# Having trouble understanding why FTL implies time travel

1. Dec 17, 2008

### 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.

2. Dec 17, 2008

### 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)

3. Dec 17, 2008

### Fredrik

Staff Emeritus
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).

4. Dec 17, 2008

### 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.

5. Dec 17, 2008

### JesseM

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 recieve 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

6. Dec 17, 2008

### JesseM

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.

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.

Last edited: Dec 17, 2008
7. Dec 17, 2008

### kronnyq

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?

8. Dec 17, 2008

### 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

9. Dec 17, 2008

### JesseM

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.

10. Dec 17, 2008

### RandallB

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.

11. Dec 17, 2008

### JesseM

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:
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?

Last edited: Dec 17, 2008
12. Dec 18, 2008

### 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.

13. Dec 18, 2008

### JesseM

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".

14. Dec 18, 2008

### Fredrik

Staff Emeritus
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?

Last edited: Dec 18, 2008
15. Dec 18, 2008

### Fredrik

Staff Emeritus
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).

16. Dec 18, 2008

### 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.

17. Dec 18, 2008

### JesseM

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.

18. Dec 18, 2008

### JesseM

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.

Last edited: Dec 18, 2008
19. Dec 18, 2008

### JesseM

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".
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.

20. Dec 18, 2008

### Fredrik

Staff Emeritus
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.

This is a good example.

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.

Did I say it was an inertial frame?

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).

21. Dec 18, 2008

### JesseM

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).
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.
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.

Last edited: Dec 18, 2008
22. Dec 18, 2008

### RandallB

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

23. Dec 18, 2008

### Fredrik

Staff Emeritus
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?

Last edited: Dec 18, 2008
24. Dec 18, 2008

### JesseM

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

25. Dec 19, 2008

### DrGreg

RandallB's problem with understanding this was discussed in another thread here. 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!