Having trouble understanding why FTL implies time travel

[Austin0]

Originally Posted by Austin0
It looks to me like in that case, the greater the velocity of the particle, the lower relative velocity you derive from the formula.
Is that your understanding?

Fredrik No

Would you mind sharing your understanding of this. Are you saying that higher velocities wouldn't return lower relative velocities from the formula?

You really need to understand simultaneity in SR to understand this stuff. When you do, it's pretty easy. So what you need to do is to learn about simultaneity and then re-examine the argument for why SR+FTL implies "time travel" (i.e. that you can receive a reply to a message you haven't sent yet).

I think I have a fair grasp of simultaneity. I can certainly understand all the various results
as outlined in the various scenarios. I understand with no difficulty its application to all normal phenomena ie. c and sub c
and its role in the various paradoxes.

The separation between these two events is spacelike. That means that some observers will disagree about which event came first, i.e. some coordinate systems will assign a smaller time coordinate to A and some will assign a smaller time coordinate to B. You chose to consider a frame in which detection happens before emission, so in that frame the tachyon is described as moving from the detector to the emitter. That doesn't mean that the information is going that way.

What does this have to do with simultaneity? This purely a matter of logic and interpretation.
I am just trying to establish some definite parameters here.
1) Jesse has been referring to the signal moving from the transmitter in A to the receiver in B thus going back in time. OK I can agree with the logic of this, given the events.
I would think that actual observers in the case would come to this same conclusion, partly based on the direction of flow of information and the nature of transmission and reception.

2) Now you are viewing this as motion from the receiver to the transmitter forward in time. This does not make any sense to me , certainly not as pertaining to actual observers with any intelligence. Do you see how this might seem a bit circular.We now have a single signal going forward and backward simultaneously in the same frame??
3) I can understand that on a certain abstract level you could say it doesn't make any difference but it certainly makes a difference when deriving velocities etc.
Is there some way to come up with a single interpretation to work with?


.

 

[Austin0]

He didn't say that the next larger prime after N is given by N+1. The proof tells you that if you assume N is the largest prime, then the new number M = (2·3·5·7·...·N)+1 [i.e. the number obtained by multiplying N by every prime smaller than it, then adding 1] won't be divisible by any other prime number smaller than itself, which would mean M is itself prime by definition. So if you assume N is the largest prime number, you can then show there must be a prime number larger than N, contradicting your original premise and proving that there is no largest prime number.

Note that proving M is prime here depends on the initial assumption that N is the largest prime number smaller than M; it's not true in reality that every number of the form (2*3*5*...*N)+1 is a prime if N is prime, the page here mentions that (2*3*5*7*11*13)+1 = 30031, which isn't prime because it's equal to 59*509.

I am losing my mind. I read it as a series of primes not as series of multiplications.
I think I have too much else on my mind.

 

[Fredrik]

Would you mind sharing your understanding of this. Are you saying that higher velocities wouldn't return lower relative velocities from the formula?

I'm not really sure what you're asking. I assume that we're talking about the formula that says that if the velocity of frame F' in frame F is u and the velocity of a particle in frame F' is v, then the velocity of that particle in frame F is

w=\frac{u+v}{1+uv}

What exactly are you asking? Which of these variables (u,v and w) do you want to make bigger, and which one(s) do you think will be smaller as a consequence? (Note that by definition we have u<1, but if the particle is a tachyon, both v and w will be >1).

I think I have a fair grasp of simultaneity. I can certainly understand all the various results
as outlined in the various scenarios. I understand with no difficulty its application to all normal phenomena ie. c and sub c
and its role in the various paradoxes.

Then it should be very easy for you to see that if I send a message, and the person who receives it is moving away from me, he can send a reply that reaches me before I sent the first message, providing that: a) he's moving fast enough, b) his tachyons are moving fast enough.

We now have a single signal going forward and backward simultaneously in the same frame??

No, we don't. The signal (the message) is going back in time, but the tachyons wouldn't be described as going back in time. Try drawing the world line of a tachyon going left and being detected before it was emitted. Isn't it obvious that it would be interpreted as a tachyon emitted going to the right from the detector to the emitter?

 

[Dale]

Try drawing the world line of a tachyon going left and being detected before it was emitted. Isn't it obvious that it would be interpreted as a tachyon emitted going to the right from the detector to the emitter?

I understand what you're saying. It could be interpreted either way, but since it is carrying information from the emitter to the detector I think it would be better interpreted as going backwards in time from the emitter to the detedtor rather than forwards in time from the detector to the emitter.

 

[JesseM]

Part of the problem is that relativity itself does not carry any notion of whether a particle is moving "backwards" or "forwards" on a given worldline--the particle's motion is completely defined by the worldline, and the worldline is just the set of points in spacetime that the particle passes through. If we know a particle passed through events A: (x=5,t=0) and B: (x=6,t=3) there isn't really any basis in relativity for saying the particle went forwards in time from A to B or backwards in time from B to A. This is why I didn't want to talk about tachyons themselves, but about tachyon signals which carry information; if Bob sees some event in his local neighborhood and sends a signal about it, and at some other point in spacetime Alice receives this signal, then if the event of Alice receiving the signal happens before the event of Bob sending it in some frame, this frame has to say that she has information about the event in Bob's neighborhood before it actually happened, even if in this frame you choose to say that the tachyons themselves were moving forward in time from Alice to Bob.

 

[neopolitan]

I found a decent page explaining this but it's a little deep for my understanding.

I think I understand the basics of special relativity where the speed of light remains constant regardless the velocity of 2 observers, the laws of physics do not depend on location or motion, and that length, time, and mass depends on motion relative to a chosen frame of reference.

I can't seem to hack why faster than light speed would suggest time travel however. If anyone would care to elaborate or point me to a page/thread that doesn't require a PhD in physics to comprehend, that would be swell.

Hi Kronnyq,

Not sure if anyone has taken this tack (but I doubt it).

You start with the idea that FTL suggests time travel. The way you put it is as if we don't do time travel every day. But we do. We travel ahead at a rate of 1 second per second (where the second is defined in terms of our own rest frame).

If we watch another person, they can either be stationary in our rest frame or moving. If they move, we will note that they seem to exchange some of their time travel for space travel. Think of it like this, we have two monitors in front of us. One shows our time, according to us, and our position according to us. The other shows the other guy's time, according to his clock and his position, according to us (because he can claim he doesn't move). Now there are some more complex issues, but let's try to see past them for a moment.

What we will see is that the time on our clock will be related to the time on the other guy's clock and the distance travelled, and each side of the spacetime ledger can be balanced out using an equation which also brings in the speeds involved (both the speed of the other guy and the speed of light). Precisely what equation you use depends on what "time on the other guy's clock" you use.

The upshot of this is that you can sort of exchange time travel for space travel. But it is a zero sum equation. Our spacetime distance will equal his spacetime distance.

If the other guy exchanges all of his time travel for space travel, he will be doing light speed (and there are major reasons why he can't do that).

If you do more than light speed, then you no longer have a zero sum equation, and it is equivalent to traveling more than our standard one second per second while at (spatial) rest. It is sort of like using bonus time travel credits and I don't know if there is a mechanism for accessing bonus time travel credits.

I think that this is what you mean by "FTL implies time travel".

An important issue is that you can't actually go backwards in time. Even if this sort of time travel were possible, then all you could do is get to a future event quicker than someone else. The event would still be in the future for both of you when you set out on your journey.

cheers,

neopolitan

 

[JesseM]

An important issue is that you can't actually go backwards in time. Even if this sort of time travel were possible, then all you could do is get to a future event quicker than someone else. The event would still be in the future for both of you when you set out on your journey.

When people say that FTL implies "time travel", they are talking specifically about sending objects or information backwards in time and violating causality. Tachyons wouldn't allow us to send sublight objects like people back in time, but they would allow information to be sent back in time if SR is correct, look at the first page or two of this thread for the reasons why (or else google the 'tachyonic anti-telephone').

 

[neopolitan]

When people say that FTL implies "time travel", they are talking specifically about sending objects or information backwards in time and violating causality. Tachyons wouldn't allow us to send sublight objects like people back in time, but they would allow information to be sent back in time if SR is correct, look at the first page or two of this thread for the reasons why (or else google the 'tachyonic anti-telephone').

I did look on the first page. Specifically I looked at the OP's post, in which he used the phrase "I can't seem to hack why faster than light speed would suggest time travel however." I used the paraphrase "FTL implies time travel" which I thought was valid. I can't see where the OP is saying anything about sending stuff back in time, information or objects.

I might be wrong, of course.

cheers,

neopolitan

(PS Causality-wise, I don't see how sending information back in time which could then be acted upon would be substantially different to sending back a thing. For example, you get into trouble if you send a bomb back in time and kill your grandfather, but surely you get into trouble if you send a convincing message to your grandfather that your grandmother has chlamydia and is to be avoided at all costs? I'd fall on the side of the fence which says you can't violate causality which indicates to me that you can't send information back. If SR says you can, it is either wrong or misinterpreted. Misinterpretation seems more likely.)

 

[JesseM]

I did look on the first page. Specifically I looked at the OP's post, in which he used the phrase "I can't seem to hack why faster than light speed would suggest time travel however." I used the paraphrase "FTL implies time travel" which I thought was valid. I can't see where the OP is saying anything about sending stuff back in time, information or objects.

Right, but the OP was talking as though this was an idea he had read or heard somewhere, and when scientists talk about the connection between FTL and time travel, they're always referring to causality violations due to sending particles or information backwards in time...if they just wanted to talk about traveling into the future at different rates, there would be no need to refer to FTL, since time dilation is a feature of slower-than-light travel.

