Discuss events which are simultaneous in one frame?

[neopolitan]

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.

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.)

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.

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.

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

<snip> 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

 

[JesseM]

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.

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?

(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.

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?)

I also seem to be lost, since you have written the following in different posts #23 and #25 respectively.

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.

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.

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.

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.

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.

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.

(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"

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.

I also don't quite know what you mean by

<snip> 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."

 

[neopolitan]

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.

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.

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

 

[neopolitan]

<snip> 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 traveling to events rather than events traveling 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?

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?

 

[JesseM]

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).

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.

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 &lt; 0...if you had c^2 * \Delta t^2 - \Delta x^2 &gt; 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.

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 traveling to events rather than events traveling 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).

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?

 

[neopolitan]

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?

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

 

[JesseM]

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

Sorry if I'm telling you something you already know, but you said "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"--are the ball being whacked and the ball ending up in the pocket not causally related? Did you mean to write "what apparently can't happen"?

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.

Please, please, please, stop with the paranoid fantasies about my secret motives. Making rather unsubtle hints about my motives and then saying "I am trying my best not to impugn motives" is not somehow more acceptable to me, if anything it is even more irritating. And the posts I respond quickly to are just the ones I can immediately think of an obvious response to--could be because there's an error, could be just to answer a question that has a simple answer, could just be to confirm that what someone is thinking is correct. I tend to respond slower to posts where I'm not sure what the person is trying to say and I don't know what I can say or ask to bring things into focus (as has been true with many of your posts on this thread). Sometimes I respond slower when I know basically what I'd like to say but I know the response will be rather involved, so it's something I put off. Sometimes it's just random laziness or getting distracted by something else in my life. But it's not like I owe you my time here--and I've spent quite a lot of accumulated time so far responding to your posts and emails--and this demanding, impatient attitude (it's only been a day since you posted the post you're now complaining I haven't gotten to yet!) is really not the best way to convince me to continue.

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)?

I don't know what you mean by "the relationship between them is skewed". Every frame agrees on which of three causally related events happens first, middle, and last, the only difference is in the amount of time between them (but that's basically just time dilation).

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

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).

I can't really see what you mean here either, the language is again pretty vague. 'There is an "event" now (what event? now in what frame?) in which a past event (what past event? past of what, and in what frame?) and future event (what future event? future of what, and in what frame?) are observed simultaneously (simultaneously in what frame?)' Can you give some kind of specific example--preferably a numerical example--and be consistently clear about what frame every statement you're making is supposed to refer to?

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.

If you're talking only about events which are not causally related, what point were you making about the cue ball?

 

[Dale]

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?

Correct, that is exactly what I was saying.

In SR this is called "timelike". When two events have timelike separation one will be inside the future light cone of the other. The inside of the future light cone contains only future events (but not all future events). Because the light cone is preserved in all frames, it should come as no surprise that events with timelike separation in one frame will have timelike separation in all frames and therefore the temporal ordering of timelike separated events is preserved in all frames.

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.

No, it is not equivalent to the rocket scenario.

In the rocket scenario the event that the nose clock reads 12:00 is not in the future nor past light cones of the event that the tail clock reads 12:00. In SR this is called "spacelike". Again, because the light cone is preserved in all frames it should come as no surprise that events with spacelike separation in one frame will have spacelike separation in all frames. However, what is surprising is that due to the relativity of simultaneity the temporal ordering of spacelike separated events is not preserved in all frames. This can occur because outside of the light cones are future, past, and simultaneous events .

 

[Dale]

JesseM and neopolitan,

Here is a pair of spacetime diagrams depicting the situation in various frames. The primed frame is the rest frame of the rocket and the unprimed frame is a frame where the rocket is moving at .6c (aka "observer frame"). In each frame the rocket's position at a specific time is shown with the solid outline. The dashed outline is the transform of the other frame's solid outline.

The argument here boils down to one of you looking at one frame and saying "the nose is further up the diagram" and the other looking at the other frame and saying "the nose is further down the diagram". Otherwise the argument is purely semantics.

 

[JesseM]

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?

