Having trouble understanding why FTL implies time travel

[kronnyq]

I found a decent page explaining this but it's a little deep for my understanding.

I think I understand the basics of special relativity where the speed of light remains constant regardless the velocity of 2 observers, the laws of physics do not depend on location or motion, and that length, time, and mass depends on motion relative to a chosen frame of reference.

I can't seem to hack why faster than light speed would suggest time travel however. If anyone would care to elaborate or point me to a page/thread that doesn't require a PhD in physics to comprehend, that would be swell.

 

[Dmitry67]

If something (A->B) is transmitted faster then light in one frame, then there is another frame where the effect (B) occurs *before* then the cause (A)

 

[Fredrik]

I can't seem to hack why faster than light speed would suggest time travel however.

It doesn't. At least not the kind of time travel you probably have in mind. Maybe you saw Heroes the other day when Daphe got "supercharged" and ran back in time. What really would have happened (if we can accept all the other ridiculous things) is that from Matt's point of view, she would have arrived at her destination at a later time than her departure time. However, from the point of view of a person in a spaceship going fast in the same direction, Daphne started at her "destination" and ran backwards until she reached Matt at some later time. Different observers can disagree about the order in which events occur, if their separation is "spacelike" (i.e. not enough time for a light signal to get from one event to the other). That's it.

So the "time travel" suggested by special relativity is pretty boring, especially since only objects with an imaginary mass (a mass that's a real number times the complex number i that satisfies i²=-1). Matt said he paid attention in high school, but the writers certainly didn't.

If FTL particles ("tachyons") exist, they must have some special features that prevent the paradoxes discuessed in this thread (mostly by me, on the first page).

 

[RandallB]

Still missing is the point on why FTL (tachyons) in SR cannot imply “backwards time”.
In the example of Daphe becoming a “Tachyon” to change her position in space to a distance further than can be traveled by light. Both Matt (at her starting position) and the fast moving spaceship have clocks and additional clocks at all locations in there frames that indicate what they believe are simultaneous times in their respective frames.

Before she even begins, Matt and the Spaceship both define can define a location that represents where Daphe is found to be and the end of her FTL trip. Therefore both Matt and the spaceship can define where and when that destination is in there own frames of reference. Setting those frames at t=0 and x=0 for the start position Matt both frames define a the time at the location where Daphe will be seen after she moves as simultaneously being at time = 0.
However this is where SR is very clear both Matt and the Spaceship disagree about what the correct “current” time is at those distant locations. They are two different locations since because of the respective motions they do not come together at the same place until Daphe arrives there at so point in the future.
Both frames claim the other is completely wrong and an inaccurate reference for the standard of simultaneous because when the review problems from the POV of only their own frame they always get good rational results, which include showing that all other frames are irrationally incorrect.
So from the POV of Matt and all observers in his frame when they perform the SR Transforms to show what the clocks at various locations in the spaceship frame say they are all still out of synchronization and total useless as a correct measure of when things happen as far as Matt and his Observes know.

The flaw being applied in claiming to see “backwards” time is comparing the times at different locations in the spaceship frame as define by the Matt frame as being correct!
Matt and his observers will tell you:
“Hey duh; we have already defined all those times in the other frame as out of sync and unreliable they cannot be “correct” – of course they show weird things like “backwards time” those clocks are just WRONG!”
SR Simultaneity completely supports them in this statement, because it also supports the very same statement made by the spaceship about the Matt view of time being wrong.

It is just more interesting (even sells books) to say “look backwards time travel” then to say what this thought experiment really shows – And that is:
Two different frames cannot agree on a common version of ‘simultaneous’

Therefore you must remain only in one frame of reference from start to finish when working this kind of problem.
So when you “do the math” using only the spaceship frame from the start, you see only normal causality and a Matt POV for time that cannot be correct.

But since it is boring to just recognize that simple SR fact (know for decades), I’ve no doubt the myth of, backwards time caused by tachyons, will continue without justification.

 

[JesseM]

It doesn't. At least not the kind of time travel you probably have in mind.

Yes it does, as long it's possible to send information FTL and as long as the principle of relativity is obeyed and tachyon signals follow the same laws all frames. Different frames have different definitions of simultaneity, and if two events have a spacelike separation, like the event of the tachyon being sent out and the event of it being received, then different frames will disagree on the order of these events, with some frames saying the signal was received before it was sent. And if it's possible in every frame for tachyon signals to be received at an earlier time than they're sent, then I can send you a tachyon signal which in your frame is received at an earlier time than I sent it, and you can send a reply which in my frame is received at an earlier time than you sent it, with the net result being that I receive your reply before I sent the original message. There's a spacetime diagram of such a two-way tachyon communication scheme here:

http://www.theculture.org/rich/sharpblue/archives/000089.html

 

[JesseM]

The flaw being applied in claiming to see “backwards” time is comparing the times at different locations in the spaceship frame as define by the Matt frame as being correct!

No, there is no such assumption. The idea that tachyons imply causality violation requires two tachyon signals, an original message and a reply, such that in frame A the original message moves FTL but forwards in time while in frame B the original message moves backwards in time, whereas in frame A the reply moves backwards in time while in frame B the reply moves FTL but forward in time. No one is assuming there is any "objective" truth about whether either of the two signals is individually moving forwards or backwards in time, but the combination of the two is such that the reply is received in the past light cone of the the event of the original signal being sent, which is a clear causality violation in all frames.

Of course this depends on the assumption that not only are FTL signals possible, but that they obey the same laws in all inertial frames (the first postulate of SR). If there was a "preferred frame" for FTL signals, such that in that frame you could send signals FTL but you could not send signals back in time according to that frame's definition of simultaneity, then FTL would not imply any causality violations.

So when you “do the math” using only the spaceship frame from the start, you see only normal causality and a Matt POV for time that cannot be correct.

For pedagogical purposes, you need to use two separate frames to demonstrate that the original signal's speed in frame A is the same as the reply's speed in frame B, and that each frame sees one of the two signals moving backwards in time, with the net result that they both agree the reply is received before the original signal was sent (of course once you have satisfied yourself that tachyons can move backwards in time in every frame, then you don't need to use two separate frames, you can analyze everything from a single frame which sees one signal moving FTL but forwards in time and the other moving backwards in time). Again, it all comes down to the first postulate of relativity--if there is any frame that sees a tachyon signal being received at an earlier time-coordinate than it was sent, then unless the tachyons violate the first postulat (i.e. they do not obey Lorentz-invariant laws), then it must be possible in every frame to send a tachyon signal such that it arrives before it was sent in that frame.

