Having trouble understanding why FTL implies time travel

[Austin0]

=JesseM;2048835]It's been proven that EPR effects cannot be used for FTL communication according to orthodox QM

,
I would be interested in sources for this as I haven't encountered it. Any google hints would be appreciated , thanks.

 

[Dale]

But what if you have an inertial frame A with v< c and tachyons traveling v> c do think that clocks in A could not be synched by the light method using tachyons instead??

No, clocks could not be synchronized by tachyons any more than they could be synchronized by baseballs or proton beams today. The Einstein synchronization procedure relies on the fact that light has the same speed in all reference frames. Baseballs, protons, and tachyons do not have the same speed in different reference frames.

SO you think [SR] wouldn't apply to imaginary causal tachyons but would apply to imaginary time traveling tachyons ?

Yes, exactly.

 

[JesseM]

In principle I would [and have] agree
I agree that any event that could possibly occur would have coordinates.
The question of assigning specific coordinates to hypothetical events is the question I am posing.

That doesn't make any sense--the very idea of taking a hypothetical about physics as a premise is to imagine a universe where the hypothetical really occurs and see what consequences would follow in such a universe. If you are imagining a universe where FTL is still purely hypothetical, then you aren't taking FTL as a premise in the first place!

If gave the if-then conditional "if I was standing in the open and it was raining, then I would get wet", would you then disagree since hypothetical rain can't get people wet the way real rain does? Your own statement above appears every bit as senseless.

Once again I would [and have] in principle agree completely. But dt<dx is a range of possible coordinates and the methods and logic of assigning a specific quantitative dt is the core of the question.

Again that doesn't make any sense. If we have a general proof that for any set of coordinates that satisfy dx>dt in some inertial frame, there must then be an inertial frame where the events occur in reverse order, then naturally this proof would apply to whatever "specific quantitative dt" and dx you happen to imagine occurring in the hypothetical. Perhaps you are arguing that there would be some difficulty calculating dt in the first place, but that doesn't make sense either--you agreed earlier that in a relativistic universe we should be able to assign x and t coordinates to any event, so that means you can find the t coordinates of the event of the signal being sent and the event of the signal being received, and dt is just the second t coordinate minus the first t coordinate.

Do you realize these questions are a physics version of the classic "Do you like women , yes or no?" Well , yes
DO you think it is wrong to hit women, yes or no?"
Yes
"If you answered yes to the first two, then have you stopped beating your wife ,,,yes or no?"

That analogy doesn't make any sense, because there is no logical reason that answering yes to the first two questions would compel you to answer yes to the question about beating your wife. In contrast, I'm just trying to lead you through the inescapable logic of the proof, so I've specifically chosen questions such that if you answer yes to all of them, it becomes obvious that you have no choice but to answer yes to the question of whether the premises of SR and FTL signaling together imply the conclusion of backwards-in-time signaling.

Through the course of this discussion I think I have come to understand your point of view and can see how, from that perspective , some of what I have been saying would seem "illogical" . I also completely agree that in this situation with many if-conditional premises it is necessary to focus on the center. The premise/argument that
"the events had a dx of 20 and a dt of 10 in the first frame"
This is the focus , both the quantitative value of dt and also the assumption that was the basis of this assigment.

No, that particular value of dt is not the focus. As I said, it is easy to come up with a general mathematical proof that if the coordinates of two events in one frame are such that dx>dt, then it is always possible to come up with a velocity v such that when you use that v in a Lorentz transformation, the order of the two events is reversed in the second frame. Would you like to see this proof, or do you agree that such a general proof is possible?

If you do agree, then it should be easy to see that for any specific choice of coordinates for the transmission-event and the reception-event such that dx>dt--whether (0,0) and (20,10) or (50,70) and (60,79.999) or (-16.5,3000) and (501,3007)--it will be possible to find a different inertial frame where the events happen in reverse order according to t-coordinates assigned by the new frame.

Can I assume that if you had simply assigned a dt=(-10 ) in this premise that you would understand how I would see it as "including the conclusion in the premises" ??

Of course, but it is not obvious that the premise "FTL" is synonymous with the possibility that the reception-event happens before the transmission-event, while it is obvious that FTL should be synonymous with the notion that dx>dt in some inertial frame. Of course the point of the proof is to show that if you take SR as a premise, then the latter "obvious" implication of the premise FTL implies the former "not-so-obvious" implication of the premise FTL. That's the difference between a vacuous tautology and a non-vacuous proof where the conclusion is still logically implied by the premise but it may not be immediately obvious that it follows just by looking at the premises.

AS I understand your point; because the actual assignment dt=10 did not obviously imply time travel and therefore required a transformation between frames to arrive at dt=-10 there was no inclusion of this conclusion in the premises.
OK I can see your point, even if the two times are effectively the same through a simple transform and the only real difference is that by deriving B from A instead of
A from B was ,,that this way it was not directly including the conclusion in the premises.