(PS Causality-wise, I don't see how sending information back in time which could then be acted upon would be substantially different to sending back a thing. For example, you get into trouble if you send a bomb back in time and kill your grandfather, but surely you get into trouble if you send a convincing message to your grandfather that your grandmother has chlamydia and is to be avoided at all costs? I'd fall on the side of the fence which says you can't violate causality which indicates to me that you can't send information back. If SR says you can, it is either wrong or misinterpreted. Misinterpretation seems more likely.)

You're correct, sending information back would be a causality violation just as much as sending matter back. But this is exactly why physicists think that FTL signaling is probably impossible--certainly there is no evidence that any tachyons exist in the real world. The point is that if you have FTL signalling in a universe that respects SR, that leads to causality violations...you can avoid causality violations by saying that one of those two premises are wrong, and most physicists would consider it unlikely there's a preferred reference frame, in which case it must be the premise of FTL signalling that's wrong.

 

[neopolitan]

<snip>in which case it must be the premise of FTL signalling that's wrong.

It really seems to me that part of the problem is the simplification of the diagrams followed by treating the diagrams as if they more than representative (ie as in the first link you gave explaining why FTL is not possible). I suspect that FTL signalling resulting in causality violations is not just practically impossible (because of the sad lack of tachyons), but also theoretically impossible (and a more rigorous treatment would show that even if you did have tacyons they would not result in causality violations). To clarify: FTL is not possible and even if it were it would not result in causality violations.

The other part is that the theory is based on two postulates and of course you will get crazy results if you introduce something which those postulates proscribe. What would be the speed of light in the rest frame of a tachyon? How would the laws of physics work in the rest frame of a tachyon?

cheers,

neopolitan

 

[JesseM]

It really seems to me that part of the problem is the simplification of the diagrams followed by treating the diagrams as if they more than representative

The argument is not based specifically on diagrams, it's based on the mathematics of the Lorentz transformation, as well as the assumption that any laws of physics applying to tachyons would have to respect the first postulate of SR (that is, the laws would work the same way in all the inertial frames given by the Lorentz transform).

The other part is that the theory is based on two postulates and of course you will get crazy results if you introduce something which those postulates proscribe.

The postulates don't forbid tachyons. They just say that the speed of light must be c in all inertial frames, and that the laws of physics must work the same way in all inertial frames.

What would be the speed of light in the rest frame of a tachyon? How would the laws of physics work in the rest frame of a tachyon?

Tachyons wouldn't have their own inertial rest frame, just like photons don't. It's not too hard to show that for the two postulates to be correct, the only inertial frames must be sublight frames.

 

[Fredrik]

Neopolitan, it's very easy to see that if you can send messages with arbitrary speeds and the emission/detection time doesn't grow at least linearly with the distance the message travels, we do get causality violations.

+ what Jesse said.

 

[Dale]

To clarify: FTL is not possible and even if it were it would not result in causality violations.

That is fine, but in that case you would have to reject the principle of relativity. Again, you can have only two of relativity, FTL, and causality. If FTL and causality, then not relativity.

Do you understand why you can have only two of FTL, causality, and relativity?

 

[neopolitan]

That is fine, but in that case you would have to reject the principle of relativity. Again, you can have only two of relativity, FTL, and causality. If FTL and causality, then not relativity.

Do you understand why you can have only two of FTL, causality, and relativity?

I don't think you can have FTL. But what I am saying is that if in the real universe you could (since what I think has little bearing on what the universe will permit), then I think we would find that that FTL would not lead to causality violations. Perhaps, if we found that FTL was possible, then we would find that relativity, like Newton's law of gravitation, was just a very very good approximation in the circumstances. Not wrong per se, but incomplete. But since I don't think that you can have FTL, then this is a purely academic exercise for me - I'm fundamentally saying that I would not be able to accept FTL unless, somehow, we worked out that we could have it without tossing out the other two.

Since we have had such long relatively fruitless discussions on simultaneity, I don't think it helps to go through the specifics of why I think that FTL wouldn't violate causality, but might necessitate that relativity is incomplete.

Covering some of the other comments:

Jesse. Tachyons that don't have their own inertial rest frame is a cop-out. Even if they don't, it's suddenly not SR (which I don't think we would disagree about). I am not convinced that you would have GR either, but certainly any equation with sqrt(1-v²/c²) would be looking very dodgy. In other words, and in response to your statement "it's based on the mathematics of the Lorentz transformation", you can't use the Lorentz transformation once v > c. So you can't base anything on it. The diagrams are dodgy and the maths is dodgy.

Fredrik. FTL doesn't have to mean that "emission/detection time doesn't grow linearly with the distance the message travels". But sure, if you had instantaneous translation, or negative "time growth" (which I assume is stuff going back in time), then you do get causality violations. I don't see the relevance, but I agree with you.

cheers,

neopolitan

 

[JesseM]

I don't think you can have FTL. But what I am saying is that if in the real universe you could (since what I think has little bearing on what the universe will permit), then I think we would find that that FTL would not lead to causality violations.

And do you understand that this could only be true if tachyons did not behave the same way in different sublight inertial reference frames (i.e. in some frames a tachyon could be received before it was emitted, in other frames it couldn't), which would be a violation of the first postulate of SR?

Jesse. Tachyons that don't have their own inertial rest frame is a cop-out.

That isn't really any sort of logical argument, just name-calling. Why isn't it also a "cop-out" that photons don't have their own inertial rest frame? And the set of inertial rest frames is defined completely by the Lorentz transform, which itself is derived from the two postulates of relativity, it has nothing to do with what particles happen to actually exist in the universe (even if the only particles were photons and there was no such thing as a particle moving slower than light, it would still logically have to be true that if the two postulates were statisfied, all inertial frames would have to be slower-than-light frames).

Even if they don't, it's suddenly not SR (which I don't think we would disagree about).

Are you saying that if tachyons exist, then it's not SR? If so, of course I'd disagree about that, I just said "The postulates don't forbid tachyons" in the previous post. Can you tell me specifically why tachyons would violate either of the two fundamental postulates of SR? Those two postulates define what is meant by "SR", so if neither is violated then you're still dealing with SR.

I am not convinced that you would have GR either, but certainly any equation with sqrt(1-v²/c²) would be looking very dodgy.

You also get nonsense if you substitute v=c into any equation with the term 1/\sqrt{1 - v^2/c^2}, but that doesn't mean you can't have things moving at c. Again, fundamentally relativity is defined by the two postulates, as long as the laws of physics respect those postulates it doesn't matter if certain equations only make sense when v is set to be a sublight velocity.

In other words, and in response to your statement "it's based on the mathematics of the Lorentz transformation", you can't use the Lorentz transformation once v > c. So you can't base anything on it.

And nothing about the existence of tachyons would obligate you to plug v > c into the Lorentz transformation, just like nothing about the existence of photons obligates you to plug v = c into the Lorentz transformation. As long as photons/tachyons behave the same way in all inertial reference frames, there is no reason for them to violate the two postulates of SR (and again, it's not hard to show that the two postulates themselves logically imply that an 'inertial reference frame' must by definition have a sublight velocity).

 

[Chewy0087]

I am not convinced that you would have GR either, but certainly any equation with sqrt(1-v²/c²) would be looking very dodgy. In other words, and in response to your statement "it's based on the mathematics of the Lorentz transformation", you can't use the Lorentz transformation once v > c. So you can't base anything on it. The diagrams are dodgy and the maths is dodgy.

neopolitan

Well...i'm not really an expert however if tachyons do exist wouldn't it simply mean that they have an imaginary mass?

m0 * 1 / sqroot (1 - v²/c²) * c² , sureley m0 would have to be imaginary giving an actual figure for energy? (presuming you can't have imaginary energy =D)

 

[neopolitan]

Jesse, Jesse, Jesse ...

From you:

"The postulates don't forbid tachyons. They just say that the speed of light must be c in all inertial frames, and that the laws of physics must work the same way in all inertial frames."

My interpretation:

SR is talking about how things work in inertial frames.

From you:

"Tachyons wouldn't have their own inertial rest frame"

My interpretation:

If we are talking about tachyons which don't have an inertial rest frame, then we aren't talking about SR. This seems to accord with the local habit (in the forums) of quickly shutting down any discussion which touches on "the perspective of a photon" or the like.

I see giving tachyons the ability to zip around the universe without their own inertial rest frame, just like the photon and any other particle which may travel at c, and then also giving the tachyon the ability to travel faster than light, which otherwise seems to be a universal upper speed limit, does seem to be at the very best questionable. My apologies if I offended you by referring to bestowing the tachyon with the effective equivalent of a get out of jail free card, or immunity from further discussion, as "a cop-out"; but note that I didn't say you copped out. I am sure you are not the original proponent of tachyons without inertial rest frames.

I don't see why anyone should get hot under the collar about an imaginary particle, it only saddens me that neither pi nor e are involved, since I can't make a pun about irrational numbers.

cheers,

neopolitan

 

[neopolitan]

Well...i'm not really an expert however if tachyons do exist wouldn't it simply mean that they have an imaginary mass?

m0 * 1 / sqroot (1 - v²/c²) * c² , sureley m0 would have to be imaginary giving an actual figure for energy? (presuming you can't have imaginary energy =D)

Since v>c the equation here would end up being imaginary as well. Unless we find that our equations are only locally applicable, and reflections of a higher level of theory which incorporates FTL without violating causality or the local applicability of relativity, then I suggest we just leave tachyons as imaginary in their entirety.

Some of the arguments to leave the door open to tachyons seem to border on messianic. If you want to have faith in tachyons, that's all well and good, but I think such faith is as helpful in mainstream physics as intelligent design is in the field of biology.

