Special Relativity We have seen that relativity requires a correction to the speed of an object as measured from a different inertial frame—specifically, this denominator: 1 – vv /c . Notice, however, that for small values of v or v , this corrective factor is virtually unity. Assume that we can ignore this factor until it falls to 0.99 so it will not affect the classical answer by more than one part in a hundred: 1 – vv /c ≤ 0.99 means that vv ≥ 0.01c . Taking the square root of the right side (a shortcut) tells us that we need not worry about the relativistic correction until the speed of either object exceeds a tenth of the speed of light. The fastest machine ever made by human beings (the Helios space probes launched by Germany) is slower than one-four-thousandth of the speed of light. Other than for subatomic particles in our accelerators, you can usually ignore the effects of relativity. It isn’t just speed that is affected by relativity: For objects and people traveling at very
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