Dingle's Dilemma: Solve the Puzzle

[Doc Al]

Arrrrr, I missed that. They do tick at the same rate though, correct?

Sure.

Thanks. Luckily I don't think any of that changes the results I predicted though.

1. Any time after C passes A, C will see both A and B ticking slower while A and B will see C ticking slower.

Sounds good.

2. A collision will occur.

3. B and C will not agree on the time the collision occurred.

Sounds good. Assume that clocks A & B are a distance L apart (along the direction of motion) and are synchronized and that C passes A when both read t = 0. Then when C collides with B, B will read t = L/v and C will read $L/(\gamma v)$.

(If I misunderstood the scenario, please correct me.)

4. After collision C will have accumulated more proper time than B.

Not sure what you mean. Proper time between what two events?

 

[paw]

Sounds good. Assume that clocks A & B are a distance L apart (along the direction of motion) and are synchronized and that C passes A when both read t = 0. Then when C collides with B, B will read t = L/v and C will read $L/(\gamma v)$.

(If I misunderstood the scenario, please correct me.)

No, you didn't misunderstand. That's exactly how I saw the scenario.

Not sure what you mean. Proper time between what two events?

Between t=0, that is when C passed A, and when C collides with B. But I see you answered in the affirmative anyway in the previous quote.

 

[AntigenX]

the acceleration (or de-acceleration) requires collision. And without (or before) collision, there won't be any acceleration (or de-acceleration). In turn collision requires same spacetime coordinates, which as you correctly pointed out, can not happen without acceleration (or de-acceleration) within the domain of SR.

This is like running in circles...

Three inertial frames A, B and C...
...though there is no absolute time, they defined their own relative time by synchronization of their clocks, so at the time of synchronization, they were both at the origin of the time axis, yet having different spatial coordinates (x, y, z) and thus they did not collide. Similarly, if one of the observer is moving away from the other observer on time axis, even if their spatial coordinates coincide, they must not collide. This further clarifies why should their all four spacetime coordinates be same for a collision to occur. (this has also been pointed out in earlier posts)...

Is this correct? Do we require all four spacetime coordinates equal for a collision?

 

[Doc Al]

Do we require all four spacetime coordinates equal for a collision?

By definition, a collision means that two things are at the same place at the same time.

 

[AntigenX]

By definition, a collision means that two things are at the same place at the same time.

But if collision occurs, whose coordinates we should consider? For event collision, the coordinates of space will naturally be same for two frames colliding, but the time coordinates of both will be different, because one is moving and other is stationary. And if both are moving, then also their time coordinates will be different. This means that two things can never collide!

 

[Doc Al]

But if collision occurs, whose coordinates we should consider? For event collision, the coordinates of space will naturally be same for two frames colliding, but the time coordinates of both will be different, because one is moving and other is stationary. And if both are moving, then also their time coordinates will be different. This means that two things can never collide!

You can use anyone's coordinates.

For any two things to collide they must have the same spacetime coordinates at the time of collision, according to anyone's frame of reference. Of course, different observers will use different coordinates to represent the same event. So what?

 

[AntigenX]

I can't say I understand much of what you just wrote.

For any two things to collide they must have the same spacetime coordinates at the time of collision, according to anyone's frame of reference. Of course, different observers will use different coordinates to represent the same event. So what?

What I want to ask is, is it when a collision occur when all four coordinates of observer in one frame match those of an observer in another frame? Or is it that they may match their coordinates and they are different according to them, and even though the colision will occur?

 

[Doc Al]

When two things collide everyone will agree that they are at the same time and place. Of course, the particular spacetime coordinates depend on what frame you are measuring with respect to. Make sense?

 

[AntigenX]

When two things collide everyone will agree that they are at the same time and place. Of course, the particular spacetime coordinates depend on what frame you are measuring with respect to. Make sense?

Ok, I think the question is not "LOUD AND CLEAR", as it should be...

The question is, after the collision has happened, obviously, everybody will be sharing the same frame of reference and so will agree about the same time and same place, however, will observers of colliding frames agree upon the spacetime coordinates of the event "collision"?

Because, being in relative motion, even their clocks may have been synchronized earlier, they will be observing different time coordinates of the other frame, and will be unable to extrapolate their own spacetime coordinates leading to collision. Simply saying, they will not be able to predict the collision, which is bound to happen, by virtue of their different readings of the other frame of reference.

 

[Doc Al]

The question is, after the collision has happened, obviously, everybody will be sharing the same frame of reference and so will agree about the same time and same place, however, will observers of colliding frames agree upon the spacetime coordinates of the event "collision"?

