Having trouble understanding why FTL implies time travel

[JesseM]

[
So are you saying that given the coincidence of( t=0 at x=0 )and (t'=0 at x'=0) and assuming the same, at rest ,metric, you could NOT apply the trasnsformation and determine that x'=15 would at that T be positioned at x=12 in A ?

You're being kind of vague, "apply the transformation" to what, exactly? You can only apply the Lorentz transformation to a pair of x,t coordinates (or x',t' coordinates) representing a single event, to find the coordinates of that same event in another frame. So what event are you interested in, and what coordinates does it have in B, that would give x=12 in A when you apply the transformation? Note that when you go back from B to A, since in B's frame A is moving in the -x' direction rather than the +x' direction, the Lorentz transformation will look a little different:

x = gamma*(x' + vt')
t' = gamma*(t' + vx'/c^2)

The only two events I was interested in where the event of the tachyon signal being sent and the event of it being received, and neither had position coordinate x=12 in A.

Are you saying that you could NOT calculate the degree of desynchronization at time t'=0 at x'=0 for a clock located at x'=15 in B ?

Whose clock? In B's frame, all of B's own clocks--which are used to define the t' coordinate of events that take place next to any given clock of B's--are synchronized. Are you asking what B's clock at x'=15 would see if it looked at A's clock right next to it at time t'=0? If so you're not expressing yourself very clearly, and I also don't really see the relevance of that question, but it can certainly be calculated using the Lorentz transformation.

By the way, I also realized I messed up the math somewhat before, if the velocity is 0.8c then gamma should be 1.666..., not 1.25 (I was thinking of the fact that with a velocity of 0.6c you get sqrt(1 - 0.6^2) = 0.8, so gamma = 1/0.8 = 1.25 in this case). So if the event of the signal being received has coordinates x=20, t=10 in A, the coordinates of this event in B are:

x' = 1.666...*(20 - 0.8*10) = 20
t' = 1.666...*(10 - 0.8*20) = -10

So if you restate your question in terms of these corrected coordinates, are you asking what B's clock at x'=20 will see at t'=0 if it looks at the clock of A right next to it? If so, applying the Lorentz transformation to this case gives:

x = 1.666...*(20 + 0.8*0) = 33.333...
t = 1.666...*(0 + 0.8*20) = 26.666...

So, if B's clock at x'=20 looks at the clock of A that's right next to it at t'=0, it'll see the clock attached to the x=33.333... mark on A's ruler, and that clock will be reading t=26.666... seconds.

Ay, there's the rub. Proving that FTL signalling would go back in time in ANY frame.
It appears to me that you and others who have proposed this hypothesis have set out with two a priori assumptions:
(1) FTL signals go back in time.

I certainly don't think an individual FTL signal is objectively going forwards or backwards in time; different frames disagree about whether the event of it being received happens before or after the event of it being sent, because of different definitions of simultaneity, and there can be no objective truth in relativity about frame-dependent questions. However, if you assume the first postulate of relativity holds (that the laws of physics work identically in all the different frames given by the Lorentz transform), then it must be possible to send a pair of FTL signals between two observers A and B moving away from each other such that the first one goes forwards in time in A's frame but back in time in B's frame, then B's reply goes forward in time in B's frame but backwards in time in A's frame, such that both frames agree that A gets B's reply before A sent the original signal. This is a widely recognized consequence of FTL signalling + the first postulate of relativity, it's a thought-experiment sometimes known as the "tachyonic anti-telephone", see my post #30 to Max where I linked to a physics paper that mentions it.

(2) That block time is an accepted physical reality.

No philosophical assumptions are required, it's just a straightforward consequence of the fact that some observers will measure an FTL signal to be received at an earlier time than it's sent in their coordinate system, combined with the assumption of the first postulate of relativity which says that any measurements obtained in one coordinate system during a given experiment can be repeated in a different coordinate system with an analogous experiment. The first postulate says that if you perform any experiment, then whatever observations you get about the results of the experiment in one frame (in terms of that frame's coordinates), it must always be possible to perform an analogous experiment which gives the same results in some other frame (in terms of that frame's own coordinates). See my comments to RandallB earlier:

Just to be clear, when I say "same experiment", I mean that whatever the coordinates of events that take place in the first experiment as seen in the first frame, one can run a second experiment such that identical events happen at the same coordinates in the second frame. For instance, suppose in frame A you have a clock which starts at position x=5 light-seconds, t=10 seconds with the clock reading T=30 seconds, and the clock is moving at 0.8c in the +x direction of frame A so it'll be at position x=13 light-seconds at time t=20 seconds, and because of time dilation it only reads T=36 seconds at that point. Do you agree that the first postulate automatically implies we can have a different clock moving at 0.8c in the +x' direction of frame B, which starts out reading T=30 seconds at x'=5 light-seconds and t'=10 seconds (in the x', t' coordinates of frame B), and then it must be true that the clock will read T=36 seconds at coordinates x'=13 light-seconds and time t'=20 seconds? If so, do you agree that any experiment in frame A can be replicated in this way in frame B, and vice versa?

Do you agree that this is an accurate description of the implications of the first postulate?

Forget for the moment the question of FTL signalling. Assume that A sends up a flare at the moment of transmission and B likewise sends up a flare on reception.
How is this situation any different from two lightning bolts in the classic demonstration of the relativity of simultaneity? How is the absolute chronology of these two events [flares] any more determinable than the absolute chronology of the two lightning bolts,, which appear simultaneous to a track observer while the train observer perceives the one at the front occurring before the back and some other observer would see the back occurring before the front?

I have never said anything about the "absolute chronology" of any two events. Again, there is no objective fact of the matter about whether the event of a given FTL signal being received happens at an earlier or later time than the event of that signal being sent, different frames disagree. However, if A can send a signal to B which travels forward in time at 2c as measured in A's frame, then the first postulate says it must be possible for B to send a reply to A which which travels forward in time at 2c as measured in B's frame. The consequence of this is that A's original message was traveling backwards in time in B's frame, and B's reply was traveling backwards in time in A's frame, and if the relative velocity between A and B is large enough then both frames agree that B's reply reaches A before A sent the original signal. This conclusion is an unavoidable result of the assumptions that FTL signaling is possible plus the first postulate of relativity; you can have FTL signaling without such causality violations only if you drop the first postulate of relativity and say that one of these observers is unable to send signals forward in time at 2c as measured in their own coordinates.

Maybe I should come up with a full numerical example to illustrate. To make the numbers a little easier, I'll assume that two observers A and B can both send signals forward in time at 5c in their own frames, and they are moving apart from one another at 0.6c. So, say A sends a signal at x=0,t=0 in the A frame and the signal is received by B at x=100,t=20 in the A frame. This means that in the B frame, the event of the signal being sent was x'=0,t'=0, while the event of it being received was:

x' = 1.25*(100 - 0.6*20) = 110
t' = 1.25*(20 - 0.6*100) = -50

In the B frame, we know A is moving in the -x' direction at 0.6c and was at position x'=0 at t'=0, so in this frame A's position as a function of time is x'(t') = -0.6*t'. If B sends an FTL signal in the -x direction at 5c from position x'=110 at t'=-50, then 50 seconds later at t'=0 the signal will have moved 5*50 = 250 in the -x direction, so it'll be at x'=110 - 250 = -140. So, the signal's position as a function of time is x'(t') = -5*t' - 140. So to figure out the coordinates in B that the reply catches up with A, just set -5*t' - 140 = -0.6*t', which gives -4.4*t' = 140, or t' = -31.8181... Since A's position as a function of time is -0.6*t' in this frame, the position of A in this frame when the reply reaches him must be x' = -0.6*-31.8181... = 19.0909...

So, in the B frame, A receives B's reply at (x'=19.0909..., t'=-31.8181...) which is earlier than the time A sent the original message at (x'=0, t'=0). You can use the Lorentz transform to find the time that A receives B's reply in the A frame:

x = 1.25*(19.0909.. + 0.6*-31.8181...) = 0
t = 1.25(-31.8181... + 0.6*19.0909...) = -25.4545...

So, you can see it's also true in the A frame that A received B's reply before A sent the original message. The only assumption being made here is that both of them can send a signal at 5c in their own frame.

 

[Austin0]

[

QUOTE=JesseM;2011725]You're being kind of vague, "apply the transformation" to what, exactly? You can only apply the Lorentz transformation to a pair of x,t coordinates (or x',t' coordinates) representing a single event, to find the coordinates of that same event in another frame. So what event are you interested in, and what coordinates does it have in B, that would give x=12 in A when you apply the transformation?

I thought it was assumed that you were doing this from the perspective of frame A.
That at x=0 and t=0 in A it was seen that x'=0 and t'=0 in B was coincident with that location and time in A.
That given that information in A it would be calculated that the clock located at x'= 15 in B would at that time [t=0 in A] read -12 So do you disagree with this ?
That an observer in A at x=12 ,t=0 would see a clock at x'=15 reading -12. No?

The only two events I was interested in where the event of the tachyon signal being sent and the event of it being received, and neither had position coordinate x=12 in A.

But in actuallity aren't there more than two relevant events to consider?
There is the event at time t=0 of the transmission.
There is the event of the reception at x'= 15 in B at time t'=-7.5 = [ t=10 in A]
There is the event of the observer at x'=15 looking at his clock and noting the time at time t=0 ,[the beginning of the exercise] Is this not correct?
So chronolgy of the events in B would be determined by comparison of the beginning and end time as perceived from a single clock at x'=15 in B.
Which in this case as calculated from A would be t'= -12 > -7.5 a forward progression of time. DO you disagree with this assessment?

Whose clock? In B's frame, all of B's own clocks--which are used to define the t' coordinate of events that take place next to any given clock of B's--are synchronized.

It appears that from the perspective of A you are deriving a time of reception in B at x'=15 of [-7.5]
and then suddenly assuming that the clocks in B are absolutely synchronized ie. That t'=0 at x'=0 means that at that time [the beginning t=0] that the clock at x'=15 also read t'=0
That based on this t'=0 > - 7.5, a backward progression of time. Is this your thinking?

.

However, if you assume the first postulate of relativity holds (that the laws of physics work identically in all the different frames given by the Lorentz transform),

That assumption is not in any way in question.

No philosophical assumptions are required, it's just a straightforward consequence of the fact that some observers will measure an FTL signal to be received at an earlier time than it's sent in their coordinate system,

To even seriously consider this question requires an assumption of the reality of an eternalist universe. That you ,in a physical sense, still exist, are present at breakfast this morning to be able to receive a back in time message from yourself ,warning you not to go out today because you're going to break a leg.
Without this assumption the whole question becomes moot, absurd.

The mathematical structure of SR , the lorentzian equations, were based on the invarience of c and c as a finte limit of velocity.
SO if you input a velocity of c or above, the system returns gibberish, infinities or imaginary numbers, without real world interpretation or meaning. Time itself is defined in terms of propagation at c. Clocks are synchronized on the basis of propagation at c.
So how can a system, within which, the very concept of FTL is meaningless , invalid, "garbage in" be expected to produce meaningful results from data derived from this idea. Be used to validate and prove conclusions based on premises "impossible" within the system itself?

 

[Fredrik]

To even seriously consider this question requires an assumption of the reality of an eternalist universe. That you ,in a physical sense, still exist, are present at breakfast this morning to be able to receive a back in time message from yourself ,warning you not to go out today because you're going to break a leg.
Without this assumption the whole question becomes moot, absurd.

SR is already a theory that describes time in an "eternalist" way, so it makes no sense to try to add eternalism as an separate axiom. Such concepts are mostly nonsense anyway. Time is a subject that should be dealt with by physicists, not by philosophers, and the way to deal with it is to find theories that accurately predict the results of experiments. Special relativity does that very well.

The mathematical structure of SR , the lorentzian equations, were based on the invarience of c and c as a finte limit of velocity.
SO if you input a velocity of c or above, the system returns gibberish, infinities or imaginary numbers, without real world interpretation or meaning.

No one here is doing that. Certainly not JesseM.

So how can a system, within which, the very concept of FTL is meaningless , invalid, "garbage in" be expected to produce meaningful results from data derived from this idea. Be used to validate and prove conclusions based on premises "impossible" within the system itself?

The concept of FTL speeds is not meaningless or invalid in SR. The fact that the velocity difference between two inertial frames can't be FTL doesn't in any way make it impossible for things to move at FTL speeds.

The paradox that JesseM describes is what makes it impossible for things to move at FTL speeds. You should think of it as a proof of the reductio ad absurdum variety. (But you should also be aware of the loophole. If the detection process is slow enough, it won't be possible for the other guy to send me the reply soon enough for me to receive the reply before I sent the original message).

 

[JesseM]

[
I thought it was assumed that you were doing this from the perspective of frame A.

What do you mean "from the perspective of"? I'm calculating the coordinates of the events in both frames--do you just mean that I'm assuming the signal is moving at 2c in the A frame?

That at x=0 and t=0 in A it was seen that x'=0 and t'=0 in B was coincident with that location and time in A.
That given that information in A it would be calculated that the clock located at x'= 15 in B would at that time [t=0 in A] read -12 So do you disagree with this ?

How could I have disagreed with this when you never specified before what coordinates you wanted to translate from one frame to another? Like I said, you were phrasing the question in a very vague way.

That an observer in A at x=12 ,t=0 would see a clock at x'=15 reading -12. No?

Can we use my revised numbers instead of these incorrect ones? As I said, I mistakenly thought that gamma for 0.8c would be 1.25, in fact at 0.8c gamma should be 1.666... instead. So, if the coordinates of the signal being received in A was x=20, t=10, in B the coordinates of the signal being received would x'=20, t'=-10. So in this case, would you be interested in what time the clock at x'=20 in B would show at t=0 in A? In this case the answer is it would show a time of t'=-16. In other words, if we look at the event x'=20, t'=-16 the corresponding coordinates in A would be:

x = 1.666... * (20 + 0.8*-16) = 12.
t = 1.666... * (-16 + 0.8*20) = 0.

Is this analogous to what you were asking? If so, what is the relevance of knowing the coordinates of this event in both frames, since it does not represent the event of the FTL signal being sent or received?

But in actuallity aren't there more than two relevant events to consider?
There is the event at time t=0 of the transmission.
There is the event of the reception at x'= 15 in B at time t'=-7.5 = [ t=10 in A]

Again, the corrected coordinates would be x'=20, t'=-10.

There is the event of the observer at x'=15 looking at his clock and noting the time at time t=0 ,[the beginning of the exercise] Is this not correct?

