# Time dilation at an unchanging velocity

1. Oct 10, 2009

### ryuunoseika

Help me settle an arguement:

Say you have two clocks, one moving at 2/3 the speed of light (for explantory purposes called "A") and another at rest ("B"). Which clocks tics faster?

2. Oct 10, 2009

### Staff: Mentor

According to whom?

3. Oct 10, 2009

### ryuunoseika

According to an observer that percieves B as stationary.

4. Oct 10, 2009

### Staff: Mentor

According to that observer, clock B clicks faster.

5. Oct 10, 2009

### ryuunoseika

Thank you, i just won \$10.

6. Oct 10, 2009

### ryuunoseika

My friend still refuses to accept that he's wrong. I've been trying to explain it for two hours, maybe you can explain it to him better than i can.

He claims the clocks should be the same because they haven't accelerated or decelerated thus they're still in the same inertial reference frame. I've been trying to explain that that doesn't matter and that it's the second object's relative velocity that sets it off. I still don't see what he's trying to say.

7. Oct 10, 2009

### JesseM

What does he mean by "in the same inertial reference frame"? The two clocks have different inertial rest frames. Obviously you can use a single inertial frame to analyze both, but the same is true of accelerating clocks, a "frame" is just a coordinate system. If your friend is confused about this issue, you might show him this little hypothetical dialogue between a student (bold) and teacher from p. 43 of Taylor and Wheeler's Spacetime Physics:

8. Oct 10, 2009

### ryuunoseika

ok, i think i get where he's going wrong now...

he says that if two objects are moving at different speeds, but not accelerating relative to each other then they are experiencing the same time and that only when one accelerates or decelerates relative to the other does time dilation become a factor.

then he went off on some rant about the twin paradox and that, relative to the twin in the rocket ship, the one on earth is accelerating, thus the one in the rocket ship should be younger and the grounded should be younger.

he lost me again. i thinks he might just be stupid...

9. Oct 10, 2009

### DaveC426913

Cut him some slack. It is a very difficult subject to comprehend.

He has a point about the subjective viewpoint. At some point in his voyage (the outbound leg), the guy in the spaceship will see the guy and the clock on Earth moving slowly. So your friend is not entirely out to lunch.

The catch is that the guy in the spaceship must turn around. And to do this he will experience non-inertial acceleration. Which is what distinguishes him as the moving observer.

10. Oct 10, 2009

### JesseM

Well, this is the classic mistake that leads people to think it's a genuine paradox, but it's wrong--inertial frames have a special role in relativity, the standard time dilation equation only works in inertial frames. The guy an the rocket has to objectively accelerate to turn around and return to Earth, it's objective because he'll feel G-forces when he accelerates, whereas an inertial observer feels weightless (here we're talking about special relativity where gravity is neglected, think of inertial vs. accelerating observers in deep space). So, the guy on the rocket knows it was him that accelerated and not the Earth, and so if he understands relativity he'll know that any frame where he remains at rest throughout the journey must be a non-inertial one, and thus the time dilation equation cannot be used in this frame to calculate the aging of the twin on Earth.

For more on the twin paradox, here's a good page to show him: