SR, LET, FTL & Causality Violation

[Fredrik]

I didn't notice that signature until now. It made me laugh, so maybe you should have been nominated for the humor award.

 

[Dale]

DaleSpam, no fair electioneering in your sig!

Yeah, it's probably not the intended use of the signatures, but this is a very low-budget campaign so I have to use cheap options!

I didn't notice that signature until now. It made me laugh, so maybe you should have been nominated for the humor award.

Excellent! You can just put me as a write-in

 

[PeterDonis]

Yeah, it's probably not the intended use of the signatures, but this is a very low-budget campaign so I have to use cheap options!

I'll get hold of McCain and Feingold and tell them PF needs campaign finance reform.

 

[D H]

DaleSpam, no fair electioneering in your sig!

The PF Sitting (it's easier to sit than stand when typing on a computer) Yearly Committee on Fair and Open Awards (PSYCo FOA¹) has met and has deemed that such electioneering violates neither the rules nor the spirit of the awards process.¹This committee is so new that we don't even have an official name, let alone a cool acronym, for it. Probably never will.

 

[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.

When we ordinary nonphysicist men who mainly experience Newtonian limit have to visualize 4 dimensional thing that can move backward in time, we sometimes get confused. But we can get back on track. The following is where I first learned relativity about frame being 4D.. so you guys are talking of 3D frame as simply coordinate, right). Anyway Martin Gardner of "Relativity Simply Explained" explained:

"The important point to grasp here is that the spacetime structure, the four-dimensional structure, of the spaceship is just as rigid and unchanging as it is in classical physics. This is the essential difference between the discarded Lorentz contraction theory and the Einstein contraction theory. For Lorentz, the contraction was a real contraction of a three-dimensional object. For Einstein, the "real" object is a four-dimensional object that does not change at all. It is simply seen, so to speak, from different angles. It's three-dimensional projection in space and its one-dimensional projection in time may change, but the four-dimensional ship of spacetime remains rigid.

Here is another instance of how the theory of relativity introduces new absolutes. The four-dimensional shape of a rigid body is an absolute unchanging shape. We can slice spacetime so the shape of a spaceship depends on the motion of the frame or reference from which we make the slice, but (as J.J.C. Smart writes in the introduction to his anthology, Problems of Space and Time), "the fact that we can take slices at different angles through a sausage does not force us to give up an absolute theory of sausages".

Agree with him? So the "frame" in "general frame", "Inertial frame", etc. are all 3D while the above is referring to a 4D "frame"? Ok. I guess where you first learned relativity can make impressions last.

 

[PeterDonis]

Agree with him?

Yes, his description does a good job of capturing the essence of the 4-D spacetime viewpoint. However:

So the "frame" in "general frame", "Inertial frame", etc. are all 3D while the above is referring to a 4D "frame"?

Not quite; a "frame" is a particular way of *describing* the 4-D spacetime by slicing it up (in Gardner's terminology) into 3-D slices (which are then called "surfaces of simultaneity" or "slices of constant time" or something like that) such that (a) each 3-D slice is labeled by a unique value of a fourth coordinate, "time" ("fourth" because it takes three coordinates to specify a point in each 3-D slice), and (b) each event in the spacetime appears in one and only one 3-D slice. Particular objects are then 4-D subregions of the whole 4-D spacetime, and different ways of slicing will "cut" the subregions at different angles, so the shapes of the slices of the objects will be different.

I'll briefly rephrase my previous descriptions of the types of frames in this terminology:

#1: A general "reference frame" imposes no constraints on how the slicing is done, as long as it meets the above requirements (a) and (b).

#2/#4: An "inertial frame" or "Lorentz frame" imposes the following additional constraints on the slices: (c) each 3-D slice is spatially flat, i.e., it's a Euclidean 3-space; (d) the spatial coordinates in the slices are assigned such that the spatial coordinates of any object that is moving inertially (i.e,. it feels no force--it is weightless) are linear functions of the time coordinate. (The coefficients in these linear functions are the "velocity components" in each spatial direction.)

As I noted before, in a flat spacetime, an inertial frame can cover the entire spacetime and meet the above requirements. In a curved spacetime, it can't; it can only cover a small local piece of the spacetime around a given event.

