Very simple relativity questions

[starthaus]

The GPS clocks are only synchronized in the earth-centered inertial frame (ECIF). Any time you are using GPS you are implicitly using the ECIF.

Sure. I am not talking about synchronization, I am talking about the transmission of timestamps from the satellite clocks to the ground clocks. What I have said (repeatedly) is that this process can be used in comparing the clock readouts in lieu of reuniting the clocks.

 

[Dale]

Sure. I am not talking about synchronization, I am talking about the transmission of timestamps from the satellite clocks to the ground clocks. What I have said (repeatedly) is that this process can be used in comparing the clock readouts in lieu of reuniting the clocks.

Understood. What I have said (repeatedly) is that this procedure requires the specification of some reference frame as jtbell mentioned.

The point is that Loonwolf does not recognize that his question is incomplete, that he needs to specify the reference frame whenever he compares distant clocks. Your method of comparison will not relieve him of the need to specify the reference frame.

 

[JesseM]

For example, the spacecraft are moving towards each other (or else one is moving while the other is still, it makes no difference), then the two clocks can be next to each other for a moment if you REALLY need them to be.

But in this case different frames disagree about which clock was ahead of the other one in the past before they crossed paths, so different frames can still disagree about which clock has been ticking slower (and has elapsed more time since some previous moment) despite the fact that they both agree about what times the two clocks read when they meet. For example, suppose the two clocks are moving towards each other at 0.6c, and when they meet, clock A reads 30 years while clock B reads 28 years. Then in the rest frame of clock A, 10 years earlier clock A read 20 years while clock B also read 20 years, so in this frame clock B elapsed less time in the 10 years before they met. But in the rest frame of clock B, 10 years earlier clock A read 22 years while clock B read 18 years, so in this frame clock A elapsed less time in the 10 years before they met. Again it's just a matter of the relativity of simultaneity, the two frames cannot agree on how the readings of the two clocks compared when they were far apart.

It just seems to me people are making excuses why they can't answer the question simply. I don't want to hear the excuse, "Well, how would they be synchronised in the first place?" or anything like that, just looking for the simple answer to the question. They show the same time in the beginning.

It's not an "excuse", it's a basic feature of relativity that clocks far apart cannot be "synchronized" in any frame-independent way. If in one frame two clocks far apart "show the same time in the beginning", then in other frames the two clocks do not show the same time in the beginning, there's no getting around this in relativity. You seem to want a "simple answer" that is "simple" in the sense of rejecting the relativity of simultaneity, and thus in rejecting relativity itself!

 

[Loonwolf]

OK, I give up then, I'm never going to get my answer. It's a simple question. The two clocks showed the same time in the beginning. Whether they could or couldn't be synchronised in any "frame-independent way" when they are far away is irrelevant - I was specifically asking for the answer in the case when they WERE showing the same time in the beginning. They don't need to be physically synchronised, they just happen to be showing the same time in the beginning. - by coincidence if necessary. From BOTH reference frames they showed the same time in the beginning. There, specified.

When they are next to each other which clock is showing the earlier time? Why can I not get the answer to this simple question?

 

[JesseM]

OK, I give up then, I'm never going to get my answer. It's a simple question. The two clocks showed the same time in the beginning. Whether they could or couldn't be synchronised in any "frame-independent way" when they are far away is irrelevant - I was specifically asking for the answer in the case when they WERE showing the same time in the beginning.

It's still not clear whether you are understanding the relativity of simultaneity. There is no case where it is objectively true that they "were showing the same time in the beginning", if they were far apart. The very words "showing the same time in the beginning" only have meaning relative to a particular choice of coordinate system (a way of labeling events with position and time coordinates). No matter what physical procedure you use to synchronize the clocks at the beginning, there will be one inertial coordinate system where the events of both clocks showing some reading (12 noon, say) happen at the same t-coordinate in that system, and other inertial coordinate systems where the those same events happen at different t-coordinates so the clocks are out-of-sync. Saying the clocks were "showing the same time at the beginning" is like saying the clocks "had the same x-coordinate at the beginning"--this can only be true relative to a particular choice of how you orient your x-axis (one where the x-axis is perpendicular to the line between the two clocks), it would always be possible to describe the exact same physical situation using a different coordinate system with an x-axis oriented at a different angle so the same clocks don't have the same x-coordinate at the beginning.

If you understand that all claims about simultaneity are coordinate-dependent, and you're just asking about a case where we choose to use a coordinate system where the clocks are synchronized at the beginning, then just say so and no one will object to your question. But as long as you continue to use language like "the clocks show the same time at the beginning" without making clear you understand that this can only be true in one choice of coordinate system, people are going to continue to try emphasize this point about how simultaneity can only be defined in a coordinate-dependent way.

 

[Dale]

Whether they could or couldn't be synchronised in any "frame-independent way" when they are far away is irrelevant - I was specifically asking for the answer in the case when they WERE showing the same time in the beginning.

It is not irrelevant, it is critically important. Your statement that "they WERE showing the same time in the beginning" is meaningless because you aren't saying which reference frame it refers to. When you say that two distant clocks are showing the same time you have to specify the reference frame. It is as simple as that. Your failure to obtain an answer is because your question is incomplete, as you have been told over, and over, and over, ...

 

[thack45]

When they are next to each other which clock is showing the earlier time? Why can I not get the answer to this simple question?

Are you just wanting to understand why two initally syncronyzed clocks read different times after one of them has traveled at higher speeds for some time?

 

[Loonwolf]

So now people are saying that it is IMPOSSIBLE that one clock can be showing the same time as another clock which is in a different place? And that ten thousand billion trillion clocks all over the universe would each show a time that wasn't even approximately the same as any other?