Yes, but again, in all mathematical proofs you can show that the conclusion is logically implicit in the premises, but in the case of non-vacuous proofs you have to go through some steps--like the "simple transform" above--to demonstrate this. Incidentally, for a specific choice of coordinates like (0,0) and (20,10) it's true that you just need to apply the transform with a particular choice of velocity to show that they can happen in reverse order in another frame, but it may not be obvious that for any choice of coordinates for the events such that dx>dt, it would always be possible to find a velocity such that when you plug that velocity and those coordinates into the Lorentz transform, the result is that the events happen in reverse order in the new frame. This is why I offered to provide a proof of this claim if you doubt it.

But in actuality there is reason to see ( dt=10 ) as directly indicating and requiring time travel. That for that dt to occur would mean going back in time 6 sec in frame A
That at t=0 ,x=0 x'=0, t'=0 from the perspective of frame B ( x=20) in A was colocated with x'=12 and had a time of t=16 AS frames always have local agreement and overall agreement this would seem to indicate a time discrepancy at x=20 from 16 --> 10 sec.=(-6)
What is your take on this?

Are you asking where the x=20 marking on A's ruler was at time t'=0 in B's frame? If so, yes, the answer is that it was next to the x'=12 mark on B's ruler, and at the moment the x=20 mark on A's ruler was passing next to the x'=12 mark on B's ruler, the clock attached to the x=20 mark on A's ruler must have read:

t = 1.666... *(0 + 0.8*12) = 16.

So, when you say "this would seem to indicate a time discrepancy at x=20 from from 16 --> 10 sec.=(-6)", are you talking about the time between the moment the clock at x=20 on A's ruler is next to the event of the tachyon signal being received, and the moment the clock at x=20 on A's ruler is next to the x'=12 mark on B's ruler? If so, then yes, according to A's clock at x=20, the event of the tachyon signal being received happens 6 seconds prior to the event of passing next to the x'=12 mark on B's ruler. Why do you bring this up? How is it relevant to the discussion?

That simply translates to "Well we know that time travel will happen in one frame so it must happen in all frames"

I am talking about an explicit premise IF a tachyon goes back in time 6 sec in frame A THEN time travel and how that would effect the significance of the overall argument.

Huh? The tachyon doesn't go back in time 6 seconds in A's frame. In A's frame, the event of the clock at x=20 passing next to the x'=12 mark on B's ruler is not simultaneous with the event of the tachyon signal being sent, these events are only simultaneous in B's frame. So, the fact that in A's frame the event of receiving the signal happens 6 seconds before the event of x=20 passing next to x'=12 in no way implies that the tachyon has gone backwards in time in this frame. In A's frame the order of the events is this:

t=0: tachyon signal emitted next to x=0 mark on A's ruler (and next to x'=0 mark on B's ruler)
t=10: tachyon signal received next to x=20 mark on A's ruler (and next to x'=20 mark on B's ruler)
t=16: x=20 mark on A's ruler passes next to x'=12 mark on B's ruler

On the other hand, in B's frame the order of these events is this:

t'=-10: tachyon signal received next to x'=20 mark on B's ruler (and next to x=20 mark on A's ruler)
t'=0: tachyon signal emitted next to x'=0 mark on B's ruler (and next to x=0 mark on A's ruler), AND simultaneously at a different location, x'=12 mark on B's ruler is passing next to x=20 mark on A's ruler.

I assume that by now you understand about the relativity of simultaneity, so you should be able to see that the fact that those two events happen simultaneously at t'=0 in B's frame does not imply they should be simultaneous in A's frame.

The applicability of the addition of velocities equation.

There is absolutely no need to use the addition of velocities equation in the proof, you can just focus on the coordinates assigned to the events of the signal being sent and the signal being received. However, it's also not hard to show that if you take two events on the worldline of an object moving at constant speed, and calculate dx and dt between these events in one frame and define the velocity in that frame as dx/dt, then if you apply the Lorentz transformation to these two events and calculate dx'/dt' in the new frame, you will find that the velocities in the two frames are related by the velocity addition equation, even in the case that dx>dt (i.e. you are looking at the worldline of a tachyon). If you'd like to see a proof of this, just ask.

The overall results of the application of the basic assumption to bi-directional assigments and the many questions that arise from those results. Questions of logic, physics and conformity to the first postulate.

I don't understand what "bi-directional assignment" means, and I don't know what "questions of logic, physics and conformity to the first postulate" you're referring to. Let me restate the steps in the proof as clearly as I can, and since you've already said you agree with the first 4 steps, maybe you can point out specifically what step you have a problem with:

1. Given the premise SR, we must assume that any events can be assigned space and time coordinates x and t in any inertial frame.

2. Given the premise FTL, there must be some inertial frame where, if you have the coordinates (x1,t1) of the signal being sent and the coordinates (x2,t2) of the signal being received, then in units where c=1, dx=|(x2-x1)| > dt=|(t2-t1)|

3. Given the premise SR, the coordinates assigned to the same event by different inertial frames must be related by the Lorentz transform.

