SR, LET, FTL & Causality Violation

[stglyde]

Sure, but that is not a separate assumption from LET. If, as LET asserts, the laws governing physical experiments are invariant under the Lorentz transform then this follows.

Certainly, but then the tachyons would be measurably inconsistent with the Lorentz transform, disproving LET, or at least requiring modifications to say that the Lorentz transform had limited applicability.

In other words, if we found a lorentz violation in experiments.. this is still possible that "travel backwards in time relative to the aether frame was impossible because tachyons always have to travel at some fixed velocity v > c *relative to the aether frame*" as PeterDonis put it. So far, how have experiments measured up. I mean has any experiments already totally refuted this? Or is this still in the agenda for future experiments to search for lorentz violations?

Note I'm not proposing any new theories. I just want to see the flexibilies of the existing theory to understand it from all angles (and frames of reference.. pun intended).

 

[PeterDonis]

Sure, but that is not a separate assumption from LET. If, as LET asserts, the laws governing physical experiments are invariant under the Lorentz transform then this follows.

Certainly, but then the tachyons would be measurably inconsistent with the Lorentz transform, disproving LET, or at least requiring modifications to say that the Lorentz transform had limited applicability.

Good points, you're right, any such rule as I proposed for the "LET theorist" would require modifying LET to claim violation of Lorentz invariance in at least one case (tachyon emission).

 

[PeterDonis]

So far, how have experiments measured up. I mean has any experiments already totally refuted this? Or is this still in the agenda for future experiments to search for lorentz violations?

No violations of Lorentz invariance have been found to date, according to the section of the living reviews site that discusses tests of Lorentz invariance (I can't remember if I've linked to this site before in this thread or if it was another one):

http://relativity.livingreviews.org/Articles/lrr-2005-5/

From what I can see there, nobody is really considering the kind of scenario we've been discussing when testing for Lorentz violations; the work that's being done seems more aimed at narrowing the limits on what kinds of quantum gravity theories are plausible candidates.

 

[stglyde]

Good points, you're right, any such rule as I proposed for the "LET theorist" would require modifying LET to claim violation of Lorentz invariance in at least one case (tachyon emission).

In other words:

Tachyon emission + Lorentz Invariance = Backward in time and A getting hit before shooting
Tachyon emission + Lorentz Violation = A can't be hit before shooting but in some frames backward in time can be seen.

No Tachyon has been detected. But if ever in the future Tachyon were detected, why must Lorentz Invariance of Tachyon be assumed when Tachyon are strange stuff and so Lorentz Violation can also theoretically occur. Right?

Again I'm just asking to have versatile understanding of the concept and not proposing anything.

 

[PeterDonis]

Tachyon emission + Lorentz Invariance = Backward in time and A getting hit before shooting
Tachyon emission + Lorentz Violation = A can't be hit before shooting but in some frames backward in time can be seen.

Yes, for the particular kind of "Lorentz Violation" described earlier (tachyons have to always travel at a fixed velocity v > c relative to the fixed LET aether frame).

No Tachyon has been detected. But if ever in the future Tachyon were detected, why must Lorentz Invariance of Tachyon be assumed when Tachyon are strange stuff and so Lorentz Violation can also theoretically occur.

Violation of Lorentz invariance and existence of tachyons are two separate things, and they don't necessarily go together. In some thread recently (can't seem to find which one) I pointed out that, strictly speaking, Lorentz invariance does not absolutely rule out "things moving faster than light"; it just requires that spacelike separated experiments must commute, i.e., the experimental results can't depend on which one occurs "first". The reason the "tachyon pistols" scenario creates a problem is that it doesn't seem like the spacelike separated events can possibly commute; in the original scenario you linked to, the result depends critically on who fires "first" (and as the scenario is constructed, there is no consistent resolution to that question).

In the alternate scenario I described, where A kills B with a tachyon pistol but C, moving past them at a high speed, sees B get a sudden wound that emits a tachyon which A catches, the two alternate interpretations of events are not exactly inconsistent, but the interpretation C would have to adopt does seem physically unreasonable; people don't just spontaneously develop gunshot wounds. (Probably this objection can be made more rigorous by bringing in the second law of thermodynamics.)

