Having trouble understanding why FTL implies time travel

[JesseM]

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.

But you still haven't given a coherent explanation as to what you think the flaw in the demonstration was. All your talk about the conclusion being included in the premises was obviously irrelevant to showing that the demonstration is flawed, since you've agreed there are plenty of if-then conditionals where the conclusion is included in the premises and yet you believe the if-then statement is true.

Perhaps it would help if you answered another question. Do you agree that the premise [the laws of physics respect relativity AND FTL signalling is physically possible] is synonymous with the premise [the laws of physics respect relativity AND there is some inertial frame where, if we consider the difference in space coordinates dx and the difference in time coordinates dt of the events of a signal being sent and received, then dx > dt (in units where c=1)]? Do you agree that in any hypothetical universe where the first statement applies, the second statement should apply too, or do you think it is meaningful to talk about a hypothetical universe where the first applies but the second does not?

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.

You can only include the initial and final conditions as premises if you have already checked they are consistent with "the pertinent applicable molecular physics". If it is impossible that the specified final outcome could follow from the specified initial conditions according to the specified laws of physics, then you're using logically inconsistent starting assumptions. Of course, you're free to drop any specific assumptions about the laws of molecular physics beyond the notion that the laws of physics are such that the initial conditions would lead to the specified final outcome--no matter what initial and final conditions we choose, presumably some possible laws would predict that the initial condition would lead to the final one.

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?

Isn't it true that in any proof where the conclusion follows mathematically or logically from the starting assumptions, the conclusion is included in the premise? That still doesn't show why the demonstration is false. If it's mathematically impossible that there could be a universe where the laws were such that the premises were true (including both the initial and final results and whatever constraints you want to place on the laws of physics) but that the "specific intermediate result" did not occur, then surely that means the if-then conditional "IF [specified initial condition + specified final condition + specified laws of physics, if any] THEN [specified intermediate result]" would be true! Do you agree? If so, this has no relevance to showing why the if-then conditional about FTL and backwards-in-time signalling is false.

Of course in this situation it would be subject to direct empirical determination while tachyons are so hard to catch.

What part of it would be subject to empirical determination? If you found that the final conditions didn't follow the initial conditions, that would show your premises were false, but it wouldn't show the if-then conditional "IF [specified initial condition + specified final condition + specified laws of physics, if any] THEN [specified intermediate result]" was false. An if-then conditional is only false if it's logically possible for the premises to be true while the conclusion is false, as long as that's not logically possible then the if-then conditional is true, regardless of whether the premises are true or not in the real world. On the other hand, if all the premises were found to hold but the conclusion did not, then you must have been wrong when you said that the premises were "only possible through a single specific intermediate result and also directly determined the intermediate result".

It would be great ,if you have time, to get your perspective on my post #65

No problem, see my post above.

 

[Austin0]

=JesseM;2021713]What does "reception in B" mean?

What terminology should I correctly use.? reception event in B ?.

Not "a" tachyon, but two different tachyon signals going in different directions and received at different points in spacetime.

Yes , when I said "a" tachyon it was meant in the generic sense of a hypothetical abstract particle not as meaning a single particle.

Originally Posted by Austin0
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?

No , as specified the receivers are clearly in B.
As specified,, from within B the signals reception would be measured as being slower and taking longer in transit from the source to the receiver that is moving toward it x'=-46.66 than it takes in transit to the receiver moving away from it x'=20
In B this would be directly derived from the observed dx'/dt' .
In A this same conclusion would be derived from transformation of the observations in A.
or from direct observations of the events in B in the manner you described. Observers in A (10,20 ), (10,-20 ) looking over and observing the events and clocks in B.
Would you agree that both frames would agree on this?
Can you suggest any comparable situation where this could take place ie. where the signal ,particle , whatever would be observed to move slower and take longer to reach a location moving towards it that it does to reach a location moving away from it?

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

. We are not considering sub light occurences in this case are we?
But a particle like light with a velocity independant of the source.
Can you think of a situation where such a particle could possibly be observed to have an equal bidirectional measurement [like light] unless you assume 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

Thanks for reminding me of the difference between speed and velocity.
Here again we are not talking about sub light signals are we ?
Thanks for taking a look

 

[Austin0]

=JesseM;2021728]But you still haven't given a coherent explanation as to what you think the flaw in the demonstration was. All your talk about the conclusion being included in the premises was obviously irrelevant to showing that the demonstration is flawed, since you've agreed there are plenty of if-then conditionals where the conclusion is included in the premises and yet you believe the if-then statement is true.

IN all the places where I have encountered this proposition , here ,other threads in this forum , any number of books,Roger Penrose et al,,, the presentation has been made as pure assertion with no hint of conditionality. SR + FTL implies time travel. In some cases " neccessarily" implies t.t. In cases, just the direct "if we have FTL we can kiss causality and freewill goodby". Never any suggestion whatever that any other eventuallity was even remotely possible.
In this particular case, as soon as you introduced the assumption of the observation in A,, there was, in fact, no other possible conclusion. Would you disagree with this?

And this assumption was introduced without any suggestion of conditionality. But rather as a self sufficient axiom or established fact of physics. Actually, just as part of a process.
Would you disagree with this??

So there is NO question regarding SR or the actually stated "if" conditionality of FTL.

It is a question of the the inevitability of the transition from these premises to the unqualified assumption of the observation in A.
Would you agree this assumption completely determined the outcome from that point,
was in fact equivalent to that conclusion (A = B) ?
Can you say how this is any different from simply assuming the actual reception in B (-10,20) ??

Perhaps it would help if you answered another question. Do you agree that the premise [the laws of physics respect relativity AND FTL signalling is physically possible] is synonymous with the premise [the laws of physics respect relativity AND there is some inertial frame where, if we consider the difference in space coordinates dx and the difference in time coordinates dt of the events of a signal being sent and received, then dx > dt (in units where c=1)]? Do you agree that in any hypothetical universe where the first statement applies, the second statement should apply too, or do you think it is meaningful to talk about a hypothetical universe where the first applies but the second does not?

As far as I can see this is just a simple statement of the possibility of FTL in which case of course this is understood . Am I missing something here?


Isn't it true that in any proof where the conclusion follows mathematically or logically from the starting assumptions, the conclusion is included in the premise? That still doesn't show why the demonstration is false. If it's mathematically impossible that there could be a universe where the laws were such that the premises were true (including both the initial and final results and whatever constraints you want to place on the laws of physics) but that the "specific intermediate result" did not occur, then surely that means the if-then conditional "IF [specified initial condition + specified final condition + specified laws of physics, if any] THEN [specified intermediate result]" would be true! Do you agree? If so, this has no relevance to showing why the if-then conditional about FTL and backwards-in-time signalling is false.

What part of it would be subject to empirical determination? If you found that the final conditions didn't follow the initial conditions, that would show your premises were false, but it wouldn't show the if-then conditional "IF [specified initial condition + specified final condition + specified laws of physics, if any] THEN [specified intermediate result]" was false. An if-then conditional is only false if it's logically possible for the premises to be true while the conclusion is false, as long as that's not logically possible then the if-then conditional is true, regardless of whether the premises are true or not in the real world. On the other hand, if all the premises were found to hold but the conclusion did not, then you must have been wrong when you said that the premises were "only possible through a single specific intermediate result and also directly determined the intermediate result".

That was not premises ,plural but only the one premise #2
I think I am not making myself clear. I was not talking about the logic in this case per se.
I was talking about the validity of the conclusions as a proof when they arbitraily assumed a premise that determined the conclusion. ie. premise =final result >>>conclusion.
If you were presented with a demonstration like this wouldn't you question its significance and procedure?
Wouldn't you consider that it did not establish any compelling reason why it should be considered any more possible than the other possible eventualities or even neccessarily itself possible, except as a logical maybe?
Wouldn't you question its validity as a proof??
Thanks

No problem, see my post above

Thanks

 

[JesseM]

What terminology should I correctly use.? reception event in B ?.

I think it would be best just to talk about the coordinates that B assigns to the reception-event, since it's misleading to suggest that the event itself takes place "in" any particular coordinate system. To see why, imagine I want to define the position of a certain tree using a 2D spatial coordinate grid on a map--if I place the origin at one spot, then in that coordinate system I might say the tree is at 3.25 km north, 5.71 km east, but if I place the origin at a different spot, then in coordinate system #2 perhaps the tree is at 2.55 km north, 1.28 km east. Is the tree "in" one coordinate system or another? No, it's just there, in the ground, the two coordinate systems are just different ways of labeling its position. If I wished to I could physically realize each coordinate system by laying out a giant grid of rulers with the specified origins, and note which ruler-markings the tree was next to, but this isn't actually necessary, I can measure the coordinates of the tree without ever having to physically construct either coordinate system. It's the same with coordinate systems in SR--physical events are just events, they are just assigned different sets of coordinates by different systems, and although you can theoretically define each coordinate system in terms of a network of rulers and clocks there is no actual need to have such a grid in place.

No , as specified the receivers are clearly in B.

When did you specify that? And when you say they are "in" B, do you just mean they are at rest in B? There is certainly no need for them to be at rest in B in order for B to assign coordinates to the event of each receiver picking up a signal, they could just as well be moving at 0.9999c in B, it makes no difference.

As specified,, from within B the signals reception would be measured as being slower and taking longer in transit from the source to the receiver that is moving toward it x'=-46.66 than it takes in transit to the receiver moving away from it x'=20

Now I'm really confused--if the receivers are moving towards or away from the signals in B, obviously the receivers aren't at rest in B! So what did you mean when you said the receivers are "in" B, exactly? Again, in no sense are events or objects "native" to one coordinate system or another, any more than a tree in the ground is native to a particular 2D coordinate grid. But I thought you had already agreed with this, since back in post #50 you said:

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

So if you don't mean to suggest either the receivers or the reception-events were native to frame B, and you also don't mean the receivers are at rest in B, what do you mean when you say the receivers are "in" B?

Also, why do you say that one receiver is moving towards the signal and one is moving away from it, as seen in B? What frame are you imagining the receivers are at rest in? As I said before, if you imagine the receivers are at rest in frame A, that should mean that in B, the receiver that is moving towards from the origin where the signals were emitted is the one that receives it at x'=20 and t'=-10, while the receiver that's moving away from the origin is the one that receives it at x'=-46.666... and t'=43.333..., which seems to be the opposite of what you say above, so either you got it wrong or you're imagining the receivers are neither at rest in A nor at rest in B (in which case please explain how the receivers are supposed to be moving in both A and B).

In B this would be directly derived from the observed dx'/dt' .

What does "this" refer to, the fact that the signal received at x'=-46.666... was moving more slowly in B, or your claim that the tachyon receiver that received the signal at x'=-46.666... was moving away from rather than towards the signal it received?