Did you mean to write "C" rather than "B" here? B was the rocket's frame, in that frame the nose doesn't read less than the tail, assuming the two clocks are synchronized in their own rest frame. But in the C frame, yes, the tail clock could read 10 s simultaneously with the nose clock reading 2 seconds, so if we go back to the observer's frame A where the tail clock reads 8 s simultaneously with the nose clock reading 2 seconds (using the numbers from my example near the end of post #28), then the tail reading 10 s is still in the future.

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.

OK, but "special" and "different" in what sense? Also, one of the reasons I brought up frame C was because it sounded a little like you were saying the whole thing about the nose being further in the future for the outside observer only required us to think about the outside observer's frame A, not to even bother with thinking about how things work in other frames, even the rocket's rest frame. I was just making the point that your argument does require us to consider another frame, although I agree that it seems more "elegant" or more intuitive to use the rocket's rest frame as the other one rather than another frame like C. But saying it's more elegant/intuitive doesn't mean it's somehow fundamentally more correct in terms of actual physics, and I wasn't sure if you were suggesting that the statement "the nose is further in the future" was supposed to be something more fundamental than just a comparison of simultaneity in two different reference frames...I was thinking specifically of your comment in post #25:

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.

Your comments about it being "less like semantics and more like something interesting", and more than "that's just relativity", made it sound like you thought there was something more to this than just a comparison of simultaneity in frame A and frame B, something more like new physics of some kind. So that's one of the reasons I brought up the frame C, to show that which clock is "more in the future" for the observer A really does crucially depend on your choice of the second frame to use, even if frame B may be the most natural choice in this situation...but we are in no way forced to use frame B by nature here.

Also, in some later posts you seemed to deny that your comments about the nose being further in the future for A depended on using a second frame at all...like your comments in post #27 about not being interested in the perspective of a "dorky physics guy" on the rocket, only in the perspective of the outside observer, and then especially your comment in post #29 where you said:

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).

So, are you now in agreement that your comment about the nose clock being further in the future for the outside observer A depends crucially on looking at the rocket frame B and picking events which are simultaneous in that frame, then seeing the order of the same events in frame A?

If we can agree on that, then I guess we really need to go back to the question of whether you're just trying to talk about how to conceptualize the different definitions of simultaneity in the rocket's frame vs. the outside observer's frame, or if your comment that this is "less like semantics and more like something interesting", and your question about whether we can "model" that, suggests you're talking about something more, perhaps a new physical model. If the former, then sure, I think this is an OK way to conceptualize the relation between the two frames' definitions of simultaneity, but if the latter, then I'm still having trouble understand what you're trying to get at, and I'm not sure what I can ask you to get you to state it in a way that makes more sense to me. If this is a case, maybe a start would be for you to try to address my questions from post #28:

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?

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?

It makes a difference in being harder to conceptualize intuitively, but if you're talking about some other kind of "difference", then what kind of difference do you mean?

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)?

Again, when you say you want only one observer, it worries me a little because of my concern that you might be suggesting that your comments about the nose clock being further in the future do not require us to think about two different frames, both the outside observer's frame and the rocket's frame, but can somehow be understood purely in terms of the observer's frame. If you agree we need to think about two different frames to make sense of your comments, then I don't see why you don't want to consider two different observers, since as I was saying in post #30, talking about particular observers is usually just understood as a kind of shorthand for talking about what's going on in particular frames.

 

[JesseM]

The argument here boils down to one of you looking at one frame and saying "the nose is further up the diagram" and the other looking at the other frame and saying "the nose is further down the diagram". Otherwise the argument is purely semantics.

I appreciate you drawing the diagrams, and the argument was about that at one point, but I think it's moved on a little. In post #26 I think I figured out what neopolitan meant about the nose being further in the future (as illustrated in your second diagram where at a single instant in the rocket frame, the nose is crossing a later line of simultaneity from the outside observer's frame than the line of simultaneity the tail is crossing), but I have some questions about some of neopolitan's other comments as explained in the post immediately above, and that's what the more recent discussion has been oriented around.

 

[neopolitan]

Did you mean to write "C" rather than "B" here? B was the rocket's frame, in that frame the nose doesn't read less than the tail, assuming the two clocks are synchronized in their own rest frame. But in the C frame, yes, the tail clock could read 10 s simultaneously with the nose clock reading 2 seconds, so if we go back to the observer's frame A where the tail clock reads 8 s simultaneously with the nose clock reading 2 seconds (using the numbers from my example near the end of post #28), then the tail reading 10 s is still in the future.