But there are plenty of other possible scenarios where things could in principle travel faster than light without creating such problems. For example, in the quantum experiments that confirmed violation of the Bell inequalities, spacelike separated measurements show a degree of correlation that should not be possible unless there was some sort of FTL connection between them. But this effect can't be used to send any signals (or gunshots); the measurement results are independent of which one is taken to occur "first", so they meet the above requirement.

 

[stglyde]

Yes, for the particular kind of "Lorentz Violation" described earlier (tachyons have to always travel at a fixed velocity v > c relative to the fixed LET aether frame).



Violation of Lorentz invariance and existence of tachyons are two separate things, and they don't necessarily go together. In some thread recently (can't seem to find which one) I pointed out that, strictly speaking, Lorentz invariance does not absolutely rule out "things moving faster than light"; it just requires that spacelike separated experiments must commute, i.e., the experimental results can't depend on which one occurs "first". The reason the "tachyon pistols" scenario creates a problem is that it doesn't seem like the spacelike separated events can possibly commute; in the original scenario you linked to, the result depends critically on who fires "first" (and as the scenario is constructed, there is no consistent resolution to that question).

In the alternate scenario I described, where A kills B with a tachyon pistol but C, moving past them at a high speed, sees B get a sudden wound that emits a tachyon which A catches, the two alternate interpretations of events are not exactly inconsistent, but the interpretation C would have to adopt does seem physically unreasonable; people don't just spontaneously develop gunshot wounds. (Probably this objection can be made more rigorous by bringing in the second law of thermodynamics.)

But there are plenty of other possible scenarios where things could in principle travel faster than light without creating such problems. For example, in the quantum experiments that confirmed violation of the Bell inequalities, spacelike separated measurements show a degree of correlation that should not be possible unless there was some sort of FTL connection between them. But this effect can't be used to send any signals (or gunshots); the measurement results are independent of which one is taken to occur "first", so they meet the above requirement.

Ok. Principle of relativity says that the laws of physics must be the same in all inertial frames. What I can't understand now is this. In LET and the tachyon pistol example, the tachyon velocity v is fixed relative to the emitter. This is why you have the paradox. But if the velocity v > c is relative to the aether frame, then no paradox. But what does it mean the velocity is relative to the aether frame. When "A" shoots after 8 seconds, the bullet must pass thru the aether and hit B. So what is the difference between the tachyon velocity v relative to emitter or relative to aether? What is the difference physically since both has to pass thru space (and hence aether). This is the last thing I want to understand before I forgot LET and have a clearer perspective and understanding of the relativity concepts and the extremes it can take. Thanks.

 

[stglyde]

If you understand the scenario in SR then you almost have it in LET also. To make the final step from SR to LET simply boost your scenario by an unknown v to get to the aether frame. You get a causality violation regardless of v.

The key is the velocity addition. In LET measured velocities still follow the usual relativistic velocity addition rule. In the tachyon pistol scenario this allows things to go backwards in time in the aether frame.

...

Here is a brief introduction:
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel2.html

If a tachyon pistol fires projectiles at any v>c then there is some frame where it would go backwards in time relative to the aether frame. I can work out the math for you if you like.

I have studied the above hyperphysics link. But it doesn't mention any backward in time travel for superluminal Tachyons. And still can't understand the following you mentioned "To make the final step from SR to LET simply boost your scenario by an unknown v to get to the aether frame. You get a causality violation regardless of v."

I thought you said LET and SR being compatible means the velocity is not relative to the aether frame but to the emitter frame. But in the above you mentioned the aether frame. Why not the emitter frame? Can you please work out the math as you mentioned above using the Tachyon pistol example of how adding velocity can create the effect? Thanks.

 

[PeterDonis]

But if the velocity v > c is relative to the aether frame, then no paradox. But what does it mean the velocity is relative to the aether frame.

It means just what it says; when determining how a tachyon moves, you have to know which frame is the aether frame; then you assign the tachyon a velocity v > c relative to that specific frame. For example, suppose that the aether frame just happened to be the frame of the "referee" in the original tachyon pistol scenario you linked to; and suppose, for simplicity, that the tachyon velocity v in that frame is infinite. Then both tachyon worldlines would be vertical lines in the diagram as drawn (the usual convention is to have time vertical and space horizontal, in which case the tachyon worldlines would be horizontal as drawn in the referee frame); the referee would see both tachyons instantaneously hit their targets when fired, at the same instant.

