# discuss events which are simultaneous in one frame?

by neopolitan
Tags: discuss, events, frame, simultaneous
 P: 645 Dale, It could be just the English, but the way I see it the nose end of the rocket will be more in the future, due to its being skewed in spacetime by virtue of its speed (relative to an observer who is not at rest relative to the rocket). Possibly Jesse is confused because I used the word "relative" in an attempt to indicate that the nose is more in the future than the tail is (so in the future relative to the tail). I can see how this could be confusing. But his understanding seems to be the reverse - that the nose is more in the past (because the nose clock reads an earlier time than one at the tail). For me, this is just plain wrong, but it could be a matter of perspective. The question then is whose perspective is more valid. I feel that Jesse's perspective almost presupposes absolute time, linked to clocks. Clocks don't tell you "when" you are any more than odometers tell you where you are. They just tell you how much time has elapsed. He seems to think that when you are in time is related to what your clock says. What I am saying instead is that while the rocket is in motion, the nose will reach the instant when it is observed before the tail reaches that same instant (relative to an observer who is not at rest relative to the rocket). It therefore could be said to be "in the future" - although of course when it is observed it is "in the now". cheers, neopolitan
P: 8,430
 Quote by neopolitan Or it could be no more than some sort of willful (albeit most likely subconscious) incomprehension on your part, Jesse, since at the end of your post, you seem to grudgingly accept that what I have to say has some sort of twisted validity anyway. I am not totally sure where the problem lies.
How did I grudgingly accept it? I just said that ultimately, how you conceptualize it doesn't matter as long as you get the right answers. But I still don't understand how you're conceptualizing it. Why does older = further in the past and younger = further in the future for you? Can you try to explain again?
 Mentor P: 15,610 Neopolitan, you are arguing over really unimportant things now compared to your initial question. There are two important points in this thread. 1) in SR all observers are intelligent, meaning that they correct for the light propagation delay to figure out when an event really occured not merely when it was observed. 2) when they do that they find that they disagree on wether or not two distant events really occured simultaneously. I'm not going to engage you in an unimportant debate about semantics.
P: 8,430
 Quote by DaleSpam I know what you mean, but I don't think it is an important argument. I can say "New York is an hour earlier than Chicago" meaning something like the sun rises in NY an hour before it rises in Chicago, or I can say "New York is an hour later than Chicago" meaning that the clock in NY shows 08:00 when the clock in Chicago shows 09:00. I don't think your post 11 is saying anything more important than that. It isn't a confusion about the math or physics, just an ambiguity in the english. Not worth arguing.
OK, this kind of helps me see what neopolitan might have been talking about actually, although "New York is an hour later" (i.e., it's later in realtime to reach the same clock time) is a little different from "New York is an hour in the future", the latter just seems like really confusing phrasing if New York actually shows an earlier time than Chicago. Neopolitan, is this basically what you meant? If so, would you agree it's just a matter of ambiguity in language, that neither version is "more correct" than the other?
P: 8,430
 Quote by neopolitan But his understanding seems to be the reverse - that the nose is more in the past (because the nose clock reads an earlier time than one at the tail). For me, this is just plain wrong, but it could be a matter of perspective. The question then is whose perspective is more valid. I feel that Jesse's perspective almost presupposes absolute time, linked to clocks. Clocks don't tell you "when" you are any more than odometers tell you where you are. They just tell you how much time has elapsed. He seems to think that when you are in time is related to what your clock says.
I'm not presupposing absolute time, I'm comparing the opinions about simultaneity of two different frames. In the ship's own frame, both clocks show the same reading at the same time, i.e. simultaneously. In that frame (call it frame A), the event of the tail clock reading 4 seconds would be one second in the future of the event of the nose clock reading 3 seconds. So, in the frame where the ship is moving forwards (call it frame B), if the event of the tail clock reading 4 seconds and the nose clock reading 3 seconds are simultaneous, then in this frame one can observe, in a single moment, a reading on the tail clock that is "in the future" of the reading on the nose clock as understood in frame A. That's all I meant! One could find another frame (call it frame C) in which the rocket is moving backwards, and in this frame the event of the tail clock reading 4 seconds might happen earlier than the event of the nose clock reading 3 seconds. So, going back to frame B, in frame B one can observe, in a single moment, a reading on the tail clock that is "in the past" of the reading on the nose clock as understood in frame C. There's obviously no absolute truth about whether one event is "really" in the future or the past of another event (unless one event lies in the other event's future light cone, in which case all frames agree on the order), all we can do is talk about the opinions of different frames, and perhaps relate them to one another as I do above.
 Quote by neopolitan What I am saying instead is that while the rocket is in motion, the nose will reach the instant when it is observed before the tail reaches that same instant (relative to an observer who is not at rest relative to the rocket). It therefore could be said to be "in the future" - although of course when it is observed it is "in the now".
What do you mean by "reaching an instant"? By instant do you mean something different than just a given reading on each clock? After all, if we pick any give reading--say, 3 seconds--then in the frame B where the rocket is moving forward, the tail will get to that reading first, not the nose, so I don't see what you mean by "the nose will reach the instant when it is observed before the tail reaches that same instant".
 P: 645 re DaleSpam and arguments about semantics - it is possible that what I am thinking about it not merely semantics. I don't know what is inside your head and, I hope, you don't know what is inside mine. I am trying to gain a better understanding of whether what Jesse and I are saying are the same thing or not. re JesseM's reply to DaleSpam - it could be an ambiguity of language, but I have the benefit of being biligual (English is my mothertongue though) and know that sometimes limitations in language make it impossible to convey certain concepts. It is possible that what I am trying to express is being converted in your mind to precisely what you originally thought, but isn't what I meant. It seems it is just you, me and Dale - so I will have another crack at explaining.
P: 645
 Quote by JesseM What do you mean by "reaching an instant"? By instant do you mean something different than just a given reading on each clock? After all, if we pick any give reading--say, 3 seconds--then in the frame B where the rocket is moving forward, the tail will get to that reading first, not the nose, so I don't see what you mean by "the nose will reach the instant when it is observed before the tail reaches that same instant".
An instant I mean as a "line of simultaneity", the events which share the same value of t in the frame to which it pertains.

So I am thinking of the rocket's frame, in which the rocket is not moving, and an observer's frame, in which the rocket is moving. An instant in the observer's frame is the set of events which share the same value of t. This "observer's instant" is not an instant in the rocket's frame, but a set of events which we can work out using lorentz transformations.

An instant in the rocket's frame, in which clocks at the nose and the tail read the same, is similarly not an instant in the observer's frame.

If we pick any instant in the observer's frame, and look at the rocket, we will see that clock on the nose reads less than the clock on the tail. We agree about this.

What I am saying is that the nose reaches any given observer's instant before the tail.

Imagine that we sit in two separate time machines, machines that shunt us into the future at faster rate than normal life (like fun events seem to do). We each have a watch, and we synchronise them before we switch our machines on.