Looking over it again, yes, I meant C rather than B. It think it is reasonably clear that I was referring to another frame which was not at rest relative to the rocket. I am not 100% sure that we are there yet with what I meant about "the nose being more in the future as compared to the tail" - noting that I was only referring to a frame where two synchonised clocks were at rest and one observer who was not at rest relative to the clocks such that one "nose" clock is ahead of the other "tail" clock in terms of their relative motion according to the observer. In that limited scenario, do you agree?

To try to clarify again, in a now moment in the observer's frame (all now moments are relative, since "now" changes all the time), the observer may observe the tail clock reading 10s and the nose clock reading 2s. IF the clocks are synchonised relative to their rest frame - noting that the observer can work this out from the relative velocity of the clocks and their apparent separation from each other - THEN the observer can further deduce that the nose clock he sees "now" is a younger version of the nose clock and an older version of the tail clock (the observed nose clock manifests earlier in the clocks's rest frame than the observed tail clock - in our example 8s earlier). The nose clock, if you like, has reached the observer's "now" before the tail clock has.

I am sorry to have to do this, but I hope I can justify it. Let's introduce a third clock - on the rocket, in the midpoint between the nose and the tail. That clock will read a midpoint value. Without thinking too deeply about the specifics, I suspect it is 6s (midway between 10s and 2s) but the acutal reading is immaterial - what is important is that it is more than 2s and less than 10s.

If the observer not at rest relative to the clocks observes a reading of 6s on the midpoint clock, 2s on the nose clock and 10s on the tail clock - and knows from his deductions that in their own rest frame the clocks are synchonised then he can say, taking the midpoint clock as his reference, that the nose clock he "should" (see since the clocks are synchronised) is in the future and the tail clock he "should" see is in the past. Whose past and whose future? the past and future of the observer.

What that observer sees, as you point out (I think), is a past version of the nose clock, relative to the midpoint clock, and a future version of the tail clock, relative to the midpoint clock.

You don't really need the third clock, since the same logic applies with only two points, but hopefully the temporary introduction of a third clock makes it easier to understand.

DaleSpam is most probably right, we are probably arguing over semantics.

More later, I must attend a meeting.

cheers,

neopolitan

 

[neopolitan]

<snip>
Also, in some later posts you seemed to deny that your comments about the nose being further in the future for A depended on using a second frame at all...like your comments in post #27 about not being interested in the perspective of a "dorky physics guy" on the rocket, only in the perspective of the outside observer,
<snip>

Fortunately I like my sense of humor, so to have an example of it reflected back at me gave me a good laugh.

Then I read a bit closer.

Please please please reread the second paragraph of post #27.

There was only one observer and that observer was not on the rocket, not at rest relative to the rocket or the clocks. The "dorky physics guy" was the observer, the only observer, the observer who I specifically stated was not on the rocket. There was no other observer on the rocket who could observe the "dorky physics guy", which was the whole point.

It is as if I have said "there is only one observer, an observer who is not at rest relative to the rocket or the clocks and we calculate things like this and come out with this answer" then you have effectively said "okay, so I take your observer and put him on the rocket, bring in another observer to replace yours, do my calculations from a different perspective than the one you have used and - look! - your results are wrong".

I am not saying you have done this deliberately, intentionally or with malice. It's an "as if". Can you see how I arrived at it?

cheers,

neopolitan

 

[neopolitan]

Jesse,

I think that most of your other questions in #40 are possibly answered by the contents of #42 where I use the midpoint clock to explain what I mean by "the nose clock is in the future".

The only that remains open is about why the rocket's frame is "special". Well, it is not special other than it is the one that the "outsider observer" is observing. The two items being observed share that frame. In your way of thinking there is a virtual observer at rest in the rest frame of the rocket and the clocks and there is an "outside observer". The virtual observer, observer B, is special because this observer is the only one of the three you discussed before who is at rest in the B frame, along with the rocket and the clocks being observed, neither A nor C are at rest in the B frame.