 

[kronnyq]

It doesn't. At least not the kind of time travel you probably have in mind. Maybe you saw Heroes the other day when Daphe got "supercharged" and ran back in time. What really would have happened (if we can accept all the other ridiculous things) is that from Matt's point of view, she would have arrived at her destination at a later time than her departure time. However, from the point of view of a person in a spaceship going fast in the same direction, Daphne started at her "destination" and ran backwards until she reached Matt at some later time. Different observers can disagree about the order in which events occur, if their separation is "spacelike" (i.e. not enough time for a light signal to get from one event to the other). That's it.

So the "time travel" suggested by special relativity is pretty boring, especially since only objects with an imaginary mass (a mass that's a real number times the complex number i that satisfies i²=-1). Matt said he paid attention in high school, but the writers certainly didn't.

If FTL particles ("tachyons") exist, they must have some special features that prevent the paradoxes discuessed in this thread (mostly by me, on the first page).

That's funny you mentioned that, ha...because I did see that episode and FTL time travel has always interested me, after watching that I decided to do some more research on it.

I'm still not quite gettin it though...I don't understand the basic SR behind it. Granted that Daphne ran back in time was quite preposterous and she could only go forward in time, why exactly does this occur when you are moving at FTL speed? Is this because it takes a bit for light to catch up to her so she is visible, that is skipping ahead of the speed of visible light relative to Matts frame of perception?

 

[Crazy Tosser]

Ok. so let's say you travel faster than light. Guess what, you see an empty universe. Why? Because since you are traveling faster than light, you cannot transmit any information to the surrounding object and no surrounding objects can transmit any information to you (that's what SR says). And now, that would be a violation of the 2nd law, wouldn't it? Heck, from your frame of reference the entire universe just disappeared - that's what I call decrease in entropy :D

 

[JesseM]

I'm still not quite gettin it though...I don't understand the basic SR behind it. Granted that Daphne ran back in time was quite preposterous and she could only go forward in time, why exactly does this occur when you are moving at FTL speed? Is this because it takes a bit for light to catch up to her so she is visible, that is skipping ahead of the speed of visible light relative to Matts frame of perception?

Have you heard of the idea of the relativity of simultaneity? The idea is that different reference frames in relativity disagree about whether events at different locations happened at the "same time" or "different times". This can be understood in terms of the fact that all frames say light moves at the same speed in all directions--if I'm on a ship and I have clocks at the front and back, then in my reference frame where the ship is at rest, if I set off a light flash at the center of the ship I must believe the event of the light hitting the back happens at the "same time" as the event of the light hitting the front. But if in your frame the ship is moving forward, from your perspective the front end of the ship is moving away from the position where the light flash happened while the back end is moving towards that position, so if you say the light moved at the same speed in both directions in your frame, you must conclude the light caught up with the back end before the light caught up with the front end. You can see a youtube video illustrating a similar thought-experiment here, and the link I posted earlier also has a good illustration.

Anyway, it turns out that the relativity of simultaneity works in such a way that if two events could both lie on the path of a signal moving slower than light (in which case physicists say there is a 'timelike separation' between the events) or exactly at the speed of light (in which case there is a 'lightlike separation' between them), then all reference frames will at least agree on the order of the two events, although they can disagree on how much time elapsed between the first and the second. On the other hand, if two events could only be connected by a signal moving faster than light--like an event happening on Earth in 2008 and an event happening at Alpha-Centauri, 4 light-years away, at some date less than 4 years past 2008, like 2010--then there is said to be a 'spacelike separation' between them, and some frames will say event A happened before event B, others will say event B happened before event A, and one frame will say event A and event B happened at the same time (note that the time events happen in a given frame is not based on when an observer at rest in that frame sees them--two events can happen at the same time-coordinate in my rest frame, but because one happens at a greater distance from me, the light from it doesn't reach me until later than the light from the other one).

So, this means that if I send a signal which moves faster than light but forward in time in my frame--so, for example, in my frame I send the signal from Earth in 2008 and my friend on Alpha Centauri receives it 2 years later in 2010--then there will be other frames where the event of the signal being received by my friend actually happened before the event of my sending it, so in these frames it is as if the signals moved "back in time". But this is still not "really" transmitting information backwards in time in any objective sense, it's just different frames disagreeing on the order, with no single "right" answer. However, the first postulate of special relativity says that the laws of physics must work exactly the same way in every frame, so anything that can happen in one frame must be replicable in every other frame (the second postulate of special relativity says that light moves at the same speed in all frames, and from these two postulates you can derive the rest of special relativity). That means that if there's at least one frame where it's possible for tachyon signals to be received at an earlier time than they were sent, it must be possible in all frames. So, I could send a signal to a friend in motion relative to me (so he would have a different rest frame than mine) which traveled FTL in my frame but backwards in time in his frame; then he could send a reply which traveled FTL in his frame but backwards in time in my frame, in such a way that I received his reply before I even sent the original signal. Although there is no objective truth about whether either of the two signals was traveling backwards in time individually, all frames agree that I received the reply before I sent the signal, so this is a case where information has objectively gone backwards in time.

 

[RandallB]

For pedagogical purposes, you need to use two separate frames to demonstrate that the original signal's speed in frame A is the same as the reply's speed in frame B, and that each frame sees one ...

No the only result that comes from using two different frames as valid frames when the both claim the other as not correct is to violate an chance of following SR rules. SR is very clear, you must work the problem from only one (assumed to be correct) referance frame - from the start ot he very end with all other frames considered as "wrong".
Nothing in SR allows using two different frames as if both could be thought of as prefered.

 

[JesseM]

No the only result that comes from using two different frames as valid frames when the both claim the other as not correct is to violate an chance of following SR rules. SR is very clear, you must work the problem from only one (assumed to be correct) referance frame - from the start ot he very end with all other frames considered as "wrong".

