Twin Paradox Animationdiagramming special relativity in anabsolute frame of reference
The animations below illustrate two basic possibilities for completing a round trip between two parties. They produce identical time differentials, demonstrating the impossibility of anyone determining their true motion status relative to the universe. i.e.  none of the parties involved can assume anything about their actual state of motion; thus they cannot know whether they are participating in scenario 1 or scenario 2. The blue circle in the diagram represents nothing but a point in space where a clock start/stop event occurs. For maximum clarity, the trips themselves involve just a light second or two in distance, and all parties make use of photon clocks which are a whopping 1/2 light second in width. The photon clocks tell the story of time contraction. The horizontal white lines represent the travelers. They each carry a photon clock. There are three clock start/stop events  A, B, and C. The fact that time differential is identical in both scenarios (twin paradox animation 1 and twin paradox animation 2) confirms that one cannot experimentally detect ones true motion status with respect to the universe. In the animations below, the space station is considered to be at rest with the cosmos. One can also make the analyses when assuming the station is in motion relative to the cosmos. The diagrams, and therefore the animations, become more complicated, but the results are identical. Scenario 1: In the twin paradox animation below, an astronaut and a space station occupant start their clocks as the astronaut passes by. A second, incoming, astronaut starts his clock as he passes by the first astronaut. The incoming astronaut and the space station occupant stop their clocks as the incoming astronaut passes by the space station. If the video has ended, and you want to replay it, click on the replay button at the lower left corner of the video box. Scenario 2: In the twins paradox animation below, an astronaut and a space station occupant start their clocks as the astronaut passes by. A second, also outbound, astronaut starts his clock as he passes by the space station. This second astronaut chases down the first astronaut. As the first astronaut is caught, both astronauts stop their clocks. The time contraction formula is easily obtained from the above diagrams. For instance, in the first diagram (animation), the clock at rest with the universe ticks off one cycle while the traveling clock ticks off .8 of a cycle. A simple application of the Pythagorean Theorem yields the following formula: t' = t * sqr rt of ( 1  V^2 ) where t' is the time recorded by the traveler, t is universal time (full clock rate, since at rest with the universe), and v is the speed of the traveler. Keep in mind that the traveler, moving at .6 light second per second of universal time, went a distance, in absolute terms, of .6 light second. A photon went the same distance in the station's clock as it did in the traveler's clock, namely, 1 light second. Thus, 0.8 = 1 * sqr rt of ( 1  0.6^2) = 1 * sqr rt of ( 1  0.36) = 1 * sqr rt of ( 0.64 ) = 0.8 (There is no need to use c (light speed) in the equation, since we are using units of light seconds. Light travels one light second in one second.) See the book Relativity Trail for more details, including an analysis of how all parties involved assess each other's clock speed and lengths in symmetrical fashion, as well as detailed derivations of length contraction, the Lorentz transformations and e = mc^2.