If my machine shunts me into the future twice as quickly than yours, which one of us will have more time on their watch? I put it to you that the one who reaches the future first will have less time on their watch (that means me).

I agree that if we were worried about who is able to say 5 minutes have elapsed on their watch first, then that will be you. If we both turn off our machines when five minutes have elapsed on our watches (inside the time machines), you will have to wait around a while for me to turn my machine off, and will be able to say that your watch read 5 minutes first. But ... I will have gone further into the future than you.

Now, this was just an explanation, I am not suggesting that such time machines are possible. Just try to apply the same logic to the rocket and the two clocks. Relative to an observer not at rest relative to the rocket, the clock on the nose travels into the observer's future faster than the clock on the tail. The clock on the tail travels into the observer's future faster than the observer.

The observer also moves into the clocks' future faster than the clocks do.

This is where it gets less like semantics and more like something interesting ... can you model that? Not just wave it away, not just say "that's just relativity", not just show the mathematics on what must happen, but describe a model in which that is possible.

This also may be the point at which I get stomped on, so if you feel like coming back with "can you?" then I will have to politely decline.

cheers,

neopolitan
P: 8,430
 Quote by neopolitan So I am thinking of the rocket's frame, in which the rocket is not moving, and an observer's frame, in which the rocket is moving. An instant in the observer's frame is the set of events which share the same value of t. This "observer's instant" is not an instant in the rocket's frame, but a set of events which we can work out using lorentz transformations. An instant in the rocket's frame, in which clocks at the nose and the tail read the same, is similarly not an instant in the observer's frame. If we pick any instant in the observer's frame, and look at the rocket, we will see that clock on the nose reads less than the clock on the tail. We agree about this. What I am saying is that the nose reaches any given observer's instant before the tail.
But as you point out, different observers have different "instants"...whose are you talking about above? If we talk about a given instant (line of constant t) in the rocket frame, then as seen in the outside observer's frame, the clock on the tail will intersect with this line before the clock on the nose. Maybe you're taking the opposite perspective, and considering a line of constant t in the observer's frame, and then pointing out that, in the rocket's frame, the clock on the nose will reach a given point on this line before the clock on the tail? If so let me know, this would help clear up my confusion about what you're trying to say (and if it is what you're saying, would you agree either perspective is equally valid?)
 Quote by neopolitan Imagine that we sit in two separate time machines, machines that shunt us into the future at faster rate than normal life (like fun events seem to do). We each have a watch, and we synchronise them before we switch our machines on. If my machine shunts me into the future twice as quickly than yours, which one of us will have more time on their watch? I put it to you that the one who reaches the future first will have less time on their watch (that means me).
I don't think that's a good analogy, because no matter what frame you pick, the rate at which each clock is advancing forward in that frame will be identical, it's not like one is being "shunted into the future" faster, just that one has a "head start" of sorts.
 Quote by neopolitan Now, this was just an explanation, I am not suggesting that such time machines are possible. Just try to apply the same logic to the rocket and the two clocks. Relative to an observer not at rest relative to the rocket, the clock on the nose travels into the observer's future faster than the clock on the tail. The clock on the tail travels into the observer's future faster than the observer.
Like I said, there's no difference in the rate no matter what frame you pick, so I would say "faster". But if my guess above is right, do you mean that in the rocket's frame at any given instant, the time on the nose-clock at that instant would be further in the outside observer's future than the time on the tail-clock at the same instant? In other words, if both clocks show a time of 3 seconds simultaneously in the rocket frame, we can note that in the outside observer's frame, the event of the nose clock showing 3 seconds happens further in the future than the event of the tail clock showing 3 seconds. So is that what you mean?

If so, I just want to note that even if we talk in this way, which clock is "further in the outside observer's future" depends on your choice of frame. We might take the frame of an observer who's moving relative to the first observer outside the rocket, but in the opposite direction as the rocket...in this new observer's frame, the time on the nose-clock at a given instant would be further in the first outside observer's past than the time on the tail-clock at the same instant.
 Quote by neopolitan The observer also moves into the clocks' future faster than the clocks do. This is where it gets less like semantics and more like something interesting ... can you model that? Not just wave it away, not just say "that's just relativity", not just show the mathematics on what must happen, but describe a model in which that is possible. This also may be the point at which I get stomped on, so if you feel like coming back with "can you?" then I will have to politely decline.
As I said above, I think the problem with your analogy is that no matter which frame you choose both clocks tick at the same rate, and also that the question of which clock is further in the outside observer's future in the frame you're using will be different depending on the choice of frame (in the rocket's rest frame the nose clock will be, but in the frame of a third observer moving in the opposite direction relative to the outside observer the tail clock will be). But maybe I'm still not understanding what you're saying here, let me know.
P: 645
 Quote by JesseM But as you point out, different observers have different "instants"...whose are you talking about above? If we talk about a given instant (line of constant t) in the rocket frame, then as seen in the outside observer's frame, the clock on the tail will intersect with this line before the clock on the nose. Maybe you're taking the opposite perspective, and considering a line of constant t in the observer's frame, and then pointing out that, in the rocket's frame, the clock on the nose will reach a given point on this line before the clock on the tail? If so let me know, this would help clear up my confusion about what you're trying to say (and if it is what you're saying, would you agree either perspective is equally valid?)
We are discussing physics aren't we, not social work?

We have a rocket with two clocks and we have an observer who is not at rest relative to the rocket. If I want to know what it observed I expect to hear "I see a rocket in motion with two clocks on it, one on each end" not "I see some dorky physics guy observing me".

Of course I am discussing the observer's instant. Why is that so hard for you to grasp?

 Quote by JesseM I don't think that's a good analogy, because no matter what frame you pick, the rate at which each clock is advancing forward in that frame will be identical, it's not like one is being "shunted into the future" faster, just that one has a "head start" of sorts. Like I said, there's no difference in the rate no matter what frame you pick, so I would say "faster". But if my guess above is right, do you mean that in the rocket's frame at any given instant, the time on the nose-clock at that instant would be further in the outside observer's future than the time on the tail-clock at the same instant? In other words, if both clocks show a time of 3 seconds simultaneously in the rocket frame, we can note that in the outside observer's frame, the event of the nose clock showing 3 seconds happens further in the future than the event of the tail clock showing 3 seconds. So is that what you mean?
Yes, that is what I mean. See how even if the analogy is not perfect (I knew it wasn't by the way) it did help you to understand? More perfect and it would be too complex, and you would have been running around point out other errors and uncertainties rather than concentrating on the issue I wished to convey.

 Quote by JesseM If so, I just want to note that even if we talk in this way, which clock is "further in the outside observer's future" depends on your choice of frame. We might take the frame of an observer who's moving relative to the first observer outside the rocket, but in the opposite direction as the rocket...in this new observer's frame, the time on the nose-clock at a given instant would be further in the first outside observer's past than the time on the tail-clock at the same instant.
I guess I implied that you were willfully incomprehending so an implication here of stupidity on my part is fair enough. Your scenario is precisely the same as "what if the rocket was going backwards relative to the observer so that the tail was effectively the nose and the nose was effectively tail". Relabel nose and tail and we are back where we started, just as both of us expect. I am pretty sure that most of us understand that "nose" is the front bit and "tail" is the back bit. If you were thinking I had each part labeled permanently on the rocket so that the nose clock would behave the same way irrespective of the direction it travelled in relative to the observer then you did not read an earlier post properly.

