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THE SPECIAL THEORY OF RELATIVITY
The following mathematical expressions summarize the basics of special relativity: l' = l * sqrt(1 - (v/c)^2) (length contraction) t' = t / sqrt(1 - (v/c)^2) (time dilation) m' = m / sqrt(1 - (v/c)^2) (mass increase) The quantity sqrt(1 - (v/c)^2), where v is the velocity of an object and c is the speed of light, is known as the Lorentz factor. (Sometimes the term refers to the reciprocal of that expression - be careful.) The Lorentz factor, named after the Nobel Prize-winning Dutch physicist who articulated it, is always less than or equal to one, and approaches zero as v increases. The variables l, l', t, t', m, and m' are confusing as well; so be sure to remember that if you are moving, distances grow shorter, time runs slower, and mass goes up - hence the terms "length contraction," "time dilation," and "mass increase." If you are moving, you will experience less time than a non-moving observer who's watching you. Also, if you are moving, you will see shorter distances than a non-moving observer looking at the same spot. And if you are moving, a non-moving observer will see your mass get larger. Remember that the speed of light is given by c = 2.997 * 10^8 m/sec. This is equivalent to 186,282 miles per second, or about 5.8 trillion miles per year. |