The special theory of relativity is the result of two postulates:
This java applet invites you to the world of space and time in special relativity.
There are two devices that utilize photons to measure time differences (some kind of clock).
First, press Start button to begin the animation. Both devices are synchronized.
Now, change the relative velocity from the selections ( 0.6c or 0.8c ) ,
You can change your frame of reference by moving your mouse button,
The width of the moving device becomes smaller, ( From the marks, figure out the shinking factor! )
and the photons are not synchronized.
Light from the two devices is initiated when the sources touch each other.
Two light cones (in yellow) from two ends will reach the center of the device
So those two events are simultaneous in your frame.
So, those two events are not simulataneous in the moving frame.
Try to change your frame of reference by moving your mouse
The period of the clock in your frame is 1.0 s.
The number T at the left shows the period
for the photon's motion measured in your rest frame.
The period of the moving frame large than 1.0s , so the moving clock runs slower.
An observer at rest with the clock sees the pulse moving up and down with speed c.
The picture is very different when viewed from the other frame.
the pulse travels a distance given by ( c t' ). ( red path in the following figure)
In your frame, the pulse travels a longer diagonal path (white path ).
The speed of light is the same to all observers in inertial frames.
The pulse seen by you must take a longer time t,
It follows from the Pythagorean Theorem that
( c t )2 = ( v t )2 + ( c t' )2
t'2 = t2 ( c2 - v2 )/c2
t = ( 1 - (v/c)2 )-1/2 t' = t'
seen by the inside observer with respect to whom the clock is stationary.
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Author: Fu-Kwun Hwang, Dept. of physics, National Taiwan Normal UniversityLast modified : More physics related java applets
Thank you Prof. Fred Trexler , for your suggestions to this web page.
Fred Trexler Professor of Physics , Spring Arbor College, MI U.S.A.