 Quote by neopolitan Such an observer will see the front end first (so see the tick from that one first) and then the rear end (so the tick from this one will be seen second) - of course travelling times for the photons have to be accounted for, if the separation between a departing rocket's nose and tail are sufficiently large or the speed is sufficiently low, then the nose may be seen second but still sooner than it may otherwise would have been expected.
Perhaps this is too confusing for you, but if you think about it, I am discussing a rocket which is departing from the observer - a rocket which is going forwards since the nose is further away than the tail. If you want to change the scenario so that the tail is further away than the nose, fine, then I agree the tail will reach the future before the nose and the clock on the tail will read a lower elapsed time than the nose - if the rocket is in reverse relative to the observer.

 Quote by JesseM As I said above, I think the problem with your analogy is that no matter which frame you choose both clocks tick at the same rate, and also that the question of which clock is further in the outside observer's future in the frame you're using will be different depending on the choice of frame (in the rocket's rest frame the nose clock will be, but in the frame of a third observer moving in the opposite direction relative to the outside observer the tail clock will be). But maybe I'm still not understanding what you're saying here, let me know.
Which analogy are you referring to? The explanation analogy with the time machines? If so, they have done their job. Forget the analogy and go back to trying to understand what I said originally.

You can try to describe the model now as requested, if you like.

cheers,

neopolitan
P: 8,430
 Quote by neopolitan We are discussing physics aren't we, not social work? We have a rocket with two clocks and we have an observer who is not at rest relative to the rocket. If I want to know what it observed I expect to hear "I see a rocket in motion with two clocks on it, one on each end" not "I see some dorky physics guy observing me". Of course I am discussing the observer's instant. Why is that so hard for you to grasp?
If I've understood you correctly, you're discussing how the outside observer's instant is seen from the perspective of an observer on the rocket (i.e if we look at two simultaneous readings in the rocket-observer's frame, you're talking about which reading is in the future and which is in the past according to the outside observer's definition of simultaneity). I had been thinking you were talking about the perspective of an observer outside the rocket, and what time the two clocks show simultaneously in his frame. I think this is a pretty understandable confusion given that you didn't really spell out what you were talking about (DaleSpam also seems to have interpreted your comment as involving simultaneous readings in the rocket observer's frame rather than the rocket-observer's frame), so there's no need for condescending comments like "why is that so hard for you to grasp?"
 Quote by neopolitan Yes, that is what I mean. See how even if the analogy is not perfect (I knew it wasn't by the way) it did help you to understand?
No, it didn't. It was the previous comment about "instants" that helped me to understand (especially the comment 'An instant in the rocket's frame, in which clocks at the nose and the tail read the same, is similarly not an instant in the observer's frame', which clued me in that you might be talking about simultaneous readings in the rocket-observer's frame rather than the outside observer's frame), and you can see that I divined your meaning in the response to that earlier section. I hadn't even read the following paragraph when I fired off that response, and if your post had consisted only of the time travel analogy I don't think it would have helped me at all.
 Quote by JesseM If so, I just want to note that even if we talk in this way, which clock is "further in the outside observer's future" depends on your choice of frame. We might take the frame of an observer who's moving relative to the first observer outside the rocket, but in the opposite direction as the rocket...in this new observer's frame, the time on the nose-clock at a given instant would be further in the first outside observer's past than the time on the tail-clock at the same instant.
 Quote by neopolitan guess I implied that you were willfully incomprehending so an implication here of stupidity on my part is fair enough.
I have to say neopolitan, I consider your constant attempts to mind-read my motives (inevitably in uncomplimentary ways) really disrespectful. I meant no implication of stupidity here, the fact that I "want to note" something doesn't even imply that I think you would disagree with it, and it certainly doesn't imply I think you're stupid. Anyway as seen below, I think you were actually leaping to incorrect conclusions about what I was saying in that comment.
 Quote by neopolitan Your scenario is precisely the same as "what if the rocket was going backwards relative to the observer so that the tail was effectively the nose and the nose was effectively tail".
No, actually, it's a little more complicated. In your scenario, there have to be two observers whose frames we refer to--the first observer A who sees the rocket going forward, and a second B on board the rocket. Unless there's an error in my interpretation of your words, what you're saying is that if we look at readings on the two clocks which are simultaneous in the frame of B, then the reading on the nose clock has a greater time-coordinate in the frame of A than the time-coordinate of the reading on the tail clock in the frame of A. In my scenario, it's still true that the rocket is moving forward relative to A, but I'm introducing a third observer C who is moving in the opposite direction as the rocket in A's frame (so this observer C also sees the rocket moving forward, at an even greater speed than in A's frame), and saying that if we look at readings on the two clocks which are simultaneous in the frame of C, then the reading on the tail clock has a greater time-coordinate in the frame of A than the time-coordinate of the reading on the nose clock. This is an entirely different scenario from imagining that the outside observer A sees the rocket moving backwards, and then looking at readings on the two clocks which are simultaneous in the frame of an observer B on board the rocket, and noting that in this case if we look at two readings which are simultaneous in the frame of B, then the reading on the tail clock (which is now effectively the nose clock in A's frame) has a greater time-coordinate in the frame of A than the time coordinate of the reading on the nose clock (which is now effectively the tail clock in A's frame) in the frame of A.
 Quote by neopolitan Perhaps this is too confusing for you, but if you think about it, I am discussing a rocket which is departing from the observer - a rocket which is going forwards since the nose is further away than the tail.
Well, I'm sure you would agree with this, but for the rocket to be "going forward" that means the nose is further away than the tail when the rocket is moving away from the observer A, but it also means the nose is closer than the tail when the rocket is moving towards the observer A (and at some moment they will be equidistant as the rocket passes A). Whether the rocket is moving towards A or away from A makes no difference to our statements about simultaneity, as long as the rocket is moving forward in both cases.
 Quote by neopolitan If you want to change the scenario so that the tail is further away than the nose, fine, then I agree the tail will reach the future before the nose and the clock on the tail will read a lower elapsed time than the nose - if the rocket is in reverse relative to the observer.
Again, that wasn't what I was suggesting. I was still suggesting a scenario where the rocket was going forward relative to A (if the rocket was moving away from A, the nose would be further than the tail), but where instead of then looking at readings of the rocket's clocks which occur simultaneously in the frame of an observer B on board the rocket, we instead look at readings on the rocket's clocks which occur simultaneously in the frame of an observer C who is moving in the opposite direction as the rocket in A's frame, so that in C's frame the rocket is moving forward at an even greater speed than in A's frame. In this case the reading on the tail clock will be "further in the future" in A's frame than the reading on the nose clock (where again, the two readings we're talking about were chosen to be simultaneous in C's frame).