You can define an infinite number of events if you like--the observer at x'=20 looking at his clock at t'=0, then looking at his clock at t'=0.1, then looking at his clock at t'=0.2, etc. I don't see why these other events are interesting though, since they don't coincide with anything on the path of the FTL signal.

So chronolgy of the events in B would be determined by comparison of the beginning and end time as perceived from a single clock at x'=15 in B.
Which in this case as calculated from A would be t'= -12 > -7.5 a forward progression of time. DO you disagree with this assessment?

Certainly it is true that at t=0 in A, the clock of the observer at x'=20 in B reads t'=-16, so this in B (as well as A) this is prior to the event of the observer at x'=20 receiving the tachyon signal at t'=-10. Both of these two events lie on the worldline of the observer at x'=20, and this observer is moving slower than light, so of course both frames agree on the order of these two events, all frames always agree on the order of events on the worldline of any object moving slower than light (events that have what is called a 'timelike separation'). I still don't understand the relevance though--in B the event of the clock at x'=20 reading t'=-16 is not simultaneous with the event of the tachyon signal being sent like it is in A, because the two frames have different definitions of simultaneity (in B the event of the clock at x'=20 reading t'=0 is simultaneous with the event of the tachyon signal being sent at x'=0 and t'=0). Do you disagree that according to B's definition of simultaneity, the tachyon signal is sent at t'=0 but received at t'=-10? Do you agree that the first postulate of relativity implies that if a tachyon signal can be received 10 seconds before it's sent in B, it should be possible to create a different tachyon signal that's received 10 seconds before it's sent in A, since the first postulate says the laws of physics must work exactly the same in each frame?

It appears that from the perspective of A you are deriving a time of reception in B at x'=15 of [-7.5]
and then suddenly assuming that the clocks in B are absolutely synchronized ie. That t'=0 at x'=0 means that at that time [the beginning t=0] that the clock at x'=15 also read t'=0
That based on this t'=0 > - 7.5, a backward progression of time. Is this your thinking?

There is no such thing as "absolute synchronization", each frame has its own definition of synchronization, and the first postulate says that anything that's possible in the coordinates of one frame must be possible in the coordinates of any other frame (the laws of physics are identical in different frames). If we assume a tachyon signal traveling at 2c is received 10 seconds after it's sent according to A's definition of simultaneity, then using the Lorentz transformation we can see that the event of it being received happened 10 seconds before it was sent in B, do you disagree? Do you understand that neither view is "correct" in any absolute sense, that they are both equally valid ways of looking at the same event? To see a real physical causality violation, you need a pair of tachyon signals like the one I described in my second example from the previous post--if you look at the numbers there you see both frames agree the reply was received before the original signal was sent, even though the two frames disagree on whether it was the first signal or the reply that was going backwards in time.

To even seriously consider this question requires an assumption of the reality of an eternalist universe. That you ,in a physical sense, still exist, are present at breakfast this morning to be able to receive a back in time message from yourself ,warning you not to go out today because you're going to break a leg.
Without this assumption the whole question becomes moot, absurd.

Nonsense, it is simply a consequence of the first postulate and the assumption that FTL signals are possible. I suppose you could say that FTL signalling + the first postulate would imply eternalism (although some philosophers believe in backwards-in-time signals can be reconciled with a presentist metaphysics if you believe the future is already determined and thus the present can take into account future events even though they don't "exist" yet--see http://spot.colorado.edu/~monton/BradleyMonton/Articles_files/presentism%20CTC%20final.pdf), but you don't need to plug eternalism in there as a separate assumption.

If you disagree, take a look at my second numerical example involving a tachyon signal and a reply, and tell me which of the following steps requires us to assume anything beyond the first postulate and the idea of FTL signals:

1. If FTL signals moving at 5c are possible in A's rest frame, a signal could be sent at x=0, t=0 in A and be received at x=100, t=20 in A's frame.

2. If B moves at 0.6c relative to A, and is at the event of the signal being received, then by the Lorentz transformation the coordinates of the signal being are x'=0, t'=0 in B's rest frame, and the coordinates of it being received are x'=110, t'=-50 in B's frame.

3. By the first postulate of relativity, if it's possible to send a signal that moves at 5c in A's frame, it must be possible to send a different signal which moves at 5c in B's frame.

4. If B sends a reply at 5c in his frame immediately after receiving the signal from A, then the signal will reach A at coordinates x'=19.0909..., t'=-31.8181...

5. Using the Lorentz transform again, in A's frame the reply from B reaches A at coordinates x=0, t=-25.4545...

6. In both frames A received B's reply before A sent the original signal, so this is a genuine physical causality violation.

(By the way, I came up with an example of tachyon signalling with slightly simpler numbers in post #53 of this thread.)

The mathematical structure of SR , the lorentzian equations, were based on the invarience of c and c as a finte limit of velocity.
SO if you input a velocity of c or above, the system returns gibberish, infinities or imaginary numbers, without real world interpretation or meaning. Time itself is defined in terms of propagation at c. Clocks are synchronized on the basis of propagation at c.

The two postulates of SR only say that c is invariant, but they don't say that other objects or signals can't move faster than c (see this page for a discussion about how tachyons are not in principle incompatible with relativity, although virtually no physicists really think tachyons actually exist in the real world). You do get gibberish if you input a v=c into the Lorentz transformation itself because there is no such thing as an inertial frame moving faster than light, but in the analysis of the tachyon problem I've only analyzed the behavior of the tachyon signal from the perspective of sublight inertial frames, I've never suggested any notion of the tachyon signal having a rest frame of its own. This is similar to the way we can analyze the behavior of light signals from the perspective of sublight frames even though photons cannot have an inertial rest frame of their own.

 

[Austin0]

[=Fredrik;2012196]SR is already a theory that describes time in an "eternalist" way, so it makes no sense to try to add eternalism as an separate axiom.

I would appreciate it if you would care to elaborate on this point.
It leads me to question my understanding ,that I may be out of touch with the accepted interpretation of both SR and Minkowski space-time.
Self evidently SR refutes the idea of a universal present with agreement of clock time.
This is not in question. But how does eternalism fit into the system?
My understanding of the paradigm is that the time axis is explicit. That for any given point t on the axis, this denotes a singular ,specific time and place in the world line t' , x'.
That this is found by going directly horozontally from t > t' where it is assumed that t' is contemporaneously located at x'. Is this correct so far?
That planes or hypersurfaces of simultaneity refer to the perception of events , regarding their simultaneity or chronolgy as they will be perceived later when the information has propagated at c to their respective world lines.
It says nothing and implies nothing about their instantaneous or absolutely simultaeous temporal relationship.
Is this correct or not?
[/QUOTE]Such concepts are mostly nonsense anyway. Time is a subject that should be dealt with by physicists, not by philosophers. .[/QUOTE]
We are in agreement on this as far as philosophers have so far not produced anything particularly useful on this subject. On the other hand , until recently, physics has not really dealt with the subject , beyond defining a necessary variable t in terms of relative motion , beyond this ,it did not deem it either necessary or relevant to bother with conceptualizing or defining time itself and left this task to the philosophers. It seems to me that physics has reached a point where it needs to define both time and space in fundamental ways , at least theoretically if not empirically, if it is going reach any unified theory or understanding . That these are both completely open questions and are relevant to SR , GR , QM and cosmology.


Originally Posted by Austin0
The mathematical structure of SR , the lorentzian equations, were based on the invarience of c and c as a finte limit of velocity.
SO if you input a velocity of c or above, the system returns gibberish, infinities or imaginary numbers, without real world interpretation or meaning.

No one here is doing that. Certainly not JesseM.

WOuld I be correct in saying that events ,given that they are of sufficintly short duration,
say a tachyon burst, are not attached to specific frames but are equally validly attached to any frame. That for the purpose of this discussion, we could make it a tachyon bolt hitting x=0=X' at t= t' =0 between the two frames?
So from the perspective of frame B this is no different than measuring the velocity of a light burst. We don't need math to assume that in this case it would arrive at x=20 in B at x=20.
At 2c we can equally assume its arrival at t=10.
Obviously, not only does this time not agree with the figure -10 derived in frame A,
but at this time x'=20 in A is nowhere near.
So it would seem to be two incompatable realities.

It can also be seen that if we arbitrarily assign the time derived in A ie. t=-10,
then suddenly it is [as RandellB said ],like "magic" .
Now we find x'=20 in A right there at t= -10, while x'=0 in A has not yet arrived at the origen of B but will 10 seconds later ,right on time.
Marvelous. Both frames agree.
BUT WOuld you say that this was normal procedure in SR , to import data derived in one frame into another frame to achieve agreement?
Would you disagree when I say that you should be able to completely independently within each frame, arrive at this agreement?
Can you tell me how to ,either logically or mathematically, arrive at a time of t= -10 in A ,,working with the given data ,completely within that frame?

So it appears to me that there are two incompatible realities. Would this be due to a flaw or failure of the Lorentz structure or is it possible that we are simply assigning parameters , inputting data that the system is not setup to handle. Indirectly introducing velocity greater than c.
I would like to point out a curious coincidence. If we assume a time of t=10 in B,
this time would be exactly 10 sec. earlier [back in time ,,,-10 sec] from the time t=20 which is what would occur for a comparable photon signal. Which is the fastest time the system is setup to record for any possible velocity.
I haven't had time to do the math but I wouldn't be surprised to find that this would hold true for any v>c that you input for a tachyon. The system will produce numbers that only really make sense relative to the time of a comparable light signal.
As I suggested before the structure defines time on the basis of propagation at c.
I ask you to consider the method of clock synchronization and then tell me if you would disagree with that statement ?

The concept of FTL speeds is not meaningless or invalid in SR. The fact that the velocity difference between two inertial frames can't be FTL doesn't in any way make it impossible for things to move at FTL speeds.

The Lorentz structure is not setup to deal only with inertial frames, but also photons which do not have inertial frames ,correct?. I was not talking about the verbal , conceptual basis of SR but of the math itself.
I myself have no problem with the concept of FTL.
As I am sure you are aware this question is being probed in labs this very moment.
So far to me the results of EPR testing, down conversion crystal experiments etc. are far from convincing but they certaily hold open the possibiltiy that the questions under discussion FTL/time travel/ causality , will be empirically resolved in our lifetime.
I will mention one more thing. I have spent considerable time ,thinking about time.
The only result of that effort is an acute awareness that not only did I not gain any definte conclusions , I couldn't even come up with any clear conception or definition of the subject at all. To my knowledge no one else has been any more successful than I have been and all attempts in the end are either hopelessly self referential or are simply conceptions and descriptions of motion in some form, under another name and attributed with qualities that are once again undefined and unconceived.
So I do not accept any hard-edged ,definte presentist view of now which I suspect eventually QM is going to demonstrate is essentially not a reality. I also do not accept a physical interpretation of block time but I am not in a position to judge nor did I mean to suggest that it is wrong or any less possible than other alternatives. Only that is was at this time only a possibility not a reality. In my mind it is a truly open question on all levels.
Thanks

 

[Austin0]

Again, the corrected coordinates would be x'=20, t'=-10.

Certainly it is true that at t=0 in A, the clock of the observer at x'=20 in B reads t'=-16, so this in B (as well as A) this is prior to the event of the observer at x'=20 receiving the tachyon signal at t'=-10.

SO if both the observers (at x=12 at t=0 who observes x'=20 with a clock reading of t'= -16) and (at x=20 at time t=10 in A who observes x'=20 with a clock reading of t'=-10)
and x'=20 in B all agree that time moved forward between these events[observations]
what is the significance of an observer at x'=0 later concluding that according to B's clock system one event happened before another?
How is this different from the observer on the train concluding that the forward lightning bolt occurred before the rear?

I still don't understand the relevance though--in B the event of the clock at x'=20 reading t'=-16 is not simultaneous with the event of the tachyon signal being sent like it is in A, because the two frames have different definitions of simultaneity (in B the event of the clock at x'=20 reading t'=0 is simultaneous with the event of the tachyon signal being sent at x'=0 and t'=0). Do you disagree that according to B's definition of simultaneity, the tachyon signal is sent at t'=0 but received at t'=-10?

I do not understand how you can, completely within B, derive a signal arriving x'=20 at t'= -10.
Given that a signal originates at x=0=x' at t=0 = t' how do you justify not applying the same logic and assuming that it would arrive at t'=10 in B ? If you assume tachyons actually go back in time how do you logically propose a signal that goes back in time in one frame but forward in time in another frame , to a location which is spatially coincident upon reception?

Do you agree that the first postulate of relativity implies that if a tachyon signal can be received 10 seconds before it's sent in B, it should be possible to create a different tachyon signal that's received 10 seconds before it's sent in A, since the first postulate says the laws of physics must work exactly the same in each frame?

I completely agree. If it in fact actually would go back in time.

There is no such thing as "absolute synchronization", each frame has its own definition of synchronization,

No question there.
,

I've never suggested any notion of the tachyon signal having a rest frame of its own.

Me either.
thanks

 

[Fredrik]

I would appreciate it if you would care to elaborate on this point.

SR is a theory of physics that consists of a mathematical model of spacetime called Minkowski space and a set of postulates that identify things we measure with things in the model.

Note that Minkowski space is a model of all of spacetime. A theory can't get more "eternalistic" than that.

My understanding of the paradigm is that the time axis is explicit. That for any given point t on the axis, this denotes a singular ,specific time and place in the world line t' , x'.
That this is found by going directly horozontally from t > t' where it is assumed that t' is contemporaneously located at x'. Is this correct so far?

A (global) coordinate system is just a function that maps Minkowski space (viewed as a manifold) onto $\mathbb R^4$. So the coordinate system assigns four numbers (coordinates) to each event. One of them is the time coordinate. I'm not sure if that answers your question, because I don't fully understand the question.

That planes or hypersurfaces of simultaneity refer to the perception of events , regarding their simultaneity or chronolgy as they will be perceived later when the information has propagated at c to their respective world lines.
It says nothing and implies nothing about their instantaneous or absolutely simultaeous temporal relationship.
Is this correct or not?

Probably not, but I'm not sure I understand you. It sounds like you have misunderstood simultaneity. You always compensate for the propagation time of light in discussions about simultaneity. For example, if you emit light at t=-T, x=0, and you detect the light at t=T, x=0 after one reflection, the reflection event is simultaneous with t=0,x=0.