Observer B is the only observer who can observe the clocks to be synchronised (after taking into account travel times, if he is not at the midpoint between the clocks - since the observer is virtual we can even nominate the midpoint between the clocks as her virtual location to make it easier for ourselves). Is this not special or different?

cheers,

neopolitan

 

[yuiop]

Hi Neopolitan,

Say I place two mickey mouse clocks next to each other on a table. Say the clocks are syncronised with each and nothing is moving except for the hands of the clocks advancing at the same rate as far as I am concerned. Now if I advance the hands of the right hand clock by 2 hours, is the right hand clock 2 hours in the future of the left hand clock in the meaning of "future" that you are using? Or is it just that I advanced the hands of the right hand clock and there is nothing fundamental about the time displayed. For instance the atoms of the two clock cases would have (near enough) the same "age".

 

[JesseM]

Fortunately I like my sense of humor, so to have an example of it reflected back at me gave me a good laugh.

Then I read a bit closer.

Please please please reread the second paragraph of post #27.

There was only one observer and that observer was not on the rocket, not at rest relative to the rocket or the clocks. The "dorky physics guy" was the observer, the only observer, the observer who I specifically stated was not on the rocket. There was no other observer on the rocket who could observe the "dorky physics guy", which was the whole point.

I understood that you only wanted to talk about one observer outside the rocket--that was why I described the paragraph as "Also, in some later posts you seemed to deny that your comments about the nose being further in the future for A depended on using a second frame at all...like your comments in post #27 about not being interested in the perspective of a "dorky physics guy" on the rocket, only in the perspective of the outside observer". I thought your point was to denigrate the notion of a second observer on the rocket by calling him a "dorky physics guy"...what you said was:

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".

In this paragraph, I thought you were saying that if you asked the observer outside what he saw, you wanted him to just see a rocket, not a dorky physics guy on board the rocket observing him back. But I guess what you're telling me is that I misunderstood, and you actually meant that if you asked what was observed by anyone, you only wanted to hear the observations of the guy outside, you didn't want to hear the observations of someone on the rocket who looks outside and sees a "dorky physics guy" (the outside observer) watching him. However, you can see that although I misunderstood who the dorky physics guy was supposed to be, I understood your main point just fine--that you didn't want to have a second observer on the rocket, just the guy outside the rocket. So this is a "difference that makes no difference".

Anyway, as I said in my last post, I don't understand why you're adamant that there be only one observer--do you agree that in relativity we basically just talk about "observers" as shorthand for different frames? Do you agree with my point that it's impossible to understand the meaning of "the nose clock is farther in the future" if we talk solely about the frame of the outside observer, that this is really a comparison of the definitions of simultaneity in the outside observer's frame and in the rocket's frame? If you agree that we have to talk about the rocket's frame in order to pick two clock readings which are simultaneous in that frame (since again, your statement about which clock is further in the future shouldn't depend on assuming the clocks are actually properly synchronized in their own rest frame), then why not just talk about the observations of the two clocks by someone on the rocket as shorthand for statements about simultaneous readings in the rocket's frame?

It is as if I have said "there is only one observer, an observer who is not at rest relative to the rocket or the clocks and we calculate things like this and come out with this answer" then you have effectively said "okay, so I take your observer and put him on the rocket, bring in another observer to replace yours, do my calculations from a different perspective than the one you have used and - look! - your results are wrong".

I am not saying you have done this deliberately, intentionally or with malice. It's an "as if". Can you see how I arrived at it?

I think it was you who was not reading my own words carefully enough here. Although I misunderstood who the "dorky physics guy" was supposed to represent, I made it clear that I understood that your point in that paragraph was that you didn't want to talk about any observations made on the rocket, only about the observations of the observer outside.

 

[yuiop]

Now say I get 3 lumps of radioactive material that decay in a consistant and predictable manner at the same rate. The half life of the material is defined as the time it takes for half the remaining atoms of isotope1 to convert to isotope2. These lumps provide a fundamental clock that cannot be arbitarily advanced, retarded or syncronised with respect to each other when they are at rest wrt each other.

I place one lump at the back of the rocket and one at the nose while the rocket is at rest wrt me. I keep one lump for reference and there are also the 3 conventional clocks of your original experiment (one alongside each lump). The rockets accelerates away for a time until coming to a final cruising speed where the rear and the nose of the rocket are going at the same speed relative to us. We note that the rocket has length contracted and conclude that the rear of the rocket must have been going faster than the nose of the rocket in order to "catch up" a little bit. It is reasonable to assume the rear clock and the rear isotope lump have time dilated the most out of all the clocks. In that sense the isotope lump at the nose of the rocket will have decayed more than the lump at the rear and so is in a fundamental sense in the future of the rear clock (but also in the past of reference lump that remained with us).