I'll be happy to retract that statement if tachyons are required to explain phenomena which can't otherwise be explained by the standard models. (Note that I do not accept that a theory may require tachyons as sufficient (and even less the weaker "permit tachyons"), since that indicates to me that the theory in question may be incomplete. Explanations of phenomena only, not wriggle room for popular theories.)

However, this thread was about why FTL implies time travel. I tried to address that but am being dragged off course into arguments about a particle I don't think exists. So, if nothing arises to persuade me there is any value in continuing to invest time in considering this highly unlikely particle, I will be bowing out.

cheers,

neopolitan

 

[Dale]

I think that FTL wouldn't violate causality, but might necessitate that relativity is incomplete.

This is fine. I also would tend to pick causality over relativity if FTL were unavoidable and I were given the choice.

 

[JesseM]

Jesse, Jesse, Jesse ...

From you:

"The postulates don't forbid tachyons. They just say that the speed of light must be c in all inertial frames, and that the laws of physics must work the same way in all inertial frames."

My interpretation:

SR is talking about how things work in inertial frames.

Of course, but an inertial frame is just a spacetime coordinate system used to label events, you can describe absolutely any event or series of events in the universe from the perspective of a sublight inertial frame, including events associated with things that are moving at v=c or hypothetical things moving at v > c.

From you:

"Tachyons wouldn't have their own inertial rest frame"

My interpretation:

If we are talking about tachyons which don't have an inertial rest frame, then we aren't talking about SR. This seems to accord with the local habit (in the forums) of quickly shutting down any discussion which touches on "the perspective of a photon" or the like.

This is not a local habit of these forums, it's the standard understanding of all physicists that photons don't have their own inertial rest frame. This is not to say you couldn't design a coordinate system where a photon was at rest, and you could do the same for a tachyon, but it would not be an "inertial" frame and the laws of physics would not obey the same equations in such a coordinate system as they do in inertial coordinate systems.

You say "If we are talking about tachyons which don't have an inertial rest frame, then we aren't talking about SR"--so, do you think that when we talk about photons (which don't have an inertial rest frame either), then "we aren't talking about SR"? If not, what's the difference? You can certainly analyze the movements of a photon from the perspective of sublight inertial frames, and write down equations which predict how they behave in terms of the coordinates of these frames, so why couldn't you do the same with tachyons?

I see giving tachyons the ability to zip around the universe without their own inertial rest frame, just like the photon and any other particle which may travel at c, and then also giving the tachyon the ability to travel faster than light, which otherwise seems to be a universal upper speed limit, does seem to be at the very best questionable.

But questionable why? In physics you aren't supposed to call things "questionable" just because they doesn't match your personal aesthetic tastes, there has to be some actual physical reason for questioning an idea, like the idea leading to implausible predictions about the results of specific experiments.

My apologies if I offended you by referring to bestowing the tachyon with the effective equivalent of a get out of jail free card, or immunity from further discussion, as "a cop-out"; but note that I didn't say you copped out. I am sure you are not the original proponent of tachyons without inertial rest frames.

When I described "cop-out" as mere name-calling without an actual argument, it wasn't because I was personally insulted--I didn't mean to suggest you were calling me names, I meant that you were using name-calling to try to call into question the statement that in SR the only inertial frames possible are sublight frames, so even if tachyons existed they wouldn't have their own inertial frame. Unless you have a coherent argument as to why this statement is wrong, this is indeed mere name-calling.

Please just answer these questions for me: do you think is there anything about tachyons that would violate either of the two fundamental postulates of SR? And do you agree that SR is defined by these postulates, so as long as we're talking about a universe where neither postulate is violated, then we're talking about a universe where SR holds? Finally, do you agree that the two postulates logically imply that all "inertial frames" must be sublight frames, i.e. it would be impossible to imagine a universe where both postulates are correct and yet some inertial frames move at speeds greater than or equal to c?

 

[JesseM]

Since v>c the equation here would end up being imaginary as well.

If you assume the equation E = m0 * 1 / sqroot (1 - v²/c²) * c² works for tachyons, then if their rest mass was imaginary this would give a real value for energy. See this article for a discussion.

Unless we find that our equations are only locally applicable, and reflections of a higher level of theory which incorporates FTL without violating causality or the local applicability of relativity, then I suggest we just leave tachyons as imaginary in their entirety.

Do you disagree that some equations of relativity that work for sublight particles already give nonsensical answers when we plug in v=c, including the one above? If so, it makes no sense to argue that tachyons are incompatible with SR on the basis of equations breaking down, unless you are also willing to argue that photons are incompatible with SR for the same reason.

Some of the arguments to leave the door open to tachyons seem to border on messianic.

Um, they are merely theoretical arguments about what the logical consequences of the theory of SR--it's just an objective fact that there is nothing in the theory of SR that would absolutely rule out tachyons. No one is actually saying tachyons are remotely plausible in the real world! The point is that your arguments against tachyons show a misunderstanding of the theory of SR on your part, which is the only reason people are arguing with you, not because they want to convince you that you should believe tachyons have a non-negligible likelihood of actually existing.

However, this thread was about why FTL implies time travel. I tried to address that but am being dragged off course into arguments about a particle I don't think exists.

Come again?? How can you possibly discuss the theoretical question of whether FTL implies time travel if you refuse to even discuss the hypothetical that FTL is possible? We don't need to believe that FTL is possible in the real world to deduce what the theoretical consequences would be if FTL were possible. And one of those theoretical consequences is that if the two postulates of SR remain valid in a universe where FTL is possible, then logically this implies the possibility of time travel in such a universe. That theoretical consequence is what this thread is all about!

 

[neopolitan]

Repeating for Jesse's benefit:

Some of the arguments to leave the door open to tachyons seem to border on messianic. If you want to have faith in tachyons, that's all well and good, but I think such faith is as helpful in mainstream physics as intelligent design is in the field of biology.

I'll be happy to retract that statement if tachyons are required to explain phenomena which can't otherwise be explained by the standard models. (Note that I do not accept that a theory may require tachyons as sufficient (and even less the weaker "permit tachyons"), since the stronger comment indicates to me that the theory in question may be incomplete. Explanations of phenomena only, not wriggle room for popular theories.)

However, this thread was about why FTL implies time travel. I tried to address that but am being dragged off course into arguments about a particle I don't think exists. So, if nothing arises to persuade me there is any value in continuing to invest time in considering this highly unlikely particle, I will be bowing out.

Perhaps I wasn't being entirely clear. I would see value if and only if tachyons are required to explain phenomena which can't otherwise be explained by standard models. Otherwise the discussion seems to be based on no more than wishful thinking.

I'll keep an eye on the thread, but until that condition is met, I won't be involving myself deeply in any tachyon discussion.

cheers,

neopolitan

PS About the imaginary energy, I was assuming m0 was more a magnitude (with mass units, rather than imaginary mass units). If m0 is imaginary, then you end up with two imaginary numbers multiplying and that results in negative energy. Perhaps you could use tachyons to power your perpetual motion machine. Of course, I think that the perpetual motion machine is imaginary as well, so I imagine that using imaginary tachyons with imaginary mass would be totally appropriate.

 

[JesseM]

Perhaps I wasn't being entirely clear. I would see value if and only if tachyons are required to explain phenomena which can't otherwise be explained by standard models. Otherwise the discussion seems to be based on no more than wishful thinking.

Tachyons are the only form of FTL I know of that are compatible with SR (obviously you can't have things like wormholes in SR because they involve curved spacetime, and in any case wormholes lead to the same sorts of problems with causality in GR). Would you say it's not worth discussing the theoretical consequences of FTL in general? If so, why did you bother posting on this thread, which is specifically about the question of what consequences FTL would have for causality in a relativistic universe?

And please stop using phrases like "wishful thinking" when I've made it clear I don't believe in tachyons, and I assume the same is true for other participants on this thread. In a theoretical discussion you can discuss anything that isn't specifically forbidden by the theory in question, even possibilities that you don't think are remotely plausible in real life. Theoretical physicists do this sort of thing all the time to test the limits of existing theories (it's especially common in GR which allows for a lot of very weird spacetimes).

PS About the imaginary energy, I was assuming m0 was more a magnitude (with mass units, rather than imaginary mass units). If m0 is imaginary, then you end up with two imaginary numbers multiplying and that results in negative energy.

No, \sqrt{1 - v^2/c^2} is the denominator so you'd have an imaginary rest mass divided by an imaginary number, so the energy would be a positive real number.

Perhaps you could use tachyons to power your perpetual motion machine.

Even if negative energy were possible it would not lead to any violations of conservation of energy, which is what is normally meant by "perpetual motion machine". Note that unlike the implausible but theoretically possible tachyons, negative energy is a theoretical possibility that many physicists think there is actually experimental evidence for, in the form of the Casimir effect in quantum physics.

 

[neopolitan]

PS About the imaginary energy, I was assuming m0 was more a magnitude (with mass units, rather than imaginary mass units). If m0 is imaginary, then you end up with two imaginary numbers multiplying and that results in negative energy.

No, sqrt{1 - v^2/c^2} is the denominator so you'd have an imaginary rest mass divided by an imaginary number, so the energy would be a positive real number.

JesseM,

Read your own link - http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html"

Now another familiar relativistic equation is E = m*[1-(v/c)²]^-1/2. Tachyons (if they exist) have v > c. This means that E is imaginary! Well, what if we take the rest mass m, and take it to be imaginary? Then E is negative real

You could be right and he is wrong. In which case you need to let him know, since the remainder of the article is pretty much based on negative energy. But if that is the case, I suggest you don't tell us all to go off reading incorrect articles.

