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:  S' system is moving "inside" stationary S system with velocity v 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 S' system versus Moving Clock (b) in S 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 S, time in Moving system S'

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 S and Moving system S'

Inside the Moving system S', 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"
[ note: for those who cannot view this page whole, see quicktime movie ]


source: PBS's NOVA Science - "Time Dilation Experiment, 1971"
[ note: for those who cannot view this page whole, see quicktime or flash movie ]

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.