You don't consider any frame to be "right" or "wrong", you just understand that frame-dependent statements are only a matter of convention, like kilometers vs. miles (and just like with units you have to make sure you keep your conventions consistent throughout the problem). But yes, you can analyze any problem in SR from the perspective of a single frame. Read what I wrote again:

For pedagogical purposes, you need to use two separate frames to demonstrate that the original signal's speed in frame A is the same as the reply's speed in frame B, and that each frame sees one of the two signals moving backwards in time, with the net result that they both agree the reply is received before the original signal was sent (of course once you have satisfied yourself that tachyons can move backwards in time in every frame, then you don't need to use two separate frames, you can analyze everything from a single frame which sees one signal moving FTL but forwards in time and the other moving backwards in time).

Once you accept that FTL + the first postulate of relativity implies that tachyon signals can move back in time in any frame, then of course you don't need to use more than one frame. Analyzing things from two different frames is a pedagogical device designed to demonstrate that, in fact, FTL + the first postulate of relativity does automatically imply that in every frame it must be possible for tachyon signals to arrive at an earlier time-coordinate than they were sent.

If you disagree that these assumptions lead to that conclusion, I have two simple questions for you:

1. Do you agree that the first postulate of relativity demands that any experiment that gives certain results in one frame (in terms of that frame's coordinates), if replicated in any other frame, must give identical results (in terms of the new frame's coordinates)?

2. Do you agree, therefore, that if you can run an experiment that in one frame will result in a signal being received before it was sent (in terms of the time-coordinates that frame assigns to the events of the signal being sent and the signal being received), then it must be possible to run an identical experiment which gives the same results in any other frame (in terms of that frame's own coordinates), assuming the first postulate of relativity is not violated?

 

[LURCH]

If it helps, try looking at the time-travel idea as an extension of time dilation. If you travel fast enough, time slows down. At lightspeed, time freezes. Above lightspeed, time goes backward.

That's only a starting point, and way oversimplified; what JesseM is trying to egt at is a bit more advanced.

 

[JesseM]

If it helps, try looking at the time-travel idea as an extension of time dilation. If you travel fast enough, time slows down. At lightspeed, time freezes. Above lightspeed, time goes backward.

No, that's wrong--an FTL object doesn't have an inertial frame of its own, so the time dilation equation (derived from the Lorentz transformation relating different inertial frames) tells you nothing whatsoever about how the ticks of an FTL "clock" would compare to sublight clocks (anyway, a naive application of the time dilation equation to v > c would give an imaginary time dilation factor, not a negative one). The relation of FTL to time travel comes from analyzing the behavior of tachyons from the perspective of sublight inertial frames, just like we analyze the behavior of photons from the perspective of sublight inertial frames without any notion of allowing the photon to have its own "perspective".

 

[Fredrik]

Yes it does,

Your explanation is just what I said in the thread I linked to (this post in particular), so it wasn't really helpful, but I think you're right, sort of. Let's say that Daphne runs west with speed 2c relative to Matt, and then turns around and runs east with speed 2c relative to a spaceship that's going west with speed 0.99c relative to Matt, she will get back to Matt before she started. To Matt, the second run would look like this: At an earlier time, Daphne appears out of nowhere and immediately splits in two. One of the Daphnes is acting normal, and the other is running backwards, going west at an FTL speed v<2c until she meets the Daphne who's running west at 2c. The two become one for an instant, and then disappear out of existence.

I have a few problems with this though. How about energy conservation, and Daphne's conscious experience? When she runs west, she just puts one foot in front of the other at some rate, say n steps per second of her own time. Then she runs east, at a lesser speed, so she's taking m<n steps per second of her own time. If the just decides to run west at a rate of m steps per second, she'll end up in the future, not in the past. So she must be doing something more than that. What exactly is she doing in addition to putting one foot in front of the other? Flapping her ears?

 

[Fredrik]

No, that's wrong--an FTL object doesn't have an inertial frame of its own, so the time dilation equation (derived from the Lorentz transformation relating different inertial frames) tells you nothing whatsoever about how the ticks of an FTL "clock" would compare to sublight clocks (anyway, a naive application of the time dilation equation to v > c would give an imaginary time dilation factor, not a negative one). The relation of FTL to time travel comes from analyzing the behavior of tachyons from the perspective of sublight inertial frames, just like we analyze the behavior of photons from the perspective of sublight inertial frames without any notion of allowing the photon to have its own "perspective".

A photon's point of view doesn't make sense of course, but we can easly define a tachyon's point of view by taking an inertial frame such that the x-axis coincides with the tachyon's world line and then swapping the x and t axes. (I'm not sure how useful this is though).

 

[Crazy Tosser]

Time is defined as changes of state from one state to another. These changes are not like your computer, they are not stored on the hard disk. Seeing these changes as slowed down or stopped from a frame of reference makes sense, but going back through the changes? Face it, time travel is impossible, and going faster than the speed of light is impossible, at least here on the Relativity forum. FTL does not imply time travel because neither exist.

 

[JesseM]

Your explanation is almost exactly what I said in the thread I linked to, so it wasn't really helpful, but I think you're right, sort of. Let's say that Daphne runs west with speed 2c relative to Matt, and then turns around and runs east with speed 2c relative to a spaceship that's going west with speed 0.99c relative to Matt, she will get back to Matt before she started. To Matt, the second run would look like this: At an earlier time, Daphne appears out of nowhere and immediately splits in two. One of the Daphnes is acting normal, and the other is running backwards, going west at an FTL speed v<2c until she meets the Daphne who's running west at 2c. The two become one for an instant, and then disappear out of existence.

This is why I restricted the discussion to FTL signals rather than objects. Suppose I send a signal to you on Jan. 10 which moves FTL in my frame but backwards in time in your frame, and the signal contains information about some lottery numbers which have just been drawn. As soon as you receive the signal you send a copy of the message back in reply which moves FTL in your frame but backwards in time in mine, which means I could receive this signal on some earlier date, say Jan. 5, and know the lottery numbers in advance. Now, if you want to look at the whole sequence in my frame without saying anything was going "backwards in time", you can take the perspective that my device which "received" the signal on Jan. 5 was really "sending" them, so the tachyons move forward in time to you, and are "received" by you shortly after you receive the signal I sent on Jan. 10; but even if you choose to look at things this way, you can't get around the fact that I know about the lottery numbers 5 days in advance of their being drawn! And the ability to gain information about the future in this way is a necessary implication of the idea that I can reliably gain information about events outside my past light cone using FTL signals (at least if we assume the first postulate of relativity holds). Do you agree with this much?

I have a few problems with this though. How about energy conservation, and Daphne's conscious experience?

