SR, LET, FTL & Causality Violation

[kmarinas86]

Guys. In LET. As you fly in near light speed. Instead of you being 6 foot tall, you would become merely 1mm in height as length contracts. Won't this mess up or ruin any physics of the atoms (for example, the electrons being nearer the nucleus, etc)? Hope someone can explain this. Thanks.

Only if the distance and speed relative to the LET preferred frame were also known. But if they're known relative to the LET preferred frame, and we know which inertial frame the LET preferred frame is, then the distance and speed are known relative to *any* inertial frame. So if we suppose the distance and speed are unknown, that has to include being unknown relative to the LET preferred frame.

It has nothing to do with location, only relative velocity. Two inertial observers which are millions of lightyears apart but at rest wrt each other share the same rest frame. Two inertial observers passing near each other at .9c relative velocity do not share the same rest frame. The first two will always agree on simultaneity, despite the fact that they are far apart. The second two will generally disagree on simultaneity, despite the fact that they are close together.

I agree with DaleSpam, but I would add quotations around the word "simultaneity" to emphasize the subjectivity evident due to the potential for disagreeing on the "simultaneity".

 

[Dale]

About LET. Someone here says the Lorentz Transform is all that matters. SR is a way to graphically plot it. LET to physicalize it. For tachyons that travel faster than light. SR says in from other coordinates (or frames) you can see other frames going back in time (by deshifting the plane of simultaneity). How about in LET, can anyone draw any illustration of what it means for some frames able to view other frames as going backward in time when LET doesn't have the graphical interace as SR. So how do you graphically illustrate LET? I just can't imagine it since it doesn't have any minkowski spacaetime diagram. I guess this is the initial problem and concern in the original message of this thread.

Why would you say that LET doesn't have a "graphical interface"? You can use all of the same graphical techniques from SR. A spacetime diagram is nothing more than a position time diagram, which is used by every student to study Newtonian physics.

http://www.physicsclassroom.com/class/1dkin/u1l3a.cfm

 

[stglyde]

Earlier in the thread, we never resolved the tachyon pistol paradox using LET physical approach

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

Consider a duel with tachyon pistols. Two duelists, A and B, are to stand back to back, then start out at 0.866 lightspeed for 8 seconds, turn, and fire. Tachyon pistol rounds move so fast, they are instantaneous for all practical purposes.

So, the duelists both set out --- at 0.866 lightspeed each relative to the other, so that the time dilation factor is 2 between them. Duelist A counts off 8 lightseconds, turns, and fires. 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. Thus, the tachyon round hits B in the back as B's clock ticks 4 seconds.

Now B (according to relativity) has every right to consider A as moving, and thus, A is the one with the slowed clock. So, as B is hit in the back at tick 4, in outrage at A's firing before 8 seconds are up, B manages to turn and fire before being overcome by his fatal wound. And since in B's frame of reference it's A's clock that ticks slow, B's round hits A, striking A dead instantly, at A's second tick; a full six seconds before A fired the original round. A classic grandfather paradox.

Let's give a LET version or Analysis:

Based on "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."

LET physical version: A & B are in relative motion 0.866 lightspeed with 2X time dilation factor. So A length physically contract literally and its time slows down literally. Same with B. Yet in A frame, he doesn't feel the time slowing down. But when he sees B. He sees B as slowing down. In the frame of B. It's vice versa.

Now when A fires the tachyon pistol 8 sec later. B is hit in B 4 second time. LET-wise. A has physical contraction and time slowing but he doesn't feel it. When he hits B. B was hit 4 sec in his time. Pissed off. B hit back. Now he sees A as slowing down. Since A is half B time. A is hit 6secs before the pistol is fired (see the clear web example).

But this doesn't make sense in LET. Something is not right. When A is actually physically contracting and time dilated... A sees B with half his time. Then B seeing A half B time. There seems to be some kind of loop error. You can get away with this in SR because you are playing with the graphics. But in LET. It doesn't seem to follow the logic. I know SR and LET obey Lorentz Transformation and supposed to be identical. But when you imagine the LET version. Something is not right.

What do you think? Please illustrate by the Tachyon pistol example how LET can still do backward in time travel if you see the key explanation that I didn't. Thanks.

 

[Dale]

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.

 

[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.

I don't know what you are talking about with the velocity addition. I understood the SR explanation of the tachyon pistols. When things are in inertial frame. Both would see each other as slowing down. "A" 8 second would be "B" 4 sec and "B" 4 sec would be "A" 2 sec. This makes thing go backward in time. There is no addition rule or anything. So I don't know what LET and addition of velocity can make things go backward in time. Please elaborate what you mean.

Do others agree? Peterdonis, any other view?

 

[Dale]

I don't know what you are talking about with the velocity addition.

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.

 

[PeterDonis]

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.

