Having trouble understanding why FTL implies time travel

[Austin0]

[

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

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

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

 

[Fredrik]

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

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

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

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

Yes.

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

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

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

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

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

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

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

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

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

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

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

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

 

[Austin0]

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

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

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

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

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

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

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

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

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

 

[Fredrik]

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

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

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

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

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

 

[Fredrik]

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

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

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

I agree 100%.

I make no claims about tachyons whatsoever.

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

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

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

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

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

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

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

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

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

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

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

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

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

 

[Austin0]

The outline of this demonstration is as follows:

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

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

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

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

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

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

___________

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

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

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

 

[JesseM]

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

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

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

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

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

 

[Austin0]

[

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

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

2)If the two postulates of relativity hold

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

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

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

 

[Fredrik]

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

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

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

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

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

 

[JesseM]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

[Austin0]

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

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

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

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

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

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

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

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

 

[JesseM]

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

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

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

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

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

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

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

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

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

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

 

[LittleRocks]

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

 

[Austin0]

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

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

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

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

In the above example ,of course I agree.

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

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

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

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

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

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

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

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

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

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

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

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

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

As above.

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

Yes.

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

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

 

[Austin0]

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

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

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

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

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

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

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

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

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

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

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

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

 

[Fredrik]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

[JesseM]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

[Austin0]

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

Sorry and thanks for the tip.

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

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

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

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

OK

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

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

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

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

This option.

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

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

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

 

[Austin0]

=JesseM;2021006]

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

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

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

No argument there.

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

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

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

What would you say in this case ? If this was presented as a demonstration or proof of the intermediate quantitative result, would you possibly agree that this could be described as including the conclusion in a premise?
Of course in this situation it would be subject to direct empirical determination while tachyons are so hard to catch.
__________________________________________________________________________-

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

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

 

[JesseM]

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

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

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

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

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

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

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

43.33..., but close enough.

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

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

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

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

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

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

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

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

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

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

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

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

 

[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.