Very simple relativity questions

JesseM

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.

DaleSpam

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

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?

DaleSpam

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

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.

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

JesseM

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
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.
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

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, 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.