In A this same conclusion would be derived from transformation of the observations in A.

What "same conclusion"? Are you talking about conclusion about the velocities of the tachyon signals/receivers in A's frame, or are you confusingly talking about the conclusions a person at rest in A would make about the coordinate velocities in B? Imagining actual people at rest in each frame is just a crutch, we don't need them to talk about how things work in different coordinate systems, and it'd be weirdly anthropomorphic to ask what one coordinate system concludes about what's going on in a different coordinate system--if you want to talk about coordinate velocities in B, just talk about frame B, there's no need to bring frame A into it unless you already know the velocity in A and want to use the Lorentz transform (or the velocity addition formula) to derive the velocity in B.

Can you suggest any comparable situation where this could take place ie. where the signal ,particle , whatever would be observed to move slower and take longer to reach a location moving towards it that it does to reach a location moving away from it?

It's hard to think of a "comparable" situation since I don't really understand what velocities you are imagining for the receivers in B. But in general, sure, it can take longer for a receiver moving towards a signal to catch up with it than for a receiver moving away from the signal, all you need for this to work is to have the receiver moving towards the signal start out at a sufficiently larger distance when the signal is sent. For example, I can send two signals at c in opposite directions from the origin, and at the moment I send the signals (according to the definition of simultaneity of the inertial frame I'm using), one receiver is at x=-90 l.s. moving towards the origin at 0.5c, while the other is at x=10 l.s. moving away from the origin at 0.5c. In this case the light signal will catch up with the receiver moving away from the origin at t=20 s, while the light signal will catch up with the receiver moving towards the origin at t=60 s. I don't know if this is comparable to the tachyon example because I don't know what velocities you are imagining for the receivers in B, and thus I don't know their "initial" positions at t'=0 in B when the tachyon signals were sent.

We are not considering sub light occurences in this case are we?
But a particle like light with a velocity independant of the source.

Huh? Where'd you get the idea a tachyon signal speed should be independent of the source? It definitely should not be, if we construct a tachyon transmitter according to a set procedure and put it at rest in frame A and see it sends signals at 2c in A, then based on the first postulate of relativity, if we construct an identical tachyon transmitter according to the same procedure and put it at rest in frame B, it should send signals at 2c in B (the first postulate says if you perform identical experiments in different inertial frames, each frame should observe the same results). The reason light signal speed is independent of the source is that the Lorentz transformations ensure that anything with dx/dt=c in one inertial frame will also have dx'/dt'=c in every other inertial frame (they should ensure this, since the Lorentz transformations were derived from the two postulates, one of which is that things moving at c have the same speed in all inertial frames!) If you use the Lorentz transformation to find the speed of a single FTL signal or object in different frames, you do not find that different frames agree on the speed as they do with light, so in this sense tachyon signals are just like sublight signals, which is why I brought them up as an analogy.

Can you think of a situation where such a particle could possibly be observed to have an equal bidirectional measurement [like light] unless you assume a frame actually at rest?

No one said that tachyon signals are "naturally" constrained to have an equal bidirectional speed in A like with light signals, it's just that we constructed a particular experiment where both signals moved at 2c in A, just like we could easily construct an experiment where two guns fired two sublight bullets at the same speed in opposite directions in some frame. If tachyon signalling were possible and relativity were respected, then it should be equally possible to design an experiment where one tachyon signal moves at 2c in A while the other moves at 3c in A (if this wasn't possible it would be a clear violation of the first postulate, since the tachyon signal moving at 2c in A must be moving at 3c in some other inertial frame).

 

[JesseM]

IN all the places where I have encountered this proposition , here ,other threads in this forum , any number of books,Roger Penrose et al,,, the presentation has been made as pure assertion with no hint of conditionality. SR + FTL implies time travel. In some cases " neccessarily" implies t.t.

How is that not a conditional? Do you imagine the authors are assuming FTL really is possible in our universe? If not, clearly they are saying "IF [SR + FTL], THEN [time travel]", which is exactly what my conditional was saying too. And of course, any if-then conditional in logic or mathematics or theoretical physics is meant to suggest that the truth of the conclusion follows "necessarily" if the premises are satisfied (though it does not mean to suggest the premises must be true in the real world, just as physicists who say 'if SR+FTL, then time travel' don't mean to suggest that FTL is actually physically possible).

In cases, just the direct "if we have FTL we can kiss causality and freewill goodby". Never any suggestion whatever that any other eventuallity was even remotely possible.

But you used the word "if" there yourself, so don't you see it's a conditional? And again, in any if-then conditional in logic or mathematics, if the if-then conditional is true then it is absolutely impossible for the premises to be true but the conclusions to be false. "If A, then B" would be false if it were "even remotely possible" for A to be true while B was false.

In this particular case, as soon as you introduced the assumption of the observation in A,, there was, in fact, no other possible conclusion. Would you disagree with this?

I don't understand what "observation in A" means--are you treating it as distinct from the notion of FTL? In other words, are you somehow imagining it's meaningful to imagine a universe where we can say FTL signalling is possible but somehow the event of transmission and reception cannot be assigned coordinates in A, or that they can be assigned coordinates but it isn't true that dx > dt?

If you just mean that once I introduced the assumption of FTL signaling (along with the prior assumption of relativity), then the conclusion of backwards-in-time signaling became inevitable, then I agree. But you seem to be arguing it's not inevitable that FTL signaling + relativity automatically implies backwards-in-time signaling.

And this assumption was introduced without any suggestion of conditionality.

"Conditionality" in "if-then conditional" does not mean there is any possibility that the conclusions might not follow from the premises! Again, think of the if-then conditional "if the temperature today is 37 C, then the temperature is 98.6 F." There's no way the "if" part could be true and yet the "then" part might not be true! The conditionality is just in the premise that the temperature today is 37 C, which might not be true. Similarly, when I say "if relativity and FTL, then backwards-in-time signaling", the conditional part is "relativity and FTL"--although I doubt relativity will turn out to be wrong, I think it's most likely that FTL will turn out to be forbidden by the fundamental laws of physics in the real world.

But rather as a self sufficient axiom or established fact of physics. Actually, just as part of a process.
Would you disagree with this??

Since I don't know what the assumption of "observation in A" means distinct from the assumption of FTL signaling + relativity (and it's certainly part of the assumptions of relativity that every possible event can be assigned coordinates in every possible inertial frame), I can't really answer this.

It is a question of the the inevitability of the transition from these premises to the unqualified assumption of the observation in A.
Would you agree this assumption completely determined the outcome from that point,
was in fact equivalent to that conclusion (A = B) ?
Can you say how this is any different from simply assuming the actual reception in B (-10,20) ??

In any mathematical proof, I suppose you could say that using the premises to derive the conclusion is logically no different from just assuming the conclusion at the outset, but it's certainly conceptually different in the sense that it may not be obvious to the human mind that the conclusion follows from the premises without going through a chain of reasoning. Similarly, without doing the Lorentz transformation math and applying the first postulate of relativity, it may not be obvious that if it's physically possible to send signals FTL, then in relativity this automatically implies it's physically possible to send signals backwards in time.

Perhaps it would help if you answered another question. Do you agree that the premise [the laws of physics respect relativity AND FTL signalling is physically possible] is synonymous with the premise [the laws of physics respect relativity AND there is some inertial frame where, if we consider the difference in space coordinates dx and the difference in time coordinates dt of the events of a signal being sent and received, then dx > dt (in units where c=1)]? Do you agree that in any hypothetical universe where the first statement applies, the second statement should apply too, or do you think it is meaningful to talk about a hypothetical universe where the first applies but the second does not?

As far as I can see this is just a simple statement of the possibility of FTL in which case of course this is understood . Am I missing something here?

To me they'd be synonymous, but it's not clear to me that you would agree, given the weird distinction you are making between FTL signaling and "observation in A" of FTL signaling. So you agree that if we have FTL signaling in a universe that obeys relativity, that automatically implies that using whichever inertial frame we have chosen, we can assign coordinates (x1,t1) to the event of the signal being sent and coordinates (x2,t2) to the event of the signal being received, and that (x2 - x1) > (t2 - t1)? If you agree with this much, do you not agree that if we transform the coordinates into other inertial frames, there will be frames where the time-coordinate of the signal being received is earlier than the time-coordinate of it being sent?


Isn't it true that in any proof where the conclusion follows mathematically or logically from the starting assumptions, the conclusion is included in the premise? That still doesn't show why the demonstration is false. If it's mathematically impossible that there could be a universe where the laws were such that the premises were true (including both the initial and final results and whatever constraints you want to place on the laws of physics) but that the "specific intermediate result" did not occur, then surely that means the if-then conditional "IF [specified initial condition + specified final condition + specified laws of physics, if any] THEN [specified intermediate result]" would be true! Do you agree? If so, this has no relevance to showing why the if-then conditional about FTL and backwards-in-time signalling is false.

On the other hand, if all the premises were found to hold but the conclusion did not, then you must have been wrong when you said that the premises were "only possible through a single specific intermediate result and also directly determined the intermediate result".

That was not premises ,plural but only the one premise #2

But surely if we only have premise #2 giving the final outcome, that alone isn't enough to directly determine the intermediate result, we at least need to add some premises about the laws of physics, if not also the premise about the initial condition.

I think I am not making myself clear. I was not talking about the logic in this case per se.
I was talking about the validity of the conclusions as a proof when they arbitraily assumed a premise that determined the conclusion. ie. premise =final result >>>conclusion.

Wait, you're saying the final condition of the system was the "conclusion" here, not the intermediate step? It would help if you explicitly wrote the if-then conditional you're referring to as I have done--would it be something like "IF [specified laws of physics + initial conditions X + final conditions Y], THEN [final conditions Y]"? If so, then obviously this is quite a trivial statement since the conclusion is directly stated as a premise rather than just implicitly determined by them, but the if-then conditional is nevertheless a logically valid one. But if that's not the if-then conditional you meant, then please spell it out. If you indeed meant the intermediate step to be the "conclusion" as I originally assumed, then when you say the intermediate step is "determined" by the final result, does that mean it is logically impossible for the final result to have occurred without the system passing through the intermediate step (or at least physically impossible in a universe obeying our laws of physics, which you included as a separate premise)? Or is there supposed to be some remote possibility that if we did an experiment we could see the final result in a system that never passed through the intermediate step?

 

[Fredrik]

In this case I think it is appropriate for clarity.

It isn't. Events don't happen in a frame. They are points in spacetime that are assigned coordinates by a frame. You didn't improve the clarity by saying "sees the reception in B". You just made it impossible to know what you meant.

Maybe you were trying to emphasize that you were talking about the B frame coordinates of the event, rather than about the event itself, but then you should have just said it the way I'm saying it now.

