Faster Than Light Travel

[Schneibster]

One way to put what reletivity says(and observations hold to) is this

1. Effects can not precede causes
2. The laws of physics are the same for everyone no mater their innertial reference frame
3. Something can travel faster than light

Pick two.

This is a really good way of looking at this. I like this post a lot; please accept my congratulations, this is one of the more original ideas I have encountered in quite a while.

 

[Yllanes]

So do they go back in time, or is there a privileged refernce frame? Or what about Inertial reference frame translations of Special Reletivity is wrong?

A tachyon going forward in time on a reference frame can be going back in time on another. Someone who knows about spacetime diagrams can convince himself with this:

The world line of the tachyon is the green line. In the black reference frame it is going forward in time with speed greater than c. In the red reference frame, the point labelled B has a negative time coordinate, t'_B. So the tachyon is going back in time in R'.

If you don't know about this diagrams you are going to have a hard time with this one. The vertical axis is time, the horizontal axis space. Time is measured in meters (or c =1), so a light ray travels with a 45º slope. Something travelling faster than light would cross more distance in the same time, so it would have a less steep worldline. Ordinary matter, travelling v < c, has a slope greater than 45º. You can find the coordinates (x,t) of an event in the usual way.

If we add a new frame, with the same origin but travelling with v < c with respect to the first, we must draw slanted axes to use the same diagram. Now, to find the t' coordinate of a point we draw a line parallel to the x' axis and notice the point of intersection with the t' axis. This is the generalisation of what you do with normal, perpendicular axes. The coordinates of A are (0,0) in both systems. The coordinates of B are both positive in R, while in R' the time is negative.

This seems to violate causality, but if one were to do all the calculations for an attempt at FTL communication, he would probably find that it is not possible (something like a received tachyon going backwards in time is indistinguishable from an emitted tachyon going forward in time). I think the FAQ article I linked discusses this a bit.

Anyway, my point in the earlier post was

• They have never been found, so their existence is very unlikely.
• However, they can be accommodated in our current theories, provided they can only travel FTL and never cross the c barrier

 

[ponderingturtle]

This is a really good way of looking at this. I like this post a lot; please accept my congratulations, this is one of the more original ideas I have encountered in quite a while.

Oh I didn't phrase it that way myself, but heard it else where. But it very clearly states what you need to be true for FTL travel that is consistent with what we already know.

 

[Ziggurat]

This seems to violate causality, but if one were to do all the calculations for an attempt at FTL communication, he would probably find that it is not possible (something like a received tachyon going backwards in time is indistinguishable from an emitted tachyon going forward in time).

No, this is wrong. If tachyons exist and if reference frames are all equivalent, then you can send messages backwards in time using tachyons, including to your past self (using a parter at a distance to send the signal back). This violates causality. There is one, and ONLY one, way to accomodate tachyons without violating causality. It has already been mentioned (very succintly by ponderingturtle), but just to hammer it in, the only way out of causality violations with tachyons is to make a prefered reference frame. If we allow for one prefered reference frame, then we can impose the requirement that tachyons never go backwards in time with respect to this preference reference frame, which would mean that nobody in any frame can send messages backwards in time to their past selves. But without a prefered reference frame, tachyons REQUIRE the possibility of causality violation.

 

[Yllanes]

I agree with you if we only take SR into account. But if we use Relativistic Quantum Mechanics, the concept of going faster than c is not so simple (seeing as how we are dealing with waves and all that). What I meant is that in some 'realistic' calculations taking QM into account, it was not so clear that causality would be violated. The FAQ I linked earlier says something about this. I do not know all the details.

 

[drkitten]

No, this is wrong. If tachyons exist and if reference frames are all equivalent, then you can send messages backwards in time using tachyons, including to your past self (using a parter at a distance to send the signal back).

Er, no.

There is one, and ONLY one, way to accomodate tachyons without violating causality. It has already been mentioned (very succintly by ponderingturtle), but just to hammer it in, the only way out of causality violations with tachyons is to make a prefered reference frame.

Er, no.