 

[stglyde]

If you understand the scenario in SR then you almost have it in LET also. To make the final step from SR to LET simply boost your scenario by an unknown v to get to the aether frame. You get a causality violation regardless of v.

The key is the velocity addition. In LET measured velocities still follow the usual relativistic velocity addition rule. In the tachyon pistol scenario this allows things to go backwards in time in the aether frame.

Ah. I think what you meant by aether frame here is as observer of A and B and not how the tachyon velocity traveling relative to the aether frame. I thought you were referring to the latter.

You mention adding velocities. You seem to be saying that the aether is moving. Is it not supposed to be fixed. Why must one boost by an unknown v to get to the aether frame?
Even without adding velocities. Causality should still be violated since LET and SR are compatible. So why add velocities?

 

[atyy]

In the case where tachyons and Lorentz invariance produce contradictions, the attempted construction is incoherent.

I doubt it makes any sense to say LET (defined as a set of Poincare invariant dynamical laws in particular Lorentz inertial frame) and X are equivalent in the case where X is incoherent.

 

[PeterDonis]

You mention adding velocities. You seem to be saying that the aether is moving. Is it not supposed to be fixed.

If you are moving relative to the aether, then the aether is moving relative to you. So if you want to see how things look in the aether frame, but all you have are measurements made in your frame, you will have to apply a Lorentz transformation to convert from your frame to the aether frame. That's what DaleSpam is talking about.

 

[stglyde]

If you are moving relative to the aether, then the aether is moving relative to you. So if you want to see how things look in the aether frame, but all you have are measurements made in your frame, you will have to apply a Lorentz transformation to convert from your frame to the aether frame. That's what DaleSpam is talking about.

I see. Thanks. So in LET. It is the aether that is resisting the object to make it not able to get pass the speed of light isn't it.. the stronger the object push, the stronger the aether will time dilate and length contract the object. It's as if the object atoms can't move freely that is why the object atoms slow down. Is this the explanation or is there no physical explanation for LET?

Also. Is there just no way even in principle to distinguish between LET and SR even in any future time. Meaning a million years from now. There is just no way they can be distinguished and the aether frame is forever unmeasurable and unknowable by any future scientists in all the universe? Or are there gedankens in which the aether frame can be detected?

 

[atyy]

Also. Is there just no way even in principle to distinguish between LET and SR even in any future time. Meaning a million years from now. There is just no way they can be distinguished and the aether frame is forever unmeasurable and unknowable by any future scientists in all the universe? Or are there gedankens in which the aether frame can be detected?

What is LET? Here we are discussing LET that is by definition SR in a particular inertial frame. By definition it can never be distinguished from SR.

Could we discover in the future that Lorentz invariance is only approximate? Yes.

Would that imply that Galilean invariance is a better description of nature? Not neessarily, but possibly yes.

 

[ghwellsjr]

What is LET? Here we are discussing LET that is by definition SR in a particular inertial frame. By definition it can never be distinguished from SR.

Exactly right.

What is the distinguishing characteristic of that particular inertial frame? It's the only frame in which light actually travels at c because it is the medium that propagates light. But it can never be found.

That is until Einstein came along. He said that any inertial frame is exactly like that one particular frame in which light actually travels at c. He calls it his second postulate.

 

[PeterDonis]

So in LET. It is the aether that is resisting the object to make it not able to get pass the speed of light isn't it.. the stronger the object push, the stronger the aether will time dilate and length contract the object. It's as if the object atoms can't move freely that is why the object atoms slow down. Is this the explanation or is there no physical explanation for LET?

I think you would have to ask an actual LET theorist. I can talk about experimental predictions of LET since they're the same as those of SR; but I don't really know what LET claims to be the "physical explanation" of those predictions. I suspect there isn't a coherent physical explanation within the LET framework, but that's because I don't think there's an aether in the first place, and if that's true then trying to explain things by postulating an aether is going to run into problems at some point.

