Why does FTL imply causality violation?

[Iggy]

While you may be correct in actuality, that is not how it works in either of the two thought experiments linked above. The speed of the sender isn't an objective measurement. The sender's speed is in fact the sender's speed relative to the receiver, so the path the tachyons take through spacetime is different for different receivers, and observers at different speed but in the same location will indeed find that they don't receive the tachyon signal at the same time.

I'm not sure you took what I said how I meant it to be taken. The speed of the tachyon relative to the observer depends on the speed of the sender relative to the observer.

 

Can you make a light cone diagram or similar where what you describe (tachyon signal speed depending on the sender) pans out?

I'm not the best with space-time diagrams but I can give it a go...

 

 

eh.. :-/

 

Sender-B travels .6c relative to sender-A

 

The tachyons are the dotted lines. They are sent from the senders and received by the observer. Sender-B figures that tachyon-B goes 2c. Sender-A figures that tachyon-A goes 2c. The observer (who is at rest relative to sender-A) figures that tachyon-A goes 2c and tachyon-B goes back in time (she receives tachyon B before it was sent in her coordinate system).

 

Meanwhile, in Universe-A, Hermes-A heads towards the Sun... A...

 

I personally can't get the SR math to work out to anything else either. It seems you need to drop the relativity of motion to get FTL signals to not cause such contradictions. And the idea of an objective frame of reference is a pretty big leap to make.

I'm not sure what that means.

 

A cannonball that goes 2 m/s relative to one person might go 1 m/s relative to another person. This doesn't mean we've dropped the relativity of motion. The speed of light is the only invariant speed. Tachyons don't travel at c, so their speed won't be invariant. They would go different speeds relative to different people.

 

Is that what you're referring to? I'm not sure.

[Mystery111]

 

 

Sounds interesting. How does that work?

 

I'll see if I can find the relevent papers.

[Mystery111]

 

 

 

Sounds interesting. How does that work?

 

A reinterpretation of tachyons moving back in time was speculated all the way back in the 60's

 

O. M. P. Bilaniuk, V. K. Deshpande, and E. C. G. Sudarshan,

Am.J.Phys. 30 (1962) 718.

 

G. Feinberg, Phys. Rev. 159 (1967) 1089.

 

The other way to avoid causality problems is to introduce a kinematic time under a non-standard form of Lorentz Transformations

 

R. Tangherlini, Nuov. Cim Suppl., 20 (1961) 1.

 

P. Caban and J. Rembielinski, Phys. Rev., A 59 (1999) 4187.

 

Here are the first two

 

http://prola.aps.org/abstract/PR/v159/i5/p1089_1

 

http://wildcard.ph.utexas.edu/~sudarshan/pub/1962_006.pdf

[Moontanman]

If FTL is possible you can send a signal and get the response before you sent it.

 

 

Isn't that only true if you are only able to communicate at light speed? If a faster than light signal is possible wouldn't that fact change the whole "get the response before you send it" thing?

[swansont]

Isn't that only true if you are only able to communicate at light speed? If a faster than light signal is possible wouldn't that fact change the whole "get the response before you send it" thing?

 

We can communicate at light speed now.

[Moontanman]

We can communicate at light speed now.

 

 

While i am sure I am wrong, your answer ignores my point, if we discover a method of communicating faster than light then light is no longer the limit to communication, wouldn't that negate the idea that you would get the response before you sent the message?

[Mystery111]

I know what you mean. You could be right.

[swansont]

While i am sure I am wrong, your answer ignores my point, if we discover a method of communicating faster than light then light is no longer the limit to communication, wouldn't that negate the idea that you would get the response before you sent the message?

 

I wasn't sure what your point was; you seemed to be saying you can get a signal before you send it if you can communicate at the speed of light. That's not true.

 

 

I don't see why FTL would somehow negate the causality violation. If the rest of relativity still held, the example given shows how you can violate causality.

[Mystery111]

I wasn't sure what your point was; you seemed to be saying you can get a signal before you send it if you can communicate at the speed of light. That's not true.

 

 

I don't see why FTL would somehow negate the causality violation. If the rest of relativity still held, the example given shows how you can violate causality.

