Understanding Temporal Dilation: The Time Vs. Velocity Equation - Part 3
If the speed that the light travels does not change, then something else must change. That something is time. Time is not constant, as hard as that is to imagine. One second for Jenny is not the same as one second for Johnny. Since their perceptions of time are different, that explains the paradox. The faster that Johnny chases after the light, the more that his time slows down, making it impossible for him to catch the light. Johnny's one second is longer than Jenny's one second, so the light has time to catch up to where Johnny thinks it should be after one second.
In order to better understand this, a more realistic example is needed. Johnny's rocket has now become his new hot rod, and Jenny's flashlight is now a stopwatch. They stand on a mile long drag strip. On Jenny's signal Johnny goes zooming down the mile long stretch at 120 miles per hour. After precisely one mile Jenny stops the stopwatch. It reads exactly 30 seconds. Johnny, feeling suspicious about Jenny's measuring ability, had brought along his own watch and timed himself in his car, stopping it exactly at the one mile mark. His watch reads 29.99999999999952 seconds, a tiny bit less than Jenny's watch. They may just brush off the difference as either human or instrumentation error, but, in fact, both watches are correct. Time is not the same for everyone. A person who is moving experiences time more slowly than someone who is standing still. Two people who are moving in relation to each other, like Johnny and Jenny, will not agree on the elapsed time between two events.
The reason that this difference in time is not evident under ordinary conditions, is that we travel at too low of speeds for the effects of the special theory of relativity to have a large enough effect. Remember, the difference in Jenny's and Johnny's time was miniscule, only a tiny fraction of a second. Because the effect of relativity is not normally experienced, it is not intuitive. We do not see its consequences at low speeds, so it seems completely unfathomable to many. In order for there to be a significant affect, the person traveling must be going a large portion of the speed of light. Light travels so fast that it can go around the earth more than seven times every second. Naturally, with present technology it is impossible to achieve those kinds of speeds in everyday life. However, GPS satellites have to be constantly time adjusted as their orbital speed allows for an extremely minute but nonetheless significant discrepancy with the time flow on the surface of the planet.
To better make sense of this remarkable phenomenon, a more profound example is needed, one that in the physics world is known as the "twin paradox." Suzie and Sarah are identical twins. On their twentieth birthday, Sarah has to leave and spend twenty years on a spaceship for some unknown reason. Sarah boards the ship and zips around the galaxy at eighty-seven percent the speed of light, or 580 million miles per hour. Finally, when the twenty years are up, Sarah returns to earth to celebrate her fortieth birthday with her twin. Much to Sarah's surprise, Suzie is celebrating her sixtieth birthday when she returns. While 20 years have passed for Sarah, 40 years have gone by for Suzie. This is because at high speeds time actually slow downs. Einstein thought of space and time as being linked together in a new entity called space-time. Because Sarah, traveling 580 million miles per hour, was exerting so much of her energy in moving through space, little energy was left over to travel through time. Compared to a nearly stationary Suzie, Sarah was living her life in slow motion, at one-half the normal speed.