4. Given 2 and 3, if you have a signal such that dx>dt for the transmission-event and the reception-event in one inertial frame, it is always possible to find a new inertial frame such the reception-event happens at an earlier time than the transmission-event in the new frame.

5. By the first postulate of SR, if it is possible in one frame to send a tachyon signal in such way that the reception-event happens at an earlier time than the transmission-event in that frame, it must be possible in any frame to send a tachyon signal in such a way that the reception-event happens earlier than the transmission-event in that frame.

6. If it's possible in any frame to send a tachyon signal in such a way that the reception-event happens earlier than the transmission-event in that frame, then it must be possible for one observer to send a tachyon message to the other and the second to then send a tachyon reply in such a way that the event of the first observer receiving the reply lies in the past light cone of the event of the first observer sending the original message, which is a clear violation of causality in every frame.

Can you point to a specific step that you disagree with here, where you think that it doesn't follow from the previous steps and the original premises of SR and FTL?

 

[Austin0]

=JesseM;2050830]


Huh? The tachyon doesn't go back in time 6 seconds in A's frame.

There is absolutely no need to use the addition of velocities equation in the proof, you can just focus on the coordinates assigned to the events of the signal being sent and the signal being received. However, it's also not hard to show that if you take two events on the worldline of an object moving at constant speed, and calculate dx and dt between these events in one frame and define the velocity in that frame as dx/dt, then if you apply the Lorentz transformation to these two events and calculate dx'/dt' in the new frame, you will find that the velocities in the two frames are related by the velocity addition equation, even in the case that dx>dt (i.e. you are looking at the worldline of a tachyon). If you'd like to see a proof of this, just ask.

No that is not necessary I have confirmed that for myself.

I don't understand what "bi-directional assignment" means, and I don't know what "questions of logic, physics and conformity to the first postulate" you're referring to. Let me restate the steps in the proof as clearly as I can, and since you've already said you agree with the first 4 steps, maybe you can point out specifically what step you have a problem with:

Perhaps I should say omnidirectional if a frame is considered at rest.
Without SR the concept of light being measured at the same speed traveling in the same direction as the inertial frame as it is measured traveling counter to the motion of the frame is a logical impossibility yes? SR provided a rational consistent explanation for how this was possible through the desynchronization of clocks. Correct??
Or do you have a different understanding?

Without this desynchronization the difference in the "bi-directional" measurements would reveal the motion of the system. Correct??

1. Given the premise SR, we must assume that any events can be assigned space and time coordinates x and t in any inertial frame.

2. Given the premise FTL, there must be some inertial frame where, if you have the coordinates (x1,t1) of the signal being sent and the coordinates (x2,t2) of the signal being received, then in units where c=1, dx=|(x2-x1)| > dt=|(t2-t1)|

3. Given the premise SR, the coordinates assigned to the same event by different inertial frames must be related by the Lorentz transform.

4. Given 2 and 3, if you have a signal such that dx>dt for the transmission-event and the reception-event in one inertial frame, it is always possible to find a new inertial frame such the reception-event happens at an earlier time than the transmission-event in the new frame.

5. By the first postulate of SR, if it is possible in one frame to send a tachyon signal in such way that the reception-event happens at an earlier time than the transmission-event in that frame, it must be possible in any frame to send a tachyon signal in such a way that the reception-event happens earlier than the transmission-event in that frame.


If it's possible in any frame to send a tachyon signal in such a way that the reception-event happens earlier than the transmission-event in that frame, then it must be possible for one observer to send a tachyon message to the other and the second to then send a tachyon reply in such a way that the event of the first observer receiving the reply lies in the past light cone of the event of the first observer sending the original message, which is a clear violation of causality in every frame.

Can you point to a specific step that you disagree with here, where you think that it doesn't follow from the previous steps and the original premises of SR and FTL?

5) Above : It is not that I disagree with this at all. But you have just finished telling me how the reception event in frame A didnt occur earlier than the transmission event in that frame so how does this conform to the 1st postulate as you have outlined in 5)


How do you se this one:
The 1st P allows us to track a photon trans-reception happening in another frame , to observe this reception event and have complete agreement between frames. Correct??
In this case assume a photon flash was emitted simultaneous with the tachyons in A.
We can be sure that an observer in B at x'=6 could look over and observe the photon reception in A at x=10 , t=10 Correct??
Now instead of dx/2c=(dt=5) to derive tachyon time,, we instead do the equally valid ((dt=10)2c)=(dx=20) and derive the distance at that same time.
Make the normal assumption that traveling twice as fast as a photon it would cover twice the distance in the same time. From this we know that an observer in B at x'=12 should be able to look over and see the event of the tachyon reception at x=20 at t=25.99 True?

I am not saying I think this is any more valid than the former. Obviously it also makes no sense that a tachyon at 2c would take longer than a photon to reach that distance.
But as I understand the 1st P all valid physics principles should apply and produce agreement between frames. SO this seems to be a problem here where there are no problems whatever when dealing with v<or=c

As you yourself have pointed out [with the exception of light] any particle having a measured speed x in one frame cannot have the same measured speed in another frame.
Yet here we have an equal speed of 2c in both frames ,correct? Another instance where the specific values do not comply with the normal principles .