Now if some robot on the rocket is programmed to syncronise the clocks at the front and rear it will arbitarily retard the front clock by 8 seconds or advance the rear clock 8 seconds. They are both equally valid methods but the choice of adjusting the rear clock or the front clock to achieve syncronisation is arbitary and artificial. Does that make any sense?

[EDIT] Notice that after syncronisation we would be able to tell which clock was advanced or retaded by comparing the conventional clcocks to the radioactive lumps sitting next to them.

 

[JesseM]

Looking over it again, yes, I meant C rather than B. It think it is reasonably clear that I was referring to another frame which was not at rest relative to the rocket. I am not 100% sure that we are there yet with what I meant about "the nose being more in the future as compared to the tail" - noting that I was only referring to a frame where two synchonised clocks were at rest and one observer who was not at rest relative to the clocks such that one "nose" clock is ahead of the other "tail" clock in terms of their relative motion according to the observer. In that limited scenario, do you agree?

I don't think the statement about the nose clock being further in the future can make sense except as a comparison of simultaneity in two frames, the outside observer's frame and the rocket's rest frame. The idea as I understood it is to take two readings on the nose and tail clock which are simultaneous in the rocket's frame, then look at when these same two readings occur in the outside observer's frame, and note that the nose reading happens further in the future than the tail reading in the observer's frame. Do you think it is possible to explain your idea of the nose being further in the future without referring to simultaneity in the rocket's rest frame, and also without necessarily assuming the clocks themselves have been properly synchronized in the rocket's rest frame?

To try to clarify again, in a now moment in the observer's frame (all now moments are relative, since "now" changes all the time), the observer may observe the tail clock reading 10s and the nose clock reading 2s. IF the clocks are synchonised relative to their rest frame - noting that the observer can work this out from the relative velocity of the clocks and their apparent separation from each other - THEN the observer can further deduce that the nose clock he sees "now" is a younger version of the nose clock and an older version of the tail clock (the observed nose clock manifests earlier in the clocks's rest frame than the observed tail clock - in our example 8s earlier). The nose clock, if you like, has reached the observer's "now" before the tail clock has.

Well, if you talk about which clock "reaches the observer's now first", this sounds more like viewing the outside observer's plane of simultaneity (his 'now') from the perspective of the rocket rest frame--as illustrated in DaleSpam's second diagram, the observer's planes of simultaneity are tilted in the rocket's frame so that the the nose will hit a given plane before the tail (here the 'before' refers to time in the rocket's own frame). So again, considering both the outside observer's frame and the rocket's frame seems critical here, which you seemed to at leas partially acknowledge when you said above "IF the clocks are synchonised relative to their rest frame..."

I am sorry to have to do this, but I hope I can justify it. Let's introduce a third clock - on the rocket, in the midpoint between the nose and the tail. That clock will read a midpoint value. Without thinking too deeply about the specifics, I suspect it is 6s (midway between 10s and 2s) but the acutal reading is immaterial - what is important is that it is more than 2s and less than 10s.

That's right, it'd be 6s. If two clocks are synchronized in their own frame, then in a frame where they're moving at speed v they'll be out-of-sync by vx/c^2, where x is the distance between them in their own rest frame. The clock in the middle is the same distance from the clock on the nose as it is from the clock on the tail, so it must be out-of-sync with each by the same amount (ahead of one and behind the other).

If the observer not at rest relative to the clocks observes a reading of 6s on the midpoint clock, 2s on the nose clock and 10s on the tail clock - and knows from his deductions that in their own rest frame the clocks are synchonised then he can say, taking the midpoint clock as his reference, that the nose clock he "should" (see since the clocks are synchronised) is in the future and the tail clock he "should" see is in the past. Whose past and whose future? the past and future of the observer.

OK, if he takes the midpoint clock as a reference for what he "should" see (though I hope you agree he could equally well take another clock for his reference) then he'll only see the nose clock give the same reading in the future, and he's already seen the tail clock show this reading in the past. I understand, and this is equivalent to the interpretation of you're comments that I've been talking about since post #26 (again, my interpretation is just that you pick simultaneous readings in the rocket's rest frame--in this case each of the three clocks reading 6 s--and then look at the order of these same readings in the observer's frame, noting that the nose reaches its reading at a time more 'in the future' for the observer than the tail reaches its own reading, and likewise the middle clock reaches its reading at a time midway between the other two in the observer's frame).

