Having trouble understanding why FTL implies time travel

[Fredrik]

Maybe I am not following you here, but isn't the propagation of sound independent of the source but measured to be different in relative frames??
That the difference with light is that it is also measured to be the same in all frames.

Yes, you're right about that.

I was not talking about the measured speed being the same in all frames. As I have mentioned elsewhere I think that due to clock desynchronization , they not only couldn't be measured at the same speed in different frmes but that they also couldn't be measured as having equal bidirectional speed in any frame.

I still haven't figured out what you mean by "bidirectional speed".

Assume you were doing an analysis of the measurement of light within two different frames.
Wouldnt you clock emmission and reception in one frame , and then from that frame calculate the emmission and reception in the other frame??

Yes.

That within the first frame there would be actual reception of photons but within that frame there would only be the hypothetical observation
by an observer at the proximate site of the actual reception in the second frame?

Absolutely not. The "actual reception" is an event, i.e. a point in spacetime. That point is assigned coordinates by all coordinate systems, and none of the inertial coordinate systems is "preferred" over any of the others.

Excuse me but in this case isn't it that 'A' [the IF] is in fact true, but it is the THEN "B' conclusion that is false? That in fact this statement is in no way valid.

No, the A (="there's a largest prime number N) is false, since there are infinitely many primes. What I posted is the easiest way to prove that. The "if-then" statement is definitely corrrect.

Isnt it the case that the premises are IF SR + FTL THEN time travel.

No, that's the statement we proved. The premise (or postulate, axiom, or whatever you prefer to call it) is SR+FTL.

That in this case the A is A =assumption of event at ( x=20, t=10) <==> B=time travel ?
Wouldnt you agree that this is treating it as a proof of B the conclusion?

The A is "SR+FTL". The FTL part can be made explicit in many different ways, and one of them is to say that a particle emitted at the origin can be detected at (10,20). (t=10,x=20).

I'm confused by your second question. You're talking about proofs as if you can prove stuff without first assuming something. You obviously can't. We're not proving B. We're proving "if A then B". We're treating the result as a proof of "if A then B", because that's what it is.

If the statement was IF SR and IF FTL and IF a signal sent from A arrives 10 sec before it is sent in B THEN "timetravel "

Would you agree that this, although a valid argument, would be an obvious tautology and without significance as a proof of "time travel" ?

Yes, since one of the assumptions is the conclusion.

 

[Austin0]

=Fredrik;2043272]You don't need to know the mass of a tachyon to understand this thread. We can define a tachyon as something that has a spacelike world line. (A curve is "spacelike" if the slope of its tangent is <1 at all points on the curve).

I wasn't suggesting the need to know the mass of a tachyon. I was simply getting it straight what we are talking about.

But if you're curious, the answer is that it turns out that a particle with that property has m²<0, so its mass must be imaginary.

Yes that is exactly what I said 3)

Yes, you can use the standard formula to "add" the velocities of an inertial frame and a tachyon (but not the velocities of a tachyon and another tachyon).

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?

In the frame where those two events are tachyon emission/absorption events, the particle is described as moving from x=20 to x=0 while the time changes from -10 to 0, so I'd calculate v as (0-20)/(0-(-10))=-2

OK this interesting. 1) This experiment is based on the transmission of information correct?

2) This means a transmitter [which flashes on transmission]and a receiver [which flashes on reception] right?

3) There is no information passing from B to A at this point Correct?

4) So what is the basis of this spatial direction?

5) How is it that you both have been talking about dt=0 -->( -10 )=-10 seconds [back in time]

and now you are suddenly talking about forward dt= (-10) --->0 =10 sec.?

 

[Austin0]

=Fredrik;204333

I still haven't figured out what you mean by "bidirectional speed".

Two speeds : One measured with the direction of motion and one counter to that direction. If a frame is assumed at rest, then I guess to be totally correct you would have to do omni-directional measurements.

No, the A (="there's a largest prime number N) is false, since there are infinitely many primes. What I posted is the easiest way to prove that. The "if-then" statement is definitely corrrect.

Excuse me . Because you set it up with a sequence in parentheses , culminating with N
I read this as a statement: If there is a largest prime N in any designated sequence then that would yield (with the addition of 1) a larger prime number.
Since this was obviously false with any prime over 2 , I missed the literal interpretation ("there's a largest prime number N) which is also obviously false. SO it seems in actuallity both the premise and the conclusion were false No??
Just out of curiosity, it appears that it would be easy to falsify the conclusion but how would that falsify the premise, which is what you want to do , right??

 

[Fredrik]

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?

No.

OK this interesting. 1) This experiment is based on the transmission of information correct?

2) This means a transmitter [which flashes on transmission]and a receiver [which flashes on reception] right?

3) There is no information passing from B to A at this point Correct?

4) So what is the basis of this spatial direction?

5) How is it that you both have been talking about dt=0 -->( -10 )=-10 seconds [back in time]

and now you are suddenly talking about forward dt= (-10) --->0 =10 sec.?

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).

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.

Weird things like this happen all the time when tachyons are involved. That's what we've been trying to explain. For example, if you hook up a bomb to a tachyon detector and set it up so that the bomb explodes when it detects a tachyon, you might see the following sequence of events (in this order):

1. The detector emits a tachyon.
2. The bomb explodes.
3. Some guy aims his tachyon gun at the detector and pulls the trigger.
4. A tachyon that was emitted from the detector some time earlier (maybe years) hits the tachyon gun right after the trigger was pulled.