On the other hand , until recently, physics has not really dealt with the subject , beyond defining a necessary variable t in terms of relative motion , beyond this ,it did not deem it either necessary or relevant to bother with conceptualizing or defining time itself and left this task to the philosophers. It seems to me that physics has reached a point where it needs to define both time and space in fundamental ways , at least theoretically if not empirically, if it is going reach any unified theory or understanding.

I disagree. GR defines two time concepts in the framework of the mathematical model: coordinate time and proper time. It also defines time operationally as "what a clock measures", and postulates the relationship between these concepts. How is that "leaving the task to the philosophers"? Scientists haven't been able to find a better theory of time than GR, but it's not because they think such a theory would be unnecessary or irrelevant.

The mathematical structure of SR , the lorentzian equations, were based on the invarience of c and c as a finte limit of velocity.
SO if you input a velocity of c or above, the system returns gibberish, infinities or imaginary numbers, without real world interpretation or meaning.

Only if you input it as a velocity difference between inertial frames, or as the velocity of a particle that was previously moving at a speed less than c.

WOuld I be correct in saying that events ,given that they are of sufficintly short duration,
say a tachyon burst, are not attached to specific frames but are equally validly attached to any frame.

Of course. A frame (i.e. a coordinate system) is just a function that assigns coordinates to the events.

WOuld you say that this was normal procedure in SR , to import data derived in one frame into another frame to achieve agreement?

You can definitely specify a set of events using one coordinate system, and then check how another coordinate system would describe those same events. That isn't controversial at all, and it would be ridiculous to describe it as "magic".

Would you disagree when I say that you should be able to completely independently within each frame, arrive at this agreement?
Can you tell me how to ,either logically or mathematically, arrive at a time of t= -10 in A ,,working with the given data ,completely within that frame?

What agreement, and what given data? Your description is too much of a mess.

If a set of events has been specified using frame F', then I obviously can't "arrive" at any sort of conclusions about those events in frame F if I'm only allowed to use frame F. (At the very least, I would have to use the Lorentz transformation from F' to F).

So it appears to me that there are two incompatible realities. Would this be due to a flaw or failure of the Lorentz structure or is it possible that we are simply assigning parameters , inputting data that the system is not setup to handle. Indirectly introducing velocity greater than c.

It's neither. However, as I have already mentioned, if tachyons exist and the emission/detection process is fast, we get some genuine paradoxes. This is a strong argument against the existence of tachyons.

 

[JesseM]

SO if both the observers (at x=12 at t=0 who observes x'=20 with a clock reading of t'= -16) and (at x=20 at time t=10 in A who observes x'=20 with a clock reading of t'=-10)
and x'=20 in B all agree that time moved forward between these events[observations] what is the significance of an observer at x'=0 later concluding that according to B's clock system one event happened before another?

An "event" in relativity is confined to something happening at a single discrete location in space and a single discrete location in time; as Fredrik said, events are not specific to any coordinate system, they are physical things that different coordinate systems just assign different names (coordinates) to. The two events you are talking about above are not the same pair of events as the tachyon signal being sent and the tachyon signal being recieved--both observers agree about the order of the two events you mention, but don't agree about the order of the events of the tachyon signal being sent and the signal being received.

To keep things straight let's say three sparks are set off at these three points in spacetime. Spark #1 is set off at the same point in spacetime as the tachyon signal being sent, so it has coordinates x=0, t=0 in frame A and x'=0, t'=0 in frame B. Note that the property of "happening at the same location in spacetime" is transitive--if we know spark #1 happens right next to the event of the tachyon signal being sent, and we know the event of the tachyon signal being sent happens right next to the event of the clock at x=0 on A's ruler reading t=0, and the event of the clock at x=0 on A's ruler reading t=0 happens right next the event of the clock at x'=0 on B's ruler reading t'=0, then all these events happened next to each other at the same point in spacetime (for example, it must also be true that spark #1 happened right next to the clock at x'=0 reading t'=0).

Spark #2 is set off next to the clock at x=12 on A's ruler reading t=0, so it also happens next to the clock at x'=20 on B's ruler reading t'=-16 (and this event is simultaneous with spark #1 in A's frame but not in B's frame). Finally, spark #3 is set off next to the event of the tachyon signal being received, so it's at x=20 and t=10 in A's system, and x'=20 and t'=-10 in B's system. These three sparks are three separate events happening at three separate locations in spacetime. So, your question:

and x'=20 in B all agree that time moved forward between these events[observations] what is the significance of an observer at x'=0 later concluding that according to B's clock system one event happened before another?

...was too vague--you are mixing up the events of spark #1 and spark #2, where both frames agree on the order (both agree 'time moved forward between these events'), with spark #1 and spark #3, where the two frames don't agree on the order. The key difference is that spark #1 and spark #2 have what is called a "timelike separation" in spacetime, which technically means that $$\Delta x^2 - c^2 \Delta t^2$$ is negative but intuitively just means a signal moving slower than light could travel from one event to the other, while spark #1 and spark #3 have what is called a "spacelike separation, which technically means $$\Delta x^2 - c^2 \Delta t^2$$ is positive but intuitively just means a signal would have to move FTL to go from one event to the other. Different frames always agree on the order of events with a timelike separation, but they can disagree on the order of events with a spacelike separation (for any two events with a spacelike separation, it's always possible to find two inertial frames that disagree on their order, as well as a frame in which the events were simultaneous).

How is this different from the observer on the train concluding that the forward lightning bolt occurred before the rear?

The only difference is that we are imagining there can be a causal relation between the event of the signal being sent and the signal being received (or between spark #1 and spark #3, which happen at the same locations as these events, and might be imagined to be set off by the tachyon transmitter and receiver) because of the tachyon signal. In the traditional train thought-experiment, we don't imagine any FTL effects so neither of the two lightning flashes can have caused the other one, they are causally independent from one another (although they might both have been caused by some event or events which lie in the overlap of their past light cones).

I do not understand how you can, completely within B, derive a signal arriving x'=20 at t'= -10.
Given that a signal originates at x=0=x' at t=0 = t' how do you justify not applying the same logic and assuming that it would arrive at t'=10 in B ?

All inertial frames are considered equally valid in SR; you are free to calculate things from the perspective of any frame, and once you have the coordinates of events in that frame, you can just do the Lorentz transform to find the coordinates of the same events in a different frame (Again, remember that the property of 'events happening at the same location in spacetime' is transitive, so if we know event E coincides with coordinates x,t in system A, and coordinates x,t in A coincide with x'=gamma*(x - vt) and t'=gamma*(t - vx/c^2) in B via the Lorentz transform, that must mean that E coincides with x'=gamma*(x - vt) and t'=gamma*(t - vx/c^2).) If SR is correct there is no way this procedure can ever steer you wrong. The reason we don't assume it arrived at t'=10 in B is because we are talking about a signal that was moving at 2c in A's frame, so it cannot also have been moving at 2c in B's frame. Consider a more normal situation where you know an object is moving at 0.5c in A's frame, so if it started at x=0 and t=0 it will end up at x=5 at t=10; you can't then proceed to also assume it was moving at 0.5c in B's frame, and therefore will end up at x'=5 and t'=10 in B! The velocity of 0.5c was specified relative to A's frame, the velocity will necessarily be different in B's frame, you can find it using the relativistic velocity addition formula, or just by doing a Lorentz transformation on the coordinates it reaches in A (either way you'll reach the same conclusion about the velocity in B, since the velocity addition formula is itself derived from the Lorentz transformation).

You might find a geometric analogy helpful here. Suppose we have a line segment on a piece of paper (analogous to physical events in spacetime), and on top of this we lay a piece of transparent graph paper with x-y axes drawn on in order to assign coordinate to point on the line (analogous to an inertial frame in SR). If one end of the segment is at the position of the origin and the other is at position x=4, y=3, then in this coordinate system the slope of the line $$\frac{\Delta y}{\Delta x}$$ will be 3/4 (the slope is analogous to the velocity of an object in an inertial frame). Now you could put a different sheet of transparent graph paper over the first two, with the x-y axes oriented at a different angle--for example, the x-axis might be exactly parallel to the line segment, so although one end of the segment still corresponds to the origin of the new coordinate system, the other end now has coordinates x'=5, y'=0 in this system, meaning the slope of the line is 0 in the second system. Both systems are just different ways of describing the same geometry, and geometric facts like the length of the line segment given by $$\sqrt{\Delta x^2 + \Delta y^2}$$ (analogous to the spacetime interval $$\sqrt{\Delta x^2 - c^2 \Delta t^2}$$), or the localized facts like fact that some other lines #1, #2, #3 all cross at a single point while line #4 crosses them at different points, will be agreed upon by all coordinate systems.

If you assume tachyons actually go back in time how do you logically propose a signal that goes back in time in one frame but forward in time in another frame , to a location which is spatially coincident upon reception?

I don't know what you mean by "logically propose" here. It's just a fact that if different inertial frames are related by the Lorentz transformation (which is itself derived from the postulates that the laws of physics work the same in all inertial frames, and the velocity of light is c in all inertial frames), then for any pair of events 1 and 2 with a spacelike separation (and events along the worldline of an FTL signal always have a spacelike separation), different frames will disagree about the order of the two events, and according to the first postulate there can be no physical basis for considering one frame's perspective more correct than another's. Is there anything about this that violates logic, any more so than the idea that for two dots on a piece of paper, in one xy coordinate system dot 1 may have a larger y-coordinate than dot 2 while in a different xy coordinate system dot 2 may have a larger y-coordinate than dot 1? Perhaps the idea of disagreement about the order violates your own philosophical intuitions about time, but this is different from an actual logical paradox.

If you can't accept the idea that causally-related events on the worldline of an FTL particle would have different orders in different frames, and that neither frame's perspective would be more physically correct than the other's, then you have to either reject the idea that FTL signals are possible, or reject the idea that the laws of physics don't distinguish between the different inertial frames related by the Lorentz transformation. Most physicists would consider the fact that FTL + relativity destroys causality a good reductio ad absurdum argument for believing that FTL is likely to be impossible if relativity is correct, although of course it's always logically possible that causality itself is false and that backwards-in-time signalling will turn out to be possible in the real world.

I've never suggested any notion of the tachyon signal having a rest frame of its own.

Me either.

Well, what did you mean when you said "SO if you input a velocity of c or above, the system returns gibberish, infinities or imaginary numbers, without real world interpretation or meaning"? Input a velocity of c or above into what equations, exactly, if not the equations of the Lorentz transformation? (or equations derived from them like the time dilation equation)

 

[Austin0]

SR is a theory of physics that consists of a mathematical model of spacetime called Minkowski space and a set of postulates that identify things we measure with things in the model.

Note that Minkowski space is a model of all of spacetime. A theory can't get more "eternalistic" than that.

Can I assume we agree that the Lorentz math and Minkowski space-time are one and the same?
That the Lorentz math gives an accurate description and predictions of phenomena and events within a limited domain.
The bounds of that domain are explicitly delineated within the Minkowski spacetime by light cones.
The area outside these cones is dark territory . Does not really exist in the Lorentx -Minkowski mathematical universe. The system can provide no meaningful information or predictions regarding events or phenomena occurring outside this space.
That this is somewhat analogous to expecting contemporary physics to provide meaningful descriptions or predictions regarding the atomic structure of dark matter.
The math cannot tell you where or when a hypothetical tachyon would arrive in any frame.
You could just as well assume that a tachyon ,even given instantaneous transmission, would simply bounce back and forth between frames vitually instantly. The math could not prove or disprove this hypothesis either because the phenomena is outside it's realm.

Probably not, but I'm not sure I understand you. It sounds like you have misunderstood simultaneity. You always compensate for the propagation time of light in discussions about simultaneity. For example, if you emit light at t=-T, x=0, and you detect the light at t=T, x=0 after one reflection, the reflection event is simultaneous with t=0,x=0.

I take it the assumption here is : abs(-T)= T in which case it is both self evident and unquestioned.
But the discussion was about planes of simultaneity and eternalism. I am trying to understand what you mean when you say space-time is an eternalist paradigm.
I have encountered in other threads the idea that shifts in direction of one world line effect a shift in its plane of simultaneity and its itersection with the other world line and thus a significant shift in the temporal relationship of two world lines. This concept seems to imply an actual temporal relationship beyond the future perception of events as received at the speed of light. Otherwise what does it mean?

I disagree. GR defines two time concepts in the framework of the mathematical model: coordinate time and proper time. It also defines time operationally as "what a clock measures", and postulates the relationship between these concepts. How is that "leaving the task to the philosophers"? Scientists haven't been able to find a better theory of time than GR, but it's not because they think such a theory would be unnecessary or irrelevant

.
You will note I specifically said "until recently" which, within the context of the long history of science, means the last century. Physics has always defined time operationally as what a clock measures. That was my point.
Eternalism on the other hand ,does actually refer directly to the phenomenon of time itself, as an entity having actual attributes. there are others that deal directly with time also.
I myself consider it quite possible that there is an actual, underlying periodicity to the universe,,, whether or not it could ever be detectable is of course problematic. That there could be an actual physical cause for time dilation. You may disagree and consider it simply a relative phenomena , with no objective reality whatsoever. Which of course may be right.

I do not have time to do the math right now but couldn't you specify a tachyon transmission to x'= -20 in B and apply the same methods to prove tachyons actually move into the future?

 

[Fredrik]

Can I assume we agree that the Lorentz math and Minkowski space-time are one and the same?

I don't know exactly what you mean by "Lorentz math", but the existence of coordinate systems with the property that a transformation between any two of them is described by a Lorentz transformation, is implied by the properties of Minkowski space. So I guess the answer is "yes".

That the Lorentz math gives an accurate description and predictions of phenomena and events within a limited domain.
The bounds of that domain are explicitly delineated within the Minkowski spacetime by light cones.
The area outside these cones is dark territory . Does not really exist in the Lorentx -Minkowski mathematical universe. The system can provide no meaningful information or predictions regarding events or phenomena occurring outside this space.

Minkowski space is the entire spacetime, every event that "has happened", every event that "is happening" and every event that "will happen"*. Nothing can be more "eternalist" than that.

*) The separation of the set of all events into those three subsets is more or less arbitrary. The definition of simultaneity that I posted is just the conventional way to do it for an inertial observer.

The math cannot tell you where or when a hypothetical tachyon would arrive in any frame.

Of course it can. If you specify a velocity in a frame, that defines the slope of a line in Minkowski space. So if you know the coordinates of the emission event and the spatial coordintes of the detection event, you also know the time coordinate of the detection event.

I take it the assumption here is : abs(-T)= T in which case it is both self evident and unquestioned.