(1) The fact that a collision happens has nothing to do with sharing the same frame of reference. The same collision can be viewed from any frame.
(2) What do you mean by "colliding frames"? I assume you mean a case where say person A (who measures things from his own frame, moving with him) is about to collide with person B (who has his own frame). Right?
(3) If two different frames view the same event (the collision) they will not necessarily agree upon the spacetime coordinates of the event.

Because, being in relative motion, even their clocks may have been synchronized earlier, they will be observing different time coordinates of the other frame, and will be unable to extrapolate their own spacetime coordinates leading to collision. Simply saying, they will not be able to predict the collision, which is bound to happen, by virtue of their different readings of the other frame of reference.

The different frames have nothing to do with each other. (Their clocks are not synchronized.) Assuming that observers in each frame have full knowledge of what's going on, they are equally capable of predicting a collision.

Using my example from (2) above: Person A and B are on a collision course with some relative speed. A sees B moving towards him; B sees A moving towards him. They both can predict the exact time and place that they will collide according to their respective distance and time measurements. (If A and B are both located at the origin of their frames, then they will agree that the collision takes place at location x = 0! )

 

[AntigenX]

(1) The fact that ... at location x = 0! )

I think you are right about everything.
Now one question, As there is no absolute time, as the OP has insistently said, does synchronizing clocks means that obsrevers are setting themselves (both) at origin of the time axis? and one more, can two clocks, moving with relative velocity be synchronized?

 

[Doc Al]

Now one question, As there is no absolute time, as the OP has insistently said, does synchronizing clocks means that obsrevers are setting themselves (both) at origin of the time axis?

Synchronizing clocks that are in the same frame (at rest with respect to each other) is certainly meaningful and doable. The "origin" of the time axis can be arbitrarily set to be when the clocks in a frame all read t = 0. (Of course, from another frame's perspective those clocks are not synchronized.)

and one more, can two clocks, moving with relative velocity be synchronized?

No. While you can arrange for two clocks moving with relative velocity to read the same at a given instant--for example, when they pass each other--that does not mean that they are synchronized.

 

[AntigenX]

No. While you can arrange for two clocks moving with relative velocity to read the same at a given instant--for example, when they pass each other--that does not mean that they are synchronized.

What does it mean to be synchronized? I mean, Synchronization means that "at the instance of synchronization the clocks should read t=0 (or any arbitrary but same value).", Then and then we will be able to calculate the time dilation in case of relative motion, no?

 

[Doc Al]

Clocks are synchronized if they always read the same time, not just at one instant.

 

[Antenna Guy]

What does it mean to be synchronized?

Sorry to interrupt, but I'd be interested in hearing if/how "proper time" might fit into this discussion.

Regards,

Bill

 

[AntigenX]

Clocks are synchronized if they always read the same time, not just at one instant.

That seems quite useless. If the synchronized clocks are always going to show the same time, why would we synchronize clocks? Let's say we do it so that, when later anyone of them is in motion, we can compare their time and deduce time dilation. In such a case, only the instance, when one of the two clocks is set moving is of importance, and no relevance is there of their history. In other words, while comparing their rates, and calculating the accumulated time by any clock, we will only be concerned with the last time when they both read same time. Does it make sense?

 

[DocZaius]

Here is a diagram I made of this scenario. I'd like a more experienced forum-goer to take a look at it and tell me if he/she agrees with it. If there is an error in it I'll take it down and/or will advertise what is wrong with it so that we might all come to a better understanding of this supposed dilemma.

 

[Doc Al]

That seems quite useless. If the synchronized clocks are always going to show the same time, why would we synchronize clocks? Let's say we do it so that, when later anyone of them is in motion, we can compare their time and deduce time dilation. In such a case, only the instance, when one of the two clocks is set moving is of importance, and no relevance is there of their history. In other words, while comparing their rates, and calculating the accumulated time by any clock, we will only be concerned with the last time when they both read same time. Does it make sense?

Sorry, I don't really know what point you are trying to make. If you'd like to continue this discussion, I suggest using a very specific example so that we don't go around in circles.

 

[Doc Al]

Here is a diagram I made of this scenario. I'd like a more experienced forum-goer to take a look at it and tell me if he/she agrees with it. If there is an error in it I'll take it down and/or will advertise what is wrong with it so that we might all come to a better understanding of this supposed dilemma.

Very good. I like it.

Perhaps AntigenX can use this specific example to make his point.

 

[AntigenX]

Sorry, I don't really know what point you are trying to make. If you'd like to continue this discussion, I suggest using a very specific example so that we don't go around in circles.

You are right.

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.

Very good. I like it.

Perhaps AntigenX can use this specific example to make his point.

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

 

[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 occurred.

 

[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.