This "Daphne" would be made of tachyons, totally different particles than what we are made of. Asking about her conscious experience is a bit like asking about the conscious experience of a being made of photons or any other particles which move at c. Relativity simply doesn't tell you anything about the "perspective" of particles which are moving at velocities larger than or equal to c, it doesn't tell us about how the ticks of clocks moving at velocities larger than or equal to c would relate to ticks of our clocks, etc. It only deals with measurements made by familiar sublight objects, the behavior of things moving at velocities larger than or equal to c can be analyzed from the perspective of sublight inertial frames but they don't have their own inertial rest frames.

 

[JesseM]

A photon's point of view doesn't make sense of course, but we can easly define a tachyon's point of view by taking an inertial frame such that the x-axis coincides with the tachyon's world line and then swapping the x and t axes. (I'm not sure how useful this is though).

Such a coordinate system could not be considered an inertial frame without violating the first postulate of SR. (think about how light cones would look in this coordinate system if you assume more than one spatial dimension, for example--not the same as in sublight inertial frames!) And if tachyons could interact with one another in such a way as to form "clocks" of some kind, there's no physical reason to expect that they would keep time with the coordinate time in a coordinate system defined this way.

 

[JesseM]

Time is defined as changes of state from one state to another. These changes are not like your computer, they are not stored on the hard disk.

Are you arguing for the philosophy of presentism, where only things in the present can be said to exist? This is hard to reconcile with the relativity of simultaneity, which says that two events which happen at the "same time" in one inertial frame happen at "different times" in another, and that no inertial frame's perspective is physically preferred over any others. Of course you could choose to believe in a "metaphysically preferred frame" whose definition of simultaneity would correspond to the "truth" about whether two events share the same present moment, but which is experimentally indistinguishable from any other frame; this seems pretty awkward, though, which is why relativity is generally seen to favor the philosophy of eternalism where all events coexist on a 4D spacetime manifold. See here for a discussion of presentism vs. eternalism, from the online "Stanford Encyclopedia of Philosophy".

Seeing these changes as slowed down or stopped from a frame of reference makes sense, but going back through the changes? Face it, time travel is impossible, and going faster than the speed of light is impossible, at least here on the Relativity forum. FTL does not imply time travel because neither exist.

FTL particles are considered unlikely but they are not fundamentally incompatible with relativity, see here. And backwards time travel appears in certain solutions to the equations of general relativity (like spacetimes containing traversable wormholes), with paths through spacetime that revisit their past being known as "closed timelike curves"; it's an open question whether the hoped-for unification of general relativity with quantum physics will end up ruling out this possibility, I imagine most physicists would say it'll probably be ruled out but it's not certain, you certainly can't rule out closed timelike curves using mere philosophical arguments.

 

[Fredrik]

Jesse, I find your replies to me pretty confusing, not because I don't understand them or because I disagree, but because the things you're saying are just what I've been saying myself. I don't see why you're saying these things to me.

Suppose I send a signal to you on Jan. 10 which moves FTL in my frame...
...
Do you agree with this much?

This is a good example.

This is why I restricted the discussion to FTL signals rather than objects.
...
This "Daphne" would be made of tachyons...

And yet you disagreed with me when I said that FTL doesn't imply time travel in the sense the OP probably had in mind. Sending messages back in time isn't what most people would consider time travel. If you didn't mean that "if Daphne can run FTL, she can go back in time and save Hiro who's stuck in 1992", then I have no idea what you were disagreeing with me about when you answered my "it doesn't" with "yes it does" in #4.

Such a coordinate system could not be considered an inertial frame without violating the first postulate of SR.

Did I say it was an inertial frame?

And if tachyons could interact with one another in such a way as to form "clocks" of some kind, there's no physical reason to expect that they would keep time with the coordinate time in a coordinate system defined this way.

First of all, they may not need "tachyonic" clocks. They can just observe what normal matter does and calculate their coordinates from that. (Of course, calculation takes time...hmm). Second, the coordinate system I defined is consistent with a definition of simultaneity that I think is just as natural for tachyons as the standard definition is for us: Switch on a light bulb somewhere near the tachyon. We define that event to be simultaneous with (t,x)=(0,0) if the light reaches the tachyon at (-T,0) and (T,0).

 

[JesseM]

And yet you disagreed with me when I said that FTL doesn't imply time travel in the sense the OP probably had in mind. Sending messages back in time isn't what most people would consider time travel.

I guess this is the source of confusion. The OP didn't really say anything very specific about what they had in mind, and sending information back in time certainly leads to all the same time travel paradoxes as sending objects back in time (not to mention the possibility of building a Star-Trek-style transporter which reduces people to a string of bits which can be used to reconstruct them in the past); your reply didn't seem to acknowledge the idea that FTL messages + relativity does lead to time travel paradoxes, and you made dismissive-sounding comments like 'So the "time travel" suggested by special relativity is pretty boring', although I admit I didn't read the earlier thread you had linked to in that post. But the OP might not have read it either, in which case I think they would get the wrong idea about the relation between FTL and time travel paradoxes in relativity from your comments. Anyway, now that we've discussed things it's clear we don't have any actual substantive disagreements about the physics issues involved.

Did I say it was an inertial frame?

No, but suppose someone is asking questions about what it'd be like to "take the perspective" of something moving at the speed of light, and then brings up some coordinate system where light is at rest. I think it'd be worth pointing out that when physicists talk about any object's "perspective" in relativity they are normally talking about the object's inertial rest frame, and that it's a special feature of the way the laws of physics work that a physical clock will keep time with coordinate time of its inertial rest frame (including the brain's internal clock); existing physics can't really make any sense of the question of what would be "experienced" by a conscious being moving at light speed, and a coordinate system where a photon is at rest doesn't shed any light on this question (you could in fact devise an infinite variety of different non-inertial coordinate systems where a photon is at rest).

First of all, they may not need "tachyonic" clocks. They can just observe what normal matter does and calculate their coordinates from that. (Of course, calculation takes time...hmm).

But you were talking about the subjective experience of a tachyonic being, which would presumably involve questions like whether they would experience our slower-than-light clocks running forwards or backwards, whether the ticks of our clocks would seem very slow or very fast, etc. Unless you're talking about a conscious being with no sense of the flow of time, which would have to be a pretty alien sense of consciousness.

Second, the coordinate system I defined is consistent with a definition of simultaneity that I think is just as natural for tachyons as the standard definition is for us: Switch on a light bulb somewhere near the tachyon. We define that event to be simultaneous with (t,x)=(0,0) if the light reaches the tachyon at (-T,0) and (T,0).