DaleSpam is most probably right, we are probably arguing over semantics.

If you're just talking about the best way to conceptualize the relation between simultaneity in the observer's frame and the rocket's frame, then I'm not really arguing with you at all, I've said since post #26 that I think "the nose clock is further in the future" can be interpreted in a reasonable way. My issues were the ones I mentioned in post #40--that sometimes you seemed to suggest we didn't have to think about the rocket frame at all, and also that you wrote this paragraph which suggested you might be hinting at something more than just a way of conceptualizing simultaneity in relativity:

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.

If you didn't mean to suggest here that what you were talking about was anything more than a way of conceptualizing simultaneity in SR, then just say so and my mind will be put at ease that you're not making any claims I would need to argue with.

 

[yuiop]

I can partly justify the nose isotope lump being ahead of the rear lump in a fundamental sense by getting the onboard robots to slowly transport both lumps to the centre of the ship so that they are right next to each other. We would notice that the lump originally at the nose has decayed more than the isotope lump that was originally at the rear. Since both the isotope lump "clocks" are essentially at the same location any observer would agree with the comparison at that point.

 

[JesseM]

Jesse,

I think that most of your other questions in #40 are possibly answered by the contents of #42 where I use the midpoint clock to explain what I mean by "the nose clock is in the future".

The only that remains open is about why the rocket's frame is "special". Well, it is not special other than it is the one that the "outsider observer" is observing. The two items being observed share that frame. In your way of thinking there is a virtual observer at rest in the rest frame of the rocket and the clocks and there is an "outside observer". The virtual observer, observer B, is special because this observer is the only one of the three you discussed before who is at rest in the B frame, along with the rocket and the clocks being observed, neither A nor C are at rest in the B frame.

Observer B is the only observer who can observe the clocks to be synchronised (after taking into account travel times, if he is not at the midpoint between the clocks - since the observer is virtual we can even nominate the midpoint between the clocks as her virtual location to make it easier for ourselves). Is this not special or different?

Observer B is the only one who observes the clocks to be synchronized if they are indeed synchronized in their own rest frame--it would be possible, although unconventional, to set the clocks so that they were synchronized in some other frame, like the outside observer's frame. And didn't you agree with me earlier that the question of which clock is "further in the future" shouldn't depend on how they are synchronized?

Anyway, whether the rocket's frame is special really depends what you mean by "special", as I already said it is certainly the most simple and elegant choice if you're interested in comparing the outside observer's definition of simultaneity with some other frame's definition of simultaneity, but it isn't physically more special than some other frame like frame C in the sense that statements made based on using the rocket's frame (like, 'the nose clock is further in the outside observer's future') will be more "objectively true" in some sense than statements made based on using frame C (like 'the tail clock is further in the outside observer's future'). So once again we come back to the question at the end of my most recent post about whether you're just talking about a nice way to conceptualize the relation between two frames' definitions of simultaneity, or whether your "describe a model in which that is possible" was meant to suggest some kind of new truths about physics beyond what SR tells us.

 

[neopolitan]

Hi Neopolitan,

Say I place two mickey mouse clocks next to each other on a table. Say the clocks are syncronised with each and nothing is moving except for the hands of the clocks advancing at the same rate as far as I am concerned. Now if I advance the hands of the right hand clock by 2 hours, is the right hand clock 2 hours in the future of the left hand clock in the meaning of "future" that you are using? Or is it just that I advanced the hands of the right hand clock and there is nothing fundamental about the time displayed. For instance the atoms of the two clock cases would have (near enough) the same "age".

The clocks are desynchronised as soon as you move the hands. It's not what I meant at all.

cheers,

neopolitan

 

[neopolitan]

Jesse,

I will get back to you tomorrow. For the moment, I was adamant that there be only one observer so you knew which equations mattered. We have had so much trouble in other exchanges by your swapping observers.