But without a prefered reference frame, tachyons REQUIRE the possibility of causality violation.

Er, no. There are at least two other solutions, depending upon how you allow tardyons -- normal stuff like you, me, bananas, and detection equipment -- to interact with tachyons. The simplest, which the mathematics doesn't forbid, is that tachyons exist but cannot interact with tardyons at all, in which case there's no way for us either to manipulate tachyons or detect the results of such manipulations.

The physics FAQ above points out a couple more solutions, based on more detailed math.

 

[Yllanes]

I would also like to add that G. Feinberg, who was one of the first to talk about tachyons, wrote a detailed article in the late 60s in which he gave much stronger arguments than the ones in the FAQ against FTL communication. I have not read that paper, but I believe that it proves that the process of tachyon detection is indistinguishable from the process of tachyon emission or, in other words, the detection of a tachyon automatically creates another one travelling forward in time. This happens at least for the specific kind of tachyons considered by Feinberg. I can probably provide the full citation for the paper, fpublished in the Physical Review.

EDIT: Found it, Phys. Rev 159 (1967), 1089-1105. The abstract is

We consider the possibility of describing, within the special theory of relativity, particles with spacelike four-momentum, which therefore have velocities greater than that of light in vacuum. The usual objections to such particles are discussed, and they are found to be unconvincing within the framework of relativistic quantum theory. A quantum field theory of noninteracting, spinless, faster-than-light particles is described. The field theory is Lorentz-invariant, but must be quantized with Fermi statistics. The associated particle theory has the property that the particle number is not Lorentz-invariant, and the no-particle state is not Lorentz-invariant either. Nevertheless, the principle of relativity is satisfied. The Lorentz invariance implies a relation between emission and absorption processes, in contradiction to the usual case. Some comments are made about the problem of introducing interactions into the field theory. The limiting velocity is c, but a limit has two sides.

(bolding mine). From the conclusion

[...]
A description of such particles, called tachyons, is possible, at least for the case of spinless, non-interacting particles. The field theory constructed is explicitly Lorentz invariant.
[...]
As the two problems are solved, we can look forward to the solution of the more fundamental question, i.e.,

3. Do faster-than-light particles exist in nature and can they be detected?

It is the hope of the author that he has convinced the reader that an affirmative answer to this question would not necessarily be in contradiction with Einstein's theory of relativity

If anyone wants to read the whole paper he must have access to a suscription to the Physical Review archives. I don't have time to read all of it. The APS web page gives 99 citations for this paper.

Something like this paper is what I meant when I said that the finding of a tachyon need not upset our current understanding of physics.

 

[c4ts]

Anyone ever heard of Alcubier (sp)? He had the idea of generating a wormhole that goes with the ship. At least it worked mathematically, I think.

 

[Ziggurat]

Er, no. There are at least two other solutions, depending upon how you allow tardyons -- normal stuff like you, me, bananas, and detection equipment -- to interact with tachyons. The simplest, which the mathematics doesn't forbid, is that tachyons exist but cannot interact with tardyons at all, in which case there's no way for us either to manipulate tachyons or detect the results of such manipulations.

If they cannot interact with tardyons by any means, then there's no meaningful sense in which they exist at all. There are an infinite number of things we can permit to exist, if we merely specify that they cannot interact with ordinary matter in any way, but none of them are of any relevance.

The physics FAQ above points out a couple more solutions, based on more detailed math.

The other "solutions" aren't really solutions to the problem, but discussions of the Klein-Gordon equation for tachyons. None of that mentions how you can get tachyons (in the layman's sense of particles propagating faster than c, not just weird quantum particles with phase velocities faster than c) without violating causality or specifying a prefered frame. You can't. A little playing around with space-time diagrams should illustrate that pretty simply.