I would agree that it's very "natural", but it's still just a convention.

But the discussion was about planes of simultaneity and eternalism. I am trying to understand what you mean when you say space-time is an eternalist paradigm.

Only that SR is defined by postulates that identify things we measure with things in a mathematical model of the set of all events (as opposed to a model of the set events that are happening right now).

I do not have time to do the math right now but couldn't you specify a tachyon transmission to x'= -20 in B and apply the same methods to prove tachyons actually move into the future?

I'm not sure what you mean by "the same methods" or "B", or the relevance of "x'=-20", but you can describe the motion of a tachyon in one frame, and you can decide to call the earlier endpoint of its world line "emission" and the later endpoint "detection", but if you do, you will find that detection precedes emission in some other frame.

 

[MikeLizzi]

Allow me to offer this link to a presentation I did in Relativity class.

http://mysite.verizon.net/mikelizzi/Tachyons.htm

It addresses the issue of causalty more than time travel.

 

[Austin0]

An "event" in relativity is confined to something happening at a single discrete location in space and a single discrete location in time; as Fredrik said, events are not specific to any coordinate system, they are physical things that different coordinate systems just assign different names (coordinates) to. The two events you are talking about above are not the same pair of events as the tachyon signal being sent and the tachyon signal being recieved--both observers agree about the order of the two events you mention, but don't agree about the order of the events of the tachyon signal being sent and the signal being received.

To keep things straight let's say three sparks are set off at these three points in spacetime. Spark #1 is set off at the same point in spacetime as the tachyon signal being sent, so it has coordinates x=0, t=0 in frame A and x'=0, t'=0 in frame B. Note that the property of "happening at the same location in spacetime" is transitive--if we know spark #1 happens right next to the event of the tachyon signal being sent, and we know the event of the tachyon signal being sent happens right next to the event of the clock at x=0 on A's ruler reading t=0, and the event of the clock at x=0 on A's ruler reading t=0 happens right next the event of the clock at x'=0 on B's ruler reading t'=0, then all these events happened next to each other at the same point in spacetime (for example, it must also be true that spark #1 happened right next to the clock at x'=0 reading t'=0).

Spark #2 is set off next to the clock at x=12 on A's ruler reading t=0, so it also happens next to the clock at x'=20 on B's ruler reading t'=-16 (and this event is simultaneous with spark #1 in A's frame but not in B's frame). Finally, spark #3 is set off next to the event of the tachyon signal being received, so it's at x=20 and t=10 in A's system, and x'=20 and t'=-10 in B's system. These three sparks are three separate events happening at three separate locations in spacetime. So, your question:

...was too vague--you are mixing up the events of spark #1 and spark #2, where both frames agree on the order (both agree 'time moved forward between these events'

), Did you mean spark #2 and spark #3 ?

with spark #1 and spark #3, where the two frames don't agree on the order.

The reason we don't assume it arrived at t'=10 in B is because we are talking about a signal that was moving at 2c in A's frame, so it cannot also have been moving at 2c in B's frame.

What is the basis within SR for this assumption?
If we consider a tachyon moving at c, wouldn't that be exactly the logical assumption to make ,,that just like a photon it would be perceived as having the same relative velocity as measured within both frames

Consider a more normal situation where you know an object is moving at 0.5c in A's frame, so if it started at x=0 and t=0 it will end up at x=5 at t=10; you can't then proceed to also assume it was moving at 0.5c in B's frame, and therefore will end up at x'=5 and t'=10 in B! The velocity of 0.5c was specified relative to A's frame, the velocity will necessarily be different in B's frame, you can find it using the relativistic velocity addition formula, or just by doing a Lorentz transformation on the coordinates it reaches in A (either way you'll reach the same conclusion about the velocity in B, since the velocity addition formula is itself derived from the Lorentz transformation).

All of the above is understood but is it relevant in this situation?
What you have said relates to inertial frames. ANd velocities not exceeding c.
In this case we are considering a tachyon , a photon going faster than c.
This is the point exactly. SR and the Lorentz math provide NO postulates or guidlines
on which to base any assumption regarding how a tachyon would be perceived in any frame let alone between two frames.
You could, with some logical justification, assume that above c photons [just like c photons] would also be perceived at the same velocity in any frame.
You could assume that they would be perceived as moving forward in time, in any frame..
The point is that any assumption would be purely arbitrary without validation within the framework of SR.
You say that your only a priori assumption is that tachyons exist but I question this assertion.
You assign a velocity of 2c in A, yet this is NOT determined within A as an observation or measurement. There is NO observation of the tachyon in A itself.
This assumed observation in A is purely the result of your arbitrary assumption of an actual observation in B at t'=(-10)
The event in A [observation of reception in B] at t=10 at x=20 is simply a consequence of this assumption of arrival in B at t'= -10 . So also then , is the attributed speed in A.
SO the , actual , causal sequence of events is:
(1)-- the transmission at t=0 x=0 in A >>>> (2) -- the reception at x'=20 at some t'=? >>
(3) the observation of event2 at some x=? at time t=? in B.

It seems to me that the logical approach to this is ; starting with (1)
you use the math to determine (2)
and then from this ,use the math to determine (3)
Of course this is problematic because strictly speaking the math won't give a definite answer to (2) without assumptions
But you have approached it by giving (1) and then assuming ((3)-- t=10 at x=20) and from this , using the math to derive (2)
Would you agree there is a certain circularity here? Assumptions on top of assumptions.

Perhaps the idea of disagreement about the order violates your own philosophical intuitions about time, but this is different from an actual logical paradox.

I have no philosophical intuitions about time in this regard to be violated. That is not the question here.

If you can't accept the idea that causally-related events on the worldline of an FTL particle would have different orders in different frames, and that neither frame's perspective would be more physically correct than the other's, then you have to either reject the idea that FTL signals are possible, or reject the idea that the laws of physics don't distinguish between the different inertial frames related by the Lorentz transformation. Most physicists would consider the fact that FTL + relativity destroys causality a good reductio ad absurdum argument for believing that FTL is likely to be impossible if relativity is correct, although of course it's always logically possible that causality itself is false and that backwards-in-time signalling will turn out to be possible in the real world.

I neither reject the possibility FTL nor do I question the postulates of relativity.
I simply question the application of those principles in this situation.

I was talking about the Lorentz math. Am I wrong in thinking that you cannot enter a v>c into any of the equations and return a meaningful result ?
Strictly speaking I don't see any possible violation of causality here merely a different possible temporality. For me a violation of causality would be if my coffee cup suddenly turned to mercury in my hand.

 

[Fredrik]

What is the basis within SR for this assumption?
If we consider a tachyon moving at c, wouldn't that be exactly the logical assumption to make ,,that just like a photon it would be perceived as having the same relative velocity as measured within both frames

A tachyon doesn't move at c. You can't assume that a tachyon moves at the same speed in two frames. When you specify the speed in frame F, you're describing what its world line looks like in F. Now you can calculate what the world line looks like in frame F', and determine its speed in F' from that. (The speed is just the slope of the world line). That completely removes your freedom to make any assumptions at all.

In this case we are considering a tachyon , a photon going faster than c.

Particles with m²>0 move at speeds <c. (They are sometimes called "tardyons" or "bradyons", but those terms aren't in widespread use).

Particles with m²=0 move at c. (They are sometimes called "luxons", but that term isn't in widespread use).

Particles with m²=0 move at speeds >c. They are called "tachyons".

(Yes, "m" is the mass).

This is the point exactly. SR and the Lorentz math provide NO postulates or guidlines
on which to base any assumption regarding how a tachyon would be perceived in any frame let alone between two frames.

This couldn't possibly be more incorrect. Every inertial frame maps Minkowski space bijectively onto $\mathbb R^4$ and every Lorentz transformation maps $\mathbb R^4$ bijectively onto itself. Every Lorentz transformation tells you the coordinates of every event in spacetime, so of course it tells you how a world line that's been specified in one frame looks in another.

Strictly speaking I don't see any possible violation of causality here merely a different possible temporality.

Both Jesse and I have explained why tachyons (that can be detected arbitrarily fast) violate causality. You can receive an answer before you sent the question. You could even set it up so that the answer triggers a mechanism that destroys the device that's supposed to send the original message.

 

[JesseM]

Did you mean spark #2 and spark #3 ?

Yes, sorry, it's #2 and #3 that have a timelike separation and thus have the same order in both frames.

The reason we don't assume it arrived at t'=10 in B is because we are talking about a signal that was moving at 2c in A's frame, so it cannot also have been moving at 2c in B's frame.

What is the basis within SR for this assumption?
If we consider a tachyon moving at c, wouldn't that be exactly the logical assumption to make ,,that just like a photon it would be perceived as having the same relative velocity as measured within both frames

If a tachyon is moving at c it isn't a tachyon! The word "tachyon" means something moving faster than c. If you're asking why we couldn't assume the speed of a tachyon is the same in all inertial frames, keep in mind that the "speed" of anything in a given inertial frame is given by (change in position)/(change in time) for two infinitesimally close events on its worldline (if the object is moving at constant speed than the two events can be far apart). If you pick two events on the worldline of something moving at c in one inertial frame, like (x=0 light seconds, t=0 seconds) and (x=5 light-seconds, t=5 seconds), and then use the Lorentz transform to find the coordinates of these events in a different inertial frame, you'll find that (change in position)/(change of time) for the new coordinates of these events in the second frame is still c. This will not be true for a pair of events on the worldline of something moving faster than c, just like it's not true for a pair of events on the worldline of something moving slower than c. I suppose you could invent a different coordinate transformation where a particle moving at some speed faster than c (say, 5c) is moving at the same coordinate speed in all coordinate systems, but it wouldn't be the Lorentz transformation. And you certainly can't come up with a coordinate transformation that respects the two postulates of relativity and where something moving at 5c in one coordinate system is moving at 5c in all coordinate systems--the Lorentz transformation is uniquely derived from the two postulates, there can't be any other coordinate transformations that satisfy both of them.

Also remember that the postulate that all frames measure light to move at c wasn't just some ad hoc notion that Einstein came up with because he thought it'd be cool, it was based specifically on fact that he wanted Maxwell's laws to work in every inertial frame, and also on the failure of the Michelson-Morley experiment to detect differences in the speed of light in different directions. There aren't any analogous arguments for postulating that something moving at 5c should have the same speed in all inertial frames, so someone postulating that a tachyon's speed is frame-invariant would not be making the same "logical assumption" that Einstein made when he postulated that light's speed is frame-invariant, since Einstein actually had physical reasons for making this postulate.

Finally, note that in the years since Einstein many new laws of physics have been discovered, and all the most fundamental ones (like quantum field theory) have turned out to obey Lorentz-invariant equations, providing further empirical support for the idea that the laws of physics are symmetrical in inertial frames related by the Lorentz transformation, not in inertial frames related by some other coordinate transformation.

All of the above is understood but is it relevant in this situation?
What you have said relates to inertial frames. ANd velocities not exceeding c.
In this case we are considering a tachyon , a photon going faster than c.
This is the point exactly. SR and the Lorentz math provide NO postulates or guidlines
on which to base any assumption regarding how a tachyon would be perceived in any frame let alone between two frames.

The Lorentz math cannot be used to talk about the rest frame of something moving faster than c, but it can certainly be used to assign coordinates to events on the tachyon's worldline from the perspective of any given sublight frame. This is just the same as with photons, where we can't plug v=c into the Lorentz transformation to get the "rest frame" of a photon (all inertial frames move slower than light in relativity), but we can assign coordinates to events on the photon's worldline from the perspective of a sublight frame. Inertial frames are just coordinate systems for assigning position and time coordinates to every event in spacetime, and every point on a tachyon's worldline would be an event in spacetime, there's no reason you can't assign coordinates to such events using a sublight frame.

You could, with some logical justification, assume that above c photons [just like c photons] would also be perceived at the same velocity in any frame.

What "logical justification" would that be? See my above points about how Einstein's reason for postulating that c is frame-invariant had to do with specific physical arguments that would not apply to a tachyon, and also the point about how the Lorentz transformation follows uniquely from the two postulates of relativity, you can't have an FTL tachyon's speed by frame-invariant without using a coordinate transformation that violates at least one of SR's fundamental postulates.

You could assume that they would be perceived as moving forward in time, in any frame..
The point is that any assumption would be purely arbitrary without validation within the framework of SR.

Not if the "framework of SR" is assumed to include the assumption that the two fundamental postulates are correct and that the laws of physics are symmetrical under the Lorentz transformation. As long as different inertial frames are related by the Lorentz transformation, it is absolutely impossible that all frames would agree on the order of two events on the worldline of a tachyon.

You assign a velocity of 2c in A, yet this is NOT determined within A as an observation or measurement. There is NO observation of the tachyon in A itself.

Sure there is. In A the tachyon signal is observed to be emitted at a certain position and time (x=0 and t=0) and is observed to be received at a certain position and time (x=20 and t=10). This is no different than measuring the position and times that a photon signal is emitted and received; it just requires the guy who is right next to the tachyon emission when it happens to note the marking on A's ruler that he's next to at that moment, and the time on the clock attached to that marking, and likewise with the guy who is right next to the tachyon reception when it happens.

This assumed observation in A is purely the result of your arbitrary assumption of an actual observation in B at t'=(-10)

No, it's the result of the assumption that the tachyon's speed (defined as change in position/change in time) is 2c in A. Of course, you could imagine a different tachyon signal which moves at 2c in some other frame besides A, call it C, but no matter what frame you choose, you can always find some different frame D where the same tachyon signal is received before it's sent according to that frame's time coordinates.

Maybe the problem is you're imagining an event is "in" one frame or another. It's not--frames are just ways of assigning coordinates to events, events themselves aren't "native" to any particular frame. If an observer sees his tachyon detector light up because it received a signal, he can determine the coordinates in A by looking at the marking on A's ruler that was next to the detector when this happened and the time on A's clock attached to that marking, and he can also determine the coordinates in B by looking at the marking on B's ruler that was next to the detector when this happened and the time on B's clock attached to that marking. The event of the detector lighting up wasn't tied to any particular frame, its coordinates in different frames are just determined by the ruler marking/clock time of that frame's system that was in the local neighborhood of the event as it happened. And remember what I said about the fact that when events are "next to" one another this property is transitive--if we know that the detector lighting up was next to mark x on ruler A whose clock showed time t, and we know by the Lorentz transform that the event of the clock at x reading t in A was next to the event of the clock at x'=gamma*(x-vt) reading t'=gamma*(t-vx/c^2) in B, then that means the event of the detector lighting up must have been next to x'=gamma*(x-vt) and t'=gamma*(t-vx/c^2) in B.

