Time intervals measured by stationary and moving observers

[PeterDonis]

Thank you. Yes, I wrote $L' (v'^2)$ instead of $L'(v^2)$, right?

The switching was in defining $x = v^2$ and $a = v'^2$ instead of the other way around.

 

[Hak]

That's because they're not fine if you have already chosen the unprimed reference frame.

I still cannot understand this. I would be grateful if you could explain it again in a way that I can understand it. Thank you very much for your contribution.

 

[Hak]

Obviously not, because in post #21 you switched reference frames (you didn't realize that's what you were doing when you said $x = v^2$, $a = v'^2$, but it was).

I guess I didn't really understand. So you can change the frame of reference, but you can't reverse $x$ and $a$, right?

 

[PeterDonis]

I would be grateful if you could explain it again in a way that I can understand it.

I'm not sure what more I can say. When you define $x = v'^2$, $a = v^2$, you are choosing the unprimed frame. That's just a fact. There is no "explanation" for it. So if you say $x = v^2$, $a = v'^2$, that is inconsistent with choosing the unprimed frame. What more is there to say?

 

[PeterDonis]

So you can change the frame of reference, but you can't reverse $x$ and $a$, right?

Wrong. Reversing $x$ and $a$ is changing the frame of reference. But then you have to start the whole analysis over from the beginning. You can't just reverse them in one equation, that was obtained by a series of approximations that assumed you were using the unprimed frame.

 

[Hak]

When you define $x = v'^2$, $a = v^2$, you are choosing the unprimed frame. That's just a fact. There is no "explanation" for it. So if you say $x = v^2$, $a = v'^2$, that is inconsistent with choosing the unprimed frame. What more is there to say?

I did not understand what calculations I should have done to choose the primed frame of reference. Should I change all the calculations in the unfolding to do that? Thank you very much.

 

[PeterDonis]

I did not understand what calculations I should have done to choose the primed frame of reference. Should I change all the calculations in the unfolding to do that?

See post #40.

 

[Hak]

@PeterDonis Thank you so much for everything, I think I understand. You really gave me a great amount of help. Thank you again.

 

[PeterDonis]

@PeterDonis Thank you so much for everything, I think I understand. You really gave me a great amount of help. Thank you again.

You're welcome!