JesseM has described the "event" as literally looking from one frame and observing the opposite counterpart in the "act" of reception.

I don't know which of his statements you're referring to, but it doesn't matter. He was probably just saying that you can use one frame to assign coordinates to all the events, or something similar to that. If you look at the first thing he says in #74, you can see that he agrees with me about these things.

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]

If by "observation" you mean the detection of a light signal that was emitted at the tachyon transmission event, then yes, of course we have to distinguish between them, because the tachyon transmission event and the light detection event are obviously two different points in spacetime. However, there's no need to mention observation events at all in this scenario. They are completely irrelevant.

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

That makes no sense at all. You're saying that the tachyon that was emitted at (0,0) in A is never detected, but is still observed to be detected (which makes no sense), and that the detection happens in frame B (which also makes no sense).

There won't be an observation event as a consequence of the detection event unless there was a detection event! And events still don't happen in frames. They are points in spacetime that are assigned coordinates by frames.

We agree that premise #1 is that (0,0) is a tachyon transmission event, but what you have said about premise #2 makes absolutely no sense. (I'm still saying that premise #2 is that there's another tachyon transmission event involving the same tachyon at (10,20) in A).

we are only considering observers in A and B and us

I'm not. I'm considering frames A and B, and events that can be assigned coordinates by both A and B. That's all. You can think of A and B as physical observers if you want, but that adds nothing. And there's no need to think of "us" as a third frame/observer.

 

[Austin0]

=JesseM;2022794]How is that not a conditional? Do you imagine the authors are assuming FTL really is possible in our universe? If not, clearly they are saying "IF [SR + FTL], THEN [time travel]", which is exactly what my conditional was saying too.

Excuse me for adding to the confusion. I am not talking about the explicit conditionality of FTL which I thought was agreed was a completely valid premise. I was referring to the lack of conditionality in the assertion of the conclusion. Ie. not "implies the possibility of time travel" but rather " neccessarily implies time travel" ,meaning there is no other possible eventuality.
In this case it is the unstated conditionality of the assumption of a reception event A (10,20)
SO in actuality it is IF SR +IF FTL + IF (event A) then------

the actual conditionality of this event is - event A if and only if event B ( -10,20) The causality is; event A is a result of event B and could only occur as a result of this specific event B

SO we have: event A if and only if event B
If A then B
DO you not see a circularity here at all?

No problem of introducing A without explicit conditionality and without any argument to support B ,which is A's cause and necessary condition?

But you used the word "if" there yourself, so don't you see it's a conditional? And again, in any if-then conditional in logic or mathematics, if the if-then conditional is true then it is absolutely impossible for the premises to be true but the conclusions to be false. "If A, then B" would be false if it were "even remotely possible" for A to be true while B was false

.
As I said there is some confusion here as to which "if " is being referred to.
As you mentioned before it is a given in physics that if a premise is false then the conclusion is false. This is a weakness of logic in the real world. This does not pertain to the logic of mathematics where axioms can be defined on any basis and simply can not be false within the system. Just as any conclusion that is validly derived can not be false. Where true has no connotation of truth as such but is better understood as meaning consistent.
This is not the case in physics or the real world. Perfectly valid premises and valid logic can produce conclusions that are false in actuality.
120 years ago, based on perfectly valid phyics axioms of the times, you could have made a valid case for the impossibility of light being measured as having equal speed in all directions, from all inertial frames. Yes??
It was in this sense that I earlier said, I agreed with the possibility of time travel as a logical possibility but could not agree that it was more than a possibility or that it was the only inevitable possibility. It was in this sense that I asked you if you didnt see real differences between the logic of math and that of physics.

I don't understand what "observation in A" means--are you treating it as distinct from the notion of FTL?

You were the one who set the conditions of this exercise.
As stated by you; the event A (10,20) was an observation event NOT a tachyon [/B]reception event. True?
How is it not a different assumption from the conditional assumption of FTL?
Unless you retroactively apply the final conclusion of the argument and say it is the same because in the end we decided that it inevitably followed from FTL + SR.

In other words, are you somehow imagining it's meaningful to imagine a universe where we can say FTL signalling is possible but somehow the event of transmission and reception cannot be assigned coordinates in A, or that they can be assigned coordinates but it isn't true that dx > dt?

You did not assign coordinates of reception in A. Only of assumed observation of events in another frame. I also think the question of assigning any coordinates to FTL is an interesting and relevant question in itself ,and deserves discussion and inquiry. I definitely don't think it is as simple as normal assignments of c and sub c events.

"Conditionality" in "if-then conditional" does not mean there is any possibility that the conclusions might not follow from the premises! Again, think of the if-then conditional "if the temperature today is 37 C, then the temperature is 98.6 F." There's no way the "if" part could be true and yet the "then" part might not be true! The conditionality is just in the premise that the temperature today is 37 C, which might not be true.

Yes , in this case the 37 C =[a (10,20)] is not neccessarily true. Is simply assumed .


.

Since I don't know what the assumption of "observation in A" means distinct from the assumption of FTL signaling + relativity (and it's certainly part of the assumptions of relativity that every possible event can be assigned coordinates in every possible inertial frame),

But in fact I don't see where you assigned coordinates of the events [reception] in B from the perspective of B frame .

In any mathematical proof, I suppose you could say that using the premises to derive the conclusion is logically no different from just assuming the conclusion at the outset, but it's certainly conceptually different in the sense that it may not be obvious to the human mind that the conclusion follows from the premises without going through a chain of reasoning.

Wouldn't you agree that assuming the conclusion at the outset removes the neccessity and meaning of going through a chain of reasoning??
Makes the whole exercise a form of tautology?

 

[JesseM]

Excuse me for adding to the confusion. I am not talking about the explicit conditionality of FTL which I thought was agreed was a completely valid premise. I was referring to the lack of conditionality in the assertion of the conclusion. Ie. not "implies the possibility of time travel" but rather " neccessarily implies time travel" ,meaning there is no other possible eventuality.

Yes, because there is no other possible eventuality if the premises are true. That's the case for every if-then conditional in mathematics or logic.

In this case it is the unstated conditionality of the assumption of a reception event A (10,20)

The premise was that FTL signals are possible--do you think it's meaninfful to talk about sending signals at FTL speed without assuming the signal is actually received at some discrete point in space and time? If I just send out a signal but no one is ever able to receive, in what sense can I say I have sent an "FTL signal" to anyone?

What's more, I explicitly asked you if you agreed that the condition of FTL signalling was synonymous with the notion that we have a sending-event and a reception-event such that dx between the two events is larger than dt in the coordinates of some inertial frame, and you agreed that they were synonymous:

erhaps it would help if you answered another question. Do you agree that the premise [the laws of physics respect relativity AND FTL signalling is physically possible] is synonymous with the premise [the laws of physics respect relativity AND there is some inertial frame where, if we consider the difference in space coordinates dx and the difference in time coordinates dt of the events of a signal being sent and received, then dx > dt (in units where c=1)]? Do you agree that in any hypothetical universe where the first statement applies, the second statement should apply too, or do you think it is meaningful to talk about a hypothetical universe where the first applies but the second does not?

As far as I can see this is just a simple statement of the possibility of FTL in which case of course this is understood . Am I missing something here?

So, maybe you can see why I'm totally confused that you now seem to be saying FTL signalling is not synonymous with the statement that we have a sending-event and a reception event, such that in some inertial frame the dx between these events is larger than the dt between them. Or are you? I have no idea anymore, perhaps you can readdress the quoted question in light of your new complaint about the assumption of a reception-event.

SO in actuality it is IF SR +IF FTL + IF (event A) then------

the actual conditionality of this event is - event A if and only if event B ( -10,20)

There is only one reception-event. In A it has one set of coordinates, in B another, but they are not two different events (although the reception-event is different from the sending-event, which in my example happened at the origin of both frames). Please read my analogy with 2D coordinate grids from post #74 (a post you never replied to, I hope you didn't miss it):

I think it would be best just to talk about the coordinates that B assigns to the reception-event, since it's misleading to suggest that the event itself takes place "in" any particular coordinate system. To see why, imagine I want to define the position of a certain tree using a 2D spatial coordinate grid on a map--if I place the origin at one spot, then in that coordinate system I might say the tree is at 3.25 km north, 5.71 km east, but if I place the origin at a different spot, then in coordinate system #2 perhaps the tree is at 2.55 km north, 1.28 km east. Is the tree "in" one coordinate system or another? No, it's just there, in the ground, the two coordinate systems are just different ways of labeling its position. If I wished to I could physically realize each coordinate system by laying out a giant grid of rulers with the specified origins, and note which ruler-markings the tree was next to, but this isn't actually necessary, I can measure the coordinates of the tree without ever having to physically construct either coordinate system. It's the same with coordinate systems in SR--physical events are just events, they are just assigned different sets of coordinates by different systems, and although you can theoretically define each coordinate system in terms of a network of rulers and clocks there is no actual need to have such a grid in place.

The tree has a different set of coordinates in each system, but that doesn't mean there are two trees! Events in spacetime are just like physical landmarks on a 2D plane, you can assign the same event two different sets of coordinates in two different frames but it would be improper to refer to these two sets of coordinates as "two events".

The causality is; event A is a result of event B and could only occur as a result of this specific event B

SO we have: event A if and only if event B
If A then B
DO you not see a circularity here at all?

Again, there is only one reception-event, call it E. Now, it is true that:
[E has coordinates x=20, t=10 in frame A] if and only if [E has coordinates x'=20, t'=-10 in frame B]
and
If [E has coordinates x=20, t=10 in frame A] then [E has coordinates x'=20, t'=-10 in frame B]

However, there's nothing "circular" about this, it just follows from the fact that the two frame's coordinates are related by the Lorentz transform, which itself can be derived from the premise that we are in a universe where the fundamental postulates of relativity hold.

And of course the idea that the signal was sent at x=0, t=0 and received at x=20, t=10 in the coordinates of frame A was just a numerical example, the condition "FTL signalling is possible" just tells us that in whatever frame we choose, whatever the coordinates of the sending-event and the receiving event in that frame, it must be true that dx > dt. And you can use the Lorentz transformation to show that for any possible coordinates of two events where dx > dt, it's possible to find a different frame where the events happened in reverse order.

This is not the case in physics or the real world. Perfectly valid premises and valid logic can produce conclusions that are false in actuality.

Not if you're talking about an if-then conditional where the logic that leads from the premises to the conclusion is indeed "valid", no. In that case, if you've shown as a pure mathematical exercise that the conclusion follows from the premise, then no later results can ever overturn this, although later results may show that some of your premises were false.

120 years ago, based on perfectly valid phyics axioms of the times, you could have made a valid case for the impossibility of light being measured as having equal speed in all directions, from all inertial frames. Yes??