Of course this is problematic because strictly speaking the math won't give a definite answer to (2) without assumptions

Yes, and the assumption is just that the tachyon is moving at 2c in A. A tachyon by definition must be moving at some v>c in some inertial frame--you're free to pick a different v>c and/or a different inertial frame if you like, but the end conclusion will be the same because it will always be possible to find a different inertial frame where the event of the signal being received happened at an earlier time-coordinate than the event of it being sent.

I was talking about the Lorentz math. Am I wrong in thinking that you cannot enter a v>c into any of the equations and return a meaningful result ?

Yes, you are wrong. You can't enter v>c into some equations, but those are specifically the equations that relate the coordinates of one frame with the coordinates of another, like the Lorentz transform or the time dilation equation (the reason you can't is that the tachyon doesn't have its own rest frame with its own coordinates). And you can't plug v=c into these equations either! But just as you can analyze the position and time coordinates of a particle moving with v=c exclusively from the perspective of sublight inertial frames, so you can do the same for a tachyon moving at v>c. Any events in spacetime whatsoever can be assigned coordinates in a sublight inertial frame, a frame is just a coordinate system covering all of the flat SR spacetime, much like Cartesian coordinates cover all of a flat 2D plane.

Strictly speaking I don't see any possible violation of causality here merely a different possible temporality. For me a violation of causality would be if my coffee cup suddenly turned to mercury in my hand.

Physicists define "violation of causality" in terms of a violation of the rule that causes always precede effects. In the case of a two-way tachyon transmission, I could receive your reply to my message before I actually sent that message, so this would be such a violation.

 

[Austin0]

If a tachyon is moving at c it isn't a tachyon! The word "tachyon" means something moving faster than c.

Can we not get off into semantics and for the purposes of this purely hypothetical discussion "consider" a tachyon traveling at c ?

Also remember that the postulate that all frames measure light to move at c wasn't just some ad hoc notion that Einstein came up with because he thought it'd be cool, it was based specifically on fact that he wanted Maxwell's laws to work in every inertial frame, and also on the failure of the Michelson-Morley experiment to detect differences in the speed of light in different directions. [/QUOTE
Understood. M-M provided empirical reasons for the assumption. SO far that is lacking in the case of tachyons.

There aren't any analogous arguments for postulating that something moving at 5c should have the same speed in all inertial frames, so someone postulating that a tachyon's speed is frame-invariant would not be making the same "logical assumption" that Einstein made when he postulated that light's speed is frame-invariant, since Einstein actually had physical reasons for making this postulate.

I was, of course, not seriously trying to make that proposal whatsoever.

Finally, note that in the years since Einstein many new laws of physics have been discovered, and all the most fundamental ones (like quantum field theory) have turned out to obey Lorentz-invariant equations, providing further empirical support for the idea that the laws of physics are symmetrical in inertial frames related by the Lorentz transformation, not in inertial frames related by some other coordinate transformation.

As I have said ,there is no argument regarding the validity of the postulates or the math.

The Lorentz math cannot be used to talk about the rest frame of something moving faster than c, but it can certainly be used to assign coordinates to events on the tachyon's worldline from the perspective of any given sublight frame. This is just the same as with photons, where we can't plug v=c into the Lorentz transformation to get the "rest frame" of a photon (all inertial frames move slower than light in relativity), but we can assign coordinates to events on the photon's worldline from the perspective of a sublight frame. Inertial frames are just coordinate systems for assigning position and time coordinates to every event in spacetime, and every point on a tachyon's worldline would be an event in spacetime, there's no reason you can't assign coordinates to such events using a sublight frame

.

Sure there is. In A the tachyon signal is observed to be emitted at a certain position and time (x=0 and t=0) and is observed to be received at a certain position and time (x=20 and t=10). This is no different than measuring the position and times that a photon signal is emitted and received; it just requires the guy who is right next to the tachyon emission when it happens to note the marking on A's ruler that he's next to at that moment, and the time on the clock attached to that marking, and likewise with the guy who is right next to the tachyon reception when it happens.

If you assume the tachyon is received in B at x'=20 at t'=+10 then the math would tell you a completely different observer in A [at a different time ], would be coincident to observe this event or would you disagree with this ?

Maybe the problem is you're imagining an event is "in" one frame or another. It's not--frames are just ways of assigning coordinates to events, events themselves aren't "native" to any particular frame.

If you will note my previous post to fredrik you will see I made the exact same point myself

If an observer sees his tachyon detector light up because it received a signal, he can determine the coordinates in A by looking at the marking on A's ruler that was next to the detector when this happened and the time on A's clock attached to that marking, and he can also determine the coordinates in B by looking at the marking on B's ruler that was next to the detector when this happened and the time on B's clock attached to that marking. The event of the detector lighting up wasn't tied to any particular frame, its coordinates in different frames are just determined by the ruler marking/clock time of that frame's system that was in the local neighborhood of the event as it happened. And remember what I said about the fact that when events are "next to" one another this property is transitive--if we know that the detector lighting up was next to mark x on ruler A whose clock showed time t, and we know by the Lorentz transform that the event of the clock at x reading t in A was next to the event of the clock at x'=gamma*(x-vt) reading t'=gamma*(t-vx/c^2) in B, then that means the event of the detector lighting up must have been next to x'=gamma*(x-vt) and t'=gamma*(t-vx/c^2) in B.

[

QUOTE]Yes, you are wrong. You can't enter v>c into some equations, but those are specifically the equations that relate the coordinates of one frame with the coordinates of another, like the Lorentz transform or the time dilation equation (the reason you can't is that the tachyon doesn't have its own rest frame with its own coordinates). And you can't plug v=c into these equations either!

Well what equations does that leave. Can you determine a meaningful relative velocity from the addition equation?

Any events in spacetime whatsoever can be assigned coordinates in a sublight inertial frame, a frame is just a coordinate system covering all of the flat SR spacetime, much like Cartesian coordinates cover all of a flat 2D plane.

Physicists define "violation of causality" in terms of a violation of the rule that causes always precede effects. In the case of a two-way tachyon transmission, I could receive your reply to my message before I actually sent that message, so this would be such a violation.

If you will note I understood and mentioned the different temporality.
But would you disagree that another fundamental aspect of the concept of causality, which you could say naturally falls out of the first law of motion, is the idea that there are no effects without cause?

IF you are attached to the conventional ideas of causality and free will AND you accept the proposition that tachyons would travel back in time, then you could say that this would constitute a strong reductio ad absurdam arguement against the physical reality interpretation of eternalism , wouldn't you agree?
I am NOT making this claim whatsoever, nor am I making ANY argument for or against block time.
I would say that it is NOT IMPOSSIBLE that EPR experimentation will eventually demonstrate that FTL interactions between entangled photons make instantaneous transmission of information possible and that even if this should prove the case it does not neccessarily mean either causality or temporality will be threatened. I would not try to prove this hypothesis either.

 

[Austin0]

[

Minkowski space is the entire spacetime, every event that "has happened", every event that "is happening" and every event that "will happen"*. Nothing can be more "eternalist" than that.

As a general statement of the system I would of course agree. COuldnt you say the same thing about a cartesian 3d system with a time element. As an abstract construct this does not neccessarily imply the continued physical existence of all points within the system.
AS a practical matter, in application you are always dealing with a bounded portion of spacetime. SO in the world line paradigm you are dealing with a limited number of discrete , specific locations and events within frames. Would you disagree that any point or event has attached a complementary pair of light cones ?
That ,of course, you can plot phenomena or events anywhere within the system but anything outside the light cones can have no direct interaction with observers inside the light cones according to the rules , as specified by the system. to my understanding that was the point.

*) The separation of the set of all events into those three subsets is more or less arbitrary. The definition of simultaneity that I posted is just the conventional way to do it for an inertial observer.

 

[Fredrik]

Can we not get off into semantics and for the purposes of this purely hypothetical discussion "consider" a tachyon traveling at c ?

Why would you want to do that? It makes even less sense than to describe a person with lots of hair on his head as "bald" or the Wednesdays in January as "the weekend".

I'm definitely not going to agree to call a massless particle a "tachyon". It would really confuse people who read my posts without reading yours, and make me look like I don't know what I'm talking about.

As a general statement of the system I would of course agree. COuldnt you say the same thing about a cartesian 3d system with a time element.

Yes.

As an abstract construct this does not neccessarily imply the continued physical existence of all points within the system.

I'm baffled by this claim. I can't make sense of it. You're saying that the mathematical model of spacetime doesn't imply that all of the events exist in that model!? That's like saying that the current standard for the design of calenders doesn't imply the existence of days labeled "Tuesday" in calenders that follow the standard! (It certainly does according to any definition of "exist" that makes sense to me).

And even if I could make sense of your statement, I would have to point out that Minkowski space describes all of the events in spacetime in exactly the same way. There are no preferred events. There's no "now". So if it doesn't "imply the continued physical existence of all points within the system" (whatever that's supposed to mean), it clearly doesn't imply the existence of the present ("within the system") either.

Maybe you should explain what you mean by "continued physical existence"? What would imply "the continued physical existence of all points within the system"? This is the sort of thing I had in mind when I said that "such concepts are mostly nonsense anyway" (in #38). What does it even mean for a moment to "exist"?

Do you understand that theories don't imply anything about the real world? All they do is make predictions about the results of experiments, and experiments can't tell you anything except how accurate those predictions are. That's all you can get from science. Science doesn't tell you anything about "existence", and as far as I know there isn't even a scientifically meaningful definition of "exist".

AS a practical matter, in application you are always dealing with a bounded portion of spacetime. SO in the world line paradigm you are dealing with a limited number of discrete , specific locations and events within frames.

That's irrelevant. The fact that a Lorentz transformation transforms the coordinates of all the events is sufficient to guarantee that if you specify a set of events using the coordinates of one frame, you know what that set looks like in another frame.

Don't forget what this part of the discussion is about. You claimed that the speed of a tachyon in one frame doesn't determine its speed in another frame. Your comment doesn't even begin to refute the fact that you can use a Lorentz transformation to find out what the tachyon's world line looks like in another frame, or the fact that if you know what the world line looks like you know the speed.

Would you disagree that any point or event has attached a complementary pair of light cones ?

No, but what does that have to do with anything?

That ,of course, you can plot phenomena or events anywhere within the system but anything outside the light cones can have no direct interaction with observers inside the light cones according to the rules , as specified by the system. to my understanding that was the point.

The correct statement is that if there are no tachyons, events outside the past light cone of an event p can't change what happens at p, and events outside the future light cone of p can't be changed by what happens at p.

 

[Austin0]

in that model[/i]!? (It certainly does according to any definition of "exist" that makes sense to me).

And even if I could make sense of your statement, I would have to point out that Minkowski space describes all of the events in spacetime in exactly the same way. There are no preferred events. There's no "now". So if it doesn't "imply the continued physical existence of all points within the system" (whatever that's supposed to mean), it clearly doesn't imply the existence of the present ("within the system") either.

Maybe you should explain what you mean by "continued physical existence"? What would imply "the continued physical existence of all points within the system"? This is the sort of thing I had in mind when I said that "such concepts are mostly nonsense anyway" (in #38). What does it even mean for a moment to "exist"?

I think you as an intelligent individual know exactly what is meant here by continued physical existence. That any ideas or contemplation of time travel neccessitate a very definite conception of past existence, whether it is going back to kill your grandfather or sending messages to your previous self.
I am not arguing against this conception per se, but I do not see it as a necessary implication of any space-time construct, even though that construct may include all space and time. It is not a question of "moments" " existing" ,,,but of matter, entities existing at past times.
AS for such nonsense concepts ,,,I did not introduce them into this topic but read them in JesseM's previous post . This led me to consider that I may be missing something relevant and so I brought it up to try and learn how it explicitly applied to Minkowski space-time , not as a generalization but specifically wrt planes of simultaneity , timelines etc.

Do you understand that theories don't imply anything about the real world? All they do is make predictions about the results of experiments, and experiments can't tell you anything except how accurate those predictions are.

In principle I understand and agree with this interpretation 100%. They are merely abstractions and can never be assumed to realistically apply to the real world.
At the same time I personally hold another view. I have no interest in physics as a form of engineering , no need to apply its math in the real world. I simply have a great curiosity and desire to gain some kind of understanding of the workings of that world. In that regard I believe that our theories are wonderful creations and however incomplete or even erroneous they may be, they still do bring us closer to understanding that reality and who knows in some cases may even be "true". In any case they are the best we have and it makes no sense to me to discontinue the quest to question and refine them , to seek new theories with some improved approximation of that "truth"

Don't forget what this part of the discussion is about. You claimed that the speed of a tachyon in one frame doesn't determine its speed in another frame.

I make no claims about tachyons whatsoever. To me they are mythological entities that could have any qualities whatsoever if they could in fact exist at all
If someone wants to posit tachyons that travel back in time and draw a spacetime picture of a tachyon transmitter as a negative cone , I can't think of any real grounds to argue with that picture. But it would seem to imply that any possible observer would receive transmissions earlier than they were sent.
On the other hand if it is considered that they travel forward in space time , have a positively sloped world line , then this to me implies that every other possible world line would move forward during the propagation interval.That if they moved forward in space they had to move forward in time . If this is a valid depiction of reality and you accept that a single observer, cannot be located at a single point in spacetime at two different times , the conclusion would seem to be that no observer could receive a tachyon at a time earlier than its transmission.That any such implications made from hypothetical observations from other inertial frames are suspect..Are artifacts due to clock desynchronization or are assumptions of actual temporality derived from clock desynchronization or simply that the system , while it may not directly exclude v >c was most definitely not designed to include this possibility and may not be applicable when this phenomena is introduced.

It may be that I am not understanding completely, the system or your interpretation of the system , but then that is almost a given. As JesseM pointed out this system was not created out of thin air . Reality itself presented a situation , the invarience of the measured speed of light , which itself refuted any common sense, common math interpretation of reality. SO by its very nature, both the universe and the mathematical description of it , are realms where common sense and normal math DO NOT APPLY. SO if you then introduce an imaginary particle which also defies common sense ,why should anyone expect logical assumptions of any kind to work?

 

[Fredrik]

I'd like to correct a typo in one of my previous posts:

Particles with m²>0 move at speeds <c. (They are sometimes called "tardyons" or "bradyons", but those terms aren't in widespread use).