 

[Fredrik]

SO it seems in actuallity both the premise and the conclusion were false No??
Just out of curiosity, it appears that it would be easy to falsify the conclusion but how would that falsify the premise, which is what you want to do , right??

This is a totally standard method of proof called "proof by contradiction", or "reductio ad absurdum". In this case, we assume that N is the largest prime number and use that to prove that there are larger prime numbers than N. That clearly implies that the assumption is false. A true statement can't imply that it's also false, but a false statement can.

 

[JesseM]

Just a couple of quick clarifications:
I was not initially aware that you were using a specific definition of the hypothetical particles, but it is your demonstration so I want to make sure what we are talking about.
Tachyons:
1) Have no mass
2) Are not massless
3) Have a negative or imaginary mass.

As Fredrik said, this is irrelevant to the current discussion, but as discussed here a tachyon's rest mass would have to be imaginary to make equations involving energy and momentum work out.

4) Are to be regarded as ballistic particles [with mass]

It's also irrelevant whether we consider tachyons as ballistic or as waves in a medium with a speed independent of source (though in this case the speed would depend on the rest frame of the medium--see this post), this would not affect the way their coordinate velocities transform in different coordinate systems (likewise, you are free to imagine photons are ballistic particles, but because of the way the Lorentz transform works, you'll still find that a photon moving at c in one frame must be moving at c in other frames).

DO you consider that the addition of velocities formula would apply to them?

Yes, because the addition of velocities formula is derived from the Lorentz transformation, and in SR the Lorentz transform tells you how the coordinates of any event (including events on the worldline of a tachyon) are assigned by different inertial frames.

What is your interpretation of B (0,0) -----> B(-10,20) as far as deriving speed??

1) (20-0)/( -10-0)=-2 OR

2) (20-0)/ abs(-10-0)=2

If it is 1) What is your idea of the meaning of this speed?

Speed is defined as the norm of the velocity vector, so it's always positive, which means the answer would be 2). On the other hand, 1) could refer to the velocity in the +x direction (because in this example the velocity vector points in the -x direction).

 

[JesseM]

This is a totally standard method of proof called "proof by contradiction", or "reductio ad absurdum". In this case, we assume that N is the largest prime number and use that to prove that there are larger prime numbers than N. That clearly implies that the assumption is false. A true statement can't imply that it's also false, but a false statement can.

For more on this point, Austin0 may want to read the wikipedia article on contraposition in logic, especially the sections "examples" and "application".

 

[Fredrik]

Speed is defined as the norm of the velocity vector, so it's always positive

Oops, this is of course true.

Austin, I thought you were asking about the velocity, not the speed, so keep that in mind when you read my answer in #90.

 

[Austin0]

Fredrik = 2. If there's a largest prime number N, then (2·3·5·7·...·N)+1 is a prime number that's larger than N. (Here "A" isn't even true. In fact, what this argument really proves is that it isn't. But the statement is still valid).

1) Excuse me but in this case isn't it that 'A' [the IF] is in fact true, but it is the THEN "B' conclusion that is false? That in fact this statement is in no way valid.

Fredrik No, the A (="there's a largest prime number N) is false, since there are infinitely many primes. What I posted is the easiest way to prove that. The "if-then" statement is definitely corrrect.

Originally Posted by Austin0 SO it seems in actuallity both the premise and the conclusion were false No??

Just out of curiosity, it appears that it would be easy to falsify the conclusion but how would that falsify the premise, which is what you want to do , right??

This is a totally standard method of proof called "proof by contradiction", or "reductio ad absurdum". In this case, we assume that N is the largest prime number and use that to prove that there are larger prime numbers than N. That clearly implies that the assumption is false. A true statement can't imply that it's also false, but a false statement can.

I am aware of the principle. It was in that light that I made the comment above.

1) In this case;
a conclusion ,validly derived from the axioms of real numbers , that proved a larger prime would falsify the premise "largest prime N"
If P then not P
But the conclusion must be validly derived, ie. true Agreed?

2) Unless I am seriously losing my mind [always possible]

In this case ,the conclusion ( N + 1 = a larger prime ) is false under all circumstances except N=2,
is not validly derived ie. is false and therefore cannot constitute a falsification under the reductio ad absurdum principle.
Agreed ?
or do you think that there is some prime that when incremented by 1 will yield another prime?

3) In actuality the premise is self evidently false so if both the premise and the conclusion are both falsifiable in what sense do you think this is a valid statement?
a) it does have an if conditional and a conclusion so it is valid in the same way "black is white" is a valid sentance because it has a subject and a verb ?

4) Using the meaning of an if conditional premise [that Jesse has been referring to] where the actual truth is not relevant , is considered automatically true,then in this case my original statement above 1) is in fact correct.
Yes or no?

 

[JesseM]

2) Unless I am seriously losing my mind [always possible]

In this case ,the conclusion ( N + 1 = a larger prime ) is false under all circumstances except N=2,
is not validly derived ie. is false and therefore cannot constitute a falsification under the reductio ad absurdum principle.
Agreed ?
or do you think that there is some prime that when incremented by 1 will yield another prime?

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.

 

[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?