As an example, suppose the rocket is 10 light-seconds long in its own rest frame, and in A's frame its moving forward at 0.6c, so in A's frame the tail clock's reading is ahead of the nose clock's reading by 6 seconds. Now choose an observer C who sees the rocket moving forward at 0.8c, so in C's frame the tail clock's reading is ahead of the nose clock's reading by 8 seconds. Pick two readings which are simultaneous in C's frame, like the tail clock reading 10 seconds and the nose clock reading 2 seconds. In A's frame when the nose clock reads 2 seconds, the nose clock reads 8 seconds and won't read 10 seconds until a later time, so the event of the tail clock reading 10 seconds is "further in the future" in A's frame than the event of the nose clock reading 2 seconds. In contrast, if we picked two readings which were simultaneous in the frame of the observer B on board the rocket, like the tail clock reading 3 seconds and the nose clock reading 3 seconds, then we'd find that the event of the nose clock reading 3 seconds is "further in the future" in A's frame than the event of the tail clock reading 3 seconds.
 Quote by neopolitan Which analogy are you referring to? The explanation analogy with the time machines? If so, they have done their job. Forget the analogy and go back to trying to understand what I said originally. You can try to describe the model now as requested, if you like.
OK, but then I don't really understand what you were asking with this earlier comment that I was responding to:
 This is where it gets less like semantics and more like something interesting ... can you model that? Not just wave it away, not just say "that's just relativity", not just show the mathematics on what must happen, but describe a model in which that is possible. This also may be the point at which I get stomped on, so if you feel like coming back with "can you?" then I will have to politely decline.
What is the difference between a "model" and just showing the "mathematics on what must happen" according to relativity? In physics when I hear the word "model" I just interpret it to mean a mathematical model, do you mean something different? And when you say "describe a model in which that is possible", what did you mean by "that" if you weren't referring back to your earlier picture involving one guy moving into the future faster than the other? Describe a model in which what is possible?
 P: 645 Ok, sorry if I offend. I am merely a little frustrated. I only ever talked about one observer. I never invited a second one (on the rocket) and certainly not a third (alternatively one relative to which the rocket is moving backwards or one relative to which the rocket is moving forwards but twice as fast as the first observer perceives). I just don't quite understand how you are helping by adding more and more observers. I accept that it is confusing if you add more and more observers, but that with time and patience you can work out what each observes. Can we dispense with the third observer at the very least. I am not sure what you want to prove with that observer. I admit that I misread it at first. But I understand less now what your intention is with the introduction of that observer than I did when I thought you wanted to somehow make the rocket appear to go backwards. I am going to leave this for a while, because I do find it rather frustrating. neopolitan
P: 8,430
 Quote by neopolitan I only ever talked about one observer. I never invited a second one (on the rocket) and certainly not a third (alternatively one relative to which the rocket is moving backwards or one relative to which the rocket is moving forwards but twice as fast as the first observer perceives). I just don't quite understand how you are helping by adding more and more observers. I accept that it is confusing if you add more and more observers, but that with time and patience you can work out what each observes.
But in relativity talking about "observers" is basically just shorthand for talking about what's true in different frames, the actual presence or absence of biological humans at rest in a particular frame doesn't affect your actual problem. It seems to me that your argument depends critically on using the definition of simultaneity in the frame where the rocket is at rest as well as the definition in the frame where it's moving; as far as I can tell what you're saying is that if we take two simultaneous readings in the rocket's rest frame B, then of those two readings, the one on the nose will be further ahead in time in the frame where the rocket is moving A (the one where you want the 'observer' to be) then the one on the tail. Is this wrong?

If not, my point in introducing a third frame C was just to show that the nose-reading being further in the future than the tail-reading in the frame A of the "observer" depends critically on the fact that you picked two clock readings which were simultaneous in the rocket's rest frame B; if you instead picked simultaneous clock readings in another frame C moving in the opposite direction relative to A (still talking about the two clocks on board the rocket, and without changing the motion of the rocket), then out of these two readings, the one on the tail will be further ahead in time in A's frame than the one on the nose. Assuming you agree with this point, then that was my only reason for introducing the third frame C, we don't have to discuss it further.
P: 645
Jesse,

Please read the whole thing before replying. Please also avoid adding complicating factors until we have clarified what we currently have. No more observers, no different rockets, no different trajectories, no different clocks. Thanks.

I have four questions (or five, depending on how you want to define "question", but two are really only one question with two options), which I have color coded red. I would appreciate you making the effort to answer them.

 Quote by JesseM But in relativity talking about "observers" is basically just shorthand for talking about what's true in different frames, the actual presence or absence of biological humans at rest in a particular frame doesn't affect your actual problem. It seems to me that your argument depends critically on using the definition of simultaneity in the frame where the rocket is at rest as well as the definition in the frame where it's moving; as far as I can tell what you're saying is that if we take two simultaneous readings in the rocket's rest frame B, then of those two readings, the one on the nose will be further ahead in time in the frame where the rocket is moving A (the one where you want the 'observer' to be) then the one on the tail. Is this wrong?
I am back at work so there is no longer any weekend to be spoilt by my getting tetchy.

I am fully aware that flesh and blood observers are not required. However the mechanism of only nominating one observer was intended to get around the problem we seem to have with you being confused about which frame's perspective I was talking about - I mean the one with an observer, the only observer I ever stipulated.

Despite this, you seem to want to observe things from the rocket, where I never specified there would be an observer, just two clocks. All we know is that the clocks are set up to be synchronous in their own frame, as you are most likely aware. I don't require that you take simultaneous readings of the clocks.

Restating: there is only one observer, the one in reference to whom the rocket is moving forward - nose first (and I initially said departing, but it doesn't really matter if it is approaching, it just may be easier to visualise a departing rocket).

If that observer observes the clocks, the nose clock will read less than the tail clock (so if the tail reads 13:55 for instance, then the nose may read 13:00).

(Question One) Can we agree on this simple point? No more new observers until we have done that please.

(I cannot answer "Is this wrong?" directly because I am not certain what you mean by "the nose will be further ahead in time". The best I can do is rephrase in the hope that my rephrasing answers your question.)

 Quote by JesseM If not, my point in introducing a third frame C was just to show that the nose-reading being further in the future than the tail-reading in the frame A of the "observer" depends critically on the fact that you picked two clock readings which were simultaneous in the rocket's rest frame B; if you instead picked simultaneous clock readings in another frame C moving in the opposite direction relative to A (still talking about the two clocks on board the rocket, and without changing the motion of the rocket), then out of these two readings, the one on the tail will be further ahead in time in A's frame than the one on the nose. Assuming you agree with this point, then that was my only reason for introducing the third frame C, we don't have to discuss it further.
If you agree on the simple point above, it would be worthwhile to try to explain what you are getting at here, because I can't see the relevance of it. I also seem to be lost, since you have written the following in different posts #23 and #25 respectively.

