Dingle's Dilemma: Solve the Puzzle

[Doc Al]

Let me try again.
I assert, the only purpose of synchronizing two clocks is to compare their rates when they are in relative motion. To compare rates, only two points on their time axis are required. Hence, If we make to read two clocks in relative motion the same arbitrary reading, the synchronization is achieved. (we have set both clocks to origin of time axis, let their space co-ordinates be different), now while comparing them, we only need their respective times at the instance of comparison.
The moral of (my ) story is, two clocks in relative motion can be synchronized, even when their space coordinates are different.

I really don't think you understand what it means for two clocks to be synchronized. At a minimum, those clocks must "tick" at the same rate. Since two clocks in relative motion tick at different rates, they cannot possibly be synchronized. (As I mentioned earlier, being synchronized does not simply mean that the two clocks once read the same time at a particular instant--it means that they continue to read the same time.)

Example is quite carefully made, but involves lots of details.

Details and precision are crucial when discussing relativity.

And I think I understand it as explained by the poster. May be I will put a more correct situation later, when I can think of it correctly.

I strongly recommend that you stick with this example. If you choose another example, be ready to provide the same level of detail.

 

[AntigenX]

I really don't think you understand what it means for two clocks to be synchronized. At a minimum, those clocks must "tick" at the same rate. Since two clocks in relative motion tick at different rates, they cannot possibly be synchronized. (As I mentioned earlier, being synchronized does not simply mean that the two clocks once read the same time at a particular instant--it means that they continue to read the same time.)

Well then let me clear my doubts about synchronization first. The questions are...
1. What is the purpose of synchronizing the clocks?
2. When can two clocks be synchronized? How?
3. Can two moving (wrt each other) clocks be synchronized, even if they are at same spatial coordinates at some instance, because their tick rates will be different due to their relative motion?

Details and precision are crucial when discussing relativity.

Certainly true, but it adds to the confusion for newcomers like me. No offense to details or precision at all.

I strongly recommend that you stick with this example. If you choose another example, be ready to provide the same level of detail.

Yes, I would, if at all I can understand synchronization.

 

[Dale]

The purpose of synchronizing clocks is to establish a time coordinate. Basically so that we can relate the time that two distant events occured.

 

[DocZaius]

I recommend you go through a special relativity textbook if you're truly interested in the subject. You'll know all about the reason for synchronizing clocks and how clocks moving relative to each other are not synchronized.

"Spacetime Physics" by Wheeler and Archibald is one I just bought and I am loving it.

 

[MeJennifer]

"Spacetime Physics" by Wheeler and Archibald is one I just bought and I am loving it.

You mean "Spacetime Physics" by Wheeler and Taylor. Archibald is Wheeler's second name.

 

[DocZaius]

You mean "Spacetime Physics" by Wheeler and Taylor. Archibald is Wheeler's second name.

Yes you're right

 

[AntigenX]

Yes, in fact I went through some texts on relativity, yet, sometimes texts can not resolve questions. A discussion can solve some problems easily, and can invoke better and detailed understanding. Unfortunately, I don't have anybody around who can possibly discuss relativity. I'll try to find the suggested book though.

I hope I haven't irritated you guys. But, basics are very important, their implementation and adaptation in any number of situations becomes easy then. I've gone through all the posts in this thread at least thrice, but am clueless about many things, and some of OP's comments have not been answered, so I thought I should start with basics.

 

[DocZaius]

Yes, in fact I went through some texts on relativity, yet, sometimes texts can not resolve questions. A discussion can solve some problems easily, and can invoke better and detailed understanding. Unfortunately, I don't have anybody around who can possibly discuss relativity. I'll try to find the suggested book though.

I hope I haven't irritated you guys. But, basics are very important, their implementation and adaptation in any number of situations becomes easy then. I've gone through all the posts in this thread at least thrice, but am clueless about many things, and some of OP's comments have not been answered, so I thought I should start with basics.

The way the textbook I am talking about approaches relativity is it first introduces the parable of the surveyors, then jumps directly into the invariance of spacetime intervals. In fact before the chapter's through, you are already calculating specific examples using the simple equation.

This approach was the best way for me to learn because it forced to think about what my answers would look like as I was calculating the problems, and it thus let me use my own mind to create the intuitiveness that is so necessary in this subject.

When the book got to the example of a "lattice of clocks" as a physical representation of a coordinate system, my experience with spacetime intervals was enough to let me fully appreciate why a gridwork of synchronized clocks was necessary to have a proper setting for measuring space and time distances between events.

I actually regard such an approach as the best way of introducing the "basics" as you say. In fact, because of the nature of SR, I think that your view of learning the conceptual basics to then be able to implement and adapt them to scenarios is actually the wrong way of learning SR. This is of course, just my opinion.

edit: The reason we seem to want to steer this conversation to specifics is because it seemed the discussion was going in circles. It is usually most beneficial for all parties involved in a discussion that is going in circles to come up with a specific problem and have one of them point to a calculation within it or a specific aspect of it and say "I disagree with this part, and here is why" or "how did you come up with this part"? I have personally had many breakthrough moments of understanding when talking about such specific things in my experience as student of all subjects.