 

 

I think what he is saying is it still ''takes time'' for a luminal signal to be taken from one point to another. A slightly faster process would be a new ''communication limit'' in his words. In that sense, it could be possible we are just dealing with a new species of particle which moves slightly faster than light, but does not physically oscillate in time. Such models have been constructed for superluminal particles.

[Iggy]

if we discover a method of communicating faster than light then light is no longer the limit to communication

I think what he is saying is it still ''takes time'' for a luminal signal to be taken from one point to another. A slightly faster process would be a new ''communication limit'' in his words.

The speed of light is special because it's invariant. That is what makes c special, and the existence of speeds faster than c would make c no less special in that regard. If something travels FTL in one frame then it travels back in time in another frame -- not because light is the fastest speed of communication, but because it is invariant (the same in every frame).

[Mystery111]

The speed of light is special because it's invariant. That is what makes c special, and the existence of speeds faster than c would make c no less special in that regard. If something travels FTL in one frame then it travels back in time in another frame -- not because light is the fastest speed of communication, but because it is invariant (the same in every frame).

 

Highlighted part: agreed.

 

Non-highlighted part: A timelike tachyon does, not a spacelike tachyon which was the point I was raising earlier. Some models go back as far as the 60's which try to circumvent the problem of a faster than light particle which would oscillate throughout time and the causality problems which closely asist it.

[Iggy]

Highlighted part: agreed.

 

Non-highlighted part: A timelike tachyon does, not a spacelike tachyon which was the point I was raising earlier. Some models go back as far as the 60's which try to circumvent the problem of a faster than light particle which would oscillate throughout time and the causality problems which closely asist it.

I don't see how that makes sense, but I'm not too familiar with tachyons.

 

When you say "time-like" do you mean a tachyon that follows a time-like geodesic, because that sounds like a contradiction in terms. Nothing that follows a time-like path would be a tachyon.

[Mystery111]

I don't see how that makes sense, but I'm not too familiar with tachyons.

 

When you say "time-like" do you mean a tachyon that follows a time-like geodesic, because that sounds like a contradiction in terms. Nothing that follows a time-like path would be a tachyon.

 

There are in fact many models which attempt to deal with the causal nature. For the timelike-spacelike references, I noted them before go back and check.

 

''It has been argued that we can avoid the notion of tachyons traveling into the past using the Feinberg reinterpretation principle^[3] which states that a negative-energy tachyon sent back in time in an attempt to challenge forward temporal causality can always be reinterpreted as a positive-energy tachyon traveling forward in time. This is because observers cannot distinguish between the emission and absorption of tachyons. For a tachyon, there is no distinction between the processes of emission and absorption, because there always exists a sub-light speed reference frame shift that alters the temporal direction of the tachyon's world-line, which is not true for bradyons or luxons. The attempt to detect a tachyon from the future (and challenge forward causality) can actually create the same tachyon and sends it forward in time (which is itself a causal event).''

 

 

I actually know a bit about negative energy tachyons. Two negative energy states in the form of two negative energy bispiners are:

 

[math]\psi_3 = \psi_{-} = N \begin{pmatrix} 1 \\ 0 \\ -a \\ 0 \end{pmatrix}[/math]

 

[math]\psi_4 = \psi_{-}' = N \begin{pmatrix} 0 \\ -a \\ 0 \\ 1 \end{pmatrix}[/math]

 

There are two positive energy bispiners as well. The four component bispiner [math]\psi_{\sigma}[/math] comes from the desription for a free particle plane wave with momentum [math]\vec{p}[/math]. Using the wiki article, this would mean that there no way we can destinguish temporal causality between the negative tachyonic description sent back in time as it can be reinterpreted as a postive energy tachyon moving forward in time.

Edited October 27, 2011 by Mystery111

[Iggy]

There are in fact many models which attempt to deal with the causal nature. For the timelike-spacelike references, I noted them before go back and check.