 Quote by JesseM One could find another frame (call it frame C) in which the rocket is moving backwards, and in this frame the event of the tail clock reading 4 seconds might happen earlier than the event of the nose clock reading 3 seconds.
 Quote by JesseM We might take the frame of an observer who's moving relative to the first observer outside the rocket, but in the opposite direction as the rocket...in this new observer's frame, the time on the nose-clock at a given instant would be further in the first outside observer's past than the time on the tail-clock at the same instant.
From what I can work out, you have two frames called C. One which has a new observer moving such that the rocket appears to be moving backwards, and one which has another new observer such that the rocket appears to be moving but faster than my single stipulated observer.

Since #25 is most recent, I now assume that you want to talk about the latter. (Question Two) Is that correct? In that case, I erred in post #27 because I was still referring to the former.

I do hope you can understand that it is getting a little crowded in our scenario with all these observers.

Anyway, dispensing with the observer introduced in #23, we have two relative velocities for the rocket, with the same direction and magnitudes such that:

relative velocity according to observer A (my "there can be only one" observer) < relative velocity according to C (as introduced in#25)

(Question Three) Is that correct?

Assuming this is indeed correct, then you want to take simultaneous readings of the clocks in the C frame. Then I am lost, I don't quite know what you want to do with those readings.

(Question Four) Do you want to take "the nose clock reads t1 and the tail clock reads t2" and see when those readings are observed by my observer (observer A) and compare the order in which these readings appear in the A frame?

Or do you want look at readings of the clocks taken by observer A which are simultaneous according to observer C, but not according simultaneous to observer A?

In either case, I still can't see the relevance of the scenario.

I also don't quite know what you mean by
 Quote by JesseM out of these two readings, the one on the tail will be further ahead in time in A's frame than the one on the nose.
If you mean that the clock on the tail will indicate that more time has elapsed than the clock on the nose indicates (for example tail clock time is 13:55 and nose clock time is 13:00), then I think I agree with you, but since I am not sure what measurements you want to take nor what "further ahead in time in A's frame" means to you, I can't be certain.

cheers,

neopolitan
P: 8,430
 Quote by neopolitan I am fully aware that flesh and blood observers are not required. However the mechanism of only nominating one observer was intended to get around the problem we seem to have with you being confused about which frame's perspective I was talking about - I mean the one with an observer, the only observer I ever stipulated. Despite this, you seem to want to observe things from the rocket, where I never specified there would be an observer, just two clocks. All we know is that the clocks are set up to be synchronous in their own frame, as you are most likely aware. I don't require that you take simultaneous readings of the clocks.
I talked about the rocket frame simply because I can't understand how to interpret your claim about the nose clock being "further in the future" than the tail clock without referring to the rocket frame as well as the outside observer's frame. More on that below.
 Quote by neopolitan Restating: there is only one observer, the one in reference to whom the rocket is moving forward - nose first (and I initially said departing, but it doesn't really matter if it is approaching, it just may be easier to visualise a departing rocket). If that observer observes the clocks, the nose clock will read less than the tail clock (so if the tail reads 13:55 for instance, then the nose may read 13:00). (Question One) Can we agree on this simple point? No more new observers until we have done that please.
Sure, I have already made the point that in the observer's frame the tail clock is ahead of the nose clock in many posts before, this was the whole reason I was having trouble understanding your claim that the nose clock was "further in the future", remember?
 Quote by neopolitan (I cannot answer "Is this wrong?" directly because I am not certain what you mean by "the nose will be further ahead in time". The best I can do is rephrase in the hope that my rephrasing answers your question.)
OK. I said:
 as far as I can tell what you're saying is that if we take two simultaneous readings in the rocket's rest frame B, then of those two readings, the one on the nose will be further ahead in time in the frame where the rocket is moving A (the one where you want the 'observer' to be) then the one on the tail. Is this wrong?
Take two simultaneous readings in the rocket frame, say the nose clock reading 13:55 and the tail clock reading 13:55. If we now switch to the frame of the outside observer, the event of the nose clock reading 13:55 actually happens at a later time-coordinate (further in the future) than the event of the tail clock reading 13:55--the tail clock reaches that time first in his frame, the nose clock reaches it later. So, this is how I interpreted your claim that the nose-clock was "further in the future" than the tail clock. If you think there is a way of making sense of that claim without referring to the rocket frame, then I still don't understand what you're saying.
 Quote by neopolitan If you agree on the simple point above, it would be worthwhile to try to explain what you are getting at here, because I can't see the relevance of it.
The relevance is:

1. The way I am interpreting your comment about the nose being "further in the future", it seems to depend on using both the outside observer's frame and the rocket frame's, since we're picking two simultaneous events on the rocket's clocks in the rocket's frame and noting that the event at the nose happens further in the future in the outside observer's frame

2. So, I just wanted to make the point that if we kept the outside observer and the rocket the same, but now used a different second frame in place of the rocket's frame, we could use the same argument to show that if we take two simultaneous events on the rocket's clocks in this new frame, then it could be that the event at the tail happens further in the future in the outside observer's frame.

