean that tachyon gets from start to finish faster than information. And that is a general problem in theory of relativity i think. It's not well defined in terms when do we think about the problem as physical matter and when in terms of information that we receive. When they sort that out, everything will be much clearer.

I think someday in future it will come as a surprise to scientists that relativity can be explained with Mach's principle and Doppler effect.

 

[JesseM]

Time dilation and tachyon speed are two different things. That negative time may in reality just mean that tachyon gets from start to finish faster than information.

The idea that tachyons could be used to communicate information backwards in time has absolutely nothing to do with the time dilation equation (tachyons don't have their own reference frame at all), it's just a product of the relativity of simultaneity (which implies that if two events have a spacelike separation, then different frames must disagree on the order of the two events) and the fact that the laws of physics are supposed to work the same way in every inertial frame.

 

[Xantos]

The idea that tachyons could be used to communicate information backwards in time has absolutely nothing to do with the time dilation equation (tachyons don't have their own reference frame at all), it's just a product of the relativity of simultaneity (which implies that if two events have a spacelike separation, then different frames must disagree on the order of the two events) and the fact that the laws of physics are supposed to work the same way in every inertial frame.

STL travel; C ; FTL travel

When you're approaching C you're making information so dense that it radiates in terms of Cerenkov radiation and traveling as fast as infromation about yourself relative to the observer towards which you're flying. So it would appear to the observer somehow like this:

Let's assume that traveler and the observer are so far apart that relativistic delay of information is observed.
Let's say that you slowly accelerate to 0.5c and then suddenly to 1c. What observer on the other side would see is a very small ship instantaniously followed by your physical self. It is very likely that he would also pick up on sensors a lot of Cerenkov radiation.

Now let's assume that we developed technology that allows us to go FTL. You accelerate to 0.5c, then to 1c (a lot of gravitational disturbance occurs at this point) and then you engage FTL drive at that point you have negative time (as seen in the equation) - you're traveling faster than the information about yourself which means you will be at the finish faster than your information (that is not backwards in time). What the observer on the finish line would see is this: you suddenly appear from nowhere followed by your own image.

 

[JesseM]

Let's say that you slowly accelerate to 0.5c and then suddenly to 1c.

Impossible according to relativity, even if you allow tachyons. Accelerating from slower-than-c to c would require infinite energy; decelerating a tachyon down to c would be equally impossible.

Now let's assume that we developed technology that allows us to go FTL. You accelerate to 0.5c, then to 1c (a lot of gravitational disturbance occurs at this point) and then you engage FTL drive at that point you have negative time (as seen in the equation)

What equation are you talking about? Again, the time dilation equation simply cannot be used for ftl velocities in relativity, because a faster-than-light reference frame would violate the postulate that the laws of physics should be the same in all frames (and if you try plugging in a v>c into the time dilation equation, you get an imaginary number, not a negative one).

you're traveling faster than the information about yourself which means you will be at the finish faster than your information (that is not backwards in time). What the observer on the finish line would see is this: you suddenly appear from nowhere followed by your own image.

This is true, but it has nothing to do with the relativity of simultaneity or the claim that tachyons could be use to send information backwards in time. Do you understand that the question of when events happen in a given reference frame is totally different from the question of when observers see signals from events--that if I see the light from an event 10 light years away in 2010 (as measured by my clocks and rulers), and then see the light from an event 20 light years away in 2020, this means that the events actually happened simultaneously in my frame? If not, you need to actually learn the basics of SR before you jump to conclusions about what physicists are saying.

 

[Xantos]

Impossible according to relativity, even if you allow tachyons. Accelerating from slower-than-c to c would require infinite energy; decelerating a tachyon down to c would be equally impossible.

Something similar was said when they were testing supersonic flight. And guess what, they broke the barrier. Now it's time to break the next barrier. With FTL I think we'll have to develope technology that allows masking the mass (or gravity). When you acomplish that, you need very little energy to travel FTL.

What equation are you talking about? Again, the time dilation equation simply cannot be used for ftl velocities in relativity, because a faster-than-light reference frame would violate the postulate that the laws of physics should be the same in all frames (and if you try plugging in a v>c into the time dilation equation, you get an imaginary number, not a negative one).

I was referring to the equation on the first page and it was almost 3 in the morning. And even with this mistake that I made, I'm 99% sure that those equations mean exactly that - information gets to the finish line behind physical object. So it would appear that event happened before it even started. And that's not sending info into the past.

This is true, but it has nothing to do with the relativity of simultaneity or the claim that tachyons could be use to send information backwards in time.

You cannot send information backwards in time. Impossibility, even with tachyons.

Do you understand that the question of when events happen in a given reference frame is totally different from the question of when observers see signals from events--that if I see the light from an event 10 light years away in 2010 (as measured by my clocks and rulers), and then see the light from an event 20 light years away in 2020, this means that the events actually happened simultaneously in my frame? If not, you need to actually learn the basics of SR before you jump to conclusions about what physicists are saying.

Yes, that is perfectly undestandable and logical because information spreads with a constant C. Those two events happened at the same time during 2000.