 

''It has been argued that we can avoid the notion of tachyons traveling into the past using the Feinberg reinterpretation principle^[3] which states that a negative-energy tachyon sent back in time in an attempt to challenge forward temporal causality can always be reinterpreted as a positive-energy tachyon traveling forward in time. This is because observers cannot distinguish between the emission and absorption of tachyons. For a tachyon, there is no distinction between the processes of emission and absorption, because there always exists a sub-light speed reference frame shift that alters the temporal direction of the tachyon's world-line, which is not true for bradyons or luxons. The attempt to detect a tachyon from the future (and challenge forward causality) can actually create the same tachyon and sends it forward in time (which is itself a causal event).''

Yes... I've heard that argument. It seems not only consistent with what I said, it says the exact same as I said...

there always exists a sub-light speed

reference frame

shift that alters the temporal direction of the tachyon's world-line

 

Now I really don't understand why you disagreed with this:

 

If something travels FTL in one frame then it travels back in time in another frame -- not because light is the fastest speed of communication, but because it is invariant (the same in every frame).

[Mystery111]

Yes... I've heard that argument. It seems not only consistent with what I said, it says the exact same as I said...

there always exists a sub-light speed

reference frame

shift that alters the temporal direction of the tachyon's world-line

 

Now I really don't understand why you disagreed with this:

 

 

 

I didn't qoute that, so you are misrepresenting the facts.

 

My post qouted you talking about knowing very little on tachyons, then asking me what a spacelike condition has to do for a tachyon. I explained to you that was one solution I referenced before and if you wanted those references you would need to go back. Secondly I explored a further option.

 

So qouting me like you did is disingenuous.

[Iggy]

I didn't qoute that, so you are misrepresenting the facts.

 

Eh? You quoted it here:

 

The speed of light is special because it's invariant. That is what makes c special, and the existence of speeds faster than c would make c no less special in that regard. If something travels FTL in one frame then it travels back in time in another frame -- not because light is the fastest speed of communication, but because it is invariant (the same in every frame).

Highlighted part: agreed.

 

Non-highlighted part: A timelike tachyon does, not a spacelike tachyon which was the point I was raising earlier. Some models go back as far as the 60's which try to circumvent the problem of a faster than light particle which would oscillate throughout time and the causality problems which closely asist it.

 

The non-highlighted part is what I repeated.

 

My post qouted you talking about knowing very little on tachyons, then asking me what a spacelike condition has to do for a tachyon. I explained to you that was one solution I referenced before and if you wanted those references you would need to go back. Secondly I explored a further option.

 

So qouting me like you did is disingenuous.

Oh, my!

 

I still don't get why you disagreed with post #35 nor what you meant by "timelike tachyons". The material you referenced reinforced the thing I said and the footnote it gave specifically equates "spacelike 4-momentum" with "faster than light" (i.e. tachyons). I don't believe that the argument you cited anywhere claims that tachyons can be taken as timelike or understood in any way to travel slower than light.

 

It seems like you disagreed with my post for reasons that don't disagree with my post.

 

Maybe it's a little off topic though and we should just leave it... ?

Edited October 27, 2011 by Iggy

[Mystery111]

Eh? You quoted it here:

 

 

 

The non-highlighted part is what I repeated.

 

 

Oh, my!

 

I still don't get why you disagreed with post #35 nor what you meant by "timelike tachyons". The material you referenced reinforced the thing I said and the footnote it gave specifically equates "spacelike 4-momentum" with "faster than light" (i.e. tachyons). I don't believe that the argument you cited anywhere claims that tachyons can be taken as timelike or understood in any way to travel slower than light.

 

It seems like you disagreed with my post for reasons that don't disagree with my post.

 

Maybe it's a little off topic though and we should just leave it... ?

 

Because I said the first part was agreed with, and not confirmed the second part, that was my fault I guess.

 

I was not disagreeing, I was adding to the different interpretations of tachyons. Nowhere in that reference you made of me:

 

''Non-highlighted part: A timelike tachyon does, not a spacelike tachyon which was the point I was raising earlier. Some models go back as far as the 60's which try to circumvent the problem of a faster than light particle which would oscillate throughout time and the causality problems which closely asist it.''