Would you agree that according to the principles of ballistic mechanics as applied to different inertial frames the closing velocity of a projectile wrt an observer frame Cw=(u+v)
must necessarily be greater than the parrallel relative velocity Pw=(u-v ) ?
That this relationship should carry through and hold with any transformation??
Would you agree?

As far as I can see it does hold true with the addition of velocities formula with all v< c
but it does not hold true for v=2c where (u+v)/ 1+uv < (u-v)/1-uv
It seems to me that this is a definite violation of the 1st P and that the conclusion from this would be that the addition formula also does not apply , just like the math for an inertial frame does not apply with v>c This seems to be clearly not physics as usual. Not to mention not logical. Or would you disagree?
I am pressed for time but I am thinking about your points. Thanks

 

[Austin0]

=DaleSpam;2050736]No, clocks could not be synchronized by tachyons any more than they could be synchronized by baseballs or proton beams today. The Einstein synchronization procedure relies on the fact that light has the same speed in all reference frames. Baseballs, protons, and tachyons do not have the same speed in different reference frames.

How do you think that light could possibly have the same speed in all directions in all frames if it weren't for clocks being desynchronized the exact right amount to make this possible?
Would you not agree that in any frame with any motion the light method actually assures desynchronization not synchronization?

 

[Austin0]

=Fredrik;2049132]No. Look at my previous reply to you (included below for completeness). If u, v and w are defined as in that post, the derivation of the velocity addition formula goes like this:

The slope of the tachyon's world line is 1/v in F' and 1/w in F. That means that the Lorentz transformation

$$\gamma\begin{pmatrix}1 & u\\ u & 1\end{pmatrix}$$

must take $$\begin{pmatrix}1\\ v\end{pmatrix}$$ to a vector proportional to $$\begin{pmatrix}1\\ w\end{pmatrix}$$. That's all we need to find w:

$$\gamma\begin{pmatrix}1 & u\\ u & 1\end{pmatrix}\begin{pmatrix}1\\ v\end{pmatrix} =\gamma\begin{pmatrix}1+uv \\ u+v\end{pmatrix} =\gamma(1+uv)\begin{pmatrix}1 \\ \frac{u+v}{1+uv}\end{pmatrix}$$

So w must be what I said before:

I thought this:
1) the gamma factor did not show up directly in the additions formula
2) the denominator in both equations looked very similar except for the sqrt operator.
I jumped to the conclusion that both u and v had been entered but that the sqrt operator had been eliminated in the course of the derivation.
I was wrong ,,not only in this conclusion but also in not taking the time to work it through before putting it out and wasting your time. For that I apologize.
My matrix math is a hazy memory so I can't follow the derivation well enough to understand how it manages to eliminate the gamma factor but that is a math mystery for another time

No. That doesn't even make sense. Lorentz and Gallilean transformations have one thing in common: they both represent a coordinate change from one inertial frame to another, but the term "inertial frame" doesn't mean the same thing in those two contexts.

Arent the definitions essentially the same?? A state of uniform [non accelerated ] motion, the difference being the added SR condition of flat space-time and the Lorentz math?

 

[Fredrik]

Arent the definitions essentially the same?? A state of uniform [non accelerated ] motion, the difference being the added SR condition of flat space-time and the Lorentz math?

The basic idea is the same in SR and pre-relativistic physics, but the details are different. Consider the properties of functions that represent a change of coordinates from one inertial frame F to another inertial frame F':

1. They are smooth functions (i.e. they can be differentiated as many times as you want).
2. They take straight lines to straight lines.
3. They take each 3-plane that's orthogonal to the 0 axis of F to a plane that's orthogonal to to the 0 axis of F'.

All of these hold in both theories, but the word "orthogonal" doesn't mean the same thing in both cases. In SR, we're talking about orthogonality with respect to the Minkowski metric instead of with respect to the Euclidean metric.

 

[Fredrik]

My matrix math is a hazy memory so I can't follow the derivation well enough to understand how it manages to eliminate the gamma factor but that is a math mystery for another time

The definition of the product of two matrices is just

$$(AB)_{ij}=\sum_k A_{ik}B_{kj}$$

where e.g. $A_{ik}$ is the entry on row i, column k of the matrix A. So in the special case where A is a 2x2 matrix and B a 2x1 matrix, we get

$$\begin{pmatrix}a & b\\ c & d\end{pmatrix}\begin{pmatrix}x\\ y\end{pmatrix}=\begin{pmatrix}ax+by\\ cx+dy\end{pmatrix}$$

 

[Dale]

How do you think that light could possibly have the same speed in all directions in all frames if it weren't for clocks being desynchronized the exact right amount to make this possible?

The two-way speed of light is isotropic, constant, and frame invariant regardless of your synchronization procedure. The Einstein synchronization procedure just makes the one-way speed match the two-way speed.