Particles with m²=0 move at c. (They are sometimes called "luxons", but that term isn't in widespread use).

Particles with m²<0 move at speeds >c. They are called "tachyons".

I typed the red "<" as a "=". That obviously wasn't my intention.

 

[Fredrik]

I think you as an intelligent individual know exactly what is meant here by continued physical existence. That any ideas or contemplation of time travel neccessitate a very definite conception of past existence, whether it is going back to kill your grandfather or sending messages to your previous self.
I am not arguing against this conception per se, but I do not see it as a necessary implication of any space-time construct, even though that construct may include all space and time. It is not a question of "moments" " existing" ,,,but of matter, entities existing at past times.

I have an intuitive idea about what "continued physical existence" means in the real world, but I have no idea what it would mean in the framework of SR. What you're saying here suggests that we should define the past to exist if we can travel there. That might make sense in the real world, but not in the theory. The "matter entities" you mention are just a bunch of timelike curves in spacetime.

I simply have a great curiosity and desire to gain some kind of understanding of the workings of that world. In that regard I believe that our theories are wonderful creations and however incomplete or even erroneous they may be, they still do bring us closer to understanding that reality and who knows in some cases may even be "true". In any case they are the best we have and it makes no sense to me to discontinue the quest to question and refine them , to seek new theories with some improved approximation of that "truth"

I agree 100%.

I make no claims about tachyons whatsoever.

You put it in the form of a question, but you suggested that we could (and should be able to) just assume what the speed of a 2c tachyon is in another inertial frame. We can't. What you seem to be missing is that "inertial frame" is a concept that has an exact definition in SR, so it doesn't make sense to make assumptions that contradicts that definition unless you say explicitly that you're trying to find a new definition of "inertial frame" that you intend to be a part of a new theory that's supposed to replace SR.

To me they are mythological entities that could have any qualities whatsoever if they could in fact exist at all

They're not mythological in SR. They are spacelike curves in Minkowski space.

If someone wants to posit tachyons that travel back in time and draw a spacetime picture of a tachyon transmitter as a negative cone , I can't think of any real grounds to argue with that picture.

No one just assumes that. The world line of a massive particle is a timelike curve. The world line of a massless particle is a null curve. The only assumption about tachyons is just that a spacelike curve can be a world line. (This can be considered the definition of a tachyon in SR).

On the other hand if it is considered that they travel forward in space time , have a positively sloped world line , then this to me implies that every other possible world line would move forward during the propagation interval.That if they moved forward in space they had to move forward in time .

You're still missing the point. If they are what you say in one frame, then they're going back in time in some other frame.

If this is a valid depiction of reality and you accept that a single observer, cannot be located at a single point in spacetime at two different times , the conclusion would seem to be that no observer could receive a tachyon at a time earlier than its transmission.

This is incorrect. Jesse and I have both explained why.

That any such implications made from hypothetical observations from other inertial frames are suspect..Are artifacts due to clock desynchronization or are assumptions of actual temporality derived from clock desynchronization or simply that the system , while it may not directly exclude v >c was most definitely not designed to include this possibility and may not be applicable when this phenomena is introduced.

The paradoxes that Jesse and I have described imply that tachyons (that can be detected in a short time) can't exist in a world that can be described by classical SR.

SO if you then introduce an imaginary particle which also defies common sense ,why should anyone expect logical assumptions of any kind to work?

Aren't we talking about the possibility of tachyons in SR? Even if you want to talk about tachyons in a broader context, it wouldn't make sense to start by throwing out SR. You have no reason to do that until you have thought about the consequences of the existence of tachyons in SR.

 

[Austin0]

The outline of this demonstration is as follows:

Hypothesis-----That given the existence of Tachyons that could travel at 2c they would travel backwards in time. Be received by some observer before the time of emmission.

Premise (#1) That a tachyon transmission is initiated in frame A at position x=0 at time t=0.
Premise (#2) That an observer in frame A located at x=20 at time t=10 observes the reception of this transmission by a proximate observer in frame B.

By application of the Lorentz transformation it is Concluded (#3) that this observer in frame B would at the moment of reception be located at x'=20 at time t'= -10

I would present some observations and conclusions of my own.
____________________________________________________________________________

(1) That whatever position and time is assumed for premise (#2) the Lorentz math can provide one , and only one, result.
(2) That this premise/assumption therefore predetermines the resulting conclusion.

(3) IF A then B
IF premise (#2) then conclusion (#3)
___________________________________________________-
.
I have since realized that it would have been clearer to go directly to the equivalence
A=B
I want to make it clear that I am not suggesting the logical operation, If A then B, is not obviously valid in the course of a chain. But rather that it is only valid if you have already established A. That in this case the link between A and B is not logical but is a simple mathematical transformation. That A and B are essentially the same thing.
[Premise] 0 deg C= 32 deg F [Conclusion
________________________________________________________________________
(4) That this is clearly inserting the desired conclusion into the premise and is not
valid under any idea of logical argument or deduction that I am aware of.
].

___________

(5) That the assumed event of premise (#2) [the observation in frame A] could only actually occur if the event in B [the reception] had occurred at the specific location and time of the conclusion and no other.
(6) A can be true if and only if B is true.
The premise (#2) can be true if and only if the conclusion (#3) is true.
(7) This is clearly inserting a premise that is directly and totally dependant on the very conclusion that is in question.
(8) I would say that this is , also , clearly not permissable or valid in any system of logic as I understand it.
(9) That in this case the premise is not only, totally dependant on the conclusion, but also ,in and of itself, directly predetermines that very conclusion. I don't see how you can get more circular than that.
(10) It appears obvious to me that the whole argument hinges on this crucial premise
and that if that premise itself is invalid, then there simply, is NO argument.
That any conclusions or further extrapolations developed from this are without validaty or meaning.

It seems to me that to present a demonstration, in effect a proof based solely on logical reasoning and argument, in a forum dedicated to physics ,is to automatically invite critique on this level. ?
And that it likewise assumes a burden of demonstrating a certain degree of rigor in this regard. Would you disagree?

Admittedly it has been a long time since I had any exposure to formal logic and my terminology and syntax may be incorrect , But I stand by my basic reasoning and am fairly certain that my recollection of the classic forms of Fallacious Argument and Deduction are somewhat accurate.
So if my understanding of logic, and its application in the science of physics, is insufficient, I am confident that you or someone else here will cheerfully set me straight.
Thanks

 

[JesseM]

(1) That whatever position and time is assumed for premise (#2) the Lorentz math can provide one , and only one, result.
(2) That this premise/assumption therefore predetermines the resulting conclusion.

(3) IF A then B
IF premise (#2) then conclusion (#3)
.
(4) That this is clearly inserting the desired conclusion into the premise and is not
valid under any idea of logical argument or deduction that I am aware of.

Uh, what? By definition, in any logical deduction, the conclusion follows necessarily from the premise. More generally, in any mathematical proof, the conclusions follow from whatever premises (axioms) you start with, if it's really a "proof" then it's logically impossible that the premises could be true while the conclusion was false. Do you disagree? If so, can you give an example of a mathematical proof or logical deduction where this is not so?

Here, the premises are just:
1) that it is possible to send signals which move "faster than light" as measured in some inertial frame, i.e. in that frame's coordinates, if dx is the coordinate distance between the signal being sent and the signal being received, and dt is the coordinate time, then dx > dt (in units where c = 1 like light-seconds and seconds)
2) the two postulates of relativity hold

From these premises (and perhaps some other implicit assumptions of SR like the idea that every event can be assigned coordinates in any inertial frame), it follows that 3) it should be possible to send signals back in time. Of course, if you don't like this conclusion you are free to reject one or both of these premises, no one is assuming that these premises are actually true in reality (most physicists would probably believe that 1 is false). The argument is just IF both 1) and 2) were true, then 3) would have to be true as well, or equivalently that the only way 3) can be false is if either 1) or 2) is false (or they both are false). So what are you trying to argue? Are you arguing that 1) and 2) could be true but 3) false? Or are you arguing that there could be a kind of "faster-than-light" signalling which would not satisfy 1), so that even though we call it "FTL" dx is not larger than dt for the sending/receiving events in any inertial frame (or the events of the signal being sent and being received somehow can't even be assigned coordinates in inertial frames?) Or are you arguing something else entirely? Either way, please explain in more detail which particular statement above you're disputing.

 

[Austin0]

[

QUOTE=JesseM;2018786]Uh, what? By definition, in any logical deduction, the conclusion follows necessarily from the premise. More generally, in any mathematical proof, the conclusions follow from whatever premises (axioms) you start with

Of course. But the key word here is follow. Not "is included." But are derived from the premise through logical progression. In this case obviously, NO logical progression is either necessary or possible because the conclusion is made inherently inevitable by the premise itself.
This is equivalent to assuming that an observer sees a polar bear in Florida in Jan. and thereby prove that there are polar bears in Florida and thus must have headed south for the winter.
Axioms are agreed upon as being self sufficient ,without need of further justification. I don't think that can reasonably be said of this premise.
GOing from the premise to the conclusion is not a matter of logical argument but is simply a matter of mathematical transformation. 0 deg. C to 32 deg. F In essence the premise and the conclusion are the same thing .
You may validly assume that a tachyon at 2c is "received" by an observer in frame A at the time and location you specified.
But you can not validly assume the event of the observation in A because this "possible" event is both causally and logically dependent on the event in B which is of course, your desired conclusion and the subject which is to be logically determined
.

2)If the two postulates of relativity hold

Once again the postulates of relativity are not in question,,,certainly not by me.

So what are you trying to argue? Are you arguing that 1) and 2) could be true but 3) false? Or are you arguing that there could be a kind of "faster-than-light" signalling which would not satisfy 1), so that even though we call it "FTL" dx is not larger than dt for the sending/receiving events in any inertial frame (or the events of the signal being

I am saying that 1) FTL is a valid assumption for these purposes.
2) You can validly assign coordinates on these terms directly into either frame as an actual reception event in that frame. And then proceed from there, through logical argument to whatever conclusions you can justify.
3) You cannot validly assign those coordinates to an event that is an observation and is not neccessarily even possible unless your conclusion is true.
Ie. If the tachyon were to be received in B at x'=20 at t'=10 [which would seem to be an equally possible occurrence] then in this case it would ,self evidently, be impossible for a proximate observer in A to be at x=20 at t=10
Would you agree with this?
Is there some other area where you think I am being too vague ??

 

[Fredrik]

Of course. But the key word here is follow. Not "is included." But are derived from the premise through logical progression. In this case obviously, NO logical progression is either necessary or possible because the conclusion is made inherently inevitable by the premise itself.

Huh?! What are you talking about? The observation that "the conclusion is made inherently inevitable by the premise itself" is the "logical progression".

Let's consider a simple example. If x is a real number that satisfies x+2=5, then x=3. We can prove this by using the properties of the real numbers:

x+2=5
(x+2)+(-2)=5+(-2)
x+(2+(-2))=5+(-2)
x+0=5+(-2)
x=5+(-2)
x=3

But these calculations show that the conclusion that x=3 is made inherently inevitable by the premise itself, so according to your logic, no logical progression could be made and it was impossible to prove that the premise implies the conclusion!?

 

[JesseM]

[ Of course. But the key word here is follow. Not "is included." But are derived from the premise through logical progression. In this case obviously, NO logical progression is either necessary or possible because the conclusion is made inherently inevitable by the premise itself.

As Fredrik says, the distinction you are making between a conclusion being "included" in the premise and "following" from the premise makes little sense to me. In both cases you can use logic to show that the conclusion is 100% inevitable if the premises are true, so what's the difference you're talking about? Are you just talking about some vague notion of how "obvious" it is that the conclusion is implied by the premises in a conceptual sense? Perhaps it will help if you address Fredrik's example where the premise is x+2=5 and the conclusion is x=3, which for anyone familiar with basic algebra is extremely obvious without needing to go through steps, but if you want to prove it in a formal way you do have to go through a series of basic algebraic steps like the ones Fredrik gave. Do you think in this case the conclusion is "included" in the premise" or is "derived from the premise through logical progression"?

This is equivalent to assuming that an observer sees a polar bear in Florida in Jan. and thereby prove that there are polar bears in Florida and thus must have headed south for the winter.

The third step--that the polar bear must have headed south--does not really follow in a purely logical way. But yes, if your premise is that an observer sees a polar bear in Florida in Jan., then that implies the conclusion that there exists at least one polar bear in Florida in Jan (at least if we include an obvious premise that the observer can only see X at a certain place and time if that X is present at that place and time). Of course this is only an "if-then" conditional, if the premise is false than the conclusion could be false too. It's the same with the FTL example, the premise that FTL signalling is possible could well be false (most scientists would probably bet it's false), in which case the conclusion of sending information backwards in time could be false too.

Axioms are agreed upon as being self sufficient ,without need of further justification. I don't think that can reasonably be said of this premise.

If you're suggesting somehow that we can only adopt axioms that we believe are self-evidently true, that's definitely wrong. In math you can pick whatever axioms you want, and explore what conclusions would follow from them, as long as they don't lead you to a logical contradiction (proving some statement is both true and false simultaneously). For example, we are free to start with the axioms of Newtonian physics and investigate the consequences even though we no longer believe these axioms are perfectly correct in the real universe. And as another example, when mathematicians like Saccheri first explored the result of rejecting the parallel postulate of Euclidean geometry, leading to the mathematics of non-Euclidean geometry, the idea that parallel lines could meet was considered self-evidently false in the real world, but they nevertheless thought it was interesting to explore the logical consequences of non-Euclidean axioms, which didn't lead to any logical contradictions. Later it was realized that if "parallel lines" were re-interpreted to mean geodesics on curved surfaces than non-Euclidean axioms could actually describe something in the real world, but not at first. Likewise, today mathematicians explore the consequences of either accepting or rejecting certain axioms in set theory, like the axiom of choice.

GOing from the premise to the conclusion is not a matter of logical argument but is simply a matter of mathematical transformation.

I'm not sure what you mean by "logical argument". If you mean a logical argument in english language, that's not how formal mathematical proofs are supposed to work--in any formal proof you're supposed to have certain axioms and certain absolute rules for generating new statements from prior ones (rules that are purely algorithmic and require no understanding of what the statements 'mean'), and then by generating a series of statements using these rules you get to the conclusion. In a formal proof a machine could check whether each step follows the rules, the entire proof just involves manipulating symbols according to the predefined rules, just like the steps Fredrik gave in going from the premise x+2=5 to the conclusion x=3.