There is just no way they can be distinguished and the aether frame is forever unmeasurable and unknowable by any future scientists in all the universe? Or are there gedankens in which the aether frame can be detected?

Well, people in the 19th century certainly thought there were experiments that would detect an aether, like the Michelson-Morley experiment. The problem was that they all failed to detect an aether. That's why LET is forced to take the position now that the aether is "unobservable". Again, I don't really know whether LET claims that some future experiment could detect an aether or not; I think you would have to ask an actual LET theorist.

 

[stglyde]

The difference between LET and SR is in the second postulate. Einstein claims that light propagates at c in any rest state whereas LET postulates that light propagates at c only in one rest state. Since we cannot know what that rest state is, LET interprets virtually all rest states as being in inertial motion with respect to that one preferred rest state and therefore experiencing time dilation and length contraction (but of some unknowable amount). SR interchanges these two rest states, any rest state is exactly like the LET preferred absolute rest state of the ether where the speed of light is c and so experiences no time dilation or length contraction--all other frames in relative inertial motion are the ones that experience the time dilation and length contraction.

Aside from that one ever-so-minor point of view, there is no difference between LET and SR.

Hi, when you shine a flashlight.. the light travels straight.. can't you say light is traveling in that one rest state hence it is the aether frame? This is my idea of an aether for many years. But it seems LET is weird in that as you said "Since we cannot know what that rest state is, LET interprets virtually all rest states as being in inertial motion with respect to that one preferred rest state and therefore experiencing time dilation and length contraction (but of some unknowable amount)." How can you put the flashlight and the light traveling ahead in this context? Are you saying that the space where the light is traveling is in inertial motion with respect to a main aether rest state (or aether frame)? Very strange concept. Is this a mainstream idea or your way of understanding it? What other words other people use?

 

[stglyde]

I reviewed up on the original MMX experiment and Lorentz invention of physical contraction to account for the negative result. In your own inertial frame. You can't tell if your body or ship has contracted because the ruler is contracted too, etc. but others outside your inertial frame can see your length contracted.. therefore by the amount of your contraction, they can calculate and detect the position of the aether. So why is it stated that the rest frame of the aether can't be found?

 

[ghwellsjr]

Hi, when you shine a flashlight.. the light travels straight.. can't you say light is traveling in that one rest state hence it is the aether frame? This is my idea of an aether for many years. But it seems LET is weird in that as you said "Since we cannot know what that rest state is, LET interprets virtually all rest states as being in inertial motion with respect to that one preferred rest state and therefore experiencing time dilation and length contraction (but of some unknowable amount)." How can you put the flashlight and the light traveling ahead in this context? Are you saying that the space where the light is traveling is in inertial motion with respect to a main aether rest state (or aether frame)? Very strange concept. Is this a mainstream idea or your way of understanding it? What other words other people use?

I'm saying, as Einstein says in his second postulate, you can pick any inertial frame and consider it to be exactly like the one and only aether frame where light travels at c. Even if there really is a single aether frame and the frame you pick is in inertial motion with respect to it, you will never know the difference so you can consider your chosen frame to be the aether frame. Thus, there is no point in being concerned about the existence of a single absolute aether rest frame.

After you pick an inertial rest frame (consider it to be the one and only aether frame in which light travels at c), then it becomes very easy to interpret the propagation of the light from a flashlight. If the flashlight is moving to the right and the flashlight is aimed upward, the photons will travel on an angle as demanded by the inertial rest frame (the aether if you want to use that to help you understand) but the beam will always be straight up from the flashlight. If the beam strikes a mirror traveling with the flashlight, it will then reflect right back to the flashlight, although the photons have taken an upside down V path. But, since it has taken a longer time for an individual photon to make the trip up to the mirror and reflect back down, (as in a vertical light clock), this means that time for this moving flashlight and mirror has slowed down. If the flashlight were aimed to the right and the mirror placed in front of it, the mirror would have to be closer in order for a photon to make the trip to the mirror and back in the same amount of time as it did for the vertical direction. This is length contraction.