I don't know, what axioms would those be? Perhaps the assumption that if different inertial observers construct their own coordinate systems using rulers and synchronized clocks at rest relative to themselves, then the coordinates of different observers will be related by the Galilei transform rather than the Lorentz transform? But of course in this case if the premises are true then it is impossible for light to have the same speed in all frames, and the fact that we find the conclusion to be false is explained by the fact that the premise is false, and in fact when different observers construct coordinate systems using inertial rulers and clocks their coordinates are actually related by the Lorentz transform. If you have a mathematical proof that certain conclusions follow from certain premises, then there is no possible way that the conclusion could be false while the premises were true, no new experimental results can change that.

You were the one who set the conditions of this exercise.
As stated by you; the event A (10,20) was an observation event NOT a tachyon [/B]reception event. True?

No, I never made this distinction between an event and the "observation" of an event, and I still have no idea what you mean by it. Could you actually explain it, in detail?

You did not assign coordinates of reception in A. Only of assumed observation of events in another frame.

Huh? Again, this looks like total gibberish to me. The event of reception had coordinates x=20,t=10 in A, which we could imagine was determined by noting that it happened right next to the x=20 marking on the ruler defining A's x-axis, and that the clock at that marking read t=10 at the moment it happened. No other frame besides A was involved here.

I also think the question of assigning any coordinates to FTL is an interesting and relevant question in itself ,and deserves discussion and inquiry. I definitely don't think it is as simple as normal assignments of c and sub c events.

Well, if you don't think any event has well-defined coordinates in every inertial frame, then this is not a universe correctly described by SR, because that assumption is built into SR. And I really don't understand how this could fail to be true, if you're talking about something like a tachyon detector that lights up at the moment it receives a tachyon, what exactly would stop you from noting what marking it was next to on a given frame's ruler when this happened, and what the reading on the clock at that marking was? Are you imagining the reception-event cannot be localized in a way that allows us to see what else was happening in the same local neighborhood of this event?

Yes , in this case the 37 C =[a (10,20)] is not neccessarily true. Is simply assumed .

Are you pulling my chain? How does the FTL proof compare to a complete gibberish statement like setting a temperature equal to a set of coordinates?

But in fact I don't see where you assigned coordinates of the events [reception] in B from the perspective of B frame .

You can imagine the coordinates in B of the event were determined in the same way as the coordinates in A, by looking at what marking on B's ruler the event happened next to, and what B's clock at that marking read at the moment. In neither case do we need to do anything but look at ruler-markings and clock-readings from a ruler/clock system at rest in one frame to define the coordinates of events in that frame. However, we are assuming as a premise that the universe is accurately described by relativity, which means that when the coordinates in A and B are determined this way, it must be true that the coordinates of the event in one frame are related to the coordinates of the event in the other frame by the Lorentz transformation. If this were not true--if, for example, the coordinates of the reception event determined by local readings on the A ruler/clock system were x=20, t=10 while the coordinates of the reception event determined by local readings on the B ruler/clock system were x'=13, t=200, then we would not be living in a universe that obeyed relativity.

 

[Austin0]

Huh? Where'd you get the idea a tachyon signal speed should be independent of the source? It definitely should not be, if we construct a tachyon transmitter according to a set procedure and put it at rest in frame A and see it sends signals at 2c in A, then based on the first postulate of relativity, if we construct an identical tachyon transmitter according to the same procedure and put it at rest in frame B, it should send signals at 2c in B (the first postulate says if you perform identical experiments in different inertial frames, each frame should observe the same results).

I clearly said independent of the source. No implication of constancy wrt measurement in any frame. I assumed we were talking about a hypothetical particle that moved with constant velocity wrt the vacuum of space in the same sense that this assumption is applied to light.
If this is not the case what other assumption could logically be adopted?.
That it behaves like a particle with mass and inherits the velocity of the source?
Where does this assumption come from?

I did not miss this post before but "events" have arisen in my life and I simply don't have the time to give them the attention I would like and that they deserve. Please excuse this and hopefully I will be able to soon. Thanks

 

[JesseM]

I clearly said independent of the source. No implication of constancy wrt measurement in any frame.

But the first postulate demands that if you repeat the same experiment in two frames, it must give the same result in each frame. For example, if you construct a source in a certain way and have it at rest in frame A, and you find that the speed of a signal emitted by the source is v as measured in A, then it must be true in relativity that if you construct an identical source and have it at rest in a different frame B, you will find that the speed of the signal emitted by the source is v as measured in B. Do you disagree that this is what the first postulate demands?

I assumed we were talking about a hypothetical particle that moved with constant velocity wrt the vacuum of space in the same sense that this assumption is applied to light.

Now you are assuming it moves at constant velocity? Didn't you just say "No implication of constancy"?

Anyway, in relativity it is possible for a non-c signal to have a constant velocity in some frame that's independent of the source, but only if it is dependent on some other physical entity which, when given a different velocity, will give the signals non-constant speed. For example, sound waves in air always move at the same speed in the rest frame of the air, so if you have a box of air at rest relative to you and a source inside the box that creates vibrations in the air, you'll find the sound waves move at the same speed in all directions regardless of the motion of the sound emitter inside the box. But then if you set the box of air in motion relative to you, by the first postulate the sound waves must have a constant speed in the box's new rest frame, and since the velocity of the sound waves is not c that must mean sound waves in different directions now have different speeds in your frame.

If this is not the case what other assumption could logically be adopted?.
That it behaves like a particle with mass and inherits the velocity of the source?
Where does this assumption come from?

It comes from the first postulate, which tells you that if the same experiment is done with the experimental apparatus having different rest frames, then each frame must see the same results when the apparatus is at rest in their frame. It also comes from the Lorentz transform, which tells you that if signals moving in different directions have the same speed in one frame, and that speed is not c, then in other frames these same signals must have different speeds. Do you disagree with either of these implications of relativity? If not, then when you consider all the physical entities relevant to determining the speed of signals (like both the box of gas and the sound emitter inside it), if the laws of physics imply that the signals move at a constant speed (other than c) in all directions when these physical entities have some particular velocities (such as the box of gas being at rest) in a given frame A, then in some other frame B the Lorentz transform implies these same signals will have different speeds in different directions; so, if you change the velocities of these entities in A so they match the earlier velocities in B (i.e. if the box was moving at 0.6c in B when it was at rest in A, you change things so it's now moving at 0.6c in A), then A must see the same result that B saw previously, namely that the speeds of the signals are different in different directions.

I did not miss this post before but "events" have arisen in my life and I simply don't have the time to give them the attention I would like and that they deserve. Please excuse this and hopefully I will be able to soon. Thanks

No problem, take your time.

 

[Fredrik]

I clearly said independent of the source. No implication of constancy wrt measurement in any frame.

This is wrong. A speed that's independent of the source is the same in all frames. (The velocity of the source defines a frame).

I assumed we were talking about a hypothetical particle that moved with constant velocity wrt the vacuum of space in the same sense that this assumption is applied to light.

It doesn't make sense to talk about a velocity relative to the vacuum, since you can't measure the speed of vacuum, or in any meaningful way assign a velocity to it. The assumption about light isn't that it moves with c relative to the vacuum. It's that the speed of light is independent of the velocity of the light source.

If this is not the case what other assumption could logically be adopted?.
That it behaves like a particle with mass and inherits the velocity of the source?
Where does this assumption come from?

Einstein's postulates lead naturally to the concept of Minkowski space, and in Minkowski space there's only one velocity that's the same in all frames. You can't have two invariant velocities unless you make a very radical change to the structure of spacetime. (I don't see how it could be done).

I would also like to remind you of something I said earlier:

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.

One last comment: I don't see how this discussion can make any progress at all unless you explain what you mean by an observation event.

 

[Austin0]

Originally posted JesseM #60
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..

Fine , by your definition as related here , it seems clear that the demonstration in question [SR +FTL implies Time Travel] is not a formal mathematical proof under these terms.. It has neither formal axioms nor absolute rules for generaating new statements. It is not an exercise in Propositional Calculas but a logical proof in english language with natural logic. It was presented with verbal conditional premises and arguments that do in fact require understanding of meaning..There is obviously nothing whatsoever wrong with that. Practically all logical arguments outside of formal mathematics are of this form. But I think it is misdirected to, now, regard it as if it were a formal mathematical proof .

Austin0 post #56
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]

I have to ask you gentlemen if you ever read this post of mine, dating from the beginning?
All your repeated responses seem to be addressed to the exact opposite statement.
You seem to either reject the concept of circular argument or think that I have come up with some kind of idiosyncratic wacky idea on my own.
You seem to not have any idea what I have meant when I said "including the conclusion in the premises"
You almost appear to be making an argument that all forms of circular reasoning are valid because ,well "the conclusion is always implicit in the premises"

I should add, in order to preclude further misinterpretation that the explicit conditionals SR and FTL are not under question or discussion here.
Only specifically and exclusively the assumption of the event A (10,20) and its equivalence to the conclusion. A (10,20) =B(-10,20)

After awhile I have begun to question my own memory, so I did a quick web search and encountered any number of references, one of which is nice and concise and I pass it on to you in the hopes that it might aid in interpreting my meaning in the points I have tried to make.
___________________________________________________________________________
But the following argument is both valid and a tautology:
• Premise: (Any statement) P.
• Conclusion (That same statement) P.
The argument has the form, 'If P, then P.' It is indeed a valid argument because there is no way that the premise can be true and the conclusion false. But it is a vacuous validity because the conclusion is simply a restatement of the premise.
In fact, all circular arguments have that character: They state the conclusion as one of the premises. Of course, the conclusion will then necessarily follow, because if a premise is true and the conclusion is simply a restatement of that premise, the conclusion will follow from the premise. But, although it is technically valid, the argument is worthless for conveying any information or knowledge or proof. That is why circular arguments should be rejected, and why showing that an argument is circular is sufficient to show that it is no good: Circular arguments are trivially valid, but are worthless for establishing their conclusion(s).
________________________________________________________________________

JesseM #74
In any mathematical proof, I suppose you could say that using the premises to derive the conclusion is logically no different from just assuming the conclusion at the outset, but it's certainly conceptually different in the sense that it may not be obvious to the human mind that the conclusion follows from the premises without going through a chain of reasoning.

Originally Posted by Austin0
Yes , in this case the 37 C =[a (10,20)] is not neccessarily true. Is simply assumed .

JesseM #74
Are you pulling my chain? How does the FTL proof compare to a complete gibberish statement like setting a temperature equal to a set of coordinates?

Excuse me , given the context of this discussion where the term [premise] 37C=96F [conclusion] and the [ premise] A(10,20) = B (-10,20) [conclusion] has been repeated in several posts I assumed that the above would be interpreted as: 37C [as a premise in its context] was logically equivalent to A(10,20) as a premise.in its context
It simply never even occurred to me that anyone would assume the absurd interpretation of this as a literal quantitative mathematical equality.
I will try to remember in the future not to take shortcuts just to save a little typing. Sorry.