There is NO physical procedure whereby the clocks are synchronised in the beginning. They just happen to be showing the same time, BY CHANCE.

I HAVE said which reference frame it refers to, BOTH.

OK, it's a case where we choose to use a coordinate system where the clocks are synchronized at the beginning. So nobody will now object to the question and will answer it?

I'm just wanting the simple answer to the question I have asked, when the two clocks are next to each other, which shows the earlier time?

 

[Dale]

So now people are saying that it is IMPOSSIBLE that one clock can be showing the same time as another clock which is in a different place?

Nobody said that, we simply said (repeatedly) that you have to specify the reference frame.

I HAVE said which reference frame it refers to, BOTH.

That is not possible. It is against the relativity of simultaneity. You have to pick one or the other or some third reference frame. It is not possible that it is simultaneous in more than one reference frame.

OK, it's a case where we choose to use a coordinate system where the clocks are synchronized at the beginning. So nobody will now object to the question and will answer it?

I'm just wanting the simple answer to the question I have asked, when the two clocks are next to each other, which shows the earlier time?

The one that was traveling faster in that "coordinate system where the clocks are synchronized at the beginning" will show the earlier time.

 

[JesseM]

So now people are saying that it is IMPOSSIBLE that one clock can be showing the same time as another clock which is in a different place? And that ten thousand billion trillion clocks all over the universe would each show a time that wasn't even approximately the same as any other?

There is NO physical procedure whereby the clocks are synchronised in the beginning. They just happen to be showing the same time, BY CHANCE.

You are either still misunderstanding or are willfully misrepresenting my point. You are talking as though there is some definite objective truth about whether two clocks are synchronized, and that I'm just saying that it's very hard to make it so they are synchronized at the beginning, that it can only happen by coincidence or something. But that's not it at all! What I'm saying is that the word "synchronized" itself has no objective frame-independent meaning, therefore it is impossible to have a situation where the clocks will be objectively synchronized at the beginning, not even by coincidence. If you just want the clocks to be synchronized in a non-objective way, relative to the coordinates of one particular frame, then it's very easy to come up with a procedure to ensure that!

If you are arguing in good faith and not willfully misrepresenting me, can you please address my analogy of the clocks "having the same x-coordinate at the beginning"? Specifically, please address these questions:

1. Do you agree that for any given pair of clocks at rest with respect to one another, we can find some coordinate system in which both clocks are at rest where the x-axis is oriented in such a way that both clocks have the same x-coordinate, and another coordinate system where both clocks are also at rest but with the x-axis at a different angle, such that the same two clocks have a different x-coordinate? Yes/No

2. If you agree with #1, then do you agree that means that it's impossible for two clocks to objectively have the same x-coordinate at the beginning, in a sense that doesn't depend on what coordinate system you use? That the very notion of "having the same x-coordinate at the beginning" can only make sense relative to a particular choice of coordinate system? Yes/No

I HAVE said which reference frame it refers to, BOTH.

Impossible. If the two clocks are moving inertially towards one another, and the clocks are synchronized at the beginning in one clock's rest frame, that automatically means they were not synchronized at the beginning in the other clock's rest frame.

OK, it's a case where we choose to use a coordinate system where the clocks are synchronized at the beginning. So nobody will now object to the question and will answer it?

Yes, in this case the question is perfectly sensible. If the two clocks are moving inertially towards each other, and they are initially synchronized relative to a particular choice of inertial coordinate system, then whichever clock has a higher velocity relative to that coordinate system will show a smaller time when the two clocks meet.

 

[Saw]

JesseM, what do you mean by "objective" and "objectively"? It seems to me you use the term as a pure synonim of "non-frame-dependent". If so, please confirm, I think it might help Loonwolf to understand the point.

 

[JesseM]

JesseM, what do you mean by "objective" and "objectively"? It seems to me you use the term as a pure synonim of "non-frame-dependent". If so, please confirm, I think it might help Loonwolf to understand the point.

Yes, that's basically all I mean, but if I just said "frame-independent" Loonwolf might get the idea that there was a real truth about the matter and that some frames were "wrong" while others were "right". I wanted to get across the idea that not only is simultaneity completely dependent on your choice of frame, but that there is also no physical basis for judging one frame's judgments about simultaneity to be more correct than any other's, since the laws of physics don't pick out a preferred frame.

 

[Saw]

Yes, that's basically all I mean, but if I just said "frame-independent" Loonwolf might get the idea that there was a real truth about the matter and that some frames were "wrong" while others were "right". I wanted to get across the idea that not only is simultaneity completely dependent on your choice of frame, but that there is also no physical basis for judging one frame's judgments about simultaneity to be more correct than any other's, since the laws of physics don't pick out a preferred frame.

Yes, you are saying that the two judgments about simultaneity are not only different (frame-dependent) but on equal footing = none is more correct. Agreed. I am not sure, though, that you should then say that none of them is objective, i.e. that what they share (equal footing) is their lack of objectivity. After all, each judgment is obtained through an objective measurement method: the Einstein convention for clock synchronization. In fact, some authors like to state the opposite, i.e. that the two judgments share (equal footing) their objectivity = they are not the result of a distorted perception due to the features of the observing subject.

In any case, whether you call them objective or not, what is important to highlight, in my opinion, is that simultaneity judgments are not final but "instrumental": they solve problems and they solve them in the same manner in all frames. So the mere fact that two observers disagree on simultaneity is not dramatic (it's not paradoxical); it would be problematic if that led to a disagreement on what happens and what does not, but such is not the case.