I want to bow out but I don't want to rudely ignore you, nor let these sort of inconsistencies stand uncorrected. I'll accept whatever corrective action you think is necessary and be on my way.

cheers,

neopolitan

 

[JesseM]

You could be right and he is wrong. In which case you need to let him know, since the remainder of the article is pretty much based on negative energy. But if that is the case, I suggest you don't tell us all to go off reading incorrect articles.

It's definitely true that a positive imaginary number (i.e. x*i where x is a positive real number) divided by a positive imaginary number gives a positive real number, I hope you wouldn't dispute this...perhaps the author of the page was assuming that the rest mass was a negative imaginary number, in which case the statement about energy being negative would be correct. I don't know what the motivation for that would be though. The wikipedia article on tachyons says here that the "Feinberg reinterpretation principle" tells us that "a negative-energy tachyon sent back in time in an attempt to violate causality can always be reinterpreted as a positive-energy tachyon traveling forward in time", which would seem to suggest the rest mass of a tachyon can be treated as either a negative or positive imaginary number.

Also, I don't know what you mean when you say "the remainder of the article is pretty much based on negative energy"--for example, the conclusion in the next paragraph that "they accelerate (p goes up) if they lose energy (E goes down)" will still be true if you assume a positive imaginary rest mass such that both E and p are positive (see the fifth paragraph here for an explanation). Nor do any of the other subsequent statements seem to depend on the idea that E and p are negative.

 

[Fredrik]

I don't think you can have FTL. But what I am saying is that if in the real universe you could (since what I think has little bearing on what the universe will permit), then I think we would find that that FTL would not lead to causality violations.

Yes, of course. (DaleSpam's thoughts about this are the same as mine). But that's not what you were saying before. At least you didn't make it clear that that's what you meant. You just jumped into a discussion about how SR+FTL implies "time travel" (in the sense that you can receive the answer to a question before you send the question), and claimed that the conclusion is wrong.

Tachyons that don't have their own inertial rest frame is a cop-out. Even if they don't, it's suddenly not SR (which I don't think we would disagree about).

This is very very wrong. A tachyon in SR is just a spacelike curve in Minkowski space, i.e. a curve such that its tangent has a slope <1 everywhere in an inertial frame.

I am not convinced that you would have GR either, but certainly any equation with sqrt(1-v²/c²) would be looking very dodgy.

The gamma factor appears in equations that describe how something changes from one inertial frame to another, and the v is the velocity of one of the frames in the other. So if there are tachyons in SR, you still won't ever have a reason to input a v>c in such a formula.

FTL doesn't have to mean that "emission/detection time doesn't grow linearly with the distance the message travels".

In the framework of SR it does. It's the only way to avoid logical inconsistencies.

But sure, if you had instantaneous translation, or negative "time growth" (which I assume is stuff going back in time), then you do get causality violations. I don't see the relevance, but I agree with you.

Now I have no idea what you're talking about. Those things that you don't see the relevance of are what this thread is about.

 

[Austin0]

Originally Posted by neopolitan
I am not convinced that you would have GR either, but certainly any equation with sqrt(1-v2/c2) would be looking very dodgy.

Fredrik-----------
The gamma factor appears in equations that describe how something changes from one inertial frame to another, and the v is the velocity of one of the frames in the other. So if there are tachyons in SR, you still won't ever have a reason to input a v>c in such a formula.

If you apply the additon of velocities formula isn't that indirectly inputting a v>c.
That the equation is basically the Lorentz transformation applied to Gallilean coordinate transforms and in the process of deriving the simplified formula the gamma factor was necessarily applied. This would seem to imply that directly deriving additive velocities through first principles would mean entering v>c into this equation [sqrt(1-v2/c2)]
Would you agree?

Or do you think this is not a problem because the (i's) might cancel out. Two imaginary velocities added together result in one meaningful , real velocity?



Originally Posted by neopolitan
FTL doesn't have to mean that "emission/detection time doesn't grow linearly with the distance the message travels".

Fredrik ----
In the framework of SR it does. It's the only way to avoid logical inconsistencies.

Two questions
1) Do you not think that this whole procedure, not to mention this whole discussion is already filled with logical inconsistancies?

2) What kind of scientific rationale is that ?? We should assume this result must be correct because otherwise we have logical inconsistancies,,, rather than logical inconsistancies might possibly indicate erroneous assumptions that should be questioned??

 

[Austin0]

=

JesseM;2048616]Tachyons are the only form of FTL I know of that are compatible with SR

Does this mean that you do not consider ,possible EPR transmission as being FTL , or that you don't consider it compatible with SR??

In either case ,why?

 

[Austin0]

This is fine. I also would tend to pick causality over relativity if FTL were unavoidable and I were given the choice.

Why do you feel that it would be a question of "choosing" one or the other if it was simply a matter of a small addition to SR.
Do you think its "OH well , we found an exception , I quess we just have to throw out SR"

Do you think it is "Impossible" that empirical discoveries in QM or cosmology might necessitate some kind of revision or expansion in just about any field of physics you can name.
Right now there are question regarding Conservation of m and E:
virtual particles and "dark" energy.

Causality: FTL is not the only assault being mounted. There are several theories and even apparent evidence in QM [delayed choice etc] that would seem to indicate the possibility that reverse causality might not only be possible but actually a fundamental reality of particle and photon interaction.

Gravity: Galactic angular mometum anomalies etc. seem to present the choice of a possible extension of GR to cover cosmic scale or a completely new form of matter [Ptolomeic epi-matter] so to speak.
I want to make it clear I am not promoting any of these possibilities, only pointing out that it is not a particularly good time to have any expectations that our current theories are the "last" word/

 

[JesseM]

Does this mean that you do not consider ,possible EPR transmission as being FTL , or that you don't consider it compatible with SR??

It's been proven that EPR effects cannot be used for FTL communication according to orthodox QM, but sure, I suppose you could imagine a universe where SR is true but QM is modified in such a way that entanglement can be used for FTL communication. In this case all the same arguments about it leading to a breakdown in causality would apply--all that's important is that there's a spacelike separation between the transmission event and the reception event for an FTL signal. If you'd answer my questions in post #88 perhaps we could make some progress in understanding exactly which part of the logic you disagree with.

Why do you feel that it would be a question of "choosing" one or the other if it was simply a matter of a small addition to SR.

What "addition" would that be? As always, SR is defined by the two postulates, and there's no way to have FTL signaling without causality violation unless one of those postulates is violated.

 

[Dale]

Why do you feel that it would be a question of "choosing" one or the other if it was simply a matter of a small addition to SR.
Do you think its "OH well , we found an exception , I quess we just have to throw out SR"

I was actually referring to the principle of relativity rather than SR. If FTL and causality then the equations describing the behavior of tachyons would necessarily have different forms in different inertial reference frames. This means that the principle of relativity is wrong.

Now, of course, there are mountains of evidence supporting SR, the Lorentz transforms, time dilation, etc., and the discovery of tachyons wouldn't negate a single piece of that evidence. Similarly, when SR was invented that did not erase Newtonian mechanics nor any of the evidence supporting it. What would happen is that we would place some currently unknown limit on the domain of applicability of the results of SR, just like SR placed a previously unknown limit (v<<c) on the domain of applicability of Newtonian mechanics. We wouldn't get rid of it (since we have so much evidence supporting it), but we would use it only where it applies and it would certainly not apply to causal tachyons.

it is not a particularly good time to have any expectations that our current theories are the "last" word

I certainly don't think that our current theories are the "last" word, and in fact I would be highly disappointed if they were.

 

[Dale]

ITachyons that don't have their own inertial rest frame is a cop-out. Even if they don't, it's suddenly not SR (which I don't think we would disagree about).

Hi neopolitan,

Sorry to interject, but don't forget that the time coordinate in SR inertial frames is defined by using the Einstein synchronization procedure on inertially moving clocks at rest wrt each other. Now, suppose that in some inertial frame you had two clocks separated by a fixed distance and traveling at some v\geq c, could you use the Einstein synchronization procedure to synchronize them? If not, then their rest frame is not a SR inertial frame.

 

[neopolitan]

You just jumped into a discussion about how SR+FTL implies "time travel" (in the sense that you can receive the answer to a question before you send the question), and claimed that the conclusion is wrong.

This will be my last comment on this thread, but it is worth pointing out where this medium seems to fail so regularly.

I didn't jump into an on-going discussion.

I specifically addressed the OP's original question, I even quoted it to highlight that I was responding solely to that question, and I ignored the rest of the discussion. I freely admit that I didn't read any of the discussion between the OP's question and my first post to the thread.

I do wonder what the OP thinks of the consequences of his rather innocent post.


To Dale: Even if that is the case (re Einstein synchronisation) then it really doesn't prove anything to me. To me the logic seems to go like this: tachyons do something impossible by going faster than light, by virtue of doing this impossible thing you can't synchronise them using Einstein synchronisation, since they can't be thus synchronised they don't have their own inertial rest frames, since they don't have their own inertial rest frames they don't have to accord with the postulates of SR, therefore SR has no dominion and can't be use to prove that tachyons don't exist, therefore they might be possible. It's akin to saying that SR can't be used to prove that god does not exist, since any god would be outside the scope of SR, therefore god exists.

I'm even willing to accept that the imaginary tachyons don't have an inertial rest frame. I just can't see how they fall under the category of SR.

It goes back to what I think you said in the second last post: if tachyons did exist then SR would be a subordinate theory to a greater one which also covers those things which can travel at v>c and so if we are talking tachyons then, strictly speaking, we are no longer talking SR.

My apologies if I've misinterpreted you.