JesseM #49
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.

This discussion is not aabout the generalalities of coordinate systems and their application, I assume [hope] we would agree on that subject..You seem to be saying that because SR does include an abstract coordinate system, within which, any point in space-time can be designated, that means that SR has FTL covered and somehow validates any specific assignment of location or time you make.
On this basis you could validly plot a trajectory of a particle undergoing gravitational acceleration with a g factor of -9.82.
Would you consider this compelling or meaningful as a demonstration of the possibility of anti-gravity?

Given the premises of this exercise it is of course logical to assume reception of transmission at any given location. Otherwise there is obviouly nothing to discuss. It is assigning a time to that reception that is the crux of the whole question.
The basis for that assignment is not to be found in the coordinate system or even explicitly in SR.
It must be derived through logic and physics. Not only the hypothetical physics of imaginary particles but also the more known physics of inertial frames with desynchronized clocks..
We know that the reason that you can expect equal bi-directional measurements of the speed of light and consider any frame at rest to assign meaningful equal bi-directional speeds and times for light is because the clocks are desynchronized the specific amount necessary to make this possible for any given relative velocity of the system.. Does it seem reasonable to assume a system is at rest and assign times to FTL on that basis and expect that the desynchronizaation will simply disappear because we're now measuring FTL.
Or that the desynchronization that works so well for light would give meaningful temporal information when dealing with phenomena that are arriving, so to speak, way ahead of schedule.?


Coming back to this discussion after time not involved , I can see that there are several basic issues that have gotten scattered out.and need to be clarified. One is as Fredrik noted the observer versus event question.It now appears there is also the basic definition of FTL and tachyons to be clarified ,among others. I have certainly learned much from you both and hope I will be able to find sufficient time to get this caught up. Thanks

 

[JesseM]

Fine , by your definition as related here , it seems clear that the demonstration in question [SR +FTL implies Time Travel] is not a formal mathematical proof under these terms.. It has neither formal axioms nor absolute rules for generaating new statements. It is not an exercise in Propositional Calculas but a logical proof in english language with natural logic. It was presented with verbal conditional premises and arguments that do in fact require understanding of meaning..There is obviously nothing whatsoever wrong with that. Practically all logical arguments outside of formal mathematics are of this form. But I think it is misdirected to, now, regard it as if it were a formal mathematical proof .

Any pure theoretical physics argument can of course be translated into a mathematical proof with the appropriate definitions, like defining spacetime as a mathematical manifold with the Minkowski metric, defining events as points in this manifold, defining the term "spacelike separation", defining a tachyon signal as one where there is an event labeled "signal is sent" and another labeled "signal received" and the two have a spacelike separation, defining the first postulate in terms of symmetry of what is seen in different Lorentzian coordinate systems, etc. This would be rather involved, and just as mathematicians do not normally write out proofs as a pure series of logical operations starting from axioms but instead avail themselves of our conceptual understanding, so similarly a theoretical proof in physics is not normally going to be written in purely symbolic form.

Austin0 post #56
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]

I have to ask you gentlemen if you ever read this post of mine, dating from the beginning?
All your repeated responses seem to be addressed to the exact opposite statement.
You seem to either reject the concept of circular argument or think that I have come up with some kind of idiosyncratic wacky idea on my own.

Yes, I would say you have "come up with some kind of idiosyncratic wacky idea". And indeed, the statement "it is only valid if you have already established A" seems like bizarro-logic. The whole point of an if-then conditional is that you are only saying the conclusion is true if the premises are true, which of course means that you don't have to establish that the premises actually hold in the real world! For example, we can talk about the theoretical implications of a universe where Newtonian gravity holds exactly, even though we know that this is not in fact true in our universe.

You seem to not have any idea what I have meant when I said "including the conclusion in the premises"

If you think we've missed the point, maybe you could actually explain it in detail...the paragraph above certainly doesn't help at all. It would help if you would actually respond to my request for examples of either purely mathematical proofs or deductions about the purely theoretical implications (i.e., no reference to experimental findings whatsoever) of certain physical premises that do not qualify as "including the conclusion in the premises" according to you.

You almost appear to be making an argument that all forms of circular reasoning are valid because ,well "the conclusion is always implicit in the premises"

Give me a single example of an if-then conditional that you think is not valid because it includes "circular reasoning" then.

I should add, in order to preclude further misinterpretation that the explicit conditionals SR and FTL are not under question or discussion here.
Only specifically and exclusively the assumption of the event A (10,20) and its equivalence to the conclusion. A (10,20) =B(-10,20)

This looks like a blatant contradiction. Do you not agree that if we take the correctness of SR as an "explicit conditional", that means we must take it as a premise that the coordinates assigned to the same event by different inertial coordinate systems must be related by the Lorentz transform? How could it possibly make sense to say that this premise could be false yet SR could be 100% correct? I have asked you variants of this question several times before and you've never given me a straight answer, please just tell me yes or no if you agree with my "must" statements above about the implications of assuming SR is accurate.

After awhile I have begun to question my own memory, so I did a quick web search and encountered any number of references, one of which is nice and concise and I pass it on to you in the hopes that it might aid in interpreting my meaning in the points I have tried to make.
___________________________________________________________________________
But the following argument is both valid and a tautology:
• Premise: (Any statement) P.
• Conclusion (That same statement) P.
The argument has the form, 'If P, then P.' It is indeed a valid argument because there is no way that the premise can be true and the conclusion false. But it is a vacuous validity because the conclusion is simply a restatement of the premise.
In fact, all circular arguments have that character: They state the conclusion as one of the premises. Of course, the conclusion will then necessarily follow, because if a premise is true and the conclusion is simply a restatement of that premise, the conclusion will follow from the premise. But, although it is technically valid, the argument is worthless for conveying any information or knowledge or proof. That is why circular arguments should be rejected, and why showing that an argument is circular is sufficient to show that it is no good: Circular arguments are trivially valid, but are worthless for establishing their conclusion(s).
________________________________________________________________________

Yes, and note that they say this is a valid if-then conditional, even if it's "vacuous". Of course it's only vacuous because anyone can see that the premise and the conclusion are precisely identical, in mathematical proofs the premise may logically imply the conclusion but it's not vacuous since you have to go through at least a few steps to demonstrate this. For example, Fredrik's "IF [x+2=5] THEN [x=3]" is not vacuous in the same way.

Yes , in this case the 37 C =[a (10,20)] is not neccessarily true. Is simply assumed .

Are you pulling my chain? How does the FTL proof compare to a complete gibberish statement like setting a temperature equal to a set of coordinates?

Excuse me , given the context of this discussion where the term [premise] 37C=96F [conclusion] and the [ premise] A(10,20) = B (-10,20) [conclusion] has been repeated in several posts I assumed that the above would be interpreted as: 37C [as a premise in its context] was logically equivalent to A(10,20) as a premise.

What? How are they "logically equivalent"? Do you even understand what "logically equivalent" means? It means you can get from one to the other using pure logical operations. This makes absolutely zero sense when applied to the premises "37C=96F" and "A(10,20) = B (-10,20)", there is no logical connection between the first and the second.

It simply never even occurred to me that anyone would assume the absurd interpretation of this as a literal quantitative mathematical equality.

I didn't say it was a literal mathematical equality, I asked "37 C =[a (10,20)]" even makes sense as an analogy for the FTL proof (how does one 'compare' to the other).

This discussion is not aabout the generalalities of coordinate systems and their application, I assume [hope] we would agree on that subject..You seem to be saying that because SR does include an abstract coordinate system, within which, any point in space-time can be designated, that means that SR has FTL covered and somehow validates any specific assignment of location or time you make.

I don't know what you mean by "SR has FTL covered". SR certainly doesn't imply that FTL should actually be possible, but it does imply that if it is, one could assign coordinates to events involving FTL particles in exactly the same way as you'd assign coordinates to any other physical events. Similarly, SR doesn't imply that it's physically possible for a wizard to wave a magic want and create a rainbow dragon that sings "happy birthday", but if you take the validity of SR as a premise, then if such a thing is possible we can assume that coordinates can be assigned to this event in any inertial frame, and that the coordinates that different inertial frames assign to this event will be related by the Lorentz transformation. Do you disagree?

On this basis you could validly plot a trajectory of a particle undergoing gravitational acceleration with a g factor of -9.82.
Would you consider this compelling or meaningful as a demonstration of the possibility of anti-gravity?

Have you forgotten all the many times I have said I do not assume FTL is an actual physical possibility? Seriously, I don't know how many times I can repeat that an if-then conditional can be valid without any assumption that the premises are actually true in the real world. Similarly, in your example if we took antigravity as a premise, then we could make theoretical deductions about how different SR frames would view the trajectory of a particle being repelled by an antigravitational field, giving us an if-then conditional of the form "IF [FTL + antigravity] THEN [theoretical conclusions]", such an if-then conditional would not be intended as a "demonstration of the possibility of anti-gravity" in the real world.

Given the premises of this exercise it is of course logical to assume reception of transmission at any given location. Otherwise there is obviouly nothing to discuss. It is assigning a time to that reception that is the crux of the whole question.
The basis for that assignment is not to be found in the coordinate system or even explicitly in SR.

If you assume SR, you must assume that any event can be assigned time and space coordinates in any inertial frame--in principle this can always be done physically by constructing a ruler/clock system representing that frame's coordinates according the procedure given by Einstein, and noting which ruler-marking and clock-reading were in the same local region as the event when and where it happened. What's more, if you assume SR, you must assume that the coordinates that different inertial frames will assign to the same event will always be related by the Lorentz transformation. Do you agree that both of these are implied by the assumption of a universe where SR is correct? Please give me a simple yes/no answer.

We know that the reason that you can expect equal bi-directional measurements of the speed of light and consider any frame at rest to assign meaningful equal bi-directional speeds and times for light is because the clocks are desynchronized the specific amount necessary to make this possible for any given relative velocity of the system.. Does it seem reasonable to assume a system is at rest and assign times to FTL on that basis and expect that the desynchronizaation will simply disappear because we're now measuring FTL.