There actually is one other assumption required in this scenario: that the spacelike curve the tachyon fired from the pistol follows is frame-dependent; the usual assumption appears to be that the tachyon velocity v is fixed relative to the emitter (the pistol in this case). For example, if you look at a typical scenario that uses tachyons to create closed loops, where A sends a message to B and then receives B's reply *before* he sent the original message, in order for the reasoning to go through, it has to be the case that tachyons emitted by B travel along spacelike curves that are not parallel to the curves followed by tachyons emitted by A--put another way, B's tachyons travel at some fixed v > c relative to B, while A's tachyons travel at the same v > c relative to A; but B's tachyons do *not* travel at v relative to A. (If they did, they would not be going backwards in time relative to A, so A could never receive B's reply before he sent his message.)

An LET theorist could, in principle, claim 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*. This would not prevent tachyons from appearing to travel backwards in time relative to some other frames, but it would prevent "closed loop" scenarios; you could never send a message using tachyons and receive the reply before you sent the message.

 

[PeterDonis]

But this doesn't make sense in LET. Something is not right. When A is actually physically contracting and time dilated... A sees B with half his time. Then B seeing A half B time. There seems to be some kind of loop error.

If you are going to be a consistent LET theorist, I would recommend working every problem in the LET frame first, to fix what happens there, before trying to translate into what observers moving relative to the LET frame would see. Though in fact, you don't even need to do any translation into other frames to determine whether tachyons can travel backwards in time relative to the aether frame. This is because of the issue I raised in my last post to DaleSpam: you have to decide what determines the velocity of the tachyons fired by the tachyon pistol, relative to the LET aether frame. Is the tachyon velocity fixed relative to that frame? Or is it fixed relative to the pistol's frame?

Until you decide that the problem is not well posed. And once you've decided that, you have also decided, implicitly, whether or not tachyons can travel backwards in time relative to the LET frame (if the tachyons move at a fixed v > c relative to the aether frame, then no; if they always move at v relative to the emitter, then yes). As you can see, this decision does not require actually working the problem out in any frame other than the aether frame.

 

[atyy]

Perhaps one difference related to what Fredrik brought up in post #13 between LET and SR is that LET requires dynamics ie. we formulate Maxwell's equations, then we find that SR is true. OTOH, SR seems to be perfectly happy with kinematics. ?

 

[stglyde]

There actually is one other assumption required in this scenario: that the spacelike curve the tachyon fired from the pistol follows is frame-dependent; the usual assumption appears to be that the tachyon velocity v is fixed relative to the emitter (the pistol in this case). For example, if you look at a typical scenario that uses tachyons to create closed loops, where A sends a message to B and then receives B's reply *before* he sent the original message, in order for the reasoning to go through, it has to be the case that tachyons emitted by B travel along spacelike curves that are not parallel to the curves followed by tachyons emitted by A--put another way, B's tachyons travel at some fixed v > c relative to B, while A's tachyons travel at the same v > c relative to A; but B's tachyons do *not* travel at v relative to A. (If they did, they would not be going backwards in time relative to A, so A could never receive B's reply before he sent his message.)

An LET theorist could, in principle, claim 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*. This would not prevent tachyons from appearing to travel backwards in time relative to some other frames, but it would prevent "closed loop" scenarios; you could never send a message using tachyons and receive the reply before you sent the message.

I've been thinking and getting familiar of what you and Dalespam have been saying for a couple of hours. Dalespam earlier in the thread also wrote:

"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)"

Ok. Let's say the tachyons travel faster than c relative to the aether frame (why must it be 2c and 1.5c Dalespam?). You said you could never send a message using tachyons and receive the reply before you sent the message. And continued "This would not prevent tachyons from appearing to travel backwards in time relative to some other frames". What other frames for example in the case of the Tachyon pistol duel scenerio? You are saying "A" won't be hit by "B" 6seconds before "A" fired the shot? Are you saying another observer "C" watching the duel would see A being hit 6 seconds before A fired the shot yet it doesn't actually happen in A or B frame? Or are you saying that B would shoot it yet it won't land in A 6 seconds before A started the shot.. then where would the bullet land (which is supposed to go back in time as you mentioned in other frames)? What other frames? Please add the observer "C" to illustrate the point. Thanks.

 

[PeterDonis]

And continued "This would not prevent tachyons from appearing to travel backwards in time relative to some other frames". What other frames for example in the case of the Tachyon pistol duel scenerio?

Drawing spacetime diagrams really helps in these kinds of situations. Unfortunately I don't have time to draw one. But in general, if we specify that tachyons always travel at some fixed velocity v > c relative to the aether frame, then we will always be able to find some observers to whom it will appear that the tachyons are moving backwards in time. Depending on the tachyon velocity v and the velocities of A and B relative to the aether frame, it is possible that A and B could be such observers; the only way to know is to specify some actual numbers for all these quantities.

