Relativity Science Calculator - Stationary vs. Moving Clocks

Stationary vs. Moving Clocks

"Science is the belief in the ignorance of the experts" - Richard Feynman ( 1918 - 1988 )

§ Assume: system is moving "inside" stationary system with velocity and is carrying the following clock consisting of a light - flash source and a receiving photocell. One "clock tick" consists of a roundtrip light - flash and photocell reception:


stationary vs. moving clock.png
suggested source of diagram: Richard Feynman's " Lectures on Physics - Vol. I "

Employing simple algebra for the above Stationary Clock (a) in system versus Moving Clock (b) in   system, we get the following: 

Lorentz factor difference.png

dilated time.png

So as 

velocity increase.png.

What this all means is that as viewed from within Stationary system , time in Moving system

dilated time2.png

will appear to move more slowly - i.e., relative units of time become comparatively expanded - as relative velocity

velocity2.png

increases as between Stationary system and Moving system

Inside the Moving system , rest time 

rest time.png

however moves at a "normal rate".

In conclusion, any "moving clock" moving at a uniform velocity in an inertial ( non - accelerating ) frame of reference relative to a stationary observer's clock will therefore appear to run slower!

§ Time dilation:

This concept of relativistic time dilation in special relativity is also shown in this American Museum of Natural History - "A Matter of Time" movie as well as PBS's NOVA Science program of the 1971 time dilation experiment aboard a transatlantic British Airways flight:

source: American Museum of Natural History - "A Matter of Time"


source: PBS's NOVA Science - "Time Dilation Experiment, 1971"

Observed Facts: Flying eastward and then westward from the stationary U.S. Naval Observatory, General Relativity predicted a time loss of 40 ± 23 nonoseconds on the eastward bound and a time gain of 275 ± 21 nanoseconds for the westward trip; the actual eastward loss was 59 ± 10 nanoseconds going eastward but gained 273 ± 7 nanoseconds for the westward trip!!

§ Another derivation partially using both (c) above and referring back to "Albert A. Michelson & the Aether-Part II":

distance-velocity-time.png

another derivation.png

§ Please also refer back to "Albert A. Michelson & the Aether-Part II" as the mathematics is identical although the problem herein is subtly different.