Again, no idea of what bizarro-logic would lead you to think this question makes sense. Of course the desynchronization is still present, why would you say it's not? If the coordinates of all events are related by the Lorentz transformation, that shows that the clocks of different frames are out-of-sync, because the Lorentz transform implies that events with different x-coordinates but the same t-coordinate in one inertial frame will have different t' coordinates in other frames. The images in my thread An illustration of relativity with rulers and clocks are nothing more than a visualization of the Lorentz transformation with two ruler/clock systems representing two inertial coordinate systems, and you can see that in one frame the other clocks are out of sync. Now just imagine drawing the events of a tachyon signal being sent and the signal being received as dots on those illustrations--for example, the sending event might be drawn next to (-346.2 meters, 0 microseconds) on the A ruler and (-692.3 meters, 2 microseconds) on the B ruler, and the event of the signal being received might be drawn next to (346.2 meters, 1 microsecond) on the A ruler and (173.1 meters, 0 microseconds) on the B ruler. Please go look at the diagrams so you can see where these events would actually be drawn in. Now, does the fact that you have drawn in these events somehow make the clocks of the B-ruler any less out of sync when drawn in the A frame (top diagram), or the clocks of the A-ruler any less out of sync in the B frame (bottom diagram)?

By the way, do you understand that it's assumed in the premise "SR is accurate" that we would continue to "synchronize" clocks at different positions in a given inertial frame using the Einstein synchronization convention involving light-signals, that even if tachyons existed we would not use them (or any other new procedure) to define what it means for clocks to be synchronized in a given frame?

Or that the desynchronization that works so well for light would give meaningful temporal information when dealing with phenomena that are arriving, so to speak, way ahead of schedule.?

Again, I don't know what this question even means--if you can assign a time-coordinate to an event, what would make that "meaningful temporal information" as opposed to "meaningless temporal information"? It's just a coordinate, which is just a matter of convention. Your question is a little like asking "how can we be sure the lines of latitude and longitude on the globe which work so well in assigning position coordinates to cities will still give meaningful positional information for mountains"?

Coming back to this discussion after time not involved , I can see that there are several basic issues that have gotten scattered out.and need to be clarified. One is as Fredrik noted the observer versus event question.

Yes, you have never clarified your own idiosycratic (and to me unintelligible) notion that the coordinates of an event in a given inertial frame only represent the "observation of an event" rather than the coordinates of the event itself in that frame.

 

[Fredrik]

I have to ask you gentlemen if you ever read this post of mine, dating from the beginning?

I probably did, but I don't remember it. The claim that "if A then B" is "only valid if you have already established A" is false. Consider these examples:

1. If x and y are real numbers, then (x+y)²=x²+y²+2xy. (It doesn't make sense to demand that we first establish that x and y are real numbers, since we haven't been given x and y).

2. If there's a largest prime number N, then (2·3·5·7·...·N)+1 is a prime number that's larger than N. (Here "A" isn't even true. In fact, what this argument really proves is that it isn't. But the statement is still valid).

Maybe you meant that the only time we're allowed to treat a proof of "if A then B" as a proof of B is when we have already established A. That's of course true. But in our case, where A="tachyons" and B="paradoxes", we're not treating the argument as a proof of B. We're treating it as an argument against tachyons.

You seem to not have any idea what I have meant when I said "including the conclusion in the premises"
You almost appear to be making an argument that all forms of circular reasoning are valid because ,well "the conclusion is always implicit in the premises"

It's not that we don't know what you meant. It's that we have no idea why you're saying it, i.e. why you think our argument (for why arbitrary signal speeds lead to paradoxes) is circular. It isn't. Do you also consider this circular? "If xy=0 for all y, then x=0".

 

[Austin0]

[Fredrik;2025339]This is wrong. A speed that's independent of the source is the same in all frames. (The velocity of the source defines a frame).

Maybe I am not following you here, but isn't the propagation of sound independant of the source but measured to be different in relative frames??
That the difference with light is that it is also measured to be the same in all frames.
That this is only possible because the clocks are specifically desynchronized the degree necessary to maintain that measurement??

It doesn't make sense to talk about a velocity relative to the vacuum, since you can't measure the speed of vacuum, or in any meaningful way assign a velocity to it. The assumption about light isn't that it moves with c relative to the vacuum. It's that the speed of light is independent of the velocity of the light source.

Do you think that it is not reasonable to assume that in flat space-time all photons move at the same constant speed??
To view c as, not only a speed of light, but also as a physical constant that applies as a limit to all particles with mass?
It certainly seems to me that this assumption is exactly why many physicists think that Tachyons are not a real possibility.
Do you think it possible that outside of gravity photons move at a range of velocities and that they are only measured at c by coincidence?

Einstein's postulates lead naturally to the concept of Minkowski space, and in Minkowski space there's only one velocity that's the same in all frames. You can't have two invariant velocities unless you make a very radical change to the structure of spacetime.

I was not talking about the measured speed being the same in all frames. As I have mentioned elsewhere I think that due to clock desynchronization , they not only couldn't be measured at the same speed in different frmes but that they also couldn't be measured as having equal bidirectional speed in any frame.

One last comment: I don't see how this discussion can make any progress at all unless you explain what you mean by an observation event

Assume you were doing an analysis of the measurement of light within two different frames.
Wouldnt you clock emmission and reception in one frame , and then from that frame calculate the emmission and reception in the other frame??

That within the first frame there would be actual reception of photons but within that frame there would only be the hypothetical observation
by an observer at the proximate site of the actual reception in the second frame?
That normally this distinction is irrelevant because there is no causal connection or temporal significnce to the order of reception and observation.
In any case this is what I meant.

 

[Austin0]

=Fredrik;2038361]I probably did, but I don't remember it. The claim that "if A then B" is "only valid if you have already established A" is false. Consider these examples:

There is some confusion here as to what conditional premises are being referred to. I have stated that it is understood ,that in general and specifically in this case, foundational ,if conditional premises, are valid and do not need to be true whatsoever.
But in this case the A is not an explicit conditional but is introduced as an argument with the tacit assumption of validity?

2. If there's a largest prime number N, then (2·3·5·7·...·N)+1 is a prime number that's larger than N. (Here "A" isn't even true. In fact, what this argument really proves is that it isn't. But the statement is still valid).

Excuse me but in this case isn't it that 'A' [the IF] is in fact true, but it is the THEN "B' conclusion that is false? That in fact this statement is in no way valid.

Maybe you meant that the only time we're allowed to treat a proof of "if A then B" as a proof of B is when we have already established A. That's of course true.

Thank you and yes that is what I meant.

But in our case, where A="tachyons" and B="paradoxes", we're not treating the argument as a proof of B. We're treating it as an argument against tachyons

Isnt it the case that the premises are IF SR + FTL THEN time travel.
That in this case the A is A =assumption of event at ( x=20, t=10) <==> B=time travel ?
Wouldnt you agree that this is treating it as a proof of B the conclusion?


If the statement was IF SR and IF FTL and IF a signal sent from A arrives 10 sec before it is sent in B THEN "timetravel "

Would you agree that this, although a valid argument, would be an obvious tautology and without significance as a proof of "time travel" ?

 

[Austin0]

This looks like a blatant contradiction. Do you not agree that if we take the correctness of SR as an "explicit conditional", that means we must take it as a premise that the coordinates assigned to the same event by different inertial coordinate systems must be related by the Lorentz transform? How could it possibly make sense to say that this premise could be false yet SR could be 100% correct? I have asked you variants of this question several times before and you've never given me a straight answer, please just tell me yes or no if you agree with my "must" statements above about the implications of assuming SR is accurate.

YES


Yes, and note that they say this is a valid if-then conditional, even if it's "vacuous". Of course it's only vacuous because anyone can see that the premise and the conclusion are precisely identical, in mathematical proofs the premise may logically imply the conclusion but it's not vacuous since you have to go through at least a few steps to demonstrate this. For example, Fredrik's "IF [x+2=5] THEN [x=3]" is not vacuous in the same way.

What? How are they "logically equivalent"? Do you even understand what "logically equivalent" means? It means you can get from one to the other using pure logical operations. This makes absolutely zero sense when applied to the premises "37C=96F" and "A(10,20) = B (-10,20)", there is no logical connection between the first and the second.

Given: "37C=96F" and "A(10,20) = B (-10,20)"

IF 1) p= any premise in a simple if -then conditional that directly determines the conclusion through a mathematical transform

IF 2) 37C= p

IF 3 ) A(10,20) = p

THEN 37C =A(10,20)

AS both 2) and 3) validly fulfill the conditions of 1) [are true] the conclusion is true.
Those specific conditions have been mentioned many times.


[QUOTE Similarly, SR doesn't imply that it's physically possible for a wizard to wave a magic want and create a rainbow dragon that sings "happy birthday", but if you take the validity of SR as a premise, then if such a thing is possible we can assume that coordinates can be assigned to this event in any inertial frame, and that the coordinates that different inertial frames assign to this event will be related by the Lorentz transformation. Do you disagree?[/QUOTE]
No. The question is what coordinates to assign ,that would then be related by the transform.
If the question was a hypothetical wand that teleported rocks and you start with a rock at x=0,z=0 that disappears at t=0 , simply assigning the coordinates x=10,z=-10 wouldn't be much proof that the rod would only work downhill would it?

Have you forgotten all the many times I have said I do not assume FTL is an actual physical possibility? Seriously, I don't know how many times I can repeat that an if-then conditional can be valid without any assumption that the premises are actually true in the real world.

Probably as many times as I have said that that is understood , and that I am not talking about that explicit conditional whatsoever. I may personally consider it an unlikely reality but that has nothing to do with this discussion.
But isn't it also true that the assumption of an event at the specific spacetime coordinates assigned in A do carry an implication that they would be true in the real world. If not what is the point?

Similarly, in your example if we took antigravity as a premise, then we could make theoretical deductions about how different SR frames would view the trajectory of a particle being repelled by an antigravitational field, giving us an if-then conditional of the form "IF [FTL + antigravity] THEN [theoretical conclusions]", such an if-then conditional would not be intended as a "demonstration of the possibility of anti-gravity" in the real world.

You apparently completely misinterpreted what was said. It was clear that antigravity was the conclusion not a premise. The correct analogy would be :
IF SR + FTL THEN antigravity. Where the assignng of coordinates that run counter to gravitational force was the proof of the conclusion.

.

What's more, if you assume SR, you must assume that the coordinates that different inertial frames will assign to the same event will always be related by the Lorentz transformation. Do you agree that both of these are implied by the assumption of a universe where SR is correct? Please give me a simple yes/no answer.

YES but once again you are talking about general principles while I am talking about the specific assigment of a specific quantitative value. See above. A specific spatial coordinate for the reappearence of the rock. I hope you don't think SR has specific quidelines for teleporting rocks.

Again, no idea of what bizarro-logic would lead you to think this question makes sense. Of course the desynchronization is still present, why would you say it's not?

I think you might want to read what I said again. I most definitely did not say or imply that I thought it would not be present.

But in fact, isn't that exactly what you are assuming when you make a direct assignment [ which implies an equal bidirectional measurement on the same basis]?