 

[stglyde]

I'm saying, as Einstein says in his second postulate, you can pick any inertial frame and consider it to be exactly like the one and only aether frame where light travels at c. Even if there really is a single aether frame and the frame you pick is in inertial motion with respect to it, you will never know the difference so you can consider your chosen frame to be the aether frame. Thus, there is no point in being concerned about the existence of a single absolute aether rest frame.

As I mentioned. I reviewed up on the original MMX experiment and Lorentz invention of physical contraction to account for the negative result. In your own inertial frame. You can't tell if your body or ship has contracted because the ruler is contracted too, etc. but others outside your inertial frame can see your length contracted.. therefore by the amount of your contraction, they can calculate and detect the position of the aether. So why is it stated that the rest frame of the aether can't be found?

After you pick an inertial rest frame (consider it to be the one and only aether frame in which light travels at c), then it becomes very easy to interpret the propagation of the light from a flashlight. If the flashlight is moving to the right and the flashlight is aimed upward, the photons will travel on an angle as demanded by the inertial rest frame (the aether if you want to use that to help you understand) but the beam will always be straight up from the flashlight. If the beam strikes a mirror traveling with the flashlight, it will then reflect right back to the flashlight, although the photons have taken an upside down V path. But, since it has taken a longer time for an individual photon to make the trip up to the mirror and reflect back down, (as in a vertical light clock), this means that time for this moving flashlight and mirror has slowed down. If the flashlight were aimed to the right and the mirror place in front of it, the mirror would have to be closer in order for a photon to make the trip to the mirror and back in the same amount of time as it did for the vertical direction. This is length contraction.

I'm familiar with this bouncing light in mirror gedanken explanation of time dilation in pure SR fashion.

 

[ghwellsjr]

I reviewed up on the original MMX experiment and Lorentz invention of physical contraction to account for the negative result. In your own inertial frame. You can't tell if your body or ship has contracted because the ruler is contracted too, etc. but others outside your inertial frame can see your length contracted.. therefore by the amount of your contraction, they can calculate and detect the position of the aether. So why is it stated that the rest frame of the aether can't be found?

First off, you don't want to say "others outside your inertial frame" because that implies that only you are in "your inertial frame". When we say "your inertial frame" we mean a frame in which you are at rest and others are traveling but they are just as much in the same frame as you are in. Every one is in all frames.

So with this in mind, in "your inertial frame", meaning in a frame in which you are at rest, you are not experiencing length contraction (or time dilation) and that is the reason why everything is normal to you. It would be just like if you happened to be at rest in the one and only aether frame, wouldn't it?

But those other people traveling with respect to you, and therefore with respect to the aether (if you want to think of it this way), will be experiencing length contraction and time dilation but they won't know it because their rulers are contracted along the direction of motion and their clocks are running slow. Now when they view you, still while in your rest frame, they will measure you to be length contracted and time dilated.

One way to help understand this is to consider what happens when they approach you and pass right by you. If you had identical spaceships, you could each measure the length of other one by seeing how long it takes the front of each spaceship to traverse the distance from the front of the other one to its rear. Since you are at rest with respect to the chosen frame, you are not experiencing length contraction or time dilation so the time according to your clock that it takes the other ship to pass you multiplied by its speed gives you its length.

Now they are doing the same thing with respect to you but remember this will all be considered from the same frame where their ship is length contracted and their clocks are running slow. Now when they are at the front of your spaceship, they note the time on their clock (just like you are doing). Then some time later, when they reach the rear of your ship, they make another note of the time on their clock. Since their clock is running slow, they will get a smaller value than they otherwise would and when they do the division, they conclude that it is your spaceship that is length contracted. See how this works? All in a single arbitrarily chosen inertial frame.

So even though they are the ones that are length contracted, they still think you are the one that is length contracted. Every measurement that you make of them, they will make of you, even though they are the ones that are "really" experiencing length contraction and time dilation, so it's impossible to tell who really is at rest with respect to the aether.

 

[PeterDonis]

As I mentioned. I reviewed up on the original MMX experiment and Lorentz invention of physical contraction to account for the negative result. In your own inertial frame. You can't tell if your body or ship has contracted because the ruler is contracted too, etc. but others outside your inertial frame can see your length contracted.. therefore by the amount of your contraction, they can calculate and detect the position of the aether. So why is it stated that the rest frame of the aether can't be found?