Note that in all this, how the two physical clocks on the rocket are actually synchronized is pretty much irrelevant, we're just talking about what events on the clocks are simultaneous in a given frame. I'm assuming that your argument that the nose clock is "further in the future" doesn't depend on whether or not the two clocks on the rocket have actually been synchronized in the rocket's rest frame, does it? Even if in the rocket's rest frame they've been synchronized incorrectly and the event of the tail clock reading 13:55 is simultaneous with the event of the nose clock reading 19:22 in this frame, and in the outside observer's frame the clock at the nose has a greater reading than the clock at the tail as a result (as opposed to the clock at the tail having a greater reading as they would if the clocks were correctly synchronized in the rocket's frame), this wouldn't make any difference to your statement that the nose clock was further in the future, would it? If you say one clock is further in the future, it seems to me you're trying to say something a little more basic than just a statement about how the clocks have been set (for example, you wouldn't say clocks in the central time zone are further in the future than clocks in the easter time zone just because clocks in the eastern time zone are set one hour ahead, would you?)
Quote by neopolitan
I also seem to be lost, since you have written the following in different posts #23 and #25 respectively.
 Quote by JesseM One could find another frame (call it frame C) in which the rocket is moving backwards, and in this frame the event of the tail clock reading 4 seconds might happen earlier than the event of the nose clock reading 3 seconds.
 Quote by JesseM We might take the frame of an observer who's moving relative to the first observer outside the rocket, but in the opposite direction as the rocket...in this new observer's frame, the time on the nose-clock at a given instant would be further in the first outside observer's past than the time on the tail-clock at the same instant.
These two quotes aren't talking about the same thing at all. In the first quote, the context was that I hadn't yet developed a hypothesis about what you meant when you said the nose is more in the future than the tail--in an earlier post I had given a short explanation about why, when I thought about what it would mean to say one clock was more in the future, I would think it was natural to say the tail was more in the future, just because it shows a greater time in the observer's frame. Then in response you said "I feel that Jesse's perspective almost presupposes absolute time", so I explained that I wasn't saying the tail was further in the future in any absolute sense, and to illustrate this I pointed out that the question of which clock was further in the future (again according to my idea of the most natural interpretation of the phrase, which was the opposite of yours) would have the opposite answer if the outside observer was in a frame where the rocket was moving backwards...here's the full paragraph so you can review the context:
 I'm not presupposing absolute time, I'm comparing the opinions about simultaneity of two different frames. In the ship's own frame, both clocks show the same reading at the same time, i.e. simultaneously. In that frame (call it frame A), the event of the tail clock reading 4 seconds would be one second in the future of the event of the nose clock reading 3 seconds. So, in the frame where the ship is moving forwards (call it frame B), if the event of the tail clock reading 4 seconds and the nose clock reading 3 seconds are simultaneous, then in this frame one can observe, in a single moment, a reading on the tail clock that is "in the future" of the reading on the nose clock as understood in frame A. That's all I meant! One could find another frame (call it frame C) in which the rocket is moving backwards, and in this frame the event of the tail clock reading 4 seconds might happen earlier than the event of the nose clock reading 3 seconds. So, going back to frame B, in frame B one can observe, in a single moment, a reading on the tail clock that is "in the past" of the reading on the nose clock as understood in frame C. There's obviously no absolute truth about whether one event is "really" in the future or the past of another event (unless one event lies in the other event's future light cone, in which case all frames agree on the order), all we can do is talk about the opinions of different frames, and perhaps relate them to one another as I do above.
In the second quote above the context was completely different. By that point I had developed a hypothesis about what you meant when you said it should be the nose that was farther in the future for the observer who sees the rocket moving forward. My hypothesis about your meaning, as I've explained earlier, involved taking two simultaneous events on the clocks in the rocket's frame, and then noting that of these two events, the event on the nose clock happens later in the outside observer's frame than the event on the tail clock. So again, I was making the point that you could keep the outside observer and the rocket the same, but now pick a different frame C to define simultaneous events on the two clocks on board the rocket, and if this frame C happens to be moving in the opposite direction as the rocket in the frame of the outside observer (which is why I said 'We might take the frame of an observer who's moving relative to the first observer outside the rocket, but in the opposite direction as the rocket'), then the result would be that the event on the tail clock happens later in the outside observer's frame than the event on the nose clock.
 Quote by neopolitan From what I can work out, you have two frames called C.
The second mention of a frame C was not meant to have any relation to the earlier mention of a frame C, sorry if using the same letters caused confusion, I don't think I remembered that I had used these labels earlier when I wrote the second quote.
 Quote by neopolitan Since #25 is most recent, I now assume that you want to talk about the latter. (Question Two) Is that correct? In that case, I erred in post #27 because I was still referring to the former.
Yes, that's correct, and now I can see that my reuse of the same letters was the cause of your confusion on that point, sorry about that.
 Quote by neopolitan relative velocity according to observer A (my "there can be only one" observer) < relative velocity according to C (as introduced in#25) (Question Three) Is that correct?
Assuming you're talking about the velocity of the rocket in each frame, yes, that's correct. Another way of putting this is that in A's frame, an object at rest in C would be moving in the opposite direction as the rocket.
 Quote by neopolitan Assuming this is indeed correct, then you want to take simultaneous readings of the clocks in the C frame. Then I am lost, I don't quite know what you want to do with those readings.
I'm just doing something directly analogous with what I did in my guess about what you meant when you said the nose clock was more in the future. My guess was that you meant we take readings on the clocks which are simultaneous in the rocket's frame (for example, the tail clock reading 10 seconds and the nose clock reading 10 seconds), and then we see which event happens later in the observer's frame (here the nose clock will not read 10 seconds until after the tail clock has already read 10 seconds, because the tail clock is ahead in this frame), and whichever clock's reading happens later, that clock is "more in the future" for the outside observer. So I was just following almost the same procedure, except instead of picking two readings which are simultaneous in the rocket's frame, I was picking two readings on the rocket's clocks which are simultaneous in the frame C (like the tail clock reading 10 seconds and the nose clock reading 2 seconds in my example near the end of post #28), and noting that of these two readings, it's actually the tail clock reading that happens later in the observer's frame, so using the same meaning of "more in the future" it's now the tail clock that's more in the future for the outside observer.
 Quote by neopolitan (Question Four) Do you want to take "the nose clock reads t1 and the tail clock reads t2" and see when those readings are observed by my observer (observer A) and compare the order in which these readings appear in the A frame? Or do you want look at readings of the clocks taken by observer A which are simultaneous according to observer C, but not according simultaneous to observer A?
I don't really see how these are distinct alternatives. I want to find two readings t1 and t2 on the nose and tail clock which are simultaneous in the frame of C but not in the frame of A, and look at the order in which these readings appear in the A frame. So I guess the answer is "all of the above"
 Quote by neopolitan In either case, I still can't see the relevance of the scenario.
Again, the only sensible way I can interpret your claim about the nose clock being further in the future is to follow a procedure just like this, except in place of frame C, use the rest frame of the rocket which I called frame B, pick clock readings which are simultaneous in B, and see which happens further in the future in the observer's frame A (in this case it will be the reading on the nose clock). I'm just saying there's nothing special about frame B, you could equally well use C and conclude that the tail clock is the one that's further in the future.
Quote by neopolitan
I also don't quite know what you mean by
 Quote by JesseM out of these two readings, the one on the tail will be further ahead in time in A's frame than the one on the nose.
If you mean that the clock on the tail will indicate that more time has elapsed than the clock on the nose indicates (for example tail clock time is 13:55 and nose clock time is 13:00), then I think I agree with you, but since I am not sure what measurements you want to take nor what "further ahead in time in A's frame" means to you, I can't be certain.
Well, to see what I was referring two when I said "these two readings", look at the context:
 if you instead picked simultaneous clock readings in another frame C moving in the opposite direction relative to A (still talking about the two clocks on board the rocket, and without changing the motion of the rocket), then out of these two readings, the one on the tail will be further ahead in time in A's frame than the one on the nose.
The "two readings" here refer to readings which are simultaneous in the frame of C; for example, in terms of my example near the end of post #28, the event of the tail clock reading 10 seconds happens simultaneously with the event of the nose clock reading 2 seconds, in the frame of C. And in this example, in the frame of the observer A, the event of the tail clock reading 10 seconds happens further ahead in time (at a later time-coordinate in A's frame) then the event of the nose clock reading 2 seconds, so that's what I mean when I say "out of these two readings, the one on the tail will be further ahead in time in A's frame than the one on the nose."
P: 645
I think we have reached another good point. We both seem to have a better understanding of the other's point of view. I think we still disagree on some key points, but on most of the basics we seem to be in accord with each other. I hope you feel the same.