But again, picture a situation where we have two space dimensions and one time dimension. Picture a regular light cone in this 3D spacetime. Now relabel the x-axis as the t axis and the t axis as the x axis, but keeping the y-axis as a space axis--a "plane of simultaneity" in this new coordinate system will now be upright like a wall instead of flat like a floor, meaning it'll be able to slice the light cone in two, so that there are photon paths which lie entirely within that single plane of simultaneity, and these photons are moving "instantaneously" rather than at c in this coordinate system. It's only if you reduce the number of space dimensions to 1, so your only coordinates are x and t, that photons moving at c in the original sublight frame would still be guaranteed to move at c in the new "tachyon" coordinate system you've defined.

 

[RandallB]

Once you accept that FTL + the first postulate of relativity implies that tachyon signals can move back in time in any frame, then of course you don't need to use more than one frame.

So what you are saying is first use two frames inappropriately to give the appearance of FTL backwards time travel by tachyons.
Then convincing your audience of that as a given, so you can use that with only one frame anytime you like and claim you are only using a single frame ...
– what do you call that kind of logic?
That is called magicians misdirection where you don’t show what the other hand has done.

1. Do you agree that the first postulate of relativity demands that any experiment that gives certain results in one frame (in terms of that frame's coordinates), if replicated in any other frame, must give identical results (in terms of the new frame's coordinates)?

No one has complained about that – at least I certainly have not.

2. Do you agree, therefore, that if you can run an experiment that in one frame will result in a signal being received before it was sent (in terms of the time-coordinates that frame assigns to the events of the signal being sent and the signal being received),

Agree therefore? What therefore, Of course not!
And you have never done so.
Frame A has all Clocks in sync no matter how far away.
When a clock 20 LY away receives a tachyon in only 10 yr it will still be LATER not before a time Zero start. And if you STAY in FRAME A you can send the tachyon back to the start across the 20 LY distance even faster in only 5 yrs that is still AFTER all the other times I.E. no backwards time change or observation to be found by the tachyon.

Sure you can pull the Rabbit Frame out of your hat with a Rabbit with a watch reading “yesterday” when looking at the Tachyon “turnaround” at the A frame 20ly location.
You want to declare that as backwards in time because the rabbit in the Rabbit Frame has a clock the reads sometime in the past! ?!
But that is exactly what the A Frame reference you picked expects – the fast moving Rabbit Frame has all their clocks WRONG, out of sync, and running SLOW.
You cannot look at a Clock SR has already defined as wrong wrt to the frame your using and call it real without breaking a SR rule. I don’t understanding why you kept pushing the fantasy.

What you need to do is complete Frame A analysis and explain WHERE and WHEN the rabbit was when the Tachyon started out in the first place!
I’ll give you half the answers:
The rabbit will have been in the same place in the rabbit frame (stationary)
The time in Frame A where ever in frame A that may be would have been Zero (Frame A in sync)
Where in Frame A the Rabbit is at the start t=0 you can set by picking a speed.
Then with a bit of math tell us: What Time was it on the Rabbit’s watch at Frame A time =0

Have you ever done that – of course not, Because no matter what speed you set for the rabbit wrt to A the Rabbit’s will read the day before “yesterday” or some time farther in the past than time the Rabbit watch will read when it gets to the 20LY frame A location to see the Tachyon arrive. Meaning from the Rabbits point of view, time passed normally, in the forward direction from when the tachyon started to when it reached the 20LY spot. And from the Rabbits POV during the Tachyon return trip; Time will still move forward for the rabbit, no matter waht any other "out of sync" Rabbit frame clock might say!

DO the math and don’t forget to tell us here what you get.

And if you want to use the time on any other location in the Rabbit frame as “correct” and in sync with each other – fine.
As you say you can pick the Rabbit frame as the “frame-dependent convention”.
SR will let you do that: IF and ONLY if you Start over from the very beginning, use all Rabbit Frame clocks as in-sync and correct, But recognize all frame A clocks as out of sync and “incorrect” as SR requires.

 

[Fredrik]

Randall, do you have a problem with this scenario? A tachyon gun is at rest in frame F. In frame F, the origin of frame F' is moving in the positive x direction with speed v=0.99c. The gun fires a tachyon that's moving in the negative x direction with speed 10c in frame F'. Would you agree that in frame F, this tachyon is going backwards in time?

 

[JesseM]

So what you are saying is first use two frames inappropriately to give the appearance of FTL backwards time travel by tachyons.

There is nothing inappropriate about it. If the first postulate is true, it must be possible for a tachyon signal to be received at an earlier time-coordinate than it was sent, in any inertial frame. Let's go to your objection to this logic:

1. Do you agree that the first postulate of relativity demands that any experiment that gives certain results in one frame (in terms of that frame's coordinates), if replicated in any other frame, must give identical results (in terms of the new frame's coordinates)?

No one has complained about that – at least I certainly have not.

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

2. Do you agree, therefore, that if you can run an experiment that in one frame will result in a signal being received before it was sent (in terms of the time-coordinates that frame assigns to the events of the signal being sent and the signal being received),

Agree therefore? What therefore, Of course not!
And you have never done so.
Frame A has all Clocks in sync no matter how far away.
When a clock 20 LY away receives a tachyon in only 10 yr it will still be LATER not before a time Zero start.

This is true as long as the tachyon signal was moving forwards in time in frame A. But do you agree that if we analyze this same signal in frame B, the event of the signal being received can happen at an earlier time-coordinate than it was sent, in the coordinates of frame B? For example, suppose in frame A the coordinates of it being sent were x=0 light-years, t=0 years and the coordinates of it being sent were x=20 light-years, t=10 years. Now suppose frame B is moving at v=0.8c in the +x direction of frame A, so gamma=1.25, giving the Lorentz transformation:

x' = 1.25*(x - v*t)
t' = 1.25*(t - vx/c^2)

This transformation assumes the origins coincide, so the event of it being sent in frame B has coordinates (x'=0, t'=0). As for the event of the signal being received, we can plug in x=20 ly, t=10 y to get:

x' = 1.25*(20 - 0.8*10) = 15
t' = 1.25*(10 - 0.8*20) = -7.5

So in frame B the event of it being sent happened at t'=0 while the event of it being received happened at t'=-7.5, which is 7.5 years earlier in this frame's time-coordinates.