Did you also read that they ran the MMX at different times of the year? The reason was that the Earth is in *different* inertial frames at different times of the year. They expected that the results of the MMX would be different because of that; even if the Earth is at rest relative to the aether in January, for example, it can't possibly be at rest relative to the aether in July, so even if no aether was detected in January they expected to detect it in July. But in fact the results were the same all year round: no aether detected.

Now suppose it's January, and I put my rocket in the exact state of motion the Earth will be in in July. Then I run the MMX in my rocket at the same time the Earth-bound lab is running the MMX. We will both get null results: no aether detected. But we can't both be at rest relative to the aether, so we can't use the null result to argue that the frame we happen to be at rest in at that moment is the aether frame.

We will also each see the other as length contracted and time dilated, and by the same amount. But if we try to use that information to calculate which frame is the aether frame, we will get different answers. So you can't find the aether frame by measuring someone else's length contraction and time dilation.

 

[zonde]

So in LET. It is the aether that is resisting the object to make it not able to get pass the speed of light isn't it.. the stronger the object push, the stronger the aether will time dilate and length contract the object. It's as if the object atoms can't move freely that is why the object atoms slow down. Is this the explanation or is there no physical explanation for LET?

Certainly not this way.
LET can be viewed as idealization where atoms are nothing more but specific configuration of ripples in aether. So obviously their maximum speed is speed of waves in aether.

 

[zonde]

One way to help understand this is to consider what happens when they approach you and pass right by you. If you had identical spaceships, you could each measure the length of other one by seeing how long it takes the front of each spaceship to traverse the distance from the front of the other one to its rear. Since you are at rest with respect to the chosen frame, you are not experiencing length contraction or time dilation so the time according to your clock that it takes the other ship to pass you multiplied by its speed gives you its length.

Now they are doing the same thing with respect to you but remember this will all be considered from the same frame where their ship is length contracted and their clocks are running slow. Now when they are at the front of your spaceship, they note the time on their clock (just like you are doing). Then some time later, when they reach the rear of your ship, they make another note of the time on their clock. Since their clock is running slow, they will get a smaller value than they otherwise would and when they do the division, they conclude that it is your spaceship that is length contracted. See how this works? All in a single arbitrarily chosen inertial frame.

So even though they are the ones that are length contracted, they still think you are the one that is length contracted. Every measurement that you make of them, they will make of you, even though they are the ones that are "really" experiencing length contraction and time dilation, so it's impossible to tell who really is at rest with respect to the aether.

This misses important point about relativity of simultaneity (or local time in LET).

This picture can illustrate the point about symmetric length contraction:

here AB is length of length contracted moving rod but AC is length of the rod in it's own frame with sloped simultaneity.
Because from perspective of moving rod everything is measured using AC length not AB things at rest are shorter than rod instead of longer (length of similar rod at rest is between AB and AC)

 

[ghwellsjr]

This misses important point about relativity of simultaneity (or local time in LET).

You're right, it does miss relativity of simultaneity, and on purpose. I was showing how two observers, one stationary in the presumed aether and one moving will still each measure the other one's length to be contracted--all without invoking the Theory of Special Relativity and without establishing separate Frames of Reference for each observer.

And of course the same analysis applies under SR using just one FoR.

 

[Dale]

So far, how have experiments measured up. I mean has any experiments already totally refuted this? Or is this still in the agenda for future experiments to search for lorentz violations?

So far there have been no reproducible mainstream experiments which have detected Lorentz violations. This is definitely "in the agenda for future experiments". In fact, it is a very active area of research since many quantum gravity theories predict Lorentz violations at sufficiently high energies.

 

[Dale]

I have studied the above hyperphysics link. But it doesn't mention any backward in time travel for superluminal Tachyons.

Correct, it is just a general link on velocity addition, since you mentioned that you didn't know what relativistic velocity addition was.

And still can't understand the following you mentioned "To make the final step from SR to LET simply boost your scenario by an unknown v to get to the aether frame. You get a causality violation regardless of v."

I mean, once you have worked out the scenario in SR then all you have to do is boost to the aether frame and you have the LET description of the scenario. Since the aether is undetectable, the best thing to do us to boost by an unknown v and see if anything changes as a function of v. It doesn't.