 Quote by JesseM I don't really see how these are distinct alternatives. I want to find two readings t1 and t2 on the nose and tail clock which are simultaneous in the frame of C but not in the frame of A, and look at the order in which these readings appear in the A frame. So I guess the answer is "all of the above".
I was thinking of something a little different, that option two would involve looking at the readings of the clocks and comparing them simply (so the order they appear in the B frame). That would be a blend of three frames and it didn't make sense to me. What you are saying now makes more sense to me, I think.

While both A and B will read the clocks so that the nose reads less than the tail, if both read the clocks simultaneously in their own frames, you are saying that it can be so that the tail reading as observed by B (10s in your example) will be observed by A later than A observes the nose reading that B reads (2s in your example) - if the readings are simultaneous to B. Simultaneous readings taken in the A frame could be something like 6s on the tail and 2s on the nose. Is that what you mean?

For me this is quite obviously the case, since the skewing of the B frame is greater relative to C than it is relative to A.

 Quote by JesseM Again, the only sensible way I can interpret your claim about the nose clock being further in the future is to follow a procedure just like this, except in place of frame C, use the rest frame of the rocket which I called frame B, pick clock readings which are simultaneous in B, and see which happens further in the future in the observer's frame A (in this case it will be the reading on the nose clock). I'm just saying there's nothing special about frame B, you could equally well use C and conclude that the tail clock is the one that's further in the future.
Here is, possibly, the crux of our misunderstanding.

I see there being something special about the frame B in that both the items which are being observed share that frame. While the actual synchronisation is not overly important as you pointed out, the fact that the clocks are in phase and at rest relative to each other is important (in phase time-wise, not necessarily timekeeping-wise, since clocks can run slow for mechanical reasons). This, I think, make a simultaneous reading in this frame different to a simultaneous reading made in another frame.

Any other (non-rest) frame will observe a skewing of spacetime in the B frame where the clocks are at rest - which makes a difference. Doesn't it?

What I think you are effectively doing by introducing a third observer is comparing the extent of skewing, which is valid enough on its own terms, but not really part of what I was getting at. Still I think we agree on what happens with third observers, can we go back to only one observer (flesh and blood) and two clocks on rocket with forward motion relative to the observer (ie nose first)?

cheers,

neopolitan
P: 645
 Quote by DaleSpam Fundamentally it appears that the universe doesn't care about simultaneity, only about causality. Two simultaneous events cannot be causally connected, so what does it matter if one happened before the other? On the other hand, a cause should always come before an effect, and this is exactly what we see in relativity. A cause will preceed the effect in all reference frames, and for the rest it doesn't really matter.
I was reviewing our thread and saw this.

I wonder what Jesse thinks of this, in reference to his third observer with a different perception of simultaneous.

Jesse was confused when I said things happen in this order "past, now, future" rather than "future, now, past". Is it easier if we call it "cause, process, result"? For example, a "cause" is me whacking a cue ball towards a pocket, the "process" is the cue ball having a rough approximation of inertial velocity across the table followed by the "result" which is cue ball in pocket (assuming my aim is true, I hit sufficiently hard and not too hard as to cause a rebound).

If I have it right, DaleSpam is saying is that we cannot skew spacetime enough to make three related events simultaneous in any frame:

event one = where and when the cue ball is just as I whack it
event two = where and when the cue ball is between event one and event three
event three = where and when the cue ball is just after it falls into the pocket.

Relative to event three, events one and two are in the past. Relative to event one, events two and three are in the future. Relative to event two, event one is in the past and event three is in the future - irrespective of which frame you observe it from. So, according to DaleSpam, you can't do is choose a frame such that me whacking the cue ball comes before the cue ball sitting the pocket.

Is this correct?

If we place two synchronised clocks on the table, one next to the start position of the cue ball and the other next to the pocket and then observe from another frame in which the table is not at rest, then this is equivalent to our rocket scenario.

In the table's frame both clocks will remain synchronised for all events. Event one is relatively in the past since when event three happens the clocks may for example all read 10s as opposed to the 2s when event one happened - something that happened 8s ago.

We talked in earlier posts about being able to observe, simultaneoulsy in a frame which is not at rest with the rocket, the clock at the nose reading 2s and the clock at the tail reading 10s.

Let us then observe the table from such a frame in which where I whack the ball is "the nose" and the pocket is "the tail". I am not interested in the relative velocity of the cue ball, I can work that out myself thank you very much. I just want to consider my three events.

What apparently can happen is that from well selected frame, you can see the cue ball being whacked and the cue ball sitting in the pocket simultaneously - in a frame which is not at rest with the table. From what DaleSpam says though, you can't select a frame where you see the cue ball in the pocket before you can see it is whacked.

This seems counterintuitive since I specified none of the following: the speed at which I hit the cue ball, the distance between the cue ball's start position and the pocket, or the relative velocity of the table in the frame from which it is observed (or the rest length of the rocket). I see no reason why I can't hit the cue ball so as to give it higher velocity, and do so when the clocks read 4s such that the ball is in the pocket at 10s. Then the observation from another frame will see the clock at the nose reading 2s (with the cue ball sitting there undisturbed) and the clock at the tail reading 10s (with the cue ball sitting there after being whacked).

This is where I think that the 2s cue ball at the nose is in the future - relative to where it "should" be since according to the observer it should be more in the past since cause should precede effect (result) - and the 10s cue ball at the tail is in the past - relative to where it "should" be. I think I can understand your perspective though since what we are observing, from a frame not at rest relative to the table, is a "past" event and a "future" event.

We tend to think of travelling to events rather than events travelling to us. For example in Sci-fi it is normally time travellers who travel to the past, rather than time-movers who bring to past to them. But in our example, I do think that we are considering something closer to the latter than the former.

In the frame not at rest relative to the table, there is an event "now" in which a past event and future event are observed simultaneously. To me that means the past event is brought forward to the future (now is in the future relative to the past) and the past event is brought back to the past (now is in the past relative to the future).

To be honest, I don't expect many people to grasp this first time around. In any event, the (apparent) potential for violated causality may be a problem. It's all nice and simple when we just talk about clocks, not so easy when you add in chains of cause and effect.