One observer, only one observer, and we should get past that.

cheers,

neopolitan

 

[neopolitan]

I can partly justify the nose isotope lump being ahead of the rear lump in a fundamental sense by getting the onboard robots to slowly transport both lumps to the centre of the ship so that they are right next to each other. We would notice that the lump originally at the nose has decayed more than the isotope lump that was originally at the rear. Since both the isotope lump "clocks" are essentially at the same location any observer would agree with the comparison at that point.

Um, where are "we"? And in any case, I think when you bring them together you should find that they have decayed equally.

I am ready to be proved wrong on this though.

cheers,

neopolitan

 

[yuiop]

Um, where are "we"? And in any case, I think when you bring them together you should find that they have decayed equally.

I am ready to be proved wrong on this though.

cheers,

neopolitan

"We" are in the original frame before the rocket accelerated away from "us". We are not onboard the rocket and have been stationary and never experienced any acceleration for the duration of the experiment. We count as one observer because we are next to each other and at rest with respect to each other. Sorry, I should have said "I" or "you" rather than "we" to stay in line with your condition of only one observer, but I get lonely sometimes :P The robots are programmed not to have an opinion and so do not count as observers ;)

When the radiactive lumps are being brought together by the inpartial robots, the rear lump is moving even faster (relative to the one and only sentient observer) than the nose lump that is transported "backwards" from the nose to the centre and so the rear lump experiences even more time dilation relative to the front lump from the point of view of the only observer.


When I get time I will do the calculations using the equations for the proper time experienced by accelerated and transported clocks.

[EDIT] Without doing the formal calculations we can note that when the rocket is cruising at constant velocity and when the convential rear and nose clocks have been syncronised that they will show the same time when brought together at the centre of the rocket. Since the radioctive lumps were not syncronised prior to bringing them together they will not show the same time when bringing them together.

 

[neopolitan]

[EDIT] Without doing the formal calculations we can note that when the rocket is cruising at constant velocity and when the convential rear and nose clocks have been syncronised that they will show the same time when brought together at the centre of the rocket. Since the radioctive lumps were not syncronised prior to bringing them together they will not show the same time when bringing them together.

I should let someone else respond, but I make two comments anyway.

Comment one: Are we not comparing the extent to which each radiactive lump has decayed? I would have thought that this implies a synchronisation at a reference event after which the decay of each lump is measured.

Comment two: I assume that, in the rest frame of the rocket, the robots move at the same speed from the nose and tail towards the middle. This means that in the rocket frame there will be a very small amount of time dilation due to the relative motion of the robots (very small because you stipulated "gradually" as the magnitude of their velocities) and that time dilation would affect each robot and lump equally. The lumps will be simultaneous at the midpoint and will have undergone the same amount of time dilation, and, if my comment one is right, still synchonised (in the rocket's frame). Since the lumps will now be collocated, and collocation applies to all frames, I believe that they will then be synchonised in all frames.

Again, I may be wrong and stand ready to be corrected :)

cheers,

neopolitan

 

[yuiop]

I should let someone else respond, but I make two comments anyway.

Comment one: Are we not comparing the extent to which each radiactive lump has decayed? I would have thought that this implies a synchronisation at a reference event after which the decay of each lump is measured.

We do a crude form of syncronisation by starting with one large lump of radioactive material that consists of billions of atoms and is essentially homogenous and then divide the large lump into 3 equal portions to form 3 crude clocks.

Comment two: I assume that, in the rest frame of the rocket, the robots move at the same speed from the nose and tail towards the middle. This means that in the rocket frame there will be a very small amount of time dilation due to the relative motion of the robots (very small because you stipulated "gradually" as the magnitude of their velocities) and that time dilation would affect each robot and lump equally. The lumps will be simultaneous at the midpoint and will have undergone the same amount of time dilation, and, if my comment one is right, still synchonised (in the rocket's frame). Since the lumps will now be collocated, and collocation applies to all frames, I believe that they will then be synchonised in all frames.

Again, I may be wrong and stand ready to be corrected :)

cheers,

neopolitan

The two robots will have undergone the same amount of time dilation in the rest frame of the rocket relative to clocks on the rocket that remain at rest with rocket. However from the point of view of our single observer not onboard the rocket the two robots will not have experienced the same amount of time dilation.

I added an edit to the end of my last post (#47) that you may have missed.