I thought you said LET and SR being compatible means the velocity is not relative to the aether frame but to the emitter frame. But in the above you mentioned the aether frame. Why not the emitter frame? Can you please work out the math as you mentioned above using the Tachyon pistol example of how adding velocity can create the effect? Thanks.

You can do it in either the aether frame or the emitter frame, but the emitter frame smacks of SR rather than LET. Here is the math (using units where c=1).

Suppose the tachyons are emitted at v=2 from the pistol at t=0, then the worldline of the tachyon in the pistol frame is x=2t, meaning e.g. that at t=1 the tachyon could hit a target at x=2. Now, further suppose that the pistol is moving at u=-.6 relative to the aether frame. Then the Lorentz transform to the aether frame gives us the world line of the tachyon in the aether frame:
$$\left( \begin{array}{cccc} 1.25 & -0.75 & 0 & 0 \\ -0.75 & 1.25 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right) \cdot \left( \begin{array}{c} t \\ 2 t \\ 0 \\ 0 \end{array} \right) = \left( \begin{array}{c} -0.25 t \\ 1.75 t \\ 0 \\ 0 \end{array} \right)$$Meaning that, although it was fired at x'=0 t'=0 it hit a target at x'=1.75 and t=-0.25 in the aether frame.

You can also find the speed of the projectile using the velocity addition formula I showed simply by substituting v=2 and u=-.6
$$\frac{u+v}{1+uv}=-7$$

 

[Dale]

Ah. I think what you meant by aether frame here is as observer of A and B and not how the tachyon velocity traveling relative to the aether frame. I thought you were referring to the latter.

No, I meant what I said. When I said aether frame I meant the aether frame.

You mention adding velocities. You seem to be saying that the aether is moving. Is it not supposed to be fixed. Why must one boost by an unknown v to get to the aether frame?

A boost is a specific coordinate transformation, i.e. changing to another coordinate system which is moving at constant velocity wrt the first. You are correct, in LET the aether is considered "stationary" and the other frames are "moving", but the mathematical operation to transform from one to the other is called "a boost" regardless of which direction you are going. So if you are in the aether frame you boost to get to the moving frame, if you are in the moving frame you boost to get to the stationary aether frame.

The reason to boost by an unknown v is simply because we cannot detect the aether so we don't know what v to use. It is unknown and unknowable.

 

[stglyde]

Guys. Isn't it LET and SR are identical because they both follow the Lorentz Tranformation, but according to someone, it is not.. this is his reasoning:

"Ah, no they are not 'identical' Lorentz says that velocity is dv = V - v and SR says dv = v. In SR one arbitrarily assumes a rest frame and in Lorentz's theory they do not. In Lorentz's theory it is ALWAY dv and in SR v relative to one's choice. Since the transform used only dv as in Sqrt(1 - [dv/c]^2) the computed results are the same. Also, since
dv is squared the sign (as in direction relative to V) is masked but actually important. There is NO symmetry in LET, the faster you move the more phyically time slowly and contracted you are, period! Finally, where in LET is relative simultaniety mentioned?"

True? If not, where is the mistake made? Thanks.

 

[Dale]

What are dv, V, and v?

I wouldn't say that they are identical, only that all of their experimental predictions are identical. I.e. The differences are philosophical only.

 

[stglyde]

What are dv, V, and v?

I wouldn't say that they are identical, only that all of their experimental predictions are identical. I.e. The differences are philosophical only.

Dunno.. saw it at google newsgroup in a comment to the same Tachyon pistol example we are discussing, and he mentions further to the statement "Now, according to A (since in relativity all inertial frames are equally valid) B's the one who's moving, so B's clock is ticking at half-speed.":


"Not true in LET! First, let's say A & B is moving at speed V wrt the
the aether as measured by its CMBR Doppler. Then the assume that both
take off in opposing directions. Then

v(A) = V + dv
v(B) = V - dv


Relative to each other


v = (V + dv) - (V - dv) = 2dv = 0.866c


each changed speed 0.433c. If V = 0.433 then:


v(A) = 0.866c
v(B) = 0.0 "


What do you think guys? If he is mistaken, which part he gets mistaken?

