SR, LET, FTL & Causality Violation

stglyde

In SR. Anything FTL or superluminal can affect causality because there would be some frame where things move backward in time. Since SR is equivalent to Lorentz Ether Theory. And LET is about additional dynamics that occurs in the backdrop of newtonian absolute space and time. Then how can you model FTL and LET and things moving back in time since the background is supposed to be absolute space and time (where things moving backward is in conflict with its main postulate)? I've been googling this but can't find the information. Thanks.

atyy

In SR and LET (the form that is equivalent to SR), every inertial frame is a preferred coordinate system, and in that sense physics in an inertial frame is "as good" as Newtonian absolute space and time (Rindler, p43).

However, what fundamentally distinguishes SR/LET and Newtonian physics, since both have inertial frames or preferred coordinate systems, is the transformation between the inertial frames. In SR/LET, the transformation between inertial frames is given by the Lorentz transforms, whereas in Newtonian physics it is given by the Galilean transform. This is why forms of FTL that violate causality are still forbidden in LET.

nitsuj

What FTL scenario would break causality? I can understand that FTL would mess up measurements of time/distance for that FoR. You mean "move backward" in propertime, not coordinate time right?.

So then what does negative propertime mean? Seems meaningless.

So I think that means FTL breaks the "all physics the same in all FoR", not causality.

I don't know for sure but isn't a postulate of SR that c is the maximum whatever? Seems like this would have to be assumed for the rest of the theory to "work". Said differently SR doesn't (directly) address FTL. Is that right?

http://www.physicsforums.com/showthread.php?t=522200

Picturing the light cone in 3D (as a sphere) was pretty enlighting, including seeing that speed of cause isn't as "important" as it preceeds effect.

Fredrik

See post #133 here (and post #138 for the correction of a typo).

nitsuj

Oh cool that's looks quite detailed. I'll read that on my lunch.

My post above though, is only suggesting that besides the point of whether FTL is possible, it would mean measurements done in that FoR aren't "transferable" / "applicable" to the reality.

nitsuj

I read that post and I don't understand this part;

"If she doesn't recieve a message at (0,0), she sends 1 at (8,0). Bob receives that message at (8,10), and replies with 1 at (8,10). So Alice receives 1 at (0,0), and we still have a contradiction."

That part I don't get. I haven't drawn the diagram (will at home). But Ima guess it's because it's a ST diagram where it's always implied that 1ct = 1x. and that slope seprates timelike from spacelike which also happens to illustrate the line between cause/effect.

Any cause effect relationship (from a time perspective, I guess the ONLY way causality can appear broken, but is propertime that's "broken" ) that's on the spacelike side means causality isn't illustrated by the photon path anymore. It would be illustrated by the tachyeon things path.

Said differently a ST diagram where 1ct=1x; 1ct=1x is the speed limit. Seen as the path of a photon (null line) on the diagram. Anything faster and wouldn't ct have to be redefined? I'd say clearly because of cause->effect.

That's my understanding of FTL and causality.

With all that being said, I see you qualified the statement with "...the standard argument for why it can't be possible to send instantaneous messages in a special relativistic universe." Which I take as meaning 1ct=1x in this context.

Fredrik

This short reply is all I have time for today, but I can probably answer follow-up questions tomorrow.

The contradiction is that she both receives a message at (0,0) and doesn't receive a message at (0,0). I'm just making sure to cover all possibilities about what can happen at (0,0). The possibilities are: a) she receives 1, b) she receives 0, c) she receives nothing. And in all three cases, we end up with a contradiction.

The most important part of what "special relativistic universe" refers to is that the simultaneity lines of an observer with speed v have slope v in the diagram. (In a Galilean spacetime, the slope would be 0, and that makes it impossible to obtain these paradoxes).

stglyde

I know FTL is forbidden in SR.. but we have many examples what would happen if FTL occured... that is.. there would be frames in which it would move backward in time. I just want to know how to model it in LET. If you don't know what I mean. Look at the following web illustration of what would happen if FTL occured in SR.

http://sheol.org/throopw/tachyon-pistols.html

Now. How do you model the same thing using LET (just for sake of discussion because we knew there was no FTL).

Fredrik

That's an interesting question that I don't know the answer to, because I've never studied LET or spent any significant time thinking about it. Is there a way to see that my Alice/Bob scenario is logically inconsistent in LET too? If someone who reads this has thought about such things, I wouldn't mind being told the answer so that I don't have to think about it.

zonde

In LET only one inertial frame is absolute frame. You just don't know which one.
For that reason Lorentz transform is not symmetric - it only appears symmetric.

And as there is only one "real" simultaneity in LET there is no paradox with FTL particles.

Fredrik

That was my initial reaction, but than I thought "that would mean that the two theories aren't equivalent". Aren't they supposed to be?

atyy

In http://www.physicsforums.com/showpos...&postcount=133 & http://www.physicsforums.com/showthr...32#post2588832 you already give the coordinates in Alice's frame. Since you only use one inertial frame for the coordinates, it is already in LET form. It looks like Bob is able to send signals back in time from (8,10) to (0,0).

Fredrik

OK, but is there something in the theory that suggests that if Bob uses the same kind of device as Alice to send messages, his answer will go back in time?

zonde

Ah, but you have to have meaningful description for FTL particle in SR to say that they are not equivalent.

Wordline of FTL particle propagating at constant speed is spacelike. That means that we can find inertial reference frame where it propagates from A to B, another inertial reference frame where it propagates from B to A and another one where it "happens" all at once along the path from A to B.
Now to send some information you have to perform some modulation of FTL signal and you have to be able to "read" that modulation of signal. Now the question is in what direction this modulation will propagate? Form A to B or from B to A? I would say that SR does not give you answer about that.

DaleSpam

Yes. The Lorentz transform still applies between two arbitrary frames in LET. So use the Lorentz transform to generate a causality violation as normal. Now, the speed of the aether is unknown, so boost your solution by an unknown v. You will see that causality is violated in the aether frame regardless of the value of v.

Any scenario which violates causality in SR violates causality in LET. The only way around it is to have the aether measurably violate the principle of relativity (eg tachyonic signals go at 2c, but only in the aether frame)

kmarinas86

They are not equivalent. There is no spacetime in LET, so in LET the Lorentz transform is something that applies to objects with respect to a single arbitrary reference frame. So time dilation and length contraction are properties of an object based on relative motion with respect that frame. Thus, this means that all particles subject to relativistic speeds must also have internal degrees of freedom (if they length contract), contrary to the view of "indivisible" particles. The is no speed limit in LET if we assume that this length contraction is a weaker or non-existent effect for some particles, such as neutrinos. The forces we know about travel up to a limit, perceived locally as c. So LET combined with the facts concerning the gravitional delay (c.f. Shapiro Delay) of light would require that the speed of light be variable even in the vacuum of space from the point of view of the single preferred frame of LET.

stglyde

In other words. Anything FTL in LET would have objects that have negative contraction and negative time dilation? Is this what you mean that objects can still go back in time in LET?

Anyway. You said there was no spacetime in LET. Are you saying the length contraction or time dilation are properties of objects that occur in newtonian absolute space and time? But PeterDonis wrote the following:

"I'm not familiar enough with Lorentz's papers to know whether he thought at first that his results could be explained by just adding on length contraction to Newtonian space and time. But I don't think it really matters, because Einstein's 1905 relativity papers did make it clear that that wasn't possible; that to make kinematics consistent with the speed of light being constant for all observers, you *had* to give up Newtonian space and time."

What do you think?