You may validly assume that a tachyon at 2c is "received" by an observer in frame A at the time and location you specified.

So you think it's valid to take as a premise that a certain signal was sent at x=0 and t=0 in A's coordinates, and received at x=20 and t=10 in A's coordinates? You don't have a problem with the idea that both the event of the sending and the event of the receiving can be localized and assigned some well-defined coordinates?

But you can not validly assume the event of the observation in A because this "possible" event is both causally and logically dependent on the event in B which is of course, your desired conclusion and the subject which is to be logically determined

Huh? What is the difference between the event of the signal being received and the event of the "observation"? Isn't the observation just noticing what ruler-marking and clock time are next to the tachyon detector at the moment it lights up (signifying it's just received a signal), specifically observing that it's next to the x=20 mark and the clock at that mark reads t=10 seconds?

I still really don't have the slightest understanding of what you're saying here. Perhaps you're arguing that although it is valid to take as a premise that the signal was sent at x=0, t=0 and received at x=20,t=10 in A's coordinate system, it is not valid to use the Lorentz transformation to find what the coordinates of these same two events would be in B's coordinate system? Is that it?

Once again the postulates of relativity are not in question,,,certainly not by me.

I didn't suggest they were, I'm just pointing out that it's logically necessary to take as a premise that the postulates of relativity are valid in order to prove that FTL signalling implies backwards-in-time signalling.

I am saying that 1) FTL is a valid assumption for these purposes.
2) You can validly assign coordinates on these terms directly into either frame as an actual reception event in that frame.

So do you accept that, for a signal to qualify as "FTL", we must be able to assign coordinates to the event of it being sent and the event of it being received in some inertial frame, and in this frame dx (the difference in x-coordinates of these events in this frame) must be larger than dt (the difference in t-coordinates of the two events)?

3) You cannot validly assign those coordinates to an event that is an observation and is not neccessarily even possible unless your conclusion is true.

Wait, you're saying I can't assign coordinates to the events of the signal being sent and the signal being received? Or are you saying I can assign coordinates to these events in any frame, but that the coordinates that different frames assign to them won't necessarily obey the Lorentz transformation? Or are you saying something else entirely? Your words are extremely unclear to me, and I still don't know what you mean by "an event that is an observation".

Ie. If the tachyon were to be received in B at x'=20 at t'=10 [which would seem to be an equally possible occurrence] then in this case it would ,self evidently, be impossible for a proximate observer in A to be at x=20 at t=10
Would you agree with this?

Of course, if you're talking about a single event of a single tachyon signal being received, I'd agree that single event cannot both have coordinates x=20, t=10 in A and coordinates x'=20, t'=10 in B, since I'd say the coordinates of anyone event in two different frames must be related by the Lorentz transform (though I'm not clear on whether you'd agree). On the other hand, if FTL signals are possible and relativity is true, I'd say it's certainly possible to send two different tachyon signals from the origin, one of which is received at x=20, t=10 in A (which by the Lorentz transform would correspond to x'=20, t'=-10 in B) and the other is received at x'=20, t=10 in B (which by the Lorentz transform would correspond to x=46.666..., t=43.333... in A)--in this case we are talking about two distinct events at different points in spacetime. Similarly, since we can send signals at 0.5c in any frame, it would be quite possible to send two different signals from the origin so that one was received at x=5, t=10 in A while the other was received at x'=5, t'=10 in B.

 

[Austin0]

Huh?! What are you talking about? The observation that "the conclusion is made inherently inevitable by the premise itself" is the "logical progression".

Let's consider a simple example. If x is a real number that satisfies x+2=5, then x=3. We can prove this by using the properties of the real numbers:

x+2=5
(x+2)+(-2)=5+(-2)
x+(2+(-2))=5+(-2)
x+0=5+(-2)
x=5+(-2)
x=3

But these calculations show that the conclusion that x=3 is made inherently inevitable by the premise itself, !?

Although the above is true it is not what I was saying and is not really applicable to the immediate question.
If x is the subject of a different enquiry,[solution to a different equation] in which x has more than one possible value and you want to prove the solution is 3 ,then inserting the premise x+2=5 is including the conclusion.
Would you disagree with this?

If it is a question of possible temperatures and you want to prove the solution is 98.6 F,
then inserting the premise 37 C, is including the conclusion in the premise.
True?
If the purpose is to prove that 98.6 F is equivalent to 37 C then this is a completely different inquiry .

The purpose of the case case in point , is not to prove that x=20 at t=10 in A is equivalent to x'=20 at t'= -10 in B , through the Lorentz transformation. That is beyond question and is "inherantly inevitable"

The question is proving that [in B] x'=20 at t'= -10 specifically , out of possible values .
In which case inserting the premise x=20 at t=10 in A is obviously precluding any other possible solutions and is including the conclusion in the premise.
It is equivalent to directly inserting the desired conclusion as a premise.
You could, of course, validly do exactly that, but then there would not be much significance to any results of the exercise , as far as demonstrating why FTL implies time travel.

 

[JesseM]

If x is the subject of a different enquiry,[solution to a different equation] in which x has more than one possible value and you want to prove the solution is 3 ,then inserting the premise x+2=5 is including the conclusion.
Would you disagree with this?

It's hard to really agree or disagree when you haven't explained what it means to say a premise "includes" the conclusion...apparently you don't just mean the premise "logically implies with 100% certainty" the conclusion, since this is true of every single mathematical proof whatsoever. Can you name a single proof in all of mathematics where the conclusion is not included in the premise?

Also, regardless of whether you feel this is too obvious to be called a mathematical proof, would you agree with the statement "IF [x+2=5] THEN [x=3]"? Do you agree it's impossible for the conclusion to be false in any situation where the premise happens to be true? If so, I wonder if you'd agree or disagree with the statement "IF [relativity is valid and FTL signalling is possible] THEN [backwards in time signalling is possible]". Regardless of whether you think the proof is too obvious somehow, do you agree that in any universe where the premise [relativity is valid and FTL signalling is possible] happens to be true, it must also be true that [backwards in time signalling is possible], it's just as impossible for the premise to be true and the conclusion false here as it is for the case of the premise [x+2=5] and the conclusion [x=3]?

If it is a question of possible temperatures and you want to prove the solution is 98.6 F,
then inserting the premise 37 C, is including the conclusion in the premise.

If it's an empirical question then obviously you can't assume anything about the temperature without making measurements. But if you just write the if-then conditional "IF [the temperature is 37 C] THEN [the temperature is 98.6 F]", this is a perfectly correct statement, it is indeed impossible for the second statement to be false IF the first is true. In saying this, there's no need to believe the first statement actually is true! Similarly, there's no need to believe the statement [relativity is valid and FTL signalling is possible] holds true in our universe--most physicist would bet that FTL signalling is not allowed by the laws of physics! The argument is simply another if-then conditional, saying that in any possible universe where the premise was true, the conclusion [backwards in time signalling is possible] would have to be true as well. Therefore, if you believe the conclusion is false (as I would bet it is in our universe), you must conclude that some aspect of the premise is false as well (either relativity fails or FTL signalling is not possible).

The question is proving that [in B] x'=20 at t'= -10 specifically , out of possible values .
In which case inserting the premise x=20 at t=10 in A is obviously precluding any other possible solutions and is including the conclusion in the premise.
It is equivalent to directly inserting the desired conclusion as a premise.

Again, please explain how any mathematical proof can avoid inserting the desired conclusion as a premise, if in every proof the conclusion follows with perfect logical certainty from the premises. If you think there's a mathematical proof where the conclusion is not inserted as a premise, give an example!

Also, as always, the proof takes the form of an if-then conditional where you're just saying that if the premise is true the conclusion follows, you're not actually endorsing the likelihood of either the premise or the conclusion. You may feel that the statement "IF [relativity is valid and FTL signalling is possible] THEN [backwards in time signalling is possible]" is too trivial to be even worth mentioning, but do you actually disagree with it? Presumably you wouldn't actually disagree with the if-then conditionals "IF [x+2=5] THEN [x=3]" or "IF [the temperature is 37 C] THEN [the temperature is 98.6 F]", right?

but then there would not be much significance to any results of the exercise , as far as demonstrating why FTL implies time travel.

So you are saying you disagree that FTL + relativity implies time travel? You think the if-then conditional "IF [relativity is valid and FTL signalling is possible] THEN [backwards in time signalling is possible]" is false in a way that the if-then conditionals "IF [x+2=5] THEN [x=3]" and "IF [the temperature is 37 C] THEN [the temperature is 98.6 F]" are not? (unless you actually think they are false too) If so, your reason in the first case can't just be that the premise is "included" in the conclusion, since it seems you would say the same thing about the second two if-then conditionals as well, but you (hopefully) don't judge them to be false.

 

[LittleRocks]

Hi,as my understanding of your question is a bit of silly maybe,but may be can be a help to you i hope.As we all know,all the forces(4 basics forces)are traveling in the speed of light,so if objectA can travel faster than the speed of light relative to the objectB,then the objectA will recive the foces which came from objectB in the previous time.

 

[Austin0]

It's hard to really agree or disagree when you haven't explained what it means to say a premise "includes" the conclusion...apparently you don't just mean the premise "logically implies with 100% certainty" the conclusion, since this is true of every single mathematical proof whatsoever. Can you name a single proof in all of mathematics where the conclusion is not included in the premise?

Also, regardless of whether you feel this is too obvious to be called a mathematical proof, would you agree with the statement "IF [x+2=5] THEN [x=3]"?

How could I not ,,,especially since I explicitly stated my agreement with this in the last post?

Do you agree it's impossible for the conclusion to be false in any situation where the premise happens to be true?

In the above example ,of course I agree.

If so, I wonder if you'd agree or disagree with the statement "IF [relativity is valid and FTL signalling is possible] THEN [backwards in time signalling is possible]".

As stated here I would have to agree completely. To think otherwise would mean being able to "prove" that in this hypothetical situation it was impossible.
Equivalent to trying to "prove" that mental telepathy or time travel itself were impossible.

Regardless of whether you think the proof is too obvious somehow, do you agree that in any universe where the premise [relativity is valid and FTL signalling is possible] happens to be true, it must also be true that [backwards in time signalling is possible], it's just as impossible for the premise to be true and the conclusion false here as it is for the case of the premise [x+2=5] and the conclusion [x=3]?

Same as above.
Are you suggesting that the term "is possible" is synonymous with "is implied"

If it's an empirical question then obviously you can't assume anything about the temperature without making measurements.

But isn't this case, in fact, a hypothetical empirical question?

But if you just write the if-then conditional "IF [the temperature is 37 C] THEN [the temperature is 98.6 F]", this is a perfectly correct statement, it is indeed impossible for the second statement to be false IF the first is true.

As before; in my last post I explicitly acknowledged the obvious validly of this statement.

In saying this, there's no need to believe the first statement actually is true! Similarly, there's no need to believe the statement [relativity is valid and FTL signalling is possible] holds true in our universe--most physicist would bet that FTL signalling is not allowed by the laws of physics! The argument is simply another if-then conditional, saying that in any possible universe where the premise was true, the conclusion [backwards in time signalling is possible] would have to be true as well. Therefore, if you believe the conclusion is false (as I would bet it is in our universe), you must conclude that some aspect of the premise is false as well (either relativity fails or FTL signalling is not possible).

Are you saying that if SR is true and FTL signalling being possible is also true then
1) backward time signally must be true as a purely logical possibility?
I would agree.
OR
2) it is impossible that time traveling signals are false as a physical possibility in reality , [even though the premises might be true]?
I disagree.
OR
3) time traveling signals are implied by these stated premises?

Again, please explain how any mathematical proof can avoid inserting the desired conclusion as a premise, if in every proof the conclusion follows with perfect logical certainty from the premises. If you think there's a mathematical proof where the conclusion is not inserted as a premise, give an example!

In the sense that the conclusion is inherently implicit in the premises , this is obviously true ,within the abstract realm of mathematics, by definition.
Would you agree that logic , like mathematics itself , is boundless? Limited only by human invention. Containing a vast array of forms ,definitons of axioms,givens,premises , proofs etc, etc. Do you believe that the forms that apply within the abstract realm of mathematics, numbers theory etc. are exactly the same as the logic and proof as it applies to physics?
Also, as always, the proof takes the form of an if-then conditional where you're just saying that if the premise is true the conclusion follows, you're not actually endorsing the likelihood of either the premise or the conclusion. You may feel that the statement "IF [relativity is valid and FTL signalling is possible] THEN [backwards in time signalling is possible]" is too trivial to be even worth mentioning, but do you actually disagree with it?

Presumably you wouldn't actually disagree with the if-then conditionals "IF [x+2=5] THEN [x=3]" or "IF [the temperature is 37 C] THEN [the temperature is 98.6 F]", right?

As above.

So you are saying you disagree that FTL + relativity implies time travel?

Yes.

You think the if-then conditional "IF [relativity is valid and FTL signalling is possible] THEN [backwards in time signalling is possible]" is false in a way that the if-then conditionals "IF [x+2=5] THEN [x=3]" and "IF [the temperature is 37 C] THEN [the temperature is 98.6 F]" are not? (unless you actually think they are false too) If so, your reason in the first case can't just be that the premise is "included" in the conclusion, since it seems you would say the same thing about the second two if-then conditionals as well, but you (hopefully) don't judge them to be false.

Me too. Hope that I am not that dim witted, that is.

 

[Austin0]

But these calculations show that the conclusion that x=3 is made inherently inevitable by the premise itself, so according to your logic, no logical progression could be made and it was impossible to prove that the premise implies the conclusion!?

[/QUOTE] If I was stating that the very validity of a proof or demonstration was then evidence that it was invalid [as you are implying here] ,then self evidently I should be placed under care , in some nice institution.

On the basis of the line reasoning of the hypothesis ,wouldn't the following apply.

We could posit a bi-directional transmission at x=0 in A .

Assume another observer in A at x=(-20 ) at t=10 who sees the reception in B.

From this, by application of the transform conclude that this reception occurred at t'=43.34 in B
Is this correct??
From this we get
_____________________________________________________________
1) A hypothetical tachyon that travels into the future in one direction but into the past in the opposite direction.

2) Moves slower and takes longer traveling to the receiver that is moving towards it than it does to the receiver moving away from it , in the same frame (B).

3) Some how, are observed at exactly equal times and distances in both directions in the other frame (A)

4) On the basis of JesseM's contention that there is no difference between observation of reception and actual reception with regard to determining velocity , we then have two wildly different relative velocities [according to direction] in one frame but the exact same relative velocity in both directions in the other frame , just as if it was light or maybe a frame actually at rest.