So if you agreed with my statement earlier about the first postulate implying that whatever the events of an experiment seen in one frame (like frame B), we can create a different experiment which will give all the same coordinates in a different frame (like frame A), then do you deny that this implies that in frame A we should be able to create a different tachyon experiment where the event of the signal being sent happens at x=0, t=0 and the event of the signal being received happens at x=15, t=-7.5? If you do deny this, can you explain your reasoning?

But that is exactly what the A Frame reference you picked expects – the fast moving Rabbit Frame has all their clocks WRONG, out of sync, and running SLOW.
You cannot look at a Clock SR has already defined as wrong wrt to the frame your using and call it real without breaking a SR rule. I don’t understanding why you kept pushing the fantasy.

You are confused if you think solving an SR problem involves declaring one frame "wrong" and another "right". As I said in my last post to you, they are simply different conventions about how to label events, analogous to using kilometers vs. miles. With units you can't get them mixed up--for instance, if you want the difference in speed between two objects you can't use kilometers/second for one and miles/second for the other--but you don't declare either right or wrong, and during the course of a problem using the metric system you can certainly make reference to other units, like saying "I know the distance between the two points was 10 miles, therefore it must be 16.09 kilometers". It's the same with SR, where during the course of solving a problem in frame A you're free to make reference to other frames, like saying "I know the object is 10 light-seconds long in its own rest frame, and it's moving at 0.8c in frame A, so in frame A it must be 6 light-seconds long". As long as you don't try to plug in measurements/coordinates from frame B in a calculation where you're supposed to use measurements/coordinates from frame A, there's no problem with juggling between talking about the way the same events look in different frames over the course of a single problem, and if you look at a relativity textbook you can see they do this sort of juggling routinely, to give students better intuitions about how the same phenomena can look different in different frames.

 

[DrGreg]

RandallB's problem with understanding this was discussed in another thread here[/color]. I gave an explicit numerical example in post #42 of that thread which RandallB failed to accept. (For the benefit of other readers, that example requires an understanding of the Lorentz transform and how to apply it (but that wasn't the issue of contention).) I tried to probe this further in post #52 but got no response.

Unfortunately I'll be offline for the next 2 weeks so won't be able to respond!

 

[madness]

Wouldn't faster than light travel imply an imaginary Lorentz factor? Which would in turn imply that a transformation to their frame would give imaginary time and position cooridnates? This doesn't look like time travel to me...

 

[JesseM]

Wouldn't faster than light travel imply an imaginary Lorentz factor? Which would in turn imply that a transformation to their frame would give imaginary time and position cooridnates? This doesn't look like time travel to me...

Have you read through the thread? The connection between FTL and backwards-in-time signalling has nothing to do with substituting v > c into the Lorentz transformation, tachyons simply wouldn't have inertial rest frames of their own for the same reasons photons don't have inertial rest frames of their own (because it would violate the first postulate of relativity, and because inertial frames are supposed to be constructed out of physical rulers and clocks which can't be accelerated to light speed or beyond). The causality violations involving tachyons are derived by analyzing their behavior from the perspective of slower-than-light frames, just like we can analyze the behavior of photons from the perspective of slower-than-light frames.

 

[daytripper]

If it helps, try looking at the time-travel idea as an extension of time dilation. If you travel fast enough, time slows down. At lightspeed, time freezes. Above lightspeed, time goes backward.

That's only a starting point, and way oversimplified; what JesseM is trying to egt at is a bit more advanced.

I used to understand FTL travel in exactly that way but then, upon studying the Lorentz factor for a long time, I realized that, as Fredrik said, v > c ==> \gamma = ai (where a is a constant and i is \sqrt{-1}).

So rather than progressing on the timeline, slowing down, then doubling back on yourself, i suppose this would imply that you would jump to another timeline at FTL speeds (if there existed a "time-plane", the 2d analogue of our timeline, where each adjacent parallel timeline is an infinitesimal change of our current one). But all of that is just complete speculation (but then again, we are talking about FTL travel here).

Wouldn't anti-matter be far closer in relationship to what kronnyq is talking about here?

edit: I posted before realizing there was a page 2 so... sorry if I'm a little behind in the discussion. I'll catch up later and revise.

 

[Max™]

Simplify it back down again.

Let's say you have a Tachyon projector that sends Tachyon signals at 2c, a Tachyon reflector 1 light-second away, and a Tachyon receiver at your position.

You also have a twin system set up with a normal laser, reflector, and receiver all at the same distances, all at rest, in a hypothetical flat spacetime (to allow us to ignore GR for simplicity).


You fire the laser and the Tachyon projector at the same moment.

The laser hits the reflector and returns at T1 and T2.

If the Tachyon was following a spacelike trajectory which resembles a real path, it would hit the reflector and return at T.5 and T1. This would involve moving through time in a manner similar to that of a body with Real mass.

A Tachyon could be defined as having imaginary mass, though, so it can be considered to move through time in a different manner.

An imaginary, or Tachyonic trajectory, could have an imaginary duration.

As I understand it, observing the beginning and end points of an imaginary trajectory from a real inertial rest frame would appear to violate causality.

There would be an effect, and then a cause.


If the Tachyon followed an imaginary trajectory, it would reach the reflector at T-.5, and reach the receiver at T-1.

 

[JesseM]

Simplify it back down again.

Let's say you have a Tachyon projector that sends Tachyon signals at 2c, a Tachyon reflector 1 light-second away, and a Tachyon receiver at your position.

You also have a twin system set up with a normal laser, reflector, and receiver all at the same distances, all at rest, in a hypothetical flat spacetime (to allow us to ignore GR for simplicity).You fire the laser and the Tachyon projector at the same moment.

The laser hits the reflector and returns at T1 and T2.

If the Tachyon was following a spacelike trajectory which resembles a real path, it would hit the reflector and return at T.5 and T1. This would involve moving through time in a manner similar to that of a body with Real mass.