#5: A "rest frame" is an inertial frame that we choose such that (e) a particular object that we're interested in has spatial coordinates (0, 0, 0) in every 3-D slice (i.e., it is "at rest" at the origin at all times).

[Edit: I should also add that the 3-D slices have to be spacelike slices, which is implicit in Gardner's description.]

 

[stglyde]

I originally wrote: "Remember that my time now can't be compared to the time "now" at Alpha Centauri.. which is the essence of Spacetime. Hence you can't say my time now is instantaneous to the time "now" at alpha centari."

Sure you can. As long as you specify the reference frame you certainly can make such comparisons and statements. They are not invalid statements, just frame-variant.

I think some confusion of mine can be traced to Martin Gardner book "Relativity Simply Explained" when he mentioned:

"Now, according to the special theory there is no "preferred" frame of reference: no reason to prefer the point of view of one observer than than another. The calculations made by the fast-moving astronaut are just as legitimate, just as "true," as the calculations made by the slow-moving astronaut. There is no universal, absolute time that can be appealed to for settling the difference between them. The instant "now" has meaning only for the spot you occupy. You cannot assume that a "now" exists simultaneously for all spots in the universe".

DaleSpam, you are saying that a "now" can indeed exist simultaneously for all spots in the universe" contrary to what Martin said (?). So quantum entangelment is indeed simulaneous here and at the edge of the universe at "now" (meaning you can imagine someone doing something now at the edge of the universe and that is simulaneous to here on earth)?

 

[Dale]

I think some confusion of mine can be traced to Martin Gardner book "Relativity Simply Explained" when he mentioned:

I have not seen that book nor that author previously. It appears to be a pop-sci book, not a serious reference book.

DaleSpam, you are saying that a "now" can indeed exist simultaneously for all spots in the universe" contrary to what Martin said (?). So quantum entangelment is indeed simulaneous here and at the edge of the universe at "now" (meaning you can imagine someone doing something now at the edge of the universe and that is simulaneous to here on earth)?

Yes, except for the idea of the universe having an edge. However, I would strongly recommend that you learn some serious relativity before worrying about quantum mechanics. The entanglement question is a non-issue, but I think that you need quite a bit more background in both SR and QM, and SR is a far easier theory to begin with.

 

[stglyde]

I have not seen that book nor that author previously. It appears to be a pop-sci book, not a serious reference book.

Yes, except for the idea of the universe having an edge. However, I would strongly recommend that you learn some serious relativity before worrying about quantum mechanics. The entanglement question is a non-issue, but I think that you need quite a bit more background in both SR and QM, and SR is a far easier theory to begin with.

So Martin Gardner is wrong when he said that "You cannot assume that a "now" exists simultaneously for all spots in the universe"?? Maybe what he meant is that since information propagates at the speed of light.. we can't know. But it doesn't mean that "now" don't exist simultaneous for all spots in the universe... what matters is that we can imagine that the now here is the same as the now say 14 billion light years away. Agree?

 

[Dale]

I am not going to explicitly say that Martin Gardner is either wrong or right. (1) I haven't read the book, (2) it is a pop-sci book, (3) I don't know the context of the quote, and (4) he is not here to explain himself. Please don't ask me again. Since the book is not a valid mainstream reference it really isn't appropriate to discuss it in detail on this forum.

Neglecting gravitational effects, you can define an inertial frame of reference which extends infinitely in all three directions in space and infinitely into the future and past. In that frame there is one "slice" labeled by t="now". That slice extends infinitely in all three directions in space but only for one instant in time.

You can also define a different inertial frame which is moving at a constant velocity wrt the first. This frame is equally valid, but will slice things differently. The "now" slice of that frame will also extend infinitely in all three directions in space.

So as long as you define your frame you can talk about the simultaneity of distant events.

 

[PeterDonis]

"Now, according to the special theory there is no "preferred" frame of reference: no reason to prefer the point of view of one observer than than another. The calculations made by the fast-moving astronaut are just as legitimate, just as "true," as the calculations made by the slow-moving astronaut. There is no universal, absolute time that can be appealed to for settling the difference between them. The instant "now" has meaning only for the spot you occupy. You cannot assume that a "now" exists simultaneously for all spots in the universe".