 

[JesseM]

I'll try to address the rest later, but just wanted to quickly post on what I think is the heart of the matter:

What's more, if you assume SR, you must assume that the coordinates that different inertial frames will assign to the same event will always be related by the Lorentz transformation. Do you agree that both of these are implied by the assumption of a universe where SR is correct? Please give me a simple yes/no answer.

YES but once again you are talking about general principles while I am talking about the specific assigment of a specific quantitative value. See above. A specific spatial coordinate for the reappearence of the rock. I hope you don't think SR has specific quidelines for teleporting rocks.

You didn't address the previous part before "what's more" which I also wanted a yes/no answer to:

If you assume SR, you must assume that any event can be assigned time and space coordinates in any inertial frame--in principle this can always be done physically by constructing a ruler/clock system representing that frame's coordinates according the procedure given by Einstein, and noting which ruler-marking and clock-reading were in the same local region as the event when and where it happened.

So, question #1, do you agree that "any event can be assigned time and space coordinates in any inertial frame"?

If the answer here is yes, then I assume this should apply to both the event of the tachyon being sent and the event of the tachyon being received (no need to comment on this unless you disagree). In this case, my question #2 is, would you also agree that the premise "FTL" implies that there must be at least one inertial frame where the difference in space coordinates dx between these two events is larger than the difference in time coordinates dt, in units where c=1?

If you answered yes to questions #1 and #2, then since you also agreed that the coordinates of different inertial frames must be related by the Lorentz transform if SR is correct, question #3 is: do you agree that if we have two events where dx > dt in some frame, it is always possible to find a second inertial frame such that when you do the Lorentz transform to find the coordinates of the same events in the second frame, their order will be reversed in the second frame?

Note that I gave an example of this where the events had a dx of 20 and a dt of 10 in the first frame and their order was reversed in the second frame moving at 0.8c relative to the first, but it's possible to prove that in general, if dx > dt for two events in one frame then it must be possible to find a different inertial frame with sufficient velocity relative to the first (a velocity less than c of course, since all inertial frames move at sublight speeds) such that when you plug that v into the Lorentz transformation equations and apply them to the coordinates of the events in the first frame, then the order of the events is reversed in the second frame. This would not be true for events where dx < dt or dx = dt, it's only true when dx > dt.

So, please address my questions 1-3 and perhaps this will help pinpoint exactly where your objection to the logic of the if-then conditional lies.

 

[Austin0]

Just a couple of quick clarifications:
I was not initially aware that you were using a specific definition of the hypothetical particles, but it is your demonstration so I want to make sure what we are talking about.
Tachyons:
1) Have no mass
2) Are not massless
3) Have a negative or imaginary mass.
4) Are to be regarded as ballistic particles [with mass]

Is this correct?

DO you consider that the addition of velocities formula would apply to them?

Jesse M Again, I don't know what this question even means--if you can assign a time-coordinate to an event, what would make that "meaningful temporal information" as opposed to "meaningless temporal information"?

What is your interpretation of B (0,0) -----> B(-10,20) as far as deriving speed??

1) (20-0)/( -10-0)=-2 OR

2) (20-0)/ abs(-10-0)=2

If it is 1) What is your idea of the meaning of this speed?
__________________________________________________________________________

I am pressed for time right now but will respond to your latest soon. Thanks

 

[Fredrik]

Just a couple of quick clarifications:
I was not initially aware that you were using a specific definition of the hypothetical particles, but it is your demonstration so I want to make sure what we are talking about.
Tachyons:
1) Have no mass
2) Are not massless
3) Have a negative or imaginary mass.
4) Are to be regarded as ballistic particles [with mass]

Is this correct?

You don't need to know the mass of a tachyon to understand this thread. We can define a tachyon as something that has a spacelike world line. (A curve is "spacelike" if the slope of its tangent is <1 at all points on the curve).

But if you're curious, the answer is that it turns out that a particle with that property has m²<0, so its mass must be imaginary.

DO you consider that the addition of velocities formula would apply to them?

Yes, you can use the standard formula to "add" the velocities of an inertial frame and a tachyon (but not the velocities of a tachyon and another tachyon).

What is your interpretation of B (0,0) -----> B(-10,20) as far as deriving speed??

1) (20-0)/( -10-0)=-2 OR

2) (20-0)/ abs(-10-0)=2

If it is 1) What is your idea of the meaning of this speed?

In the frame where those two events are tachyon emission/absorption events, the particle is described as moving from x=20 to x=0 while the time changes from -10 to 0, so I'd calculate v as (0-20)/(0-(-10))=-2.

 

[Fredrik]

Maybe I am not following you here, but isn't the propagation of sound independant of the source but measured to be different in relative frames??
That the difference with light is that it is also measured to be the same in all frames.

Yes, you're right about that.

I was not talking about the measured speed being the same in all frames. As I have mentioned elsewhere I think that due to clock desynchronization , they not only couldn't be measured at the same speed in different frmes but that they also couldn't be measured as having equal bidirectional speed in any frame.

I still haven't figured out what you mean by "bidirectional speed".

Assume you were doing an analysis of the measurement of light within two different frames.
Wouldnt you clock emmission and reception in one frame , and then from that frame calculate the emmission and reception in the other frame??

Yes.

That within the first frame there would be actual reception of photons but within that frame there would only be the hypothetical observation
by an observer at the proximate site of the actual reception in the second frame?

Absolutely not. The "actual reception" is an event, i.e. a point in spacetime. That point is assigned coordinates by all coordinate systems, and none of the inertial coordinate systems is "preferred" over any of the others.

Excuse me but in this case isn't it that 'A' [the IF] is in fact true, but it is the THEN "B' conclusion that is false? That in fact this statement is in no way valid.

No, the A (="there's a largest prime number N) is false, since there are infinitely many primes. What I posted is the easiest way to prove that. The "if-then" statement is definitely corrrect.

Isnt it the case that the premises are IF SR + FTL THEN time travel.

No, that's the statement we proved. The premise (or postulate, axiom, or whatever you prefer to call it) is SR+FTL.

That in this case the A is A =assumption of event at ( x=20, t=10) <==> B=time travel ?
Wouldnt you agree that this is treating it as a proof of B the conclusion?

The A is "SR+FTL". The FTL part can be made explicit in many different ways, and one of them is to say that a particle emitted at the origin can be detected at (10,20). (t=10,x=20).

I'm confused by your second question. You're talking about proofs as if you can prove stuff without first assuming something. You obviously can't. We're not proving B. We're proving "if A then B". We're treating the result as a proof of "if A then B", because that's what it is.

If the statement was IF SR and IF FTL and IF a signal sent from A arrives 10 sec before it is sent in B THEN "timetravel "

Would you agree that this, although a valid argument, would be an obvious tautology and without significance as a proof of "time travel" ?

Yes, since one of the assumptions is the conclusion.

 

[Austin0]

=Fredrik;2043272]You don't need to know the mass of a tachyon to understand this thread. We can define a tachyon as something that has a spacelike world line. (A curve is "spacelike" if the slope of its tangent is <1 at all points on the curve).

I wasn't suggesting the need to know the mass of a tachyon. I was simply getting it straight what we are talking about.

But if you're curious, the answer is that it turns out that a particle with that property has m²<0, so its mass must be imaginary.

Yes that is exactly what I said 3)

Yes, you can use the standard formula to "add" the velocities of an inertial frame and a tachyon (but not the velocities of a tachyon and another tachyon).

It looks to me like in that case, the greater the velocity of the particle, the lower relative velocity you derive from the formula.
Is that your understanding?

In the frame where those two events are tachyon emission/absorption events, the particle is described as moving from x=20 to x=0 while the time changes from -10 to 0, so I'd calculate v as (0-20)/(0-(-10))=-2

OK this interesting. 1) This experiment is based on the transmission of information correct?

2) This means a transmitter [which flashes on transmission]and a receiver [which flashes on reception] right?

3) There is no information passing from B to A at this point Correct?

4) So what is the basis of this spatial direction?

5) How is it that you both have been talking about dt=0 -->( -10 )=-10 seconds [back in time]

and now you are suddenly talking about forward dt= (-10) --->0 =10 sec.?

 

[Austin0]

=Fredrik;204333

I still haven't figured out what you mean by "bidirectional speed".

Two speeds : One measured with the direction of motion and one counter to that direction. If a frame is assumed at rest, then I guess to be totally correct you would have to do omni-directional measurements.

No, the A (="there's a largest prime number N) is false, since there are infinitely many primes. What I posted is the easiest way to prove that. The "if-then" statement is definitely corrrect.

Excuse me . Because you set it up with a sequence in parentheses , culminating with N
I read this as a statement: If there is a largest prime N in any designated sequence then that would yield (with the addition of 1) a larger prime number.
Since this was obviously false with any prime over 2 , I missed the literal interpretation ("there's a largest prime number N) which is also obviously false. SO it seems in actuallity both the premise and the conclusion were false No??
Just out of curiosity, it appears that it would be easy to falsify the conclusion but how would that falsify the premise, which is what you want to do , right??

 

[Fredrik]

It looks to me like in that case, the greater the velocity of the particle, the lower relative velocity you derive from the formula.
Is that your understanding?

No.

OK this interesting. 1) This experiment is based on the transmission of information correct?

2) This means a transmitter [which flashes on transmission]and a receiver [which flashes on reception] right?

3) There is no information passing from B to A at this point Correct?

4) So what is the basis of this spatial direction?

5) How is it that you both have been talking about dt=0 -->( -10 )=-10 seconds [back in time]

and now you are suddenly talking about forward dt= (-10) --->0 =10 sec.?

You really need to understand simultaneity in SR to understand this stuff. When you do, it's pretty easy. So what you need to do is to learn about simultaneity and then re-examine the argument for why SR+FTL implies "time travel" (i.e. that you can receive a reply to a message you haven't sent yet).

The separation between these two events is spacelike. That means that some observers will disagree about which event came first, i.e. some coordinate systems will assign a smaller time coordinate to A and some will assign a smaller time coordinate to B. You chose to consider a frame in which detection happens before emission, so in that frame the tachyon is described as moving from the detector to the emitter. That doesn't mean that the information is going that way.

Weird things like this happen all the time when tachyons are involved. That's what we've been trying to explain. For example, if you hook up a bomb to a tachyon detector and set it up so that the bomb explodes when it detects a tachyon, you might see the following sequence of events (in this order):

1. The detector emits a tachyon.
2. The bomb explodes.
3. Some guy aims his tachyon gun at the detector and pulls the trigger.
4. A tachyon that was emitted from the detector some time earlier (maybe years) hits the tachyon gun right after the trigger was pulled.

 

[Fredrik]

SO it seems in actuallity both the premise and the conclusion were false No??
Just out of curiosity, it appears that it would be easy to falsify the conclusion but how would that falsify the premise, which is what you want to do , right??