 

[JesseM]

Without SR the concept of light being measured at the same speed traveling in the same direction as the inertial frame as it is measured traveling counter to the motion of the frame is a logical impossibility yes? SR provided a rational consistent explanation for how this was possible through the desynchronization of clocks. Correct??

Yes, although the clocks are only "desynchronized" in the frame where they are moving of course.

Without this desynchronization the difference in the "bi-directional" measurements would reveal the motion of the system. Correct??

Yes, if all frames agreed on what it meant for clocks to be synchronized (i.e. if they all agreed about simultaneity), then it would be impossible for light to have the same speed in both directions in all frames. I still don't really understand what your original comment "The overall results of the application of the basic assumption to bi-directional assigments and the many questions that arise from those results." Application of what basic assumption? And what does "the basic assumption to bi-directional assignments" mean? I understand that in the context of light you are using "bi-directional" to mean measuring the speed of light in both directions is, but I don't understand what "bi-directional assignments" are. What is being assigned, and what is it being assigned to?

1. Given the premise SR, we must assume that any events can be assigned space and time coordinates x and t in any inertial frame.

2. Given the premise FTL, there must be some inertial frame where, if you have the coordinates (x1,t1) of the signal being sent and the coordinates (x2,t2) of the signal being received, then in units where c=1, dx=|(x2-x1)| > dt=|(t2-t1)|

3. Given the premise SR, the coordinates assigned to the same event by different inertial frames must be related by the Lorentz transform.

4. Given 2 and 3, if you have a signal such that dx>dt for the transmission-event and the reception-event in one inertial frame, it is always possible to find a new inertial frame such the reception-event happens at an earlier time than the transmission-event in the new frame.

5. By the first postulate of SR, if it is possible in one frame to send a tachyon signal in such way that the reception-event happens at an earlier time than the transmission-event in that frame, it must be possible in any frame to send a tachyon signal in such a way that the reception-event happens earlier than the transmission-event in that frame.

If it's possible in any frame to send a tachyon signal in such a way that the reception-event happens earlier than the transmission-event in that frame, then it must be possible for one observer to send a tachyon message to the other and the second to then send a tachyon reply in such a way that the event of the first observer receiving the reply lies in the past light cone of the event of the first observer sending the original message, which is a clear violation of causality in every frame.

Can you point to a specific step that you disagree with here, where you think that it doesn't follow from the previous steps and the original premises of SR and FTL?

5) Above : It is not that I disagree with this at all. But you have just finished telling me how the reception event in frame A didnt occur earlier than the transmission event in that frame so how does this conform to the 1st postulate as you have outlined in 5)

5) just said it would be possible to send a different tachyon signal that goes back in time in A's coordinates, it doesn't say that that specific tachyon signal (the one that was sent at (0,0) and received at (20,10) in A) is going back in time in A's coordinates. As an analogy, if I see a missile moving at 0.5c in my frame, and in your frame I am moving at 0.5c in the same direction so in your frame the missile is moving at (0.5c + 0.5c)/(1 + 0.5*0.5) = 0.8c, then by the first postulate it must be possible for me to see a missile moving at 0.8c in my frame...but this doesn't mean that particular missile should be measured to be moving at 0.8c in my frame, since I already measured it to be moving at 0.5c in my frame. The first postulate just implies I could send out a different missile which would be moving at 0.8c in my frame, and similarly the first postulate implies A could see a different tachyon signal which was received before it was transmitted in A's frame.

How do you se this one:
The 1st P allows us to track a photon trans-reception happening in another frame , to observe this reception event and have complete agreement between frames. Correct??

I understand what you're saying, but your language is confused here, the events of a photon being sent and received don't happen "in" any particular frame, they're just events, different frames assign them different coordinates. The second postulate (is that what you meant to write?) does say that if one frame finds that dx=dt for two events (in units where c=1, so both events would lie on the worldline of a photon), then another frame will also find that dx'=dt' when it looks at the same events in its own coordinates.

In this case assume a photon flash was emitted simultaneous with the tachyons in A.
We can be sure that an observer in B at x'=6 could look over and observe the photon reception in A at x=10 , t=10 Correct??

What do you mean by "look over"? If you're talking about a local observation, the reception event wouldn't happen next to x'=6 in B's frame, it'd happen next to x' = 1.666..*(10 - 0.8*10)=3.333... in B's frame (and so naturally it'd also happen at t'=3.333... in B's frame).

Now instead of dx/2c=(dt=5) to derive tachyon time,, we instead do the equally valid ((dt=10)2c)=(dx=20) and derive the distance at that same time.

Distance at the same time in whose frame? Since you're using A's dt of 10 I assume you mean A's frame here...it's true that in A's frame, the event of the photon being received at x=10, t=10 is simultaneous with the event of the tachyon being received at x=20, t=10. But of course, these two reception-events are not simultaneous in B's frame, where the photon reception-event happens at t'=3.333... while the tachyon reception-event happens at t'=-10. If you want to assume the tachyon signal was just measured to be passing by the origins of the two frames rather than actually being emitted at that point, then we could say that in B's frame at t'=3.333... the tachyon would have been at position x'=-6.666... (and in A's frame, this event on the tachyon's worldline would be at x=-6.666..., and t=-3.333...)