--> Without doing the formal calculations we can note that when the rocket is cruising at constant velocity and when the convential rear and nose clocks have been syncronised that they will show the same time when brought together at the centre of the rocket. Since the radioctive lumps were not syncronised prior to bringing them together they will not show the same time when bringing them together. <--

Does that additional comment help any?

 

[neopolitan]

kev,

If you check my previous post, you will see that your edit was the topic of my reply - I quoted your edit and nothing else.

I would appreciate a third opinion on this. I do still think that, when collocated, the lumps will have decayed equally - in all frames.

cheers,

neopolitan

MY EDIT - Here is an explanation for why. Perhaps it works, perhaps not. The time dilation for both lumps will be the same, relative to an outside observer - so long as the lumps are at rest in the rest frame they share with the rocket. There will just be an offset between due to their not being collocated. The reduction of that offset, to zero, can be accounted for by the different rates of time dilation as observed by the outside observer when they are not at rest in what was otherwise their shared rest frame (and, for the duration, only the rocket's rest frame).

A related effect must take place if a moving pair of clocks are slowed, so that they are and remain synchonised in their rest frame and become synchonised in a frame in which they were not at rest before deceleration but are at rest after deceleration. I am not saying it is the deceleration that does it.

 

[neopolitan]

Back to topic - Simultaneity

I would like to return to the original core topic, simultaneity.

Jesse confirmed that what we call simultaneity is "transmission simultaneity". Here is my definition:

Transmission simultaneity - photons from two events are released simultaneously, such that if the sources were equidistant (and remain equidistant - in other words the observer is at rest), the photons would reach the observer at rest together. Under most circumstances however, the photons will not reach the observer simultaneously and knowledge of where the photons were released is required to know that their release was in fact simultaneous.

If this is the case, and I have no doubt that it is, then is there validity in conceptualising an "instant", or a "surface of simultaneity"? Such an "instant" would comprise of an "event space" in which, relative to an inertial observer (at rest in that observer's own frame), all events are simultaneous. I could pick any instant, for example the instant when I absorbed the first photon from the sun to ever hit my retina (we could argue endlessly about how long that absorption process takes and the quantum uncertainty about when precisely the photon was absorbed, but the idea is to pick an instant, so we pick an instant in which the probability that the photon has just been absorbed is maximal), and label that t=0. Relative to my rest frame, there would be an event space which was the set of events (x,y,x,0) where x, y and z are unbounded. That event space would constitute an instance or a surface of simultaneity.

Are there any conceptual problems with that?

To prevent diversions, I state explicitly that I am aware that relative to other observers who might not share my rest frame the event frame I just define is not necessarily an instant or a surface of simultaneity. I will get to that later, if there are no real conceptual problems with what I am proposing.

cheers,

neopolitan

 

[yuiop]

I would like to return to the original core topic, simultaneity.

Jesse confirmed that what we call simultaneity is "transmission simultaneity". Here is my definition:



If this is the case, and I have no doubt that it is, then is there validity in conceptualising an "instant", or a "surface of simultaneity"? Such an "instant" would comprise of an "event space" in which, relative to an inertial observer (at rest in that observer's own frame), all events are simultaneous. I could pick any instant, for example the instant when I absorbed the first photon from the sun to ever hit my retina (we could argue endlessly about how long that absorption process takes and the quantum uncertainty about when precisely the photon was absorbed, but the idea is to pick an instant, so we pick an instant in which the probability that the photon has just been absorbed is maximal), and label that t=0. Relative to my rest frame, there would be an event space which was the set of events (x,y,x,0) where x, y and z are unbounded. That event space would constitute an instance or a surface of simultaneity.

Are there any conceptual problems with that?

To prevent diversions, I state explicitly that I am aware that relative to other observers who might not share my rest frame the event frame I just define is not necessarily an instant or a surface of simultaneity. I will get to that later, if there are no real conceptual problems with what I am proposing.

cheers,

neopolitan

What you are describing here is pretty standard. See this link http://casa.colorado.edu/~ajsh/sr/simultaneous.html. Ceruleans "hypersurface of simultaneity" is the tilted blue plane as seen by Vermilion whos own hypersurface of simultaneity is the red plane orthogonal to the time axis of his coordinate system.

 

[neopolitan]

Thanks kev,

I'll wait a bit to see if anyone thinks it is not standard.

cheers,

neopolitan