So I would like to know if any of the above is either incorrect or an invalid inference.

I would particularly like your commentary on 2) which to me seems like a huge violation of any kind of logically expectable behavior.

Do you think this is a reasonable picture of a possible hypothetical particle?
Thanks

 

[Fredrik]

Austin, please learn to use the quote tags properly. It would make your posts easier to read. (Tip: Use the preview feature and don't submit the reply until you get it right).

I find it hard to understand what you're trying to say because you're saying things that don't make sense to me. One example is that you're using the word "observer" in a strange way. There's no need to distinguish between the notions "physical observer" and "inertial frame" since the only thing we care about when we mention a physical observer is how he/she would assign coordinates to events. You keep talking about observers at specific locations, but it only makes sense to do that when you're introducing a new coordinate system (with the origin at the location you specified).

Another example of a phrase that doesn't make sense to me is "sees the reception in B". Seeing doesn't have anything to do with it, and I don't know if you mean that the reception happens in B or the seeing that happens in B, but it doesn't make sense either way. Events don't "happen in a frame". They are just points in spacetime that are assigned coordinates by a frame.

Let's go back to what you said earlier, and do it right:

Hypothesis-----That given the existence of Tachyons that could travel at 2c they would travel backwards in time. Be received by some observer before the time of emmission.

Premise (#1) That a tachyon transmission is initiated in frame A at position x=0 at time t=0.
Premise (#2) That an observer in frame A located at x=20 at time t=10 observes the reception of this transmission by a proximate observer in frame B.

By application of the Lorentz transformation it is Concluded (#3) that this observer in frame B would at the moment of reception be located at x'=20 at time t'= -10

Premise #1 is that there's a tachyon transmission event* at (0,0) in frame A. (It doesn't make sense to say that it happens "in" frame A. Just say that it's an event, and then specify its coordinates in some frame).

Premise #2 is that there's a tachyon transmission event at (10,20) in frame A. (The stuff you said about observers and frame B makes no sense to me).

Edit: I should of course also have mentioned that the tachyon mentioned in #2 is the same tachyon as the one mentioned in #1.

Now there are two ways to make sense of what you said next.

Option 1: We choose frame B to be the frame that has the same origin as A and a velocity of 0.8c in A. Then we do a Lorentz transformation to find the coordinates of these events in B. The results are (0,0) and (-10,20).

Option 2: We choose frame B to be a frame that has the same origin as A and a velocity v in A, but we don't specify what v is. Instead we specify that a Lorentz transformation from A to B must transform (10,20) to (-10,20) and determine v from that. We do the math and find that v=0.8c.

*) By "tachyon transmission event", I mean an event that's either an emission event or a dection event. Different observers may disagree about whether a transmission event is an emission or a detection.

 

[JesseM]

If so, I wonder if you'd agree or disagree with the statement "IF [relativity is valid and FTL signalling is possible] THEN [backwards in time signalling is possible]".

As stated here I would have to agree completely. To think otherwise would mean being able to "prove" that in this hypothetical situation it was impossible.
Equivalent to trying to "prove" that mental telepathy or time travel itself were impossible.

Regardless of whether you think the proof is too obvious somehow, do you agree that in any universe where the premise [relativity is valid and FTL signalling is possible] happens to be true, it must also be true that [backwards in time signalling is possible], it's just as impossible for the premise to be true and the conclusion false here as it is for the case of the premise [x+2=5] and the conclusion [x=3]?

Same as above.
Are you suggesting that the term "is possible" is synonymous with "is implied"

You seem to be misunderstanding what I mean by "is possible"--I am talking about whether something is physically possible, a question which depending on the laws of physics will have a definite yes or no answer, not using the word "possible" in the sense of "might be true and might not". For example, according to the laws of physics as currently understood, it would definitely be physically possible for me to move at 0.8c relative to the Earth, even though this would be hard to realize in practice; for this to be physically impossible, our current understanding of physics would have to be seriously wrong.

So, you should interpret my if-then proposition in a similar way, as "IF [relativity is valid and FTL signalling is physically possible] THEN [backwards in time signalling is physically possible]". In any universe where the laws of physics both respect relativity and allow FTL signalling, the same laws of physics must also allow backwards-in-time signalling, in other words. So, do you think this if-then conditional is false? If you do, then you need to come up with a better argument for why you think it's false than "the conclusion is included in the premise", since you'd also say the conclusion is included in the premise in the conditional "IF [x+2=5] THEN [x=3]", yet you'd agree with me that this if-then conditional is true.

If it's an empirical question then obviously you can't assume anything about the temperature without making measurements.

But isn't this case, in fact, a hypothetical empirical question?

"hypothetical empirical question" is different from "empirical question". For instance, if hypothetically my empirical measurements showed the temperature was 37 C, then the temperature would be 98.6 F--this if-then conditional is true regardless of whether this hypothetical is true in the real world! But if I want to know what the temperature is in the real world, that's a non-hypothetical empirical question that requires me to go out and make some actual measurements.

Similarly, if hypothetically empirical measurements showed that it was physically possible to transmit information faster than light, then if relativity was valid it would also be physically possible to transmit information backwards in time. This if-then conditional is true regardless of whether the hypothetical about it being physically possible to send FTL signals is true in the real world (it probably isn't).

Are you saying that if SR is true and FTL signalling being possible is also true then
1) backward time signally must be true as a purely logical possibility?
I would agree.
OR
2) it is impossible that time traveling signals are false as a physical possibility in reality , [even though the premises might be true]?
I disagree.
OR
3) time traveling signals are implied by these stated premises?

2. If relativity is respected and FTL signals are a physical possibility, then backwards-in-time signals must be a physical possibility as well.

Again, please explain how any mathematical proof can avoid inserting the desired conclusion as a premise, if in every proof the conclusion follows with perfect logical certainty from the premises. If you think there's a mathematical proof where the conclusion is not inserted as a premise, give an example!
In the sense that the conclusion is inherently implicit in the premises , this is obviously true ,within the abstract realm of mathematics, by definition.

And when you talked about "conclusions being included in the premises", is this the sense in which you meant it, that "the conclusion is inherently implicit in the premises"? Or did you have some other meaning in mind?

Would you agree that logic , like mathematics itself , is boundless? Limited only by human invention. Containing a vast array of forms ,definitons of axioms,givens,premises , proofs etc, etc. Do you believe that the forms that apply within the abstract realm of mathematics, numbers theory etc. are exactly the same as the logic and proof as it applies to physics?

I'm not sure what you mean by this question. Obviously we could write up different possible dynamical equations for the fundamental laws of physics which would lead to different possible predictions, and only one set of predictions can actually be true in our universe, so which equations accurately describe the physics of our universe is an empirical question. However, if we are just writing if-then conditionals of the form "IF [the laws of physics have property X] THEN [Y must be physically possible]", judging the truth or falsity of such propositions is a purely mathematical issue, we don't have to worry about the empirical question of whether the laws of physics do in fact have property X in our own universe. For example, would you agree the statement "IF [gravity obeys an inverse-cube force law] THEN [if I am twice as close to a gravitating point mass as you are, I will feel 8 times the force]" is true, even though we know that gravity actually obeys an inverse-square force law (at least in the Newtonian limit) in the real world?

 

[Austin0]

Austin, please learn to use the quote tags properly. It would make your posts easier to read. (Tip: Use the preview feature and don't submit the reply until you get it right).

Sorry and thanks for the tip.

Another example of a phrase that doesn't make sense to me is "sees the reception in B". Seeing doesn't have anything to do with it, and I don't know if you mean that the reception happens in B or the seeing that happens in B, but it doesn't make sense either way. Events don't "happen in a frame". They are just points in spacetime that are assigned coordinates by a frame.

In this case I think it is appropriate for clarity. JesseM has described the "event" as literally looking from one frame and observing the opposite counterpart in the "act" of reception. I am sure you are right on some level and I will try to learn the appropriate terminology to completely describe events within the system.
In this case I think it is pertinent to distinguish between events that are actual receptions of a tachyon and events which are simply the observation from another frame of the reception event [but which actually involves no tachyons]

Let's go back to what you said earlier, and do it right:

Premise #1 is that there's a tachyon transmission event* at (0,0) in frame A. (It doesn't make sense to say that it happens "in" frame A. Just say that it's an event, and then specify its coordinates in some frame).

OK

Premise #2 is that there's a tachyon transmission event at (10,20) in frame A. (The stuff you said about observers and frame B makes no sense to me).

Incorrect. That is exactly what I was attempting to clarify.
There is NO tachyon event of any kind. There is merely the observation such an event happening proximately in frame B
[

Now there are two ways to make sense of what you said next.

Option 1: We choose frame B to be the frame that has the same origin as A and a velocity of 0.8c in A. Then we do a Lorentz transformation to find the coordinates of these events in B. The results are (0,0) and (-10,20).

This option.

*) By "tachyon transmission event", I mean an event that's either an emission event or a dection event. Different observers may disagree about whether a transmission event is an emission or a detection

Undoubtedly true generally, but for now, we are only considering observers in A and B and us , so can we just for this discussion consider that we all agree on this particular transmission and reception.?

Thanks for your patience and I hope I have cleared up the meaning wrt that post enough that I might get your feedback on the main body.

 

[Austin0]

=JesseM;2021006]

So, you should interpret my if-then proposition in a similar way, as "IF [relativity is valid and FTL signalling is physically possible] THEN [backwards in time signalling is physically possible]". In any universe where the laws of physics both respect relativity and allow FTL signalling, the same laws of physics must also allow backwards-in-time signalling, in other words. So, do you think this if-then conditional is false? true.

This IS the question. Based solely on these stated premises, I think that it is not inherently inevitable or adequately demonstrated that this is neccessarily true.

"hypothetical empirical question" is different from "empirical question".

No argument there.

And when you talked about "conclusions being included in the premises", is this the sense in which you meant it, that "the conclusion is inherently implicit in the premises"? Or did you have some other meaning in mind?

If, for example , the question was the hypothetical empirical question of a chain of catalytic reactions. With several possible, reasonable quantitative outcomes.The question and conclusion being the quantitative outcome of the intermediate one.

The Axioms: the pertinent applicable molecular physics.
Premise #1: the initial quantitative combination.
Premise #2: the final quantitative outcome.
Which itself was only possible through a single specific intermediate result and also directly determined the intermediate result.

What would you say in this case ? If this was presented as a demonstration or proof of the intermediate quantitative result, would you possibly agree that this could be described as including the conclusion in a premise?
Of course in this situation it would be subject to direct empirical determination while tachyons are so hard to catch.
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It would be great ,if you have time, to get your perspective on my post #65

Thanks for your patience .I am sure neither one of us enjoys semantic questions and I hope we both agree that semantics is not the real question here but is simply a small inherant part needing clarification.

 

[JesseM]

On the basis of the line reasoning of the hypothesis ,wouldn't the following apply.

We could posit a bi-directional transmission at x=0 in A .

Assume another observer in A at x=(-20 ) at t=10 who sees the reception in B.

What does "reception in B" mean? The reception is just the physical event of the receiving device picking up the signal, physical events don't happen "in" one frame or another, and any physical event can be assigned coordinates in every frame (with the coordinates that different frames assign to the same event being related by the Lorentz transform).

But let's suppose that was just an awkward way of saying you're interested in knowing the coordinates in B of this event of the second signal being received. In that case, with v=0.8c and gamma=1.666..., the coordinates in B would be:

x' = 1.666...*(-20 - 0.8*10) = -46.666...
t' = 1.666...*(10 + 0.8*20) = 43.3333...

From this, by application of the transform conclude that this reception occurred at t'=43.34 in B
Is this correct??

43.33..., but close enough.

From this we get
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1) A hypothetical tachyon that travels into the future in one direction but into the past in the opposite direction.

Not "a" tachyon, but two different tachyon signals going in different directions and received at different points in spacetime. Yes, one goes into the past and the other into the future in B's frame. This shouldn't be all that suprising, since if FTL-and-forward-in-time signalling is possible in any frame, it must be possible in every frame; likewise, if backwards-in-time signalling is possible in any frame, it must be possible in every frame. So, in any frame it should be possible to do both with multiple tachyon signals.

2) Moves slower and takes longer traveling to the receiver that is moving towards it than it does to the receiver moving away from it , in the same frame (B).

Are you assuming the receivers are at rest in A? It makes no difference to the thought-experiment whether they are at rest in A or B or some totally different frame, all that matters is that one happens to be at position x=20 at time t=10 in A's frame, and the other happens to be at position x=-20 at time t=10 in A's frame. But note that if you do assume the receivers are at rest in A, then in B they will both be moving in the -x' direction just like the origin of A (since B's origin is moving in the +x direction in A), so in B it will take longer to reach the receiver moving away from it (but again, you could easily assume the receivers were moving in the +x' direction and it'd make no difference to the thought-experiment as long as the receivers were there to meet the signals at the same places and times).

3) Some how, are observed at exactly equal times and distances in both directions in the other frame (A)

Is it surprising to you that signals with a speed other than light could have symmetrical speeds and travel times in one frame but asymmetrical speeds and travel times in another? Aside from the whole backwards-in-time issue, this is quite possible with slower-than-light signals too. Imagine two signals are sent in opposite directions at speed 0.5c from x=0 and t=0 in the A frame, so one is received to the right of the origin at x=10, t=20 while the other is received to the left of the origin at x=-10, t=20. In B's frame, the coordinates of the one on the right being received are:

x' = 1.666...*(10 - 0.8*20) = -10
t' = 1.666...*(20 - 0.8*10) = 20

So this signal had a velocity of -0.5c in B's frame. And the coordinates of the one on the left being received are:

x' = 1.666...*(-10 - 0.8*20) = -43.333...
t' = 1.666...*(20 + 0.8*10) = 46.666...

So this signal had a larger velocity of -0.93c in B's frame.

4) On the basis of JesseM's contention that there is no difference between observation of reception and actual reception with regard to determining velocity , we then have two wildly different relative velocities [according to direction] in one frame but the exact same relative velocity in both directions in the other frame , just as if it was light or maybe a frame actually at rest.

Even in the A frame the signals have different velocities because velocity is a vector that has both magnitude and direction--the magnitude is the same for both signals in A (i.e. they have the same speed in A), but the directions are not. And as I said above, it's perfectly easy to arrange things so that two sublight signals have equal speeds in one frame but different speeds in another.