Make the normal assumption that traveling twice as fast as a photon it would cover twice the distance in the same time. From this we know that an observer in B at x'=12 should be able to look over and see the event of the tachyon reception at x=20 at t=25.99 True?

No, that doesn't make any sense. First of all, the tachyon is only "traveling twice as fast as a photon" in A's frame, that doesn't necessarily mean it is traveling twice as fast in other frames since a tachyon's speed would not be frame-invariant (in fact in B's frame it happens to be true that it is, although in B's frame the tachyon seems to be traveling in the opposite direction, so its velocity is different even if its speed is not). Second, where exactly did you get t=25.99? I don't get your argument at all.

I am not saying I think this is any more valid than the former. Obviously it also makes no sense that a tachyon at 2c would take longer than a photon to reach that distance.
But as I understand the 1st P all valid physics principles should apply and produce agreement between frames. SO this seems to be a problem here where there are no problems whatever when dealing with v<or=c

Since your argument doesn't make any sense to me I'd guess you've just made a mistake somewhere, but I can't tell where your mistake is unless you actually explain the argument in detail instead of just throwing out random numbers.

As you yourself have pointed out [with the exception of light] any particle having a measured speed x in one frame cannot have the same measured speed in another frame.

No, I said it can't have the same speed in all frames. It is certainly possible for a single sublight object to be traveling at speed S in the +x direction in one frame and speed S in the -x direction in another frame (opposite velocities but same speed). In my example above with the missile moving at 0.5c in my frame but 0.8c in yours, in your frame I am moving at 0.5c in the +x direction, while in the missile's frame I am moving at 0.5c in the -x direction. This is the same sort of thing that's going on with the tachyon, since it's going at 2c in the +x direction in frame A and 2c in the -x' direction in B's frame (since in B's frame the tachyon is further in the -x' direction at later times--at t'=-10 it's at x'=20 but at t'=0 it's at x'=0).

Would you agree that according to the principles of ballistic mechanics as applied to different inertial frames the closing velocity of a projectile wrt an observer frame Cw=(u+v)
must necessarily be greater than the parrallel relative velocity Pw=(u-v ) ?

No. In the missile example above, in your frame the missile is moving at 0.8c while I am moving at 0.5c, so in your frame the closing velocity is 0.3c. But in my frame the velocity of the missile relative to me is 0.5c.

As far as I can see it does hold true with the addition of velocities formula with all v< c

You're neglecting to consider the fact that velocity can be negative in the case of an object moving in the -x direction instead of the +x direction.

It seems to me that this is a definite violation of the 1st P

Even if what you were saying was true, how would it be a violation of the first postulate? The first postulate doesn't say that the laws that tachyons follow should be identical to the laws that sublight particles follow, it just says that whatever laws tachyons are observed to follow in one inertial frame, they must follow the same laws in every other inertial frame.

 

[Austin0]

The two-way speed of light is isotropic, constant, and frame invariant regardless of your synchronization procedure. The Einstein synchronization procedure just makes the one-way speed match the two-way speed.

It is understood that the speed of light is isotropic,constant and frame invariant regardless of your synch procedure. Otherwise the motion of a frame would be detectable, yes?
The path length of a photon moving from the front of a moving system in the direction to the rear must necessarily be shorter than the path from the rear to the front, agreed??

In a reflected, two-way measurement this is not true. The path length and the measurement is the same in either direction , agreed?

So necessarily half of the two way measurement is not going to be the same as a one way measurement in either direction. Unless the clocks are desynchronized , with the clocks in the rear running ahead of the clocks in the front.
Yes?
If for instance two way measurements were made from the center. This information [dt/2]was then sent at c [radio] to the clocks at the front and rear . It would reach the rear faster and based on the assumption of [ dx/dt=c] the clock would be set ahead. The reverse being true in the other direction ,,,yes?
I was not suggesting that the clocks had to be light synchronized to produce the invariance , I assume that is definitely not the case. I was only pointing out that the light procedure would automatically produce the exact same degree of desynchronization.
As far as I can see this desynchronization is one of the universe's little tricks on us like time dilation and length contraction. A conspiracy to keep us from being able to determine absolute motion. Just kidding.

As far as I can see the mystery of the invariance of light , which certainly twisted my mind when I first encountered it through Micholson-Morley, is only rationally explained and made possible through SR and the conception of clock desynchronization. DO you have any other way to look at it or understand it?

 

[Dale]

It is understood that the speed of light is isotropic,constant and frame invariant regardless of your synch procedure. Otherwise the motion of a frame would be detectable, yes?
The path length of a photon moving from the front of a moving system in the direction to the rear must necessarily be shorter than the path from the rear to the front, agreed??

In a reflected, two-way measurement this is not true. The path length and the measurement is the same in either direction , agreed?