How does a "tachyon reflector" work? One might imagine that it bounces back a tachyon signal at the same speed the signal hit it, but this isn't precise enough--"same speed" in whose frame? This is why the traditional thought-experiment is a little different--instead of a tachyonic reflector, suppose we have a device which receives the tachyon signal, then sends a copy of the message back with a new set of tachyons that move at 2c in its own rest frame. In this case, if this device has a different rest frame than me because it's moving away from me at some (sublight) relativistic velocity, in my frame the response won't be moving at 2c, if the difference in our rest frames is large enough the signal may be moving backwards in time in my frame, in the sense that I will receive the reply from this device at an earlier time-coordinate than it sent the reply, in my coordinate system. If the velocities and distances are chosen correctly it is possible for me to receive this reply before the time T1 when I sent the original message to the receiver, a thought experiment which some physicists term a "tachyonic anti-telephone"--see for example section 3 of this paper (on p.7 of the pdf file, although the number at the bottom of the page is 6), which says:

First, we would like to recall a well-known paradox sometimes called “tachyonic anti-telephone” [50] arising in the presence of the superluminal hypothetical particles tachyons possessing unbounded velocity c_{tachyon} &gt; 1. In this case we could send a message to our own past. Indeed, let us consider some observer, who is at rest at x = 0 with respect to the reference frame (x, t) and sends along OR a tachyon signal to an astronaut in the spacecraft R (see Fig. 1). In turn, after receiving this signal, the astronaut communicates back sending the tachyon signal, RP. As this signal propagates the astronaut proper time t′ grows. However, if the speed of the spacecraft is larger than 1 / c_{tachyon}, then the signal RP propagates backward in time in the original rest frame of the observer. Thus, the observers can in principle send information from “their future” to “their past”. It is clear that such situation is unacceptable from the physical point of view.

A Tachyon could be defined as having imaginary mass, though, so it can be considered to move through time in a different manner.

An imaginary, or Tachyonic trajectory, could have an imaginary duration.

What is the meaning of an "imaginary trajectory"? In relativity a tachyon would follow a spacelike path through spacetime, whose endpoints would just be regular coordinates like (x=10 light-seconds, t=0 seconds) and (x=20 light-seconds, t=10 seconds). It is true that if you try to calculate the "proper time" between these points the same way you would for points with a timelike separation, using the formula \Delta \tau = \sqrt{\Delta t^2 - \frac{1}{c^2}(\Delta x^2 + \Delta y^2 + \Delta z^2)}, then you get an imaginary number, but this has no relevance to the argument that tachyon messages would lead to causality violations in relativity.

If the Tachyon followed an imaginary trajectory, it would reach the reflector at T-.5, and reach the receiver at T-1.

If you're calling backwards-in-time trajectories "imaginary" while calling FTL but forwards-in-time trajectories non-imaginary, that terminology doesn't make any sense to me--all spacelike trajectories have imaginary values for the proper time when you plug the endpoints into the formula I mentioned. So what specific quantity is it that you think has an imaginary value for backwards-in-time trajectories but not FTL but forward-in-time trajectories, if not the proper time? It would have to be some frame-dependent quantity (unlike proper time which is frame-invariant), since for a single pair of sending/receiving events, different frames can disagree about whether the event of the tachyon signal being received happens before the signal being sent (a 'backwards in time' trajectory) or whether it happened after (an FTL-but-forward-in-time trajectory).

 

[Austin0]

This is true as long as the tachyon signal was moving forwards in time in frame A. But do you agree that if we analyze this same signal in frame B, the event of the signal being received can happen at an earlier time-coordinate than it was sent, in the coordinates of frame B? For example, suppose in frame A the coordinates of it being sent were x=0 light-years, t=0 years and the coordinates of it being sent were x=20 light-years, t=10 years. Now suppose frame B is moving at v=0.8c in the +x direction of frame A, so gamma=1.25, giving the Lorentz transformation:

x' = 1.25*(x - v*t)
t' = 1.25*(t - vx/c^2)

This transformation assumes the origins coincide, so the event of it being sent in frame B has coordinates (x'=0, t'=0). As for the event of the signal being received, we can plug in x=20 ly, t=10 y to get:

x' = 1.25*(20 - 0.8*10) = 15
t' = 1.25*(10 - 0.8*20) = -7.5

According to this scenario at (t=0 in A ) the position (x'=15 in B) was at location x=12 in A
At that time ( t=0 in A ) the clock at x'=15 in B would read (t'= -12 ) due to clock desynchronization ,,correct?
SO if the signal was received at x'=15 at time t'=-7.5 that is still forward in time according to the clock at that location right?

So in frame B the event of it being sent happened at t'=0 while the event of it being received happened at t'=-7.5, which is 7.5 years earlier in this frame's time-coordinates.

As you have pointed out to me you cannot make this kind of comparison between frames as a whole but only between specific clocks in frames due to desynchronization.
Between frames you can only make a generalized statement regarding elapsed time dilation through the Lorentz factor Is this not so?

 

[Austin0]

Hi RandallB
I just want to say that I think I understand what you are saying and this has also bothered me for years since encountering the back in time hypothesis. I find it hard to understand why others seem to have a completely different interpretation of your point.
So I will present my observations and see if you agree.
SR seems quite clear regrding simultaneity:
It is impossible to determine absolute simultaneity using any system of synchronized clocks, multiple observers or combinations of reference frames. PERIOD
Since absolute chronology is totally dependant on the determination of absolute simultaneity, any scheme which assumes the ability to derive absolute chronolgy implies the same methods could be employed to determine absolute simultaneity and further could then be used to determine a frame with absolute clock synchronicity or in other words, an ABSOLUTE preferred rest frame.
So it would appear that any hypothesis which purports to accomplish this is either inherantly flawed or , in itself , constitutes a falsification of one of the fundamental assertions of SR.

 

[JesseM]

According to this scenario at (t=0 in A ) the position (x'=15 in B) was at location x=12 in A
At that time ( t=0 in A ) the clock at x'=15 in B would read (t'= -12 ) due to clock desynchronization ,,correct?

You seem to have things confused, there are two separate events here: the event of the signal being sent, which has coordinates x=0, t=0 in A and x'=0, t'=0 in B, and the event of the signal being received, which has coordinates x=20, t=10 in A and x'=15, t'=-7.5 in B. There is no single event that has coordinates t=0 in A and position x'=15 in B, nor is there any event that has location x=12 in A or time t'=-12 in B. I'm not sure what you mean about clock desynchronization--the Lorentz transformation already takes into account the different synchronization of clocks in different frames when mapping the coordinates of an event in frame A to the coordinates of the same event in frame B (for example, if you pick two events with different spatial coordinates but the same time coordinate in A, and use the Lorentz transformation to find the coordinates of these events in B, they will have different time coordinates in B because B defines simultaneity differently). You may want to take a look at this thread where I provided an illustration of how the Lorentz transformation can be understood visually in terms of two ruler/clock systems moving alongside each other.