 

[Ziggurat]

Here's the problem with Tachyons and time travel:


Black lines are space and time axes (time is vertical). Blue lines are the light cone. Red lines show tachyon trajectories. The problem is that if there is no prefered reference frame, then there is no intrinsic difference between the tachyon trajectories shown in A, B and C. If tachyons can interact with matter, it is possible to send a tachyon back in time to yourself, as shown by the trajectory in D (which is just a two-leg path following the trajectories B and C). That violates causality. If there is a prefered reference frame, then A, B, and C need not all be equivalent. If there is one frame in which trajectories like B and C are not possible (that is, some frame in which tachyons must have a forward time component), then even in other reference frames which allow a backwards time component, only B- OR C-type trajectories will be permissible, never both, and causality is restored. But we cannot impose that forward-only restriction on tachyons in ALL reference frames, because if trajectory A is possible (a requirement for it to be a tachyon) in one frame, then there is a frame in which B is also possible. So we cannot keep both equivalence between all reference frames AND causality once we admit tachyons.

Gah! the picture got shrunk strangely when posted: click on it to get the original picture which doesn't make the horizontal axis disappear.

 

[Yllanes]

I fully understand that and I even drew a similar diagram above, illustrating the fact that a tachyon goes backwards in time for some reference frames. I agree that you can form closed loops with them. They would violate causality if they interacted with matter like, say, photons. But if there are some restrictions to how they can interact with matter, it is possible that they cannnot serve to send information FTL.

What do you think about the paper I referenced in my last post? I am not asking you to read it, of course, I just want to know your first impression about it. I believe that's the paper that coined the word 'tachyon'.

And another question, if I may: do you think they are at least mathematically consistent within QFT as free particles?

The other "solutions" aren't really solutions to the problem, but discussions of the Klein-Gordon equation for tachyons. None of that mentions how you can get tachyons (in the layman's sense of particles propagating faster than c, not just weird quantum particles with phase velocities faster than c) without violating causality or specifying a prefered frame. You can't. A little playing around with space-time diagrams should illustrate that pretty simply.

I don't know... the paragraph says that you cannot propagate information faster than c even with tachyons, from a QFT point of view.

And just to be clear: I don't think there are any tachyons. There are lots of reasons to dislike them. I do not believe a sensible field theory for interacting tachyons has ever been accomplished and the issue certainly looks difficult: tachyons could be some sort of perpetual motion machine, due to their negative energy, for example. Also, a free tachyon that would not interact at all with ordinary matter seems on the one hand a pointless mathematical excercise as you said. But it also introduces new problems if we bring gravity into the picture... everything must interact with gravity.

 

[Dave1001]

This is an awesome thread to observe. =)

 

[Ziggurat]

What do you think about the paper I referenced in my last post? I am not asking you to read it, of course, I just want to know your first impression about it.

I read a lot (but not all) of it. Much of what they address is non-causality arguments against tachyons, and as far as I can tell, their arguments are sound. Their argument regarding causality seems insufficient to me: they seem to be saying that if the creation and production of tachyons is sufficiently uncontrollable, then information cannot be transmitted into the past. But that doesn't strike me as nearly sufficient: if you can produce them with any nonzero efficiency, and you can detect them with any nonzero efficiency, then the causality problem still exists, even if in practice it will never be encountered. An equivalent scenario might be that we can, in principle, build black holes: simply keep chucking mass into the sun. In practice, humanity will likely never have that capability, but that doesn't matter to the theories. And I cannot imagine a scenario in which there is any interaction with ordinary matter but where it is still not possible, even in principle, to create or detect tachyons with SOME nonzero efficiency. Perhaps I'm wrong on that, but it would take quite a lot to show that such a scenario is possible.

And another question, if I may: do you think they are at least mathematically consistent within QFT as free particles?

Maybe, but I'm not even sure if QFT, by itself, requires causality either. You'd need another opinion on that, I don't have much experience with the details of QFT.

 

[Schneibster]

Since we could not detect tachyons, any interaction that produced them would result in an apparent violation of conservation of energy... and a Nobel Prize for the detector.

The link between causality violation and energy conservation violation is one of the reasons Hawking made the Chronology Protection Conjecture, I think.

 

[Yllanes]

I read a lot (but not all) of it. Much of what they address is non-causality arguments against tachyons, and as far as I can tell, their arguments are sound. Their argument regarding causality seems insufficient to me: [...]