So necessarily half of the two way measurement is not going to be the same as a one way measurement in either direction. Unless the clocks are desynchronized , with the clocks in the rear running ahead of the clocks in the front.
Yes?
If for instance two way measurements were made from the center. This information [dt/2]was then sent at c [radio] to the clocks at the front and rear . It would reach the rear faster and based on the assumption of [ dx/dt=c] the clock would be set ahead. The reverse being true in the other direction ,,,yes?
I was not suggesting that the clocks had to be light synchronized to produce the invariance , I assume that is definitely not the case. I was only pointing out that the light procedure would automatically produce the exact same degree of desynchronization.
As far as I can see this desynchronization is one of the universe's little tricks on us like time dilation and length contraction. A conspiracy to keep us from being able to determine absolute motion. Just kidding.

As far as I can see the mystery of the invariance of light , which certainly twisted my mind when I first encountered it through Micholson-Morley, is only rationally explained and made possible through SR and the conception of clock desynchronization. DO you have any other way to look at it or understand it?

I'm sorry, but it is very difficult for me to understand what you are saying when you deliberately use non-standard terminology. As far as I can tell your "clock desynchronization" is what everyone else calls "the relativity of simultaneity", and your post is just a rough sketch of how to derive the relativity of simultaneity from the two postulates. If so, I agree.

But the point is, how could you use baseballs to synchronize clocks? If Alice is 10 m away from Bob and throws a baseball at Bob when her clock reads t0, what time should Bob set his clock to when he catches it? Because the speed of baseballs is not frame invariant you don't know. Similarly for tachyons.

 

[Austin0]

=DaleSpam;2052727]I'm sorry, but it is very difficult for me to understand what you are saying when you deliberately use non-standard terminology. As far as I can tell your "clock desynchronization" is what everyone else calls "the relativity of simultaneity", and your post is just a rough sketch of how to derive the relativity of simultaneity from the two postulates. If so, I agree.

I think there is a definite difference between the two concepts; Relativity of simultaneity and clock desynchronization.
Relative simultaneity is relevant to observations and the relationship between inertial frames.
Clock desynchronization must be viewed as an intrinsic reality because it occurs with regard to light ,which we consider the only actual constant velocity.
Ie. If you have a frame at some unknown state of motion, you then accelerate the system to a new steady velocity and measure light you get the same measurement. You then accelerate to a new velocity.,,etc etc.
Obviously there is no basis to determine a quantitative velocity for any of these stages but logiclly we can assume that they are all different in relation to light propagating in both directions along the same vector.
So if SR holds and light is constant the only possible explanation that I can see for the invariance of the measurements at these different velocities is that the clocks desynchronize proportionately. If you have a different explantion I would be interested to hear it.

But the point is, how could you use baseballs to synchronize clocks? If Alice is 10 m away from Bob and throws a baseball at Bob when her clock reads t0, what time should Bob set his clock to when he catches it? Because the speed of baseballs is not frame invariant you don't know. Similarly for tachyons

Actually if the 1st P holds you should be able to use any reasonable means to synchronize clocks.
For instance linear accelerators. The degree of desynchronization derived from this method would of necessity perfectly match that of light. If it didnt then physics would not be symetric and also the state of motion would be detectable.This is assuming of course that you have already determined a velocity through normal methods for a particle at a given energy /acceleration in some frame to apply to other frames.
The reason it would agree with light , as far as I can see, is because Newtonian ballistic mechanics, which is based on the complete isotropy of direction [ie. that an equal force is going to produce an equal acceleration of a particle with the motion of a system as counter to that motion] would not hold at relativistic velocities.
Acceleration forward would mean pushing a particle up the Lorentz mass slope with increasing energy demands for further acceleration ,while acceleration counter to the system motion would be down the slope with decreasing mass.
SO a particle moving forward would have a lower relative speed than a particle moving backward if accelerated with equal energy. But of course that is exactly what is required if the clocks in back are running ahead and the ones forward are behind.Just as a photon moving forward must take longer to reach the front which is moving away than to reach the rear..
But this could not hold for FTL because the clocks are not synchronized the necessary amount. So clocks synchronized with tachyons would not and could not agree with clocks synchronized with light or any sub c particle.

 

[Austin0]

Originally Posted by Austin0
Without SR the concept of light being measured at the same speed traveling in the same direction as the inertial frame as it is measured traveling counter to the motion of the frame is a logical impossibility yes? SR provided a rational consistent explanation for how this was possible through the desynchronization of clocks. Correct??

=JesseM;2051784]Yes, although the clocks are only "desynchronized" in the frame where they are moving of course.

You mean they are only perceived to be desynchronized from a frame which is moving wrt them,,,right?
That they are not perceived to be desynched in the frame in which they are at rest.
I agree,,,the desynchronization ,just like motion is undetectable.
But it must still be assumed to be present to explain the invariant measurement of the speed of light. Without reference to any other frame but only in relation to light a single frame at any possible velocity will measure the same speed .
How do you explain this or consider it possible if the clocks are not desynchronized by comparable degrees for each of these different velocities?
Obviously it is not possible to assume any quantitative velocity for a single frame but only the general logical assumption that the velocities must be different wrt the only constant we know , the propagation of light.

