The Uncertainty Principle If the entire universe consists of waves when viewed