Why do both clocks run slower in each reference frame?

[IntuitioN]

I am having great difficulty understanding this concept. For example, a new Planet X whizzes past the Earth at v very close to c. From the Earth frame of reference, clocks on Planet X is running slower. However, from Planet X's frame of reference, clocks on Earth appears to be running slower.

How does this work? It seems impossible that both clocks can run slower.

 

[ramollari]

This is the so-called Twin Paradox, and there have been many threads here in PF about it.

https://www.physicsforums.com/showthread.php?t=61640

https://www.physicsforums.com/showthread.php?t=49092

There exist a variety of explanations to this paradox, which don't seem to be completely satisfactory.

 

[HallsofIvy]

No body said both close were slower. Each clock looks like it is running slower to a person in the other frame of reference.

 

[Doc Al]

How does this work? It seems impossible that both clocks can run slower.

To begin understanding how each observer measures the other's clock clock as running slow, and why this entails neither physical impossibility nor contradiction, you need to see how several special relativistic effects interwork:

(1) moving clocks are measured to run slow
(2) moving metersticks (or anything with length) are measured to be shorter (along the direction of motion)
(3) moving clocks that are synchronized in their own frame are measured to be out of synch​

Each of these effects are completely symmetric. Observer A will say that Observer B's clocks run slow (as measured by A) and Observer B will say the same about A's clocks. Same for the other two effects. Effect #3, clock desynchronization, is the most subtle.

It is only by combining all three of these effects that things will make sense. I recommend consulting any of the many elementary books on special relativity available for a detailed explanation.

Another place to start is with a website that explains time dilation using the infamous "light clock": http://landau1.phys.virginia.edu/classes/109/lectures/srelwhat.html
That links to a short lecture that covers time dilation; the followup lecture explains clock synchronization and simultaneity; the third explains how it all fits together. Be sure to look at all three!

PS: I don't think IntuitioN had the twin paradox in mind when he asked his question. (That will just add confusion, at this point.)

 

[ramollari]

PS: I don't think IntuitioN had the twin paradox in mind when he asked his question. (That will just add confusion, at this point.)

I just wanted to inform the thread starter about the name of the paradox and that it is well known. Yes, probably he wanted a more basic introduction to time dilation and the twin paradox.

 

[Doc Al]

I just wanted to inform the thread starter about the name of the paradox and that it is well known. Yes, probably he wanted a more basic introduction to time dilation and the twin paradox.

I understand. My point is that the example given in the first post was not an example of the twin paradox. (As I'm sure you are well aware, the twin paradox involves an asymmetry; the passing of two planets is completely symmetric.)

 

[ramollari]

This is a paradox as well, isn't it? Each observer in a planet is in an inertial frame of reference, so their observations must be correct. An observer in a planet is measuring that the clocks in the other planet are moving slower, and the observer in the other planet is measuring that the clocks in the first planet are moving slower. And they are in frames of reference that are moving at constant velocity!