Simple Nature - Light and Matter

k / Red and blue light travelat the same speed.l / Bright and dim light travelat the same speed.m / A nonsinusoidal wave.standing still in space, then the right sides of the Γ equations wouldbe zero, because there would be no change in the field over timeat a particular point. But the left sides are not zero, so this isimpossible. 13The velocity of the waves is a fixed number for a given wave pattern.Consider a typical sinusoidal wave of visible light, with a distanceof half a micrometer from one peak to the next peak. Supposethis wave pattern provides a valid solution to Maxwell’s equationswhen it is moving with a certain velocity. We then know, for instance,that there cannot be a valid solution to Maxwell’s equationsin which the same wave pattern moves with double that velocity.The time derivatives on the right sides of Maxwell’s equations forΓ E and Γ B would be twice as big, since an observer at a certainpoint in space would see the wave pattern sweeping past at twicethe rate. But the left sides would be the same, so the equationswouldn’t equate.The velocity is the same for all wave patterns. In other words,it isn’t 0.878c for one wave pattern, and 1.067c for some other pattern.This is surprising, since, for example, water waves with differentshapes do travel at different speeds. Similarly, even thoughwe speak of “the speed of sound,” sound waves do travel at slightlydifferent speeds depending on their pitch and loudness, although thedifferences are small unless you’re talking about cannon blasts or extremelyhigh frequency ultrasound. To see how Maxwell’s equationsgive a consistent velocity, consider figure k. Along the right andleft edges of the same Ampèrian surface, the more compressed wavepattern of blue light has twice as strong a field, so the circulationson the left sides of Maxwell’s equations are twice as large. 14 Tosatisfy Maxwell’s equations, the time derivatives of the fields mustalso be twice as large for the blue light. But this is true only if theblue light’s wave pattern is moving to the right at the same speed asthe red light’s: if the blue light pattern is sweeping over an observerwith a given velocity, then the time between peaks is half as much,like the clicking of the wheels on a train whose cars are half thelength. 15We can also check that bright and dim light, as shown in figurel, have the same velocity. If you haven’t yet learned much about13 A young Einstein worried about what would happen if you rode a motorcyclealongside a light wave, traveling at the speed of light. Would the light wave havea zero velocity in this frame of reference? The only solution lies in the theory ofrelativity, one of whose consequences is that a material object like a student ora motorcycle cannot move at the speed of light.14 Actually, this is only exactly true of the rectangular strip is made infinitesimallythin.15 You may know already that different colors of light have different speedswhen they pass through a material substance, such as the glass or water. Thisis not in contradiction with what I’m saying here, since this whole analysis is forlight in a vacuum.700 Chapter 11 Electromagnetism