Fair enough. I agree that the arguments presented are not completely satisfying, I just wanted to point out that the ideas are not crazy.

Let's just say that you can construct a rigorous field theory for free tachyons, but that it would be little more than a mathematical recreation (if they are free we can't see them).[1] However, a theory for interacting tachyons seems to present insurmountable problems (energetic considerations for example). Most importantly, they have never been observed (maybe we don't observe them because they are free, but this is meaningless for a physical theory).

So, to summarise for the purposes of this thread:

• From the point of view of SR, anything going FTL violates causality, which is a pretty good argument against tachyons.
• From the point of view of QFT (roughly, QM+SR), at the most fundamental level there is room for them (representations with imaginary mass), which has allowed people to build theories for non-interacting tachyons. However, still within QFT, if we try to build a theory for interacting tachyons we find huge problems and it is even possible that they cannot be solved without violating things like energy conservation! Another pretty good argument against tachyons.
• They have not been observed and they are not needed for any theory we currently have, so there's no reason to think they exist.

I think that our positions here differ only in that you consider the first point sufficient to discard them and I said there was a very small chance they could exist and not contradict current physical laws, if we took QM into account. This thread has made me think a bit more about this and I now believe the 'very small chance' is so tiny that it is probably not worth mentioning.

____
[1] For example, Introduction to Algebraic and Constructive Field Theory, by Baez, Segal and Zhou (Princeton UP, 1992).

 

[ponderingturtle]

I agree with you if we only take SR into account. But if we use Relativistic Quantum Mechanics, the concept of going faster than c is not so simple (seeing as how we are dealing with waves and all that). What I meant is that in some 'realistic' calculations taking QM into account, it was not so clear that causality would be violated. The FAQ I linked earlier says something about this. I do not know all the details.

And that does not remove the problems of shifting reference frames. On a macro scale, you can use anything that exists to send information backward in time, that is because any thing that goes faster than light will be seen by some obsevers to arive before it leaves. ANd they might well be in a position to send a message back to the start before it leaves either.

QM does not enter into it, we are not talking about that scale.

 

[ponderingturtle]

Something like this paper is what I meant when I said that the finding of a tachyon need not upset our current understanding of physics.

Finding one would. One existing might not, but for one the lorentz transformations are now wrong, or effects can preceed causes.

 

[ponderingturtle]

Anyone ever heard of Alcubier (sp)? He had the idea of generating a wormhole that goes with the ship. At least it worked mathematically, I think.

That pick three thing I mentioned, it is irrelevent as to how FTL is achieved, but if FTL exists then either there is a prefered reference frame and our theories being based on know prefered frame work out in some strange fashion with one of their fundamental premisise being wrong, or time travel happens and the idea that something happened because of what came before is wrong becuase is might have happened because of what came after.

 

[luvhumility]

I've been keepin my eye on fluid dynamic studies and of course vortex theory as it applies to accoustic waves and gravitation. I am still very new to these studies. can anyone expound on this articles...?

http://cat.inist.fr/?aModele=afficheN&cpsidt=13494064

And this paper on plasma, and possible matters creation through sound wave and plasma interaction is very interesting. It might lead to some answers for some of us who like this discussion about C and beyond...since plasma is the 5th state of matter and produces light, e.g. stars, LASRES, Neon bulbs, Arc Plasma etc. I feel this area of study certainly applies to our discussion on C and Mass interaction....anyone please expound!!

http://cat.inist.fr/?aModele=afficheN&cpsidt=13494064

lh

 

[ponderingturtle]

Fair enough. I agree that the arguments presented are not completely satisfying, I just wanted to point out that the ideas are not crazy.

Let's just say that you can construct a rigorous field theory for free tachyons, but that it would be little more than a mathematical recreation (if they are free we can't see them).[1] However, a theory for interacting tachyons seems to present insurmountable problems (energetic considerations for example). Most importantly, they have never been observed (maybe we don't observe them because they are free, but this is meaningless for a physical theory).

Is a theory that can not be tested scientific? How do we seperate tachyons from ID and accept theories that can not be tested about one and not the other?