What Gardner meant by this can be simply stated in the "slicing" language of previous posts: two observers who are in relative motion will slice up 4-D spacetime into 3-D slices at different angles. That means two events which lie in the same slice for one observer (i.e., happen at the same time in that observer's frame) will lie in *different* slices for the other observer (i.e., will happen at different times). "Now" is just a label for the particular slice corresponding to whatever time is the "current" time for a particular observer, so what is true for slices in general will be true for the "now" slice.

 

[stglyde]

Neglecting gravitational effects, you can define an inertial frame of reference which extends infinitely in all three directions in space and infinitely into the future and past. In that frame there is one "slice" labeled by t="now". That slice extends infinitely in all three directions in space but only for one instant in time.

You can also define a different inertial frame which is moving at a constant velocity wrt the first. This frame is equally valid, but will slice things differently. The "now" slice of that frame will also extend infinitely in all three directions in space.

So as long as you define your frame you can talk about the simultaneity of distant events.

Martin Gardner who is a physicist is describing something like this (although he gave another example). Supposed you can travel at the speed of light. From your frame of view, it would take you 0 second to reach the galaxy NGC 4203 that is 10.4 million light years away.. but for earth, millions of years have passed. Let's say the Earth got destroyed by china oversized nuclear arsenals 50 years after the traveller left. So from the frame of view of the traveller. He could say Earth got destroyed before he left (because his reaching NGC is simultaneous). For someone on earth. Earth got destroyed after he left. This is what Martin Garner meant the Now is not the same in the whole universe. But yet you said it can exist. Can you share the context of what you are saying with reference to this example about the traveller and NGC. How do you define an inertial frame that is common to the traveller traveling at lightspeed (or near the speed of light because I know nothing massive can move at the same of light) to the observer left on earth?

 

[Dale]

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.

 

[stglyde]

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.

 

[atyy]

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.

The only surviving form of LET is SR in a particular inertial frame. What do Maxwell's equations say the field of a moving charge in a particular inertial frame should be? See if this doesn't remind you of length contraction (set v=0.8): http://www.its.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html.

 

[PeterDonis]

Let's say the Earth got destroyed by china oversized nuclear arsenals 50 years after the traveller left. So from the frame of view of the traveller. He could say Earth got destroyed before he left (because his reaching NGC is simultaneous).

First of all, you admit that the traveller can't actually move at the speed of light, he can only get very close to it. Let's assume he moves at a speed such that, by his clock, it only takes him 1 second to get from Earth to NGC 4203.

Second, the traveller *cannot* say that the Earth got destroyed before he left, because the Earth was still there when he left; he was *at* Earth at that event, so anything that occurs on Earth after he leaves will be seen by him to have a later time than the event of his leaving. He will, however, see it take much less time for China to destroy the Earth; instead of 50 years, it will take a small fraction of a second.

How do you define an inertial frame that is common to the traveller traveling at lightspeed (or near the speed of light because I know nothing massive can move at the same of light) to the observer left on earth?

You don't, because they are in relative motion. The traveller's inertial frame is not the same as the Earth's inertial frame (or the inertial frame of anyone at rest on the Earth). They "slice" the 4-D spacetime up into 3-D slices at different angles. It would really help you to take a step back and think about what that means.

 

[stglyde]

Yes, his description does a good job of capturing the essence of the 4-D spacetime viewpoint. However:



Not quite; a "frame" is a particular way of *describing* the 4-D spacetime by slicing it up (in Gardner's terminology) into 3-D slices (which are then called "surfaces of simultaneity" or "slices of constant time" or something like that) such that (a) each 3-D slice is labeled by a unique value of a fourth coordinate, "time" ("fourth" because it takes three coordinates to specify a point in each 3-D slice), and (b) each event in the spacetime appears in one and only one 3-D slice. Particular objects are then 4-D subregions of the whole 4-D spacetime, and different ways of slicing will "cut" the subregions at different angles, so the shapes of the slices of the objects will be different.