As you have pointed out to me you cannot make this kind of comparison between frames as a whole but only between specific clocks in frames due to desynchronization.

You can certainly make a comparison between the position and time of an event in one frame with the position and time of the same event in another, that's what the Lorentz transform is all about. Each frame's position and time coordinates are defined in terms of local readings on a lattice of rulers and clocks at rest in that frame, with the clocks synchronized according to the assumption that light moves at the same speed in all directions in that frame. So, for example, if I see an explosion that happens next to the 100 light-seconds mark on the ruler defining my x-axis, and the clock sitting at that mark reads 50 seconds at the moment the explosion happens right next to it (a local measurement), then I assign that event coordinates x=100 light-seconds, t=50 seconds.

The key to understanding why FTL signalling would imply causality violation is the first postulate of relativity, which says that the laws of physics must work exactly the same in all the different inertial frames constructed this way. So if there is one frame that measures the signal to be received at an earlier time-coordinate than it was sent, this must be possible in all frames as long as the first postulate holds.

 

[Austin0]

[

QUOTE=JesseM;2010434]You seem to have things confused, there are two separate events here: the event of the signal being sent, which has coordinates x=0, t=0 in A and x'=0, t'=0 in B, and the event of the signal being received, which has coordinates x=20, t=10 in A and x'=15, t'=-7.5 in B. There is no single event that has coordinates t=0 in A and position x'=15 in B, nor is there any event that has location x=12 in A or time t'=-12 in B.

So are you saying that given the coincidence of( t=0 at x=0 )and (t'=0 at x'=0) and assuming the same, at rest ,metric, you could NOT apply the trasnsformation and determine that x'=15 would at that T be positioned at x=12 in A ?
Are you saying that you could NOT calculate the degree of desynchronization at time t'=0 at x'=0 for a clock located at x'=15 in B ?
Are you saying that a clock at that spacetime location would NOT be expected to read t'= -12 ?

You may want to take a look at this thread where I provided an illustration of how the Lorentz transformation can be understood visually in terms of two ruler/clock systems moving alongside each other.

Yes I have seen your illustration before from other threads, you did a fine and clear presentation. Reminds me of Feynmans treatment, which is where I initially learned the concepts of desynchronization some 25 years ago. Since I only recently began spending any real time considering SR again , I have a lot of brushing up to do and found your charts very helpful as I am sure many others have also. Thank you.

The key to understanding why FTL signalling would imply causality violation is the first postulate of relativity, which says that the laws of physics must work exactly the same in all the different inertial frames constructed this way. So if there is one frame that measures the signal to be received at an earlier time-coordinate than it was sent, this must be possible in all frames as long as the first postulate holds.

[/QUOTE]
Ay, there's the rub. Proving that FTL signalling would go back in time in ANY frame.
It appears to me that you and others who have proposed this hypothesis have set out with two a priori assumptions:
(1) FTL signals go back in time.
(2) That block time is an accepted physical reality.

The first is, of course , the subject in question and would seem to be questionable logic to include the conclusion in the premises.
The second appears to be unwarranted. As far as I know eternalism is not an explicit postulate of SR but simply an interpretation by some. If I am incorrect in this I would like to know?
As a concept it has great popular support among Sci FI fans and in books and movies
but as a scientific theory it has neither empirical validation nor universal acceptance.
So , as of this time, it remains a metaphysical speculation.
Right or wrong?
I think you would be at the forefront of the mass of people in this forum who would come down on anyone so unwise as to propose some scheme to establish or prove absolute simultaneity based on the, also highly speculative ,metaphysical concept of presentism.
Do you disagree?
ANd then where does that leave the question of causality, without the assumption of the actual physical existence of the recipient of an assumed backward in time message, at some previous time? Without this, even if some hypothetical signal could go back in time there could be no violation of causality because there would be nobody home to receive it.

Forget for the moment the question of FTL signalling. Assume that A sends up a flare at the moment of transmission and B likewise sends up a flare on reception.
How is this situation any different from two lightning bolts in the classic demonstration of the relativity of simultaneity? How is the absolute chronology of these two events [flares] any more determinable than the absolute chronology of the two lightning bolts,, which appear simultaneous to a track observer while the train observer perceives the one at the front occurring before the back and some other observer would see the back occurring before the front?
Perhaps I am missing something here but if you could determine absolute chronolgy/simultaneity between two events it would seem that in principle you could then find an inertial frame wherein the clocks reflected this ie. where two absolutely simulataneious events were seen to occur at the same time according to local clocks and therefore the clocks would be absolutely synchronous. I assume you do not think this is possible so I have to ask why you think it IS possible to determine absolute chronolgy between two disparate events?
By the way , my math is rusty but you might want to check the gamma factor. Thanks
for your help and patience

 

[Fredrik]

Ay, there's the rub. Proving that FTL signalling would go back in time in ANY frame.

I think you misunderstood him. I did too the first time I read the words you quoted there. He's not saying that everyone would agree that a particular signal is going back in time. He's just saying that for every inertial frame F, it would be possible to produce a signal S_F that in the coordinates of frame F is detected before its emitted.

 

[JesseM]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

[Austin0]

[

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

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

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

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

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

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

.

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

That assumption is not in any way in question.

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

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

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

 

[Fredrik]

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

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

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

No one here is doing that. Certainly not JesseM.

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

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

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

 

[JesseM]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

[Austin0]

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

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


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

No one here is doing that. Certainly not JesseM.

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

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

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

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

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

 

[Austin0]

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

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

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

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

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

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

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

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

No question there.
,

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

Me either.
thanks

 

[Fredrik]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

[JesseM]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Me either.

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

 

[Austin0]

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

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

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

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

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

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

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

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

 

[Fredrik]

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

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

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

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

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

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

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

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

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

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

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

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

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

 

[MikeLizzi]

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

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

It addresses the issue of causalty more than time travel.

 

[Austin0]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

[Fredrik]

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

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

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

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

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

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

(Yes, "m" is the mass).

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

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

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

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

 

[JesseM]

Did you mean spark #2 and spark #3 ?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

[Austin0]

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

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

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

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

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

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

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

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

.

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

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

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

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

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

[

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

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

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

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

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

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