Bed calls. I've answered everyone, I don't intend to respond anymore and I won't be monitoring the thread either.

cheers,

neopolitan

 

[Chewy0087]

If tachyons have an imaginary mass / the imaginary 'boost factor', of course they'll cancel out, giving a positive energy, quite simple maths I can't see why anyone would dispute that, so calling it 'dodgey' as an argument is invalid. The beauty of the equations done by Einstein is their amazing nature to hold in all situations (looked at so far) and it can also in theory hold for tachyons if they have an imaginary mass

I also don't see neopolitan why you want to continue talking about FTL (you don't seem to mind) and yet you have an aversion to talking about a particle which is the closest thing we have to (and basically embody) the concept?

Also, it's my understanding that it is possible to use the e = m0 gamma c2 formula for photons & tachyons however it becomes redundant due to the nature of the calculations, therefore it's far more constructive to use clear & defined inertial frames!

 

[Fredrik]

If you apply the additon of velocities formula isn't that indirectly inputting a v>c.

No. Look at my previous reply to you (included below for completeness). If u, v and w are defined as in that post, the derivation of the velocity addition formula goes like this:

The slope of the tachyon's world line is 1/v in F' and 1/w in F. That means that the Lorentz transformation

\gamma\begin{pmatrix}1 &amp; u\\ u &amp; 1\end{pmatrix}

must take \begin{pmatrix}1\\ v\end{pmatrix} to a vector proportional to \begin{pmatrix}1\\ w\end{pmatrix}. That's all we need to find w:

\gamma\begin{pmatrix}1 &amp; u\\ u &amp; 1\end{pmatrix}\begin{pmatrix}1\\ v\end{pmatrix} =\gamma\begin{pmatrix}1+uv \\ u+v\end{pmatrix} =\gamma(1+uv)\begin{pmatrix}1 \\ \frac{u+v}{1+uv}\end{pmatrix}

So w must be what I said before:

I'm not really sure what you're asking. I assume that we're talking about the formula that says that if the velocity of frame F' in frame F is u and the velocity of a particle in frame F' is v, then the velocity of that particle in frame F is

w=\frac{u+v}{1+uv}

What exactly are you asking? Which of these variables (u,v and w) do you want to make bigger, and which one(s) do you think will be smaller as a consequence? (Note that by definition we have u<1, but if the particle is a tachyon, both v and w will be >1).

That the equation is basically the Lorentz transformation applied to Gallilean coordinate transforms and in the process of deriving the simplified formula the gamma factor was necessarily applied.

No. That doesn't even make sense. Lorentz and Gallilean transformations have one thing in common: they both represent a coordinate change from one inertial frame to another, but the term "inertial frame" doesn't mean the same thing in those two contexts.

This would seem to imply that directly deriving additive velocities through first principles would mean entering v>c into this equation [sqrt(1-v2/c2)]
Would you agree?

No. See above.

1) Do you not think that this whole procedure, not to mention this whole discussion is already filled with logical inconsistancies?

2) What kind of scientific rationale is that ?? We should assume this result must be correct because otherwise we have logical inconsistancies,,, rather than logical inconsistancies might possibly indicate erroneous assumptions that should be questioned??

1. No.
2. I have no idea what you're talking about. Who says we have to assume that something is correct? As for your last question, you're missing the point, again. You won't find that logical inconsistency unless you take SR+FTL+"short emission/detection times" as the starting point. When you've found the inconsistency, you have learned something, which is that a theory that includes all of those doesn't make sense. You're right that there's more than one assumption that we might consider replacing, but the only way to realize that is to do the very thing that you're objecting against. So I really have no idea what you're complaining about. I just said that in the framework of SR, the possibility of FTL messages implies that emission/detection times grows at least linearly with distance. It makes no sense to object against that unless you think the words mean something different than what they actually mean.

 

[Fredrik]

I just can't see how they fall under the category of SR.

They do because you can define spacelike curves in Minkowski space. (Curves with slope <1 in an inertial frame). That's really all there is to it, since SR is the theory that uses Minkowski space as a model of space and time.

 

[Dale]

I'm even willing to accept that the imaginary tachyons don't have an inertial rest frame. I just can't see how they fall under the category of SR.

Photons fall under SR and do not have an inertial rest frame. Accelerating objects also fall under SR and do not have inertial rest frames.

It goes back to what I think you said in the second last post: if tachyons did exist then SR would be a subordinate theory to a greater one which also covers those things which can travel at v>c and so if we are talking tachyons then, strictly speaking, we are no longer talking SR.

My apologies if I've misinterpreted you.

Almost, I would just specify that we are talking about tachyons which do not violate causality. "if causal tachyons did exist then SR would be a subordinate theory to a greater one which also covers those things which can travel at v>c and so if we are talking causal tachyons then, strictly speaking, we are no longer talking SR". It is only causal tachyons that violate relativity.

You could theoretically have tachyons that are perfectly compatible with relativity. But relativistic tachyons would violate causality.

 

[Austin0]

=JesseM;2041873]I'll try to address the rest later, but just wanted to quickly post on what I think is the heart of the matter:

So, question #1, do you agree that "any event can be assigned time and space coordinates in any inertial frame"?

In principle I would [and have] agree
I agree that any event that could possibly occur would have coordinates.
The question of assigning specific coordinates to hypothetical events is the question I am posing.

If the answer here is yes, then I assume this should apply to both the event of the tachyon being sent and the event of the tachyon being received (no need to comment on this unless you disagree). In this case, my question #2 is, would you also agree that the premise "FTL" implies that there must be at least one inertial frame where the difference in space coordinates dx between these two events is larger than the difference in time coordinates dt, in units where c=1?

Once again I would [and have] in principle agree completely. But dt<dx is a range of possible coordinates and the methods and logic of assigning a specific quantitative dt is the core of the question.

If you answered yes to questions #1 and #2, then since you also agreed that the coordinates of different inertial frames must be related by the Lorentz transform if SR is correct, question #3 is: do you agree that if we have two events where dx > dt in some frame, it is always possible to find a second inertial frame such that when you do the Lorentz transform to find the coordinates of the same events in the second frame, their order will be reversed in the second frame?

Do you realize these questions are a physics version of the classic "Do you like women , yes or no?" Well , yes
DO you think it is wrong to hit women, yes or no?"
Yes
"If you answered yes to the first two, then have you stopped beating your wife ,,,yes or no?"

Note that I gave an example of this where the events had a dx of 20 and a dt of 10 in the first frame and their order was reversed in the second frame moving at 0.8c relative to the first, but it's possible to prove that in general, if dx > dt for two events in one frame then it must be possible to find a different inertial frame with sufficient velocity relative to the first (a velocity less than c of course, since all inertial frames move at sublight speeds) such that when you plug that v into the Lorentz transformation equations and apply them to the coordinates of the events in the first frame, then the order of the events is reversed in the second frame. This would not be true for events where dx < dt or dx = dt, it's only true when dx > dt.

So, please address my questions 1-3 and perhaps this will help pinpoint exactly where your objection to the logic of the if-then conditional lies.

Through the course of this discussion I think I have come to understand your point of view and can see how, from that perspective , some of what I have been saying would seem "illogical" . I also completely agree that in this situation with many if-conditional premises it is necessary to focus on the center. The premise/argument that
"the events had a dx of 20 and a dt of 10 in the first frame"
This is the focus , both the quantitative value of dt and also the assumption that was the basis of this assigment.
Can I assume that if you had simply assigned a dt=(-10 ) in this premise that you would understand how I would see it as "including the conclusion in the premises" ??
Ie. "assuming a signal from A arrives 10 sec before it was sent in frame B Then "time travel"

AS I understand your point; because the actual assignment dt=10 did not obviously imply time travel and therefore required a transformation between frames to arrive at dt=-10 there was no inclusion of this conclusion in the premises.
OK I can see your point, even if the two times are effectively the same through a simple transform and the only real difference is that by deriving B from A instead of
A from B was ,,that this way it was not directly including the conclusion in the premises.

But in actuality there is reason to see ( dt=10 ) as directly indicating and requiring time travel. That for that dt to occur would mean going back in time 6 sec in frame A
That at t=0 ,x=0 x'=0, t'=0 from the perspective of frame B ( x=20) in A was colocated with x'=12 and had a time of t=16 AS frames always have local agreement and overall agreement this would seem to indicate a time discrepancy at x=20 from 16 --> 10 sec.=(-6)
What is your take on this?
Please do not come back with "the first postulate says that etc etc."

That simply translates to "Well we know that time travel will happen in one frame so it must happen in all frames"

I am talking about an explicit premise IF a tachyon goes back in time 6 sec in frame A THEN time travel and how that would effect the significance of the overall argument.


Beyond the above question is :
The applicability of the addition of velocities equation.
The overall results of the application of the basic assumption to bi-directional assigments and the many questions that arise from those results. Questions of logic, physics and conformity to the first postulate.

I have started to address some of these in the past and will try to find time to get them into a clear form in the near future.
Thanks and sorry for taking so long to directly respond to this post.

 

[Austin0]

Hi neopolitan,

Sorry to interject, but don't forget that the time coordinate in SR inertial frames is defined by using the Einstein synchronization procedure on inertially moving clocks at rest wrt each other. Now, suppose that in some inertial frame you had two clocks separated by a fixed distance and traveling at some v\geq c, could you use the Einstein synchronization procedure to synchronize them? If not, then their rest frame is not a SR inertial frame.

But what if you have an inertial frame A with v< c and tachyons traveling v> c do think that clocks in A could not be synched by the light method using tachyons instead??
Without the a priori assumption of the new implicit Postulate of SR (FTL = time travel.

 

[Austin0]

=DaleSpam;2048839]I was actually referring to the principle of relativity rather than SR. If FTL and causality then the equations describing the behavior of tachyons would necessarily have different forms in different inertial reference frames. This means that the principle of relativity is wrong.

