# SR, LET, FTL & Causality Violation

## Main Question or Discussion Point

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.

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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.

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.
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?

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.

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Fredrik
Staff Emeritus
Gold Member
What FTL scenario would break causality?
See post #133 here (and post #138 for the correction of a typo).

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

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.

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

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."
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.

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.
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).

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.
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 [Broken]

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

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Fredrik
Staff Emeritus
Gold Member
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
Gold Member
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
Staff Emeritus
Gold Member
And as there is only one "real" simultaneity in LET there is no paradox with FTL particles.
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
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. In https://www.physicsforums.com/showpost.php?p=2588832&postcount=133 & https://www.physicsforums.com/showthread.php?p=2588832#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
Staff Emeritus
Gold Member
In https://www.physicsforums.com/showpost.php?p=2588832&postcount=133 & https://www.physicsforums.com/showthread.php?p=2588832#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).
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
Gold Member
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?
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.

Dale
Mentor
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. 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)

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?
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.

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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.
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?

atyy
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?
I can't think of any reason why this should be. So perhaps SR and LET are not equivalent in the realm of FTL. My inclination to try to formulate a LET tachyon was to set up a tachyonic version of Maxwell-like wave equations. Unfortunately, they don't seem to have the properties of particle tachyons in SR, at least judging by http://www.desy.de/user/projects/Physics/ParticleAndNuclear/tachyons.html. OTOH, do tachyonic waves automatically enforce FTL without paradoxes, since wave FTL requires nonlocality?

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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.
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?
I'm saying, "[L]ength contraction [and] time dilation are properties of objects that occur in [N]ewtonian 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?
http://en.wikipedia.org/wiki/Relativity_of_simultaneity

Wikipedia said:
A mathematical form of the relativity of simultaneity ("local time") was introduced by [[Hendrik Lorentz]] in 1892, and physically interpreted (to first order in ''v/c'') as the result of a synchronization using light signals by [[Henri Poincaré]] in 1900. However, both Lorentz and Poincaré based their conceptions on the [[Lorentz ether theory|aether]] as a preferred but undetectable frame of reference, and continued to distinguish between "true time" (in the aether) and "apparent" times for moving observers. It was [[Albert Einstein]] in 1905 who abandoned the (classical) aether and emphasized the significance of relativity of simultaneity to our understanding of space and time. He deduced the failure of absolute simultaneity from two stated assumptions:
* the [[Principle of relativity#In special relativity|principle of relativity]]–the equivalence of inertial frames, such that the laws of physics apply equally in all inertial coordinate systems;
* the constancy of the [[speed of light]] detected in empty space, independent of the relative motion of its source.
I would drop the first assumption immediately and say that the second is also questionable. Dropping the first assumption is sufficient to reject PeterDonis' argument. As for the second one, I do think that anytime that light changes speed due to the nature of the medium, it must refract one way or another. Light travels slower in highly refractive media, and faster in relatively non-refractive media. Our time keeping devices are not altered by such media in the same way that light is. This might also be true in the space between stars, but in the opposite way.

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zonde
Gold Member
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?
and Einsteins 1905 relativity paper - On the Electrodynamics of Moving Bodies

I we look at this quote from Einsteins 1905 paper:
"The introduction of a “luminiferous ether” will prove to be superfluous inasmuch as the view here to be developed will not require an “absolutely stationary space” provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place."

And in 1920 Einstein wrote in some letter that:
"More careful reflection teaches us, however, that the Special Theory of Relativity does not compel us to deny the Aether."

So I would like to encourage you to take "more careful reflection".

PeterDonis
Mentor
2019 Award
I would drop the first assumption immediately and say that the second is also questionable.
Really? You would drop two assumptions that are experimentally verified to a very high accuracy? (Unless by "dropping the assumptions" you actually mean "dropping the SR framework that predicts experimental results in accordance with these assumptions, and using the LET framework instead, that predicts exactly the same experimental results but claims it's for an entirely different reason.")

Also, you have mis-stated the first assumption slightly. Here's how it should read: "The laws of physics can be expressed in a form that is the same in all inertial coordinate systems." (This is the SR version; the GR version expands it to say that the laws of physics can be expressed in a form that is the same in *all* coordinate systems, inertial or not.) The first assumption does not rule out the possibility that there may be other ways of expressing the laws that look different in different inertial coordinate systems; it just says that you don't have to use such expressions. As I understand it, LET is an alternate expression of the physical laws that privileges some particular inertial coordinate system (but we don't know which one) as being the "absolute rest frame", such that the laws of physics look simplest in that frame. So LET does not really drop the first assumption.

Dropping the first assumption is sufficient to reject PeterDonis' argument.
See above; you haven't actually dropped it. Unless I'm misunderstanding something about LET and it actually makes different predictions than standard SR does, in which case it's falsified by experiment.

(Edit: See additional comment in my next post.)

As for the second one, I do think that anytime that light changes speed due to the nature of the medium, it must refract one way or another. Light travels slower in highly refractive media, and faster in relatively non-refractive media. Our time keeping devices are not altered by such media in the same way that light is. This might also be true in the space between stars, but in the opposite way.
Is this just handwaving, or does LET actually model light traveling in vacuum this way? If so, does this model make different predictions than standard SR? If it does, again, it's falsified by experiment.

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PeterDonis
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2019 Award
Dropping the first assumption is sufficient to reject PeterDonis' argument.
If you think so, you have misunderstood my argument. The local Lorentz invariance of spacetime, as opposed to Galilean invariance, is an experimental fact, not an assumption. Newtonian physics requires Galilean invariance; you can't change Galilean invariance to Lorentz invariance just by "overlaying" additional structure on top of Newtonian physics. You have to get rid of the underlying Newtonian structure altogether and replace it with the Lorentz invariant kinematics.

Dale
Mentor
They are not equivalent.
They may not be equivalent from a metaphysical or philosophical standpoint, but they are experimentally equivalent. Both SR and LET use the Lorentz transforms to make their experimental predictions, therefore they both always produce the same predictions.

If you believe that in some circumstances the Lorentz transform would not apply then you are no longer discussing LET, but perhaps some sort of generalization or extension of it.

They may not be equivalent from a metaphysical or philosophical standpoint, but they are experimentally equivalent. Both SR and LET use the Lorentz transforms to make their experimental predictions, therefore they both always produce the same predictions.

If you believe that in some circumstances the Lorentz transform would not apply then you are no longer discussing LET, but perhaps some sort of generalization or extension of it.
It doesn't appear to me that LET requires that every kind of matter be subject to contract to arbitrarily small lengths when approaching c - only those obseved to do so. If infact it does not forbid variations of this contraction (i.e. some not patterned after the "Lorentz contraction"), then it would seem that it does not forbid faster than light travel so as the contraction toward zero length could occur at a higher speed than c, or perhaps not at all.

Dale
Mentor
It doesn't appear to me that LET requires that every kind of matter be subject to contract to arbitrarily small lengths when approaching c - only those obseved to do so. If infact it does not forbid variations of this contraction (i.e. some not patterned after the "Lorentz contraction"), then it would seem that it does not forbid faster than light travel so as the contraction toward zero length could occur at a higher speed than c, or perhaps not at all.
And what equations would it use to predict the results of experiments?