Yes, if all frames agreed on what it meant for clocks to be synchronized (i.e. if they all agreed about simultaneity), then it would be impossible for light to have the same speed in both directions in all frames.

I still don't really understand what your original comment "The overall results of the application of the basic assumption to bi-directional assigments and the many questions that arise from those results." Application of what basic assumption? And what does "the basic assumption to bi-directional assignments" mean? I understand that in the context of light you are using "bi-directional" to mean measuring the speed of light in both directions is, but I don't understand what "bi-directional assignments" are. What is being assigned, and what is it being assigned to?

The basic assumption is : The assumption that a velocity of 2c could be assigned on the basis of the rational 1/2 of the dx/dt for c,,, in frame A.
For the purposes of analysis I have taken the liberty of assuming that this should apply in the same way in the opposite direction and since you seem to be applying Newtonian mechanics to a FTL particle this should be valid,,,,,, yes?

5. By the first postulate of SR, if it is possible in one frame to send a tachyon signal in such way that the reception-event happens at an earlier time than the transmission-event in that frame,

5) just said it would be possible to send a different tachyon signal that goes back in time in A's coordinates, it doesn't say that that specific tachyon signal (the one that was sent at (0,0) and received at (20,10) in A) is going back in time in A's coordinates

.


Austin0
The 1st P allows us to track a photon trans-reception happening in another frame , to observe this reception event and have complete agreement between frames. Correct??

I understand what you're saying, but your language is confused here, the events of a photon being sent and received don't happen "in" any particular frame, they're just events, different frames assign them different coordinates. The second postulate (is that what you meant to write?) does say that if one frame finds that dx=dt for two events (in units where c=1, so both events would lie on the worldline of a photon), then another frame will also find that dx'=dt' when it looks at the same events in its own coordinates.

I understand the semantic difference but is it important? Abstraction is a powerful tool but is reducing events to pure numbers necessarily useful?? Wouldnt you agree that for pedagogical purposes, for communication and even for conceptualization it is sometimes better to see things in a more natural context??
In any case it is not the 2nd P I was referring to ,, although it goes without saying both frames will agree on c.
I ws talking about the workings of the system which allows the analysis of phenomena
from the perspective of different frames and have complete agreement, to apply physics and rational assumptions and achieve rational results.

What do you mean by "look over"? If you're talking about a local observation, the reception event wouldn't happen next to x'=6 in B's frame, it'd happen next to x' = 1.666..*(10 - 0.8*10)=3.333... in B's frame (and so naturally it'd also happen at t'=3.333... in B's frame).

OUCH! This time I truly came out with nonsense. I somehow managed to completely forget about time and jumped to the absurd direct gamma (x=10) ==> x'=6,,,, obviously from this beginning everything following is to be disregarded.
The dilemma of my current life is that I am too pressed to carry on this discussion but too involved to put it on hold and stop thinking about it. Sorry.

 

[Austin0]

I'm sorry, but it is very difficult for me to understand what you are saying when you deliberately use non-standard terminology. As far as I can tell your "clock desynchronization" is what everyone else calls "the relativity of simultaneity", and your post is just a rough sketch of how to derive the relativity of simultaneity from the two postulates. If so, I agree.

But the point is, how could you use baseballs to synchronize clocks? If Alice is 10 m away from Bob and throws a baseball at Bob when her clock reads t0, what time should Bob set his clock to when he catches it? Because the speed of baseballs is not frame invariant you don't know. Similarly for tachyons.

Hi Dale If Alice has an ideally consistant fast ball that always travels 60mph in one frame
wouldn't it be expected that whatever relative frame she was placed in, the rulers and clocks within that frame would measure her throws at 60mph?

So if in some frame, a clock was placed 176ft away from another clock and a ball was clocked at t=10 by the frist clock and arrived at the second [unsynched clock] at t=49
it would be calculated that the passage should take 2 seconcds and arrive at clock 2 at t=12 so therefore clock2 was 37 secs fast and being set back that amount should then be in synch with clock 1 and would then measure light or any other phenomena just the same as any of the other clocks in that frame.
Is this not correct??
Of course baseballs would not be frame invariant like light as far as being measured the same from other outside frames but they should be invarient just like the rest of physics within fames of differing velocities. For synchronization purposes this is what's important , right??
As for my terminology; I learned what I know of SR by myself, until I discovered this forum there was never anyone with either the understanding or interest for me to discuss these things with so I am just learning the terminology and forms in common use. I am learning as fast as I can Thanks for your parience

 

[Austin0]

Yes, although the clocks are only "desynchronized" in the frame where they are moving of course.

The paradox of the invariance of light drove me crazy until I knew enough about SR and clock desynchronization to come to a consistant explanation through that clock desynchronization. As I learned this by myself , before I discovered this forum, I assumed that this was the same explanation that everyone else arrived at.
If this is not the case I would very much appreciate knowing what the other explanation might be.
How a system that is accelerated to a different steady velocity can still measure the speed of light at the same value.
Thanks