neopolitan

PS I had better admit to being a little naughty here. If you are looking for it, you can find in my scenario the reason why causality is most certainly not violated. I did want others to find it and point it out, but not so much that I am willing to risk being locked out by an overzealous moderator or give anti-relativity nuts something that may look like ammunition for their cause. Now I admit the reason is there, is anyone still willing to point it out?
P: 8,430
 Quote by neopolitan I was reviewing our thread and saw this. I wonder what Jesse thinks of this, in reference to his third observer with a different perception of simultaneous. Jesse was confused when I said things happen in this order "past, now, future" rather than "future, now, past". Is it easier if we call it "cause, process, result"? For example, a "cause" is me whacking a cue ball towards a pocket, the "process" is the cue ball having a rough approximation of inertial velocity across the table followed by the "result" which is cue ball in pocket (assuming my aim is true, I hit sufficiently hard and not too hard as to cause a rebound). If I have it right, DaleSpam is saying is that we cannot skew spacetime enough to make three related events simultaneous in any frame: event one = where and when the cue ball is just as I whack it event two = where and when the cue ball is between event one and event three event three = where and when the cue ball is just after it falls into the pocket.
Right, the only way these events could be simultaneous is if cue ball moved FTL. As long as there's no FTL in the universe, then all frames will agree on the order of causally-related events (which is why tachyons would cause serious problems for causality if they existed, see this recent thread).
 Quote by neopolitan Relative to event three, events one and two are in the past. Relative to event one, events two and three are in the future. Relative to event two, event one is in the past and event three is in the future - irrespective of which frame you observe it from. So, according to DaleSpam, you can't do is choose a frame such that me whacking the cue ball comes before the cue ball sitting the pocket. Is this correct?
Right.
 Quote by neopolitan If we place two synchronised clocks on the table, one next to the start position of the cue ball and the other next to the pocket and then observe from another frame in which the table is not at rest, then this is equivalent to our rocket scenario. In the table's frame both clocks will remain synchronised for all events. Event one is relatively in the past since when event three happens the clocks may for example all read 10s as opposed to the 2s when event one happened - something that happened 8s ago. We talked in earlier posts about being able to observe, simultaneoulsy in a frame which is not at rest with the rocket, the clock at the nose reading 2s and the clock at the tail reading 10s. Let us then observe the table from such a frame in which where I whack the ball is "the nose" and the pocket is "the tail". I am not interested in the relative velocity of the cue ball, I can work that out myself thank you very much. I just want to consider my three events. What apparently can happen is that from well selected frame, you can see the cue ball being whacked and the cue ball sitting in the pocket simultaneously - in a frame which is not at rest with the table. From what DaleSpam says though, you can't select a frame where you see the cue ball in the pocket before you can see it is whacked.
No, not only can you not see them in the wrong order, you can't see them simultaneously either. If events are simultaneous in one frame, then there is a spacelike separation between them, meaning that no matter what inertial coordinate system you use, if the spatial separation between them is $$\Delta x$$ and the temporal separation is $$\Delta t$$ in this coordinate system, then $$c^2 * \Delta t^2 - \Delta x^2 < 0$$...if you had $$c^2 * \Delta t^2 - \Delta x^2 > 0$$ then there'd be a timelike separation between them, and if $$c^2 * \Delta t^2 - \Delta x^2 = 0$$ then they have a lightlike separation. If events have a spacelike separation in one inertial frame's coordinates, they will have a spacelike separation in every inertial frame, and likewise with events that have a timelike or lightlike separation (in fact the value of $$c^2 * \Delta t^2 - \Delta x^2$$ is the same in every frame, this is the 'invariant spacetime interval'...for events with a timelike separation, it is just c^2 times the proper time elapsed on a clock that moves inertially between the events). For events with a spacelike separation, it is always possible to find an inertial frame where they are simultaneous, and also always possible to a pair of inertial frames that both say they were non-simultaneous but disagree on their order. Events with a timelike separation could be bridged by an object moving slower than light, events with a lightlike separation can only be bridged by something moving at exactly c, and events with a spacelike separation could only be bridged by a tachyon moving FTL, if such things existed.
 Quote by neopolitan This seems counterintuitive since I specified none of the following: the speed at which I hit the cue ball, the distance between the cue ball's start position and the pocket, or the relative velocity of the table in the frame from which it is observed (or the rest length of the rocket). I see no reason why I can't hit the cue ball so as to give it higher velocity, and do so when the clocks read 4s such that the ball is in the pocket at 10s. Then the observation from another frame will see the clock at the nose reading 2s (with the cue ball sitting there undisturbed) and the clock at the tail reading 10s (with the cue ball sitting there after being whacked). This is where I think that the 2s cue ball at the nose is in the future - relative to where it "should" be since according to the observer it should be more in the past since cause should precede effect (result) - and the 10s cue ball at the tail is in the past - relative to where it "should" be. I think I can understand your perspective though since what we are observing, from a frame not at rest relative to the table, is a "past" event and a "future" event. We tend to think of travelling to events rather than events travelling to us. For example in Sci-fi it is normally time travellers who travel to the past, rather than time-movers who bring to past to them. But in our example, I do think that we are considering something closer to the latter than the former. In the frame not at rest relative to the table, there is an event "now" in which a past event and future event are observed simultaneously. To me that means the past event is brought forward to the future (now is in the future relative to the past) and the past event is brought back to the past (now is in the past relative to the future). To be honest, I don't expect many people to grasp this first time around. In any event, the (apparent) potential for violated causality may be a problem. It's all nice and simple when we just talk about clocks, not so easy when you add in chains of cause and effect. Comments?
Well, tell me if I'm wrong, but it seems as if all your speculations here followed from the assumption that it would be possible for two causally-related events to be simultaneous in some frame (your comment 'What apparently can happen is that from well selected frame, you can see the cue ball being whacked and the cue ball sitting in the pocket simultaneously'), when in fact that is not possible unless FTL exists, as I explained above (and if FTL exists, the problems this causes for causality in relativity are well-known).
 Quote by neopolitan PS I had better admit to being a little naughty here. If you are looking for it, you can find in my scenario the reason why causality is most certainly not violated. I did want others to find it and point it out, but not so much that I am willing to risk being locked out by an overzealous moderator or give anti-relativity nuts something that may look like ammunition for their cause. Now I admit the reason is there, is anyone still willing to point it out?
Can you specify what you're talking about here?
P: 645
 Quote by JesseM Can you specify what you're talking about here?
I knew about the FTL limitations and the inability to violate causality (outside of the theoretical tachyon). I just didn't want someone to assume that I thought that causality was being violated and that I was therefore trying to invalidate relativity.

I am also aware that you can't see causally related events simultaneously without something going FTL.

Writing something that could be interpreted as implying that I wasn't aware of this FTL issue did get you to respond though. I note that you tend to respond very quickly when you can easily find an error. But not when it seems you can't, such as in the post before the one you are responding to here (eg #33). I am trying my best not to impugn motives, but it would help me to resist the temptation if you could respond to that one now.

In addition, while we both accept that you can't see causally related events simultaneoulsy, can we both accept that we can observe causally related events from an inertial frame such that the events are skewed (ie the events may not be simultaneous in the frame in which they occur, but the relationship between them is skewed, similarly to the relationship between the two clocks on the table are skewed)?

Can you then see if you can understand what I said here?

 Quote by neopolitan In the frame not at rest relative to the table, there is an event "now" in which a past event and future event are observed simultaneously. To me that means the past event is brought forward to the future (now is in the future relative to the past) and the _future_ event is brought back to the past (now is in the past relative to the future).
Note that I not claiming the ability to see the cue ball both unwhacked and in the pocket, just what we have talked about before - the clock at one end of the table saying 2s and the clock at the other end saying 10s. These clocks are not causally related.

cheers,

neopolitan

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