The Special theory of Relativity
Combining concepts Einstein arrived at through his own "thought experiments" and those contributed by some of the greatest scientific minds of the 19th century, Einstein formulated two postulates:
- The speed of light has the same value in all inertial reference frames
- The laws of physics are identical in all inertial reference frames
While the second postulate is simply a restatement of the principle of relativity, the first postulate is dramatically different than what common sense dictates.
Experience tells us that a fast car can catch up to a slower car or that gravel that falls out of the back of a dump truck actually has a speed that equals the speed of the dump truck plus the speed of an approaching car as the gravel bounces on the pavement. The same is not true for light, however. The light emitted from the dump truck's tail light would be measured to travel at 300,000 kilometers per second regardless of whether the light was measured by someone riding in the truck, someone following the dump truck in a car traveling at 60 miles per hour, or by someone standing by the side of the road. Taken to an extreme, a spaceship traveling at half the speed of light (0.5c) could fire a laser weapon at an enemy spaceship, but the speed of the laser beam would be simply the speed of light and not the speed of light plus the speed of the pursuing spaceship. This would be true for all observers regardless of whether the observer was on the spaceship, being fired upon, or simply watching from a nearby space station. As stated before, the constancy of the speed of light was implied by Maxwell's equations and a number of experiments hinted that this was true, but the thought experiments described on this page and the previous pages point out the bizarre results of this simple fact.
Consequences of Einstein's Postulates
Let's now investigate some of the weirdness associated with special relativity by using the example of a Formula 1 car driven by Marianne at the fabled site of the Belgian Grand Prix—Spa-Francorchamps. The vital statistics of the car are given in the table below:
Length: 14.8 ft
Mass: 1,323 lbs*
Kemmel Straight: 214 mph
Time to 125 mph: 3.8 sec
*includes Marianne
As the car is zooming around the course, let's compare the results of measurements made by Marianne as she is driving the car and by Ginger as she watches the car go around the track:
Marianne's Frame of Reference
L: 14.8 ft
m: 1,323 lbs
Kemmel Straight: 214 mph
t to 125 mph: 3.77777777777751 sec
Ginger's Frame of Reference
L: 14.7777777777773 ft
m: 1,323.00000000000059 lbs
Kemmel Straight: 214 mph
t to 125 mph: 3.8 sec
Okay, it's not a big deal, but something is amiss. Marianne and Ginger cannot agree on the length of the car, its mass, or how long it takes the car to accelerate to 125 mph! The discrepancy is infinitesimally small, however, and hardly anything to worry about in everyday racing. Things get much stranger, though, if we consider the extreme case of a race car that can travel at a significant percentage of the speed of light.
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