Are you saying another observer "C" watching the duel would see A being hit 6 seconds before A fired the shot yet it doesn't actually happen in A or B frame?

Again, it depends on C's velocity relative to the aether frame, as well as A's and B's, and the velocity v of the tachyon. It is certainly possible to have C see the tachyon appear to travel backwards in time but not A or B if the velocities are chosen appropriately.

Btw, there's another wrinkle to this, which is discussed by John Bell, IIRC, in his paper on the "tachyonic antitelephone". Suppose A has the tachyon pistol, and suppose the tachyon velocity v is such that A and B both see the tachyon moving forward in time (say they are both at rest relative to each other). Then from A's point of view he fires the pistol at B and hits him, and B sees it the same way. But suppose there is some observer C whose velocity relative to A and B are such that C sees the tachyon going "backwards in time". What C would actually see is that B suddenly develops a gunshot wound which emits a tachyon, and the tachyon is the miraculously caught in A's pistol. So if I am A, I have committed murder from mine and B's point of view, but from C's point of view I have stopped a dangerous tachyon from injuring others; as Bell puts it, "I should get a medal." So when we say the tachyon "appears to go backwards in time", we have to be careful how we interpret what that means.

 

[stglyde]

Well, you used the word "frame" yourself in the OP. What did you mean by it?

#1 is the most general term: I would define it as any way of assigning coordinates to events that meets certain very basic conditions (for example, that events which are "close together" should have coordinates which are close in value). Normally we try to have the assignment of coordinates to events be "sensible", meaning there will be some reasonable relationship between the coordinates and something with physical meaning; but in principle we don't have to do this, it just makes calculations easier.

#2 and #4 are basically the same thing: they refer to special cases of #1 in which the metric in the given coordinates assumes the standard Minkowski form: d\tau^{2} = dt^{2} - dx^{2} - dy^{2} - dz^{2}. In flat spacetime (i.e., when gravity is negligible), such a frame can be global (i.e., it can cover the entire spacetime); but in curved spacetime (i.e., when gravity is present), such a frame can only be local; it can only cover a small region of spacetime around a given event (how small depends on how accurate we want our answers to be and how strong gravity is).

#5 is a particular instance of #2 and #4 such that an object we are interested in is at rest at the spatial origin in the given frame. In flat spacetime, again, this can be true globally; but in curved spacetime it will only be true locally.

#3 has at least two meanings that I'm aware of:

#3a: A "preferred frame" can be a particular instance of #1 (i.e., it can be any kind of frame, not necessarily an inertial/Lorentz frame) that matches up in some way with a key property of the spacetime we are interested in. For example, in the FRW spacetimes that are used in cosmology, the "comoving" frame, the frame in which the universe looks homogeneous and isotropic, is a preferred frame, because it matches up with the symmetries (homogeneity and isotropy) of the spacetime. The reason such a frame is "preferred" is that calculations are easier in a frame that matches up with the symmetries of the spacetime.

#3b: A "preferred frame" can also be a particular frame that is picked out by someone's physical theory as being "special", regardless of whether there is any actual physical observable that matches up with it. For example, the "aether frame" in LET is a preferred frame in this sense.

For years before this week. I thought LET was referring to an aether that uses Galilian invariance of some kind (with no velocity limit) but found out this week the LET aether also used Lorentz invariance (with c as the speed limit). But then what if for sake of discussion, the LET aether also had unlimited speed limit with the speed of light only the speed for normal particles? This means the speed of c is not the ceiling of LET spacetime and so SR were a limiting case. Of course in particle experiments the particles can't be pushed to light speed and we assume it is the ceiling limit of spacetime. What if it is the particles properties and not spacetime. In this scenerio with unlimited velocity in the nLET, then the aether frame is the rest frame and superluminal velocity won't imply any backward in time travel anymore in the Tachyon pistols in any frames, right? I just want to compare the new view of LET with the old view I thought I knew and their differences. Thanks.

 

[Dale]

There actually is one other assumption required in this scenario: that the spacelike curve the tachyon fired from the pistol follows is frame-dependent; the usual assumption appears to be that the tachyon velocity v is fixed relative to the emitter (the pistol in this case).

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.

An LET theorist could, in principle, claim 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*.

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.

 

[Dale]

"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)"

Ok. Let's say the tachyons travel faster than c relative to the aether frame (why must it be 2c and 1.5c Dalespam?).

No reason. The "e.g." in my parenthetical comment means "for example". Any v>c would work equally well.

 

[Dale]

But then what if for sake of discussion, the LET aether also had unlimited speed limit with the speed of light only the speed for normal particles? ... In this scenerio with unlimited velocity in the nLET

You need to be careful here. It is one thing to discuss legitimate scientific theories of the past, but it is another to speculate on new personal theories.

However, any particle which does not have a speed limit c will either violate the principle of relativity or causality. You can have any two of the following three: FTL, causality, and relativity.

 

[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.