 

Contains anywhere that I disagreed with your post. You brought up causality, which is what is implied by that model you speak of. That is why my reference to the non-highlighted part was in nature of the problem of causality offerring other solutions, which I gave.

[Moontanman]

I wasn't sure what your point was; you seemed to be saying you can get a signal before you send it if you can communicate at the speed of light. That's not true.

 

 

I don't see why FTL would somehow negate the causality violation. If the rest of relativity still held, the example given shows how you can violate causality.

 

 

What i had in mind was that if you did have a method of communicating faster than light then the causality thing would only apply to observers who were limited to speed of light?

 

Here is the thought experiment i was thinking of, lets say that I somehow construct a "radio" that communicates instantaneously. I turn it on and hear a voice and manage somehow to talk to it, i find out it is originating from the Andromeda Galaxy, we talk with no time lag, I could be so far off the mark here but indulge me a second or two more. From the stand point of relativity would we both be speaking to each other in each others future? I think Andromeda is a million light years or so away, if I had immediate access to Andromeda wouldn't mean i was talking to the guy in the past and he was speaking to me in his past? One million years in our pasts because we are one million light years from each other? Ok, now I'm really confused damn it....

[granpa]

if you and the person in andromeda are stationary with respect to each other then you are both in each others present.

[Moontanman]

if you and the person in andromeda are stationary with respect to each other then you are both in each others present.

 

 

Can you elaborate? Considering the idea that there is no universal reference frame or are you saying there is a universal reference frame?

[swansont]

Can you elaborate? Considering the idea that there is no universal reference frame or are you saying there is a universal reference frame?

 

No. If you are at rest with respect to each other, you are in the same reference frame. You can synchronize clocks and can agree on what time it is.

[Moontanman]

No. If you are at rest with respect to each other, you are in the same reference frame. You can synchronize clocks and can agree on what time it is.

 

 

So if we are both traveling at the same speed we can communicate faster than light?

[swansont]

So if we are both traveling at the same speed we can communicate faster than light?

 

You offered that as a premise in your scenario. If you have a method of communicating faster than light, then you have a method of communicating faster than light.

[JohnB]

At irregular intervals I try to understand Lorentz Transformations without having my brains drain from my ears. Perhaps like others I can understand the logic as given by swansonts link, but I can't conceptualise it all.

 

I see how causality is violated due to the pretty slanted lines in the diagram, but I don't see how it works. I think of it this way. Say I have 4 ships each at a different star some 10 LY from Earth and each star is 10 LY from its neighbour. A ship takes 1 week to travel 10 LY. I send out a ship with a recall message. So the recall ship arrives at Star A after 1 week and passes on the message. The recall ship heads to the next Star while the Star A ship heads home. At the end of the second week the Star A ship arrives home and the recall ship arrives at Star B. At the end of the third week, the ship from Star B arrives home and the recall ship is at Star C. At the end of the fourth week the ship from Star C arrives home and the recall ship is at Star D. At the end of the fifth week both the Star D ship and the recall ship arrive home.

 

How is causality violated? Or is there no transformation because the ships awaiting the recall are sort of "at rest" and are therefore in the same frame as I am?

 

Now for the biggy. It strikes me that one definition of Minkowski Spacetime is that it is a construct where FTL will result in causality violations. What if when travelling FTL you are no longer in Minkowski Spacetime? Why would the same rules apply. Because I'm at the "really dumb" end of the relativity spectrum here I'm thinking in similar terms to geometry. One could define Euclidian geometry as a world where parallel lines remain the same distance apart. As soon as this basis changes, then you are no longer in Euclidian space and the rules don't apply. Probably very wrongly I'm thinking of Minkowski as defining the geometry of spacetime in a similar fashion to Euclid and surfaces.

 

Another question that I have to ask is "Does relativity apply to dark matter and energy?" I just can't see why it would. DM virtually ignores the world of baryonic matter and the EM spectrum. Why would rules formulated to describe and dependent upon the baryonic world and the EM spectrum have any relevence to non baryonic matter and non EM forms of energy?

[swansont]

I have a cold, so dissecting the problem isn't in the cards ATM, but suffice to say that FTL means you can violate causality, not that all scenarios will violate causality.