 

[Dale]

let's say A & B is moving at speed V wrt the
the aether as measured by its CMBR Doppler. Then the assume that both
take off in opposing directions. Then

v(A) = V + dv
v(B) = V - dv

This is not correct. LET uses the relativistic velocity addition formula, just like SR. The pseudo-LET described here would be inconsistent with existing observations since it would permit any ordinary particle to be a tachyon, and would have other observable consequences.

 

[stglyde]

What are dv, V, and v?

V -> Velocity with respect to (wrt) the aetherial background (CMBR)
v -> Velocity of a second moving object (Frame), again wrt the aetherial frame
dv -> net differential speed

This is not correct. LET uses the relativistic velocity addition formula, just like SR. The pseudo-LET described here would be inconsistent with existing observations since it would permit any ordinary particle to be a tachyon, and would have other observable consequences.

Lorentz explicitly uses V & v (defined above) but shows that for the transform only the net (dv) is necessary. In other words (IOW) one can assume any 'local frame' is a 'rest frame' and only the net (delta) velocity is used in the transform. You can pretend you're at rest and measure any speed wrt to you and calculated the delta coordinate changes just based on that. This is what SR does. Likewise. Lorentz NEVER! proposed relative simultaniety.

About v = (V + dv) - (V - dv) = 2dv = 0.866c

Note that the aetherial speed V factored out.

 

[Jorrie]

Lorentz NEVER! proposed relative simultaniety.

Lorentz introduced/accepted the LTs, which for time:
$t' = \gamma(t-vx/c^2)$.
Does this not imply the relativity of simultaneity?

 

[stglyde]

This misses important point about relativity of simultaneity (or local time in LET).

This picture can illustrate the point about symmetric length contraction:

here AB is length of length contracted moving rod but AC is length of the rod in it's own frame with sloped simultaneity.
Because from perspective of moving rod everything is measured using AC length not AB things at rest are shorter than rod instead of longer (length of similar rod at rest is between AB and AC)

What are you talking about? Why. How does Relativity of Simultaneity differ between SR and LET?

 

[stglyde]

First off, you don't want to say "others outside your inertial frame" because that implies that only you are in "your inertial frame". When we say "your inertial frame" we mean a frame in which you are at rest and others are traveling but they are just as much in the same frame as you are in. Every one is in all frames.

So with this in mind, in "your inertial frame", meaning in a frame in which you are at rest, you are not experiencing length contraction (or time dilation) and that is the reason why everything is normal to you. It would be just like if you happened to be at rest in the one and only aether frame, wouldn't it?

But those other people traveling with respect to you, and therefore with respect to the aether (if you want to think of it this way), will be experiencing length contraction and time dilation but they won't know it because their rulers are contracted along the direction of motion and their clocks are running slow. Now when they view you, still while in your rest frame, they will measure you to be length contracted and time dilated.

One way to help understand this is to consider what happens when they approach you and pass right by you. If you had identical spaceships, you could each measure the length of other one by seeing how long it takes the front of each spaceship to traverse the distance from the front of the other one to its rear. Since you are at rest with respect to the chosen frame, you are not experiencing length contraction or time dilation so the time according to your clock that it takes the other ship to pass you multiplied by its speed gives you its length.

Now they are doing the same thing with respect to you but remember this will all be considered from the same frame where their ship is length contracted and their clocks are running slow. Now when they are at the front of your spaceship, they note the time on their clock (just like you are doing). Then some time later, when they reach the rear of your ship, they make another note of the time on their clock. Since their clock is running slow, they will get a smaller value than they otherwise would and when they do the division, they conclude that it is your spaceship that is length contracted. See how this works? All in a single arbitrarily chosen inertial frame.

So even though they are the ones that are length contracted, they still think you are the one that is length contracted. Every measurement that you make of them, they will make of you, even though they are the ones that are "really" experiencing length contraction and time dilation, so it's impossible to tell who really is at rest with respect to the aether.

Ghwellsjr, is the above related to relativity of simultaneity in LET where it has same behavior as SR because we can't measure the aether rest frame?

Also what do you make of the concept of the aether background frame being where the CMBR has no significant dirtectional Doppler shift?