Once again I don't understand. Suppose we eventually found a matrix or some means of determining motion within a system. Do you think this would mean that SR was wrong?

SR doesn't say motion doesn't exist or have any reality ,only that it is right now undetectable and working with this reality derived a system for achieving invariance of physics.

Now, of course, there are mountains of evidence supporting SR, the Lorentz transforms, time dilation, etc., and the discovery of tachyons wouldn't negate a single piece of that evidence. Similarly, when SR was invented that did not erase Newtonian mechanics nor any of the evidence supporting it. What would happen is that we would place some currently unknown limit on the domain of applicability of the results of SR, just like SR placed a previously unknown limit (v<<c) on the domain of applicability of Newtonian mechanics.

Thank you , my point exactly and I certainly couldn't have put it better or more succinctly

Original post Austin0
if it was simply a matter of a small addition to SR.

We wouldn't get rid of it (since we have so much evidence supporting it), but we would use it only where it applies and it would certainly not apply to causal tachyons.

I certainly don't think that our current theories are the "last" word, and in fact I would be highly disappointed if they were

Me too.

But you do seem to feel that SR as it now exists should be able to simply and directly apply to phenomena that is not strictly within its domain . SO you think it wouldn't apply to imaginary causal tachyons but would apply to imaginary time traveling tachyons ?

 

[Austin0]

=JesseM;2048835]It's been proven that EPR effects cannot be used for FTL communication according to orthodox QM

,
I would be interested in sources for this as I haven't encountered it. Any google hints would be appreciated , thanks.

 

[Dale]

But what if you have an inertial frame A with v< c and tachyons traveling v> c do think that clocks in A could not be synched by the light method using tachyons instead??

No, clocks could not be synchronized by tachyons any more than they could be synchronized by baseballs or proton beams today. The Einstein synchronization procedure relies on the fact that light has the same speed in all reference frames. Baseballs, protons, and tachyons do not have the same speed in different reference frames.

SO you think [SR] wouldn't apply to imaginary causal tachyons but would apply to imaginary time traveling tachyons ?

Yes, exactly.

 

[JesseM]

In principle I would [and have] agree
I agree that any event that could possibly occur would have coordinates.
The question of assigning specific coordinates to hypothetical events is the question I am posing.

That doesn't make any sense--the very idea of taking a hypothetical about physics as a premise is to imagine a universe where the hypothetical really occurs and see what consequences would follow in such a universe. If you are imagining a universe where FTL is still purely hypothetical, then you aren't taking FTL as a premise in the first place!

If gave the if-then conditional "if I was standing in the open and it was raining, then I would get wet", would you then disagree since hypothetical rain can't get people wet the way real rain does? Your own statement above appears every bit as senseless.

Once again I would [and have] in principle agree completely. But dt<dx is a range of possible coordinates and the methods and logic of assigning a specific quantitative dt is the core of the question.

Again that doesn't make any sense. If we have a general proof that for any set of coordinates that satisfy dx>dt in some inertial frame, there must then be an inertial frame where the events occur in reverse order, then naturally this proof would apply to whatever "specific quantitative dt" and dx you happen to imagine occurring in the hypothetical. Perhaps you are arguing that there would be some difficulty calculating dt in the first place, but that doesn't make sense either--you agreed earlier that in a relativistic universe we should be able to assign x and t coordinates to any event, so that means you can find the t coordinates of the event of the signal being sent and the event of the signal being received, and dt is just the second t coordinate minus the first t coordinate.

Do you realize these questions are a physics version of the classic "Do you like women , yes or no?" Well , yes
DO you think it is wrong to hit women, yes or no?"
Yes
"If you answered yes to the first two, then have you stopped beating your wife ,,,yes or no?"

That analogy doesn't make any sense, because there is no logical reason that answering yes to the first two questions would compel you to answer yes to the question about beating your wife. In contrast, I'm just trying to lead you through the inescapable logic of the proof, so I've specifically chosen questions such that if you answer yes to all of them, it becomes obvious that you have no choice but to answer yes to the question of whether the premises of SR and FTL signaling together imply the conclusion of backwards-in-time signaling.

Through the course of this discussion I think I have come to understand your point of view and can see how, from that perspective , some of what I have been saying would seem "illogical" . I also completely agree that in this situation with many if-conditional premises it is necessary to focus on the center. The premise/argument that
"the events had a dx of 20 and a dt of 10 in the first frame"
This is the focus , both the quantitative value of dt and also the assumption that was the basis of this assigment.

No, that particular value of dt is not the focus. As I said, it is easy to come up with a general mathematical proof that if the coordinates of two events in one frame are such that dx>dt, then it is always possible to come up with a velocity v such that when you use that v in a Lorentz transformation, the order of the two events is reversed in the second frame. Would you like to see this proof, or do you agree that such a general proof is possible?

If you do agree, then it should be easy to see that for any specific choice of coordinates for the transmission-event and the reception-event such that dx>dt--whether (0,0) and (20,10) or (50,70) and (60,79.999) or (-16.5,3000) and (501,3007)--it will be possible to find a different inertial frame where the events happen in reverse order according to t-coordinates assigned by the new frame.

Can I assume that if you had simply assigned a dt=(-10 ) in this premise that you would understand how I would see it as "including the conclusion in the premises" ??

Of course, but it is not obvious that the premise "FTL" is synonymous with the possibility that the reception-event happens before the transmission-event, while it is obvious that FTL should be synonymous with the notion that dx>dt in some inertial frame. Of course the point of the proof is to show that if you take SR as a premise, then the latter "obvious" implication of the premise FTL implies the former "not-so-obvious" implication of the premise FTL. That's the difference between a vacuous tautology and a non-vacuous proof where the conclusion is still logically implied by the premise but it may not be immediately obvious that it follows just by looking at the premises.

AS I understand your point; because the actual assignment dt=10 did not obviously imply time travel and therefore required a transformation between frames to arrive at dt=-10 there was no inclusion of this conclusion in the premises.
OK I can see your point, even if the two times are effectively the same through a simple transform and the only real difference is that by deriving B from A instead of
A from B was ,,that this way it was not directly including the conclusion in the premises.

Yes, but again, in all mathematical proofs you can show that the conclusion is logically implicit in the premises, but in the case of non-vacuous proofs you have to go through some steps--like the "simple transform" above--to demonstrate this. Incidentally, for a specific choice of coordinates like (0,0) and (20,10) it's true that you just need to apply the transform with a particular choice of velocity to show that they can happen in reverse order in another frame, but it may not be obvious that for any choice of coordinates for the events such that dx>dt, it would always be possible to find a velocity such that when you plug that velocity and those coordinates into the Lorentz transform, the result is that the events happen in reverse order in the new frame. This is why I offered to provide a proof of this claim if you doubt it.

But in actuality there is reason to see ( dt=10 ) as directly indicating and requiring time travel. That for that dt to occur would mean going back in time 6 sec in frame A
That at t=0 ,x=0 x'=0, t'=0 from the perspective of frame B ( x=20) in A was colocated with x'=12 and had a time of t=16 AS frames always have local agreement and overall agreement this would seem to indicate a time discrepancy at x=20 from 16 --> 10 sec.=(-6)
What is your take on this?

Are you asking where the x=20 marking on A's ruler was at time t'=0 in B's frame? If so, yes, the answer is that it was next to the x'=12 mark on B's ruler, and at the moment the x=20 mark on A's ruler was passing next to the x'=12 mark on B's ruler, the clock attached to the x=20 mark on A's ruler must have read:

t = 1.666... *(0 + 0.8*12) = 16.

So, when you say "this would seem to indicate a time discrepancy at x=20 from from 16 --> 10 sec.=(-6)", are you talking about the time between the moment the clock at x=20 on A's ruler is next to the event of the tachyon signal being received, and the moment the clock at x=20 on A's ruler is next to the x'=12 mark on B's ruler? If so, then yes, according to A's clock at x=20, the event of the tachyon signal being received happens 6 seconds prior to the event of passing next to the x'=12 mark on B's ruler. Why do you bring this up? How is it relevant to the discussion?

That simply translates to "Well we know that time travel will happen in one frame so it must happen in all frames"

I am talking about an explicit premise IF a tachyon goes back in time 6 sec in frame A THEN time travel and how that would effect the significance of the overall argument.

Huh? The tachyon doesn't go back in time 6 seconds in A's frame. In A's frame, the event of the clock at x=20 passing next to the x'=12 mark on B's ruler is not simultaneous with the event of the tachyon signal being sent, these events are only simultaneous in B's frame. So, the fact that in A's frame the event of receiving the signal happens 6 seconds before the event of x=20 passing next to x'=12 in no way implies that the tachyon has gone backwards in time in this frame. In A's frame the order of the events is this:

t=0: tachyon signal emitted next to x=0 mark on A's ruler (and next to x'=0 mark on B's ruler)
t=10: tachyon signal received next to x=20 mark on A's ruler (and next to x'=20 mark on B's ruler)
t=16: x=20 mark on A's ruler passes next to x'=12 mark on B's ruler

On the other hand, in B's frame the order of these events is this:

t'=-10: tachyon signal received next to x'=20 mark on B's ruler (and next to x=20 mark on A's ruler)
t'=0: tachyon signal emitted next to x'=0 mark on B's ruler (and next to x=0 mark on A's ruler), AND simultaneously at a different location, x'=12 mark on B's ruler is passing next to x=20 mark on A's ruler.

I assume that by now you understand about the relativity of simultaneity, so you should be able to see that the fact that those two events happen simultaneously at t'=0 in B's frame does not imply they should be simultaneous in A's frame.