This is a totally standard method of proof called "proof by contradiction", or "reductio ad absurdum". In this case, we assume that N is the largest prime number and use that to prove that there are larger prime numbers than N. That clearly implies that the assumption is false. A true statement can't imply that it's also false, but a false statement can.

 

[JesseM]

Just a couple of quick clarifications:
I was not initially aware that you were using a specific definition of the hypothetical particles, but it is your demonstration so I want to make sure what we are talking about.
Tachyons:
1) Have no mass
2) Are not massless
3) Have a negative or imaginary mass.

As Fredrik said, this is irrelevant to the current discussion, but as discussed here a tachyon's rest mass would have to be imaginary to make equations involving energy and momentum work out.

4) Are to be regarded as ballistic particles [with mass]

It's also irrelevant whether we consider tachyons as ballistic or as waves in a medium with a speed independent of source (though in this case the speed would depend on the rest frame of the medium--see this post), this would not affect the way their coordinate velocities transform in different coordinate systems (likewise, you are free to imagine photons are ballistic particles, but because of the way the Lorentz transform works, you'll still find that a photon moving at c in one frame must be moving at c in other frames).

DO you consider that the addition of velocities formula would apply to them?

Yes, because the addition of velocities formula is derived from the Lorentz transformation, and in SR the Lorentz transform tells you how the coordinates of any event (including events on the worldline of a tachyon) are assigned by different inertial frames.

What is your interpretation of B (0,0) -----> B(-10,20) as far as deriving speed??

1) (20-0)/( -10-0)=-2 OR

2) (20-0)/ abs(-10-0)=2

If it is 1) What is your idea of the meaning of this speed?

Speed is defined as the norm of the velocity vector, so it's always positive, which means the answer would be 2). On the other hand, 1) could refer to the velocity in the +x direction (because in this example the velocity vector points in the -x direction).

 

[JesseM]

This is a totally standard method of proof called "proof by contradiction", or "reductio ad absurdum". In this case, we assume that N is the largest prime number and use that to prove that there are larger prime numbers than N. That clearly implies that the assumption is false. A true statement can't imply that it's also false, but a false statement can.

For more on this point, Austin0 may want to read the wikipedia article on contraposition in logic, especially the sections "examples" and "application".

 

[Fredrik]

Speed is defined as the norm of the velocity vector, so it's always positive

Oops, this is of course true.

Austin, I thought you were asking about the velocity, not the speed, so keep that in mind when you read my answer in #90.

 

[Austin0]

Fredrik = 2. If there's a largest prime number N, then (2·3·5·7·...·N)+1 is a prime number that's larger than N. (Here "A" isn't even true. In fact, what this argument really proves is that it isn't. But the statement is still valid).

1) Excuse me but in this case isn't it that 'A' [the IF] is in fact true, but it is the THEN "B' conclusion that is false? That in fact this statement is in no way valid.

Fredrik No, the A (="there's a largest prime number N) is false, since there are infinitely many primes. What I posted is the easiest way to prove that. The "if-then" statement is definitely corrrect.

Originally Posted by Austin0 SO it seems in actuallity both the premise and the conclusion were false No??

Just out of curiosity, it appears that it would be easy to falsify the conclusion but how would that falsify the premise, which is what you want to do , right??

This is a totally standard method of proof called "proof by contradiction", or "reductio ad absurdum". In this case, we assume that N is the largest prime number and use that to prove that there are larger prime numbers than N. That clearly implies that the assumption is false. A true statement can't imply that it's also false, but a false statement can.

I am aware of the principle. It was in that light that I made the comment above.

1) In this case;
a conclusion ,validly derived from the axioms of real numbers , that proved a larger prime would falsify the premise "largest prime N"
If P then not P
But the conclusion must be validly derived, ie. true Agreed?

2) Unless I am seriously losing my mind [always possible]

In this case ,the conclusion ( N + 1 = a larger prime ) is false under all circumstances except N=2,
is not validly derived ie. is false and therefore cannot constitute a falsification under the reductio ad absurdum principle.
Agreed ?
or do you think that there is some prime that when incremented by 1 will yield another prime?

3) In actuality the premise is self evidently false so if both the premise and the conclusion are both falsifiable in what sense do you think this is a valid statement?
a) it does have an if conditional and a conclusion so it is valid in the same way "black is white" is a valid sentance because it has a subject and a verb ?

4) Using the meaning of an if conditional premise [that Jesse has been referring to] where the actual truth is not relevant , is considered automatically true,then in this case my original statement above 1) is in fact correct.
Yes or no?

 

[JesseM]

2) Unless I am seriously losing my mind [always possible]

In this case ,the conclusion ( N + 1 = a larger prime ) is false under all circumstances except N=2,
is not validly derived ie. is false and therefore cannot constitute a falsification under the reductio ad absurdum principle.
Agreed ?
or do you think that there is some prime that when incremented by 1 will yield another prime?

He didn't say that the next larger prime after N is given by N+1. The proof tells you that if you assume N is the largest prime, then the new number M = (2·3·5·7·...·N)+1 [i.e. the number obtained by multiplying N by every prime smaller than it, then adding 1] won't be divisible by any other prime number smaller than itself, which would mean M is itself prime by definition. So if you assume N is the largest prime number, you can then show there must be a prime number larger than N, contradicting your original premise and proving that there is no largest prime number.

Note that proving M is prime here depends on the initial assumption that N is the largest prime number smaller than M; it's not true in reality that every number of the form (2*3*5*...*N)+1 is a prime if N is prime, the page here mentions that (2*3*5*7*11*13)+1 = 30031, which isn't prime because it's equal to 59*509.

 

[Austin0]

Originally Posted by Austin0
It looks to me like in that case, the greater the velocity of the particle, the lower relative velocity you derive from the formula.
Is that your understanding?

Fredrik No

Would you mind sharing your understanding of this. Are you saying that higher velocities wouldn't return lower relative velocities from the formula?

You really need to understand simultaneity in SR to understand this stuff. When you do, it's pretty easy. So what you need to do is to learn about simultaneity and then re-examine the argument for why SR+FTL implies "time travel" (i.e. that you can receive a reply to a message you haven't sent yet).

I think I have a fair grasp of simultaneity. I can certainly understand all the various results
as outlined in the various scenarios. I understand with no difficulty its application to all normal phenomena ie. c and sub c
and its role in the various paradoxes.

The separation between these two events is spacelike. That means that some observers will disagree about which event came first, i.e. some coordinate systems will assign a smaller time coordinate to A and some will assign a smaller time coordinate to B. You chose to consider a frame in which detection happens before emission, so in that frame the tachyon is described as moving from the detector to the emitter. That doesn't mean that the information is going that way.

What does this have to do with simultaneity? This purely a matter of logic and interpretation.
I am just trying to establish some definite parameters here.
1) Jesse has been referring to the signal moving from the transmitter in A to the receiver in B thus going back in time. OK I can agree with the logic of this, given the events.
I would think that actual observers in the case would come to this same conclusion, partly based on the direction of flow of information and the nature of transmission and reception.

2) Now you are viewing this as motion from the receiver to the transmitter forward in time. This does not make any sense to me , certainly not as pertaining to actual observers with any intelligence. Do you see how this might seem a bit circular.We now have a single signal going forward and backward simultaneously in the same frame??
3) I can understand that on a certain abstract level you could say it doesn't make any difference but it certainly makes a difference when deriving velocities etc.
Is there some way to come up with a single interpretation to work with?


.

 

[Austin0]

He didn't say that the next larger prime after N is given by N+1. The proof tells you that if you assume N is the largest prime, then the new number M = (2·3·5·7·...·N)+1 [i.e. the number obtained by multiplying N by every prime smaller than it, then adding 1] won't be divisible by any other prime number smaller than itself, which would mean M is itself prime by definition. So if you assume N is the largest prime number, you can then show there must be a prime number larger than N, contradicting your original premise and proving that there is no largest prime number.

Note that proving M is prime here depends on the initial assumption that N is the largest prime number smaller than M; it's not true in reality that every number of the form (2*3*5*...*N)+1 is a prime if N is prime, the page here mentions that (2*3*5*7*11*13)+1 = 30031, which isn't prime because it's equal to 59*509.

I am losing my mind. I read it as a series of primes not as series of multiplications.
I think I have too much else on my mind.

 

[Fredrik]

Would you mind sharing your understanding of this. Are you saying that higher velocities wouldn't return lower relative velocities from the formula?

I'm not really sure what you're asking. I assume that we're talking about the formula that says that if the velocity of frame F' in frame F is u and the velocity of a particle in frame F' is v, then the velocity of that particle in frame F is

$$w=\frac{u+v}{1+uv}$$

What exactly are you asking? Which of these variables (u,v and w) do you want to make bigger, and which one(s) do you think will be smaller as a consequence? (Note that by definition we have u<1, but if the particle is a tachyon, both v and w will be >1).

I think I have a fair grasp of simultaneity. I can certainly understand all the various results
as outlined in the various scenarios. I understand with no difficulty its application to all normal phenomena ie. c and sub c
and its role in the various paradoxes.

Then it should be very easy for you to see that if I send a message, and the person who receives it is moving away from me, he can send a reply that reaches me before I sent the first message, providing that: a) he's moving fast enough, b) his tachyons are moving fast enough.

We now have a single signal going forward and backward simultaneously in the same frame??

No, we don't. The signal (the message) is going back in time, but the tachyons wouldn't be described as going back in time. Try drawing the world line of a tachyon going left and being detected before it was emitted. Isn't it obvious that it would be interpreted as a tachyon emitted going to the right from the detector to the emitter?

 

[Dale]

Try drawing the world line of a tachyon going left and being detected before it was emitted. Isn't it obvious that it would be interpreted as a tachyon emitted going to the right from the detector to the emitter?

I understand what you're saying. It could be interpreted either way, but since it is carrying information from the emitter to the detector I think it would be better interpreted as going backwards in time from the emitter to the detedtor rather than forwards in time from the detector to the emitter.

 

[JesseM]

Part of the problem is that relativity itself does not carry any notion of whether a particle is moving "backwards" or "forwards" on a given worldline--the particle's motion is completely defined by the worldline, and the worldline is just the set of points in spacetime that the particle passes through. If we know a particle passed through events A: (x=5,t=0) and B: (x=6,t=3) there isn't really any basis in relativity for saying the particle went forwards in time from A to B or backwards in time from B to A. This is why I didn't want to talk about tachyons themselves, but about tachyon signals which carry information; if Bob sees some event in his local neighborhood and sends a signal about it, and at some other point in spacetime Alice receives this signal, then if the event of Alice receiving the signal happens before the event of Bob sending it in some frame, this frame has to say that she has information about the event in Bob's neighborhood before it actually happened, even if in this frame you choose to say that the tachyons themselves were moving forward in time from Alice to Bob.