Common Time: Explaining Einstein's Definition

[WilliamMGiraldo]

Hi.

Thanks for letting me ask this question. It is a stupid one.
I'm a newbie at relativity theory, and I'm reading On the electrodynamics of moving bodies, By Einstein, A. He associates time with space, and tells us that you can measure the "time" of an event if you are in the coordinates of the event with a wristwatch.

However, he says that:

¿Why does this defines a common time? ¿What is common time? ¿Is it that the two clocks display the same value?

This is the document in question: http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1905_relativity.pdf

 

[jbriggs444]

¿Why does this defines a common time? ¿What is common time? ¿Is it that the two clocks display the same value?

In context, this "common time" would be a definition of time that is common to (that is a time standard that is shared between and can be used for) both events near A and events near B. He is leading toward what we would describe as "coordinate time" and is suggesting a synchronization convention that can be used to allow times measured by clock A over here to be validly compared with times measured by clock B over there.

 

[Nugatory]

In this context "common" means "shared" or "agreed on". We can all agree that everything that happens in the vicinity of B when clearly clock B's hands point to noon happens at the same time, noon according to clock B; and likewise for clock A. But if we want to compare the times of events happening in the vicinity of A and events happening in the vicinity of B we need something more: we need to know whether clock A read noon at the same time as clock B. Einstein is describing exactly what it means to say that they do.

 

[sweet springs]

Hello
By transposition
[tex]t_B=\frac{t_A+t'_A}{2}[/tex]
Light starts A at 1:00
Light reflects back to A at 3:00
The time when light reaches B should be 2:00, the middle.
It seems reasonable to me.

 

[Orodruin]

On a side note, I strongly suggest against trying to learn relativity from the original papers. You will be missing more than 100 years' worth in didactical and pedagogical development with respect to relativity. Once you have learned the theory from modern sources, it will be of historical curiosity to go back and see how the original papers were written.

 

[WilliamMGiraldo]

Hi. Thanks to everybody for replying, I'm very excited to learn this topic.

On a side note, I strongly suggest against trying to learn relativity from the original papers. You will be missing more than 100 years' worth in didactical and pedagogical development with respect to relativity. Once you have learned the theory from modern sources, it will be of historical curiosity to go back and see how the original papers were written.

You are right, but I'm not only studying the theory; I'm also studying the man.

Hello
By transposition
[tex]t_B=\frac{t_A+t'_A}{2}[/tex]
Light starts A at 1:00
Light reflects back to A at 3:00
The time when light reaches B should be 2:00, the middle.
It seems reasonable to me.

Exactly! But, then, why not just say that at every moment, both clocks display the same value? That would satisfy [tex]t_B-t_A=t'_A-t_B[/tex] and would be a lot less confussing. So I feel I'm not understanding the ideas beneath.

In this context "common" means "shared" or "agreed on". We can all agree that everything that happens in the vicinity of B when clearly clock B's hands point to noon happens at the same time, noon according to clock B; and likewise for clock A. But if we want to compare the times of events happening in the vicinity of A and events happening in the vicinity of B we need something more: we need to know whether clock A read noon at the same time as clock B. Einstein is describing exactly what it means to say that they do.

Yeah, that's what he says. But then; is he just saying that the clocks must display the same value? Because he could have said just that [tex]t_B=t_A+\Delta t[/tex] where [tex]\Delta t[/tex] is the time it takes for the light to reach B from A.

 

[jbriggs444]

Exactly! But, then, why not just say that at every moment, both clocks display the same value? That would satisfy

tB−tA=t′A−tB​

What does it mean for two clocks to display the same value at the same moment? That is, what does "at the same moment" mean? How do you define it in terms of an experiment that can be performed?

Is there more than one procedure that could be used that would give different results? [hint: the answer is yes].

 

[WilliamMGiraldo]

What does it mean for two clocks to display the same value at the same moment? That is, what does "at the same moment" mean? How do you define it in terms of an experiment that can be performed?

Is there more than one procedure that could be used that would give different results? [hint: the answer is yes].

Let the A and B clocks be together; they resemble in all aspects each other, so you can tell that the hands of these two clocks are always at the same position with respect to each other. That is, if you put them in a bag, shake it, and randomly get any of them out of the bag, you can't tell if the one you chose is the one who belongs to A or B.

That said, and ignoring the relativistic effects of walking, you walk and put one of these clocks at A and the other at B. ¿Is this what Einstein is trying to say? ¿Why to involve light in the subject?

 

[sweet springs]

Hi.

Time Synchronize Officers who adjust their watches to a standard clock at the Central Office, travel around the country and adjust the clocks everywhere to his/her watch. Such a synchronization system works. Correct but boring as you say. The light procedures seem to be redundant.

However, when you proceed to section 3 of the paper, you will find it exciting to compare two synchronized systems that are moving each other and the relation [tex]t_B-t_A=t'_A-t_B[/tex] is quite beneficial to do that. Be patient.