The applicability of the addition of velocities equation.

There is absolutely no need to use the addition of velocities equation in the proof, you can just focus on the coordinates assigned to the events of the signal being sent and the signal being received. However, it's also not hard to show that if you take two events on the worldline of an object moving at constant speed, and calculate dx and dt between these events in one frame and define the velocity in that frame as dx/dt, then if you apply the Lorentz transformation to these two events and calculate dx'/dt' in the new frame, you will find that the velocities in the two frames are related by the velocity addition equation, even in the case that dx>dt (i.e. you are looking at the worldline of a tachyon). If you'd like to see a proof of this, just ask.

The overall results of the application of the basic assumption to bi-directional assigments and the many questions that arise from those results. Questions of logic, physics and conformity to the first postulate.

I don't understand what "bi-directional assignment" means, and I don't know what "questions of logic, physics and conformity to the first postulate" you're referring to. Let me restate the steps in the proof as clearly as I can, and since you've already said you agree with the first 4 steps, maybe you can point out specifically what step you have a problem with:

1. Given the premise SR, we must assume that any events can be assigned space and time coordinates x and t in any inertial frame.

2. Given the premise FTL, there must be some inertial frame where, if you have the coordinates (x1,t1) of the signal being sent and the coordinates (x2,t2) of the signal being received, then in units where c=1, dx=|(x2-x1)| > dt=|(t2-t1)|

3. Given the premise SR, the coordinates assigned to the same event by different inertial frames must be related by the Lorentz transform.

4. Given 2 and 3, if you have a signal such that dx>dt for the transmission-event and the reception-event in one inertial frame, it is always possible to find a new inertial frame such the reception-event happens at an earlier time than the transmission-event in the new frame.

5. By the first postulate of SR, if it is possible in one frame to send a tachyon signal in such way that the reception-event happens at an earlier time than the transmission-event in that frame, it must be possible in any frame to send a tachyon signal in such a way that the reception-event happens earlier than the transmission-event in that frame.

6. If it's possible in any frame to send a tachyon signal in such a way that the reception-event happens earlier than the transmission-event in that frame, then it must be possible for one observer to send a tachyon message to the other and the second to then send a tachyon reply in such a way that the event of the first observer receiving the reply lies in the past light cone of the event of the first observer sending the original message, which is a clear violation of causality in every frame.

Can you point to a specific step that you disagree with here, where you think that it doesn't follow from the previous steps and the original premises of SR and FTL?

 

[Austin0]

=JesseM;2050830]


Huh? The tachyon doesn't go back in time 6 seconds in A's frame.

There is absolutely no need to use the addition of velocities equation in the proof, you can just focus on the coordinates assigned to the events of the signal being sent and the signal being received. However, it's also not hard to show that if you take two events on the worldline of an object moving at constant speed, and calculate dx and dt between these events in one frame and define the velocity in that frame as dx/dt, then if you apply the Lorentz transformation to these two events and calculate dx'/dt' in the new frame, you will find that the velocities in the two frames are related by the velocity addition equation, even in the case that dx>dt (i.e. you are looking at the worldline of a tachyon). If you'd like to see a proof of this, just ask.

No that is not necessary I have confirmed that for myself.

I don't understand what "bi-directional assignment" means, and I don't know what "questions of logic, physics and conformity to the first postulate" you're referring to. Let me restate the steps in the proof as clearly as I can, and since you've already said you agree with the first 4 steps, maybe you can point out specifically what step you have a problem with:

Perhaps I should say omnidirectional if a frame is considered at rest.
Without SR the concept of light being measured at the same speed traveling in the same direction as the inertial frame as it is measured traveling counter to the motion of the frame is a logical impossibility yes? SR provided a rational consistent explanation for how this was possible through the desynchronization of clocks. Correct??
Or do you have a different understanding?

Without this desynchronization the difference in the "bi-directional" measurements would reveal the motion of the system. Correct??

1. Given the premise SR, we must assume that any events can be assigned space and time coordinates x and t in any inertial frame.

2. Given the premise FTL, there must be some inertial frame where, if you have the coordinates (x1,t1) of the signal being sent and the coordinates (x2,t2) of the signal being received, then in units where c=1, dx=|(x2-x1)| > dt=|(t2-t1)|

3. Given the premise SR, the coordinates assigned to the same event by different inertial frames must be related by the Lorentz transform.

4. Given 2 and 3, if you have a signal such that dx>dt for the transmission-event and the reception-event in one inertial frame, it is always possible to find a new inertial frame such the reception-event happens at an earlier time than the transmission-event in the new frame.

5. By the first postulate of SR, if it is possible in one frame to send a tachyon signal in such way that the reception-event happens at an earlier time than the transmission-event in that frame, it must be possible in any frame to send a tachyon signal in such a way that the reception-event happens earlier than the transmission-event in that frame.


If it's possible in any frame to send a tachyon signal in such a way that the reception-event happens earlier than the transmission-event in that frame, then it must be possible for one observer to send a tachyon message to the other and the second to then send a tachyon reply in such a way that the event of the first observer receiving the reply lies in the past light cone of the event of the first observer sending the original message, which is a clear violation of causality in every frame.

Can you point to a specific step that you disagree with here, where you think that it doesn't follow from the previous steps and the original premises of SR and FTL?

5) Above : It is not that I disagree with this at all. But you have just finished telling me how the reception event in frame A didnt occur earlier than the transmission event in that frame so how does this conform to the 1st postulate as you have outlined in 5)


How do you se this one:
The 1st P allows us to track a photon trans-reception happening in another frame , to observe this reception event and have complete agreement between frames. Correct??
In this case assume a photon flash was emitted simultaneous with the tachyons in A.
We can be sure that an observer in B at x'=6 could look over and observe the photon reception in A at x=10 , t=10 Correct??
Now instead of dx/2c=(dt=5) to derive tachyon time,, we instead do the equally valid ((dt=10)2c)=(dx=20) and derive the distance at that same time.
Make the normal assumption that traveling twice as fast as a photon it would cover twice the distance in the same time. From this we know that an observer in B at x'=12 should be able to look over and see the event of the tachyon reception at x=20 at t=25.99 True?

I am not saying I think this is any more valid than the former. Obviously it also makes no sense that a tachyon at 2c would take longer than a photon to reach that distance.
But as I understand the 1st P all valid physics principles should apply and produce agreement between frames. SO this seems to be a problem here where there are no problems whatever when dealing with v<or=c

As you yourself have pointed out [with the exception of light] any particle having a measured speed x in one frame cannot have the same measured speed in another frame.
Yet here we have an equal speed of 2c in both frames ,correct? Another instance where the specific values do not comply with the normal principles .


Would you agree that according to the principles of ballistic mechanics as applied to different inertial frames the closing velocity of a projectile wrt an observer frame Cw=(u+v)
must necessarily be greater than the parrallel relative velocity Pw=(u-v ) ?
That this relationship should carry through and hold with any transformation??
Would you agree?

As far as I can see it does hold true with the addition of velocities formula with all v< c
but it does not hold true for v=2c where (u+v)/ 1+uv < (u-v)/1-uv
It seems to me that this is a definite violation of the 1st P and that the conclusion from this would be that the addition formula also does not apply , just like the math for an inertial frame does not apply with v>c This seems to be clearly not physics as usual. Not to mention not logical. Or would you disagree?
I am pressed for time but I am thinking about your points. Thanks

 

[Austin0]

=DaleSpam;2050736]No, clocks could not be synchronized by tachyons any more than they could be synchronized by baseballs or proton beams today. The Einstein synchronization procedure relies on the fact that light has the same speed in all reference frames. Baseballs, protons, and tachyons do not have the same speed in different reference frames.

How do you think that light could possibly have the same speed in all directions in all frames if it weren't for clocks being desynchronized the exact right amount to make this possible?
Would you not agree that in any frame with any motion the light method actually assures desynchronization not synchronization?

 

[Austin0]

=Fredrik;2049132]No. Look at my previous reply to you (included below for completeness). If u, v and w are defined as in that post, the derivation of the velocity addition formula goes like this:

The slope of the tachyon's world line is 1/v in F' and 1/w in F. That means that the Lorentz transformation

\gamma\begin{pmatrix}1 &amp; u\\ u &amp; 1\end{pmatrix}

must take \begin{pmatrix}1\\ v\end{pmatrix} to a vector proportional to \begin{pmatrix}1\\ w\end{pmatrix}. That's all we need to find w:

\gamma\begin{pmatrix}1 &amp; u\\ u &amp; 1\end{pmatrix}\begin{pmatrix}1\\ v\end{pmatrix} =\gamma\begin{pmatrix}1+uv \\ u+v\end{pmatrix} =\gamma(1+uv)\begin{pmatrix}1 \\ \frac{u+v}{1+uv}\end{pmatrix}

So w must be what I said before:

I thought this:
1) the gamma factor did not show up directly in the additions formula
2) the denominator in both equations looked very similar except for the sqrt operator.
I jumped to the conclusion that both u and v had been entered but that the sqrt operator had been eliminated in the course of the derivation.
I was wrong ,,not only in this conclusion but also in not taking the time to work it through before putting it out and wasting your time. For that I apologize.
My matrix math is a hazy memory so I can't follow the derivation well enough to understand how it manages to eliminate the gamma factor but that is a math mystery for another time

No. That doesn't even make sense. Lorentz and Gallilean transformations have one thing in common: they both represent a coordinate change from one inertial frame to another, but the term "inertial frame" doesn't mean the same thing in those two contexts.

Arent the definitions essentially the same?? A state of uniform [non accelerated ] motion, the difference being the added SR condition of flat space-time and the Lorentz math?