I'll briefly rephrase my previous descriptions of the types of frames in this terminology:

#1: A general "reference frame" imposes no constraints on how the slicing is done, as long as it meets the above requirements (a) and (b).

#2/#4: An "inertial frame" or "Lorentz frame" imposes the following additional constraints on the slices: (c) each 3-D slice is spatially flat, i.e., it's a Euclidean 3-space; (d) the spatial coordinates in the slices are assigned such that the spatial coordinates of any object that is moving inertially (i.e,. it feels no force--it is weightless) are linear functions of the time coordinate. (The coefficients in these linear functions are the "velocity components" in each spatial direction.)

As I noted before, in a flat spacetime, an inertial frame can cover the entire spacetime and meet the above requirements. In a curved spacetime, it can't; it can only cover a small local piece of the spacetime around a given event.

#5: A "rest frame" is an inertial frame that we choose such that (e) a particular object that we're interested in has spatial coordinates (0, 0, 0) in every 3-D slice (i.e., it is "at rest" at the origin at all times).

[Edit: I should also add that the 3-D slices have to be spacelike slices, which is implicit in Gardner's description.]

Thanks for the clarifications. Do you have a book or something? You should write a book like "Idiot's Guide to Spacetime" or "Spacetime for Dummies". Why is there no such book when there are huge demands for it i wonder.


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.

 

[stglyde]

First of all, you admit that the traveller can't actually move at the speed of light, he can only get very close to it. Let's assume he moves at a speed such that, by his clock, it only takes him 1 second to get from Earth to NGC 4203.

Second, the traveller *cannot* say that the Earth got destroyed before he left, because the Earth was still there when he left; he was *at* Earth at that event, so anything that occurs on Earth after he leaves will be seen by him to have a later time than the event of his leaving. He will, however, see it take much less time for China to destroy the Earth; instead of 50 years, it will take a small fraction of a second.

This is a bad example.. i just don't want to quote in the book giving his original example. But altering the above example. Supposed initially NGC 4203 and Earth is at rest at a distance of 10.4 million light years (ignoring the motion of galaxies). Then you started your travel there from earth. And NGC 4203 got destroyed 100 years later in the rest frame of earth. But it took you 1 second to reach NGC 4203 from Earth . So in your frame and time. NGC 4203 was destroyed before you left Earth. In the frame of someone on earth. NGC 4203 was destroyed after you left Earth. I think this is a good example now. I'm having headache now thinking of all this thing that not even crazy people in the street imagine.

You don't, because they are in relative motion. The traveller's inertial frame is not the same as the Earth's inertial frame (or the inertial frame of anyone at rest on the Earth). They "slice" the 4-D spacetime up into 3-D slices at different angles. It would really help you to take a step back and think about what that means.

Yes I know and lorentz transformation can equalize it. But supposed the distance and speed is unknown. And there is no way to apply the Lorentz transformation. Then I guess they are completely lost not able to tell which is which. But if LET preferred frame can be distinguished. Then it can be known (but I know LET preferred frame is unknowable.. at least for now).

 

[PeterDonis]

Supposed initially NGC 4203 and Earth is at rest at a distance of 10.4 million light years (ignoring the motion of galaxies). Then you started your travel there from earth. And NGC 4203 got destroyed 100 years later in the rest frame of earth. But it took you 1 second to reach NGC 4203 from Earth . So in your frame and time. NGC 4203 was destroyed before you left Earth. In the frame of someone on earth. NGC 4203 was destroyed after you left Earth.

Yes, in this case, in your inertial frame while traveling from Earth to NGC4203, you would assign a "time" value to NGC4203 being destroyed that was before the time of your leaving Earth.

But supposed the distance and speed is unknown. And there is no way to apply the Lorentz transformation.

True.

But if LET preferred frame can be distinguished. Then it can be known (but I know LET preferred frame is unknowable.. at least for now).

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.

 

[Dale]

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.

The nucleus, the electrons, and all of their associated fields and interactions will also be length contracted. The result is that nothing will be noticeable within the moving frame. Light will still focus on the retina, enzymes will still catalyze their reactions, etc.

 

[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.