Moving Mechanical Clocks

I am enjoying reading the book written for non-scientists - The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory However, I wonder whether the thought experiment is flawed, and would appreciate your response. In summary, if you replace the photon light clock with a mechanical slingshot clock, the sliding clock should tick at the same rate as the stationary clock. Here is how we describe the modified thought experiment: Page 38: - Replace the light clock with a mechanical slingshot clock. - Replace the single photon of light a solid projectile that is shot by the slingshot. - "Ticks" on the slingshot may be thought of as occurring every time the projectile makes a round trip. Page 40: - The sliding clock's projectile travels FASTER than the stationary clock's by the added speed of the sliding clock (unlike the constant speed of light in the case of the light clock). - The moving slingshot clock therefore ticks at the at the SAME RATE (not slower) as the stationary clock. Please let me know if my conclusion for the thought experiment is correct, and if not, why not. Thank you for taking the time. I look forward to your response. (sorry I could not attach the actual book pages here)
- 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)

Mike, Thank you very much for your response. Are you saying that the constancy of the speed of light is also applicable to solid projectile? or something more nuanced? Can you please elaborate a bit? Thanks again.
- 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)

Mike, Thank you for you response. Please review my questions / comments below (in UPPER CASE so it is easier to see). The projectile speed will be just slightly different (LESS?) 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. (FOR TWO REASONS, THIS NEED NOT BE SO: 1. THE PROJECTILE SPEED IN THE STATIONARY CLOCK NEED NOT BE SET TO THE SPEED OF PHOTON; IN FACT IT WILL BE SET TO A MUCH LOWER SPEED, THIS IS PART OF THE EXPERIMENTAL SET UP AND SHOULD NOT INTERFERE WITH THE CONCLUSIONS; 2. MORE IMPORTANTLY, THE PROJECTILE SPEED IS NOT SUBJECT TO THE CONSTANCY PROPERTY THAT PHOTON IS SUBJECTED TO). 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.
- 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-v²/c²).  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-v²/c²), the same as for the light clock.

Mike W.

(published on 08/14/2013)