 

[Fredrik]

Arent the definitions essentially the same?? A state of uniform [non accelerated ] motion, the difference being the added SR condition of flat space-time and the Lorentz math?

The basic idea is the same in SR and pre-relativistic physics, but the details are different. Consider the properties of functions that represent a change of coordinates from one inertial frame F to another inertial frame F':

1. They are smooth functions (i.e. they can be differentiated as many times as you want).
2. They take straight lines to straight lines.
3. They take each 3-plane that's orthogonal to the 0 axis of F to a plane that's orthogonal to to the 0 axis of F'.

All of these hold in both theories, but the word "orthogonal" doesn't mean the same thing in both cases. In SR, we're talking about orthogonality with respect to the Minkowski metric instead of with respect to the Euclidean metric.

 

[Fredrik]

My matrix math is a hazy memory so I can't follow the derivation well enough to understand how it manages to eliminate the gamma factor but that is a math mystery for another time

The definition of the product of two matrices is just

(AB)_{ij}=\sum_k A_{ik}B_{kj}

where e.g. A_{ik} is the entry on row i, column k of the matrix A. So in the special case where A is a 2x2 matrix and B a 2x1 matrix, we get

\begin{pmatrix}a &amp; b\\ c &amp; d\end{pmatrix}\begin{pmatrix}x\\ y\end{pmatrix}=\begin{pmatrix}ax+by\\ cx+dy\end{pmatrix}

 

[Dale]

How do you think that light could possibly have the same speed in all directions in all frames if it weren't for clocks being desynchronized the exact right amount to make this possible?

The two-way speed of light is isotropic, constant, and frame invariant regardless of your synchronization procedure. The Einstein synchronization procedure just makes the one-way speed match the two-way speed.

 

[JesseM]

Without SR the concept of light being measured at the same speed traveling in the same direction as the inertial frame as it is measured traveling counter to the motion of the frame is a logical impossibility yes? SR provided a rational consistent explanation for how this was possible through the desynchronization of clocks. Correct??

Yes, although the clocks are only "desynchronized" in the frame where they are moving of course.

Without this desynchronization the difference in the "bi-directional" measurements would reveal the motion of the system. Correct??

Yes, if all frames agreed on what it meant for clocks to be synchronized (i.e. if they all agreed about simultaneity), then it would be impossible for light to have the same speed in both directions in all frames. I still don't really understand what your original comment "The overall results of the application of the basic assumption to bi-directional assigments and the many questions that arise from those results." Application of what basic assumption? And what does "the basic assumption to bi-directional assignments" mean? I understand that in the context of light you are using "bi-directional" to mean measuring the speed of light in both directions is, but I don't understand what "bi-directional assignments" are. What is being assigned, and what is it being assigned to?

1. Given the premise SR, we must assume that any events can be assigned space and time coordinates x and t in any inertial frame.

2. Given the premise FTL, there must be some inertial frame where, if you have the coordinates (x1,t1) of the signal being sent and the coordinates (x2,t2) of the signal being received, then in units where c=1, dx=|(x2-x1)| > dt=|(t2-t1)|

3. Given the premise SR, the coordinates assigned to the same event by different inertial frames must be related by the Lorentz transform.

4. Given 2 and 3, if you have a signal such that dx>dt for the transmission-event and the reception-event in one inertial frame, it is always possible to find a new inertial frame such the reception-event happens at an earlier time than the transmission-event in the new frame.

5. By the first postulate of SR, if it is possible in one frame to send a tachyon signal in such way that the reception-event happens at an earlier time than the transmission-event in that frame, it must be possible in any frame to send a tachyon signal in such a way that the reception-event happens earlier than the transmission-event in that frame.

If it's possible in any frame to send a tachyon signal in such a way that the reception-event happens earlier than the transmission-event in that frame, then it must be possible for one observer to send a tachyon message to the other and the second to then send a tachyon reply in such a way that the event of the first observer receiving the reply lies in the past light cone of the event of the first observer sending the original message, which is a clear violation of causality in every frame.

Can you point to a specific step that you disagree with here, where you think that it doesn't follow from the previous steps and the original premises of SR and FTL?

5) Above : It is not that I disagree with this at all. But you have just finished telling me how the reception event in frame A didnt occur earlier than the transmission event in that frame so how does this conform to the 1st postulate as you have outlined in 5)

5) just said it would be possible to send a different tachyon signal that goes back in time in A's coordinates, it doesn't say that that specific tachyon signal (the one that was sent at (0,0) and received at (20,10) in A) is going back in time in A's coordinates. As an analogy, if I see a missile moving at 0.5c in my frame, and in your frame I am moving at 0.5c in the same direction so in your frame the missile is moving at (0.5c + 0.5c)/(1 + 0.5*0.5) = 0.8c, then by the first postulate it must be possible for me to see a missile moving at 0.8c in my frame...but this doesn't mean that particular missile should be measured to be moving at 0.8c in my frame, since I already measured it to be moving at 0.5c in my frame. The first postulate just implies I could send out a different missile which would be moving at 0.8c in my frame, and similarly the first postulate implies A could see a different tachyon signal which was received before it was transmitted in A's frame.

How do you se this one:
The 1st P allows us to track a photon trans-reception happening in another frame , to observe this reception event and have complete agreement between frames. Correct??

I understand what you're saying, but your language is confused here, the events of a photon being sent and received don't happen "in" any particular frame, they're just events, different frames assign them different coordinates. The second postulate (is that what you meant to write?) does say that if one frame finds that dx=dt for two events (in units where c=1, so both events would lie on the worldline of a photon), then another frame will also find that dx'=dt' when it looks at the same events in its own coordinates.

In this case assume a photon flash was emitted simultaneous with the tachyons in A.
We can be sure that an observer in B at x'=6 could look over and observe the photon reception in A at x=10 , t=10 Correct??

What do you mean by "look over"? If you're talking about a local observation, the reception event wouldn't happen next to x'=6 in B's frame, it'd happen next to x' = 1.666..*(10 - 0.8*10)=3.333... in B's frame (and so naturally it'd also happen at t'=3.333... in B's frame).

Now instead of dx/2c=(dt=5) to derive tachyon time,, we instead do the equally valid ((dt=10)2c)=(dx=20) and derive the distance at that same time.

Distance at the same time in whose frame? Since you're using A's dt of 10 I assume you mean A's frame here...it's true that in A's frame, the event of the photon being received at x=10, t=10 is simultaneous with the event of the tachyon being received at x=20, t=10. But of course, these two reception-events are not simultaneous in B's frame, where the photon reception-event happens at t'=3.333... while the tachyon reception-event happens at t'=-10. If you want to assume the tachyon signal was just measured to be passing by the origins of the two frames rather than actually being emitted at that point, then we could say that in B's frame at t'=3.333... the tachyon would have been at position x'=-6.666... (and in A's frame, this event on the tachyon's worldline would be at x=-6.666..., and t=-3.333...)

Make the normal assumption that traveling twice as fast as a photon it would cover twice the distance in the same time. From this we know that an observer in B at x'=12 should be able to look over and see the event of the tachyon reception at x=20 at t=25.99 True?

No, that doesn't make any sense. First of all, the tachyon is only "traveling twice as fast as a photon" in A's frame, that doesn't necessarily mean it is traveling twice as fast in other frames since a tachyon's speed would not be frame-invariant (in fact in B's frame it happens to be true that it is, although in B's frame the tachyon seems to be traveling in the opposite direction, so its velocity is different even if its speed is not). Second, where exactly did you get t=25.99? I don't get your argument at all.

I am not saying I think this is any more valid than the former. Obviously it also makes no sense that a tachyon at 2c would take longer than a photon to reach that distance.
But as I understand the 1st P all valid physics principles should apply and produce agreement between frames. SO this seems to be a problem here where there are no problems whatever when dealing with v<or=c

Since your argument doesn't make any sense to me I'd guess you've just made a mistake somewhere, but I can't tell where your mistake is unless you actually explain the argument in detail instead of just throwing out random numbers.

As you yourself have pointed out [with the exception of light] any particle having a measured speed x in one frame cannot have the same measured speed in another frame.

No, I said it can't have the same speed in all frames. It is certainly possible for a single sublight object to be traveling at speed S in the +x direction in one frame and speed S in the -x direction in another frame (opposite velocities but same speed). In my example above with the missile moving at 0.5c in my frame but 0.8c in yours, in your frame I am moving at 0.5c in the +x direction, while in the missile's frame I am moving at 0.5c in the -x direction. This is the same sort of thing that's going on with the tachyon, since it's going at 2c in the +x direction in frame A and 2c in the -x' direction in B's frame (since in B's frame the tachyon is further in the -x' direction at later times--at t'=-10 it's at x'=20 but at t'=0 it's at x'=0).

Would you agree that according to the principles of ballistic mechanics as applied to different inertial frames the closing velocity of a projectile wrt an observer frame Cw=(u+v)
must necessarily be greater than the parrallel relative velocity Pw=(u-v ) ?

No. In the missile example above, in your frame the missile is moving at 0.8c while I am moving at 0.5c, so in your frame the closing velocity is 0.3c. But in my frame the velocity of the missile relative to me is 0.5c.

As far as I can see it does hold true with the addition of velocities formula with all v< c

You're neglecting to consider the fact that velocity can be negative in the case of an object moving in the -x direction instead of the +x direction.

It seems to me that this is a definite violation of the 1st P

Even if what you were saying was true, how would it be a violation of the first postulate? The first postulate doesn't say that the laws that tachyons follow should be identical to the laws that sublight particles follow, it just says that whatever laws tachyons are observed to follow in one inertial frame, they must follow the same laws in every other inertial frame.