# Moving Mechanical Clocks

*Most recent answer: 08/12/2013*

- Ramesh Srinivasan (age 53)

San Jose, CA, USA

The problem with that thought experiment is that you've assumed that the velocity of the projectile in the lab frame is just given by the overall clock velocity in the lab frame plus the projectile velocity in the clock frame. That assumption seems intuitively right, but it turns out to be false.

Why are we able to reason out what happens with light directly, but have to go through a bit more argument to figure out the strange behavior of the projectile? We don't have any simple universal laws describing projectile motion. We do have, however, Maxwell's equations describing light. These look like universal laws that we hope would work in all frames, and they say that light travels at a fixed speed. So we can try the assumption that they are indeed universal. It leads to all sorts of implications (special relativity) and these implications turn out to be true. Among the implications are the ones that tell us that the simple velocity addition rules don't quite work for the projectile.

Mike W.

*(published on 08/12/2013)*

## Follow-Up #1: relativity, clocks, and velocity

- Ramesh Srinivasan (age 53)

San Jose, CA, USA

The projectile speed will be just slightly different from what you'd get by simple velocity addition. With the new speed, you'll find that the clock rate for the projectile clock exactly matches that for the light-bounce clock. All clocks of any sort will continue to exactly match so long as they travel together. That's what the principle of relativity says. It turns out to be correct.

Mike W.

*(published on 08/13/2013)*

## Follow-Up #2: relativistic bouncing ball clock

- Ramesh Srinivasan (age 53)

San Jose

Certainly the projectile will not travel at c, in any frame. Say that in the clock frame it travels at speed s. In the lab frame, its velocity component along the direction between the plates, at right angles to the clock's velocity **v**, is s*sqrt(1-v^{2}/c^{2}). The distance between the two plates is the same in both frames, since the gap is at right angles to **v**. So the lab says the projectile clock is running slow by a factor of sqrt(1-v^{2}/c^{2}), the same as for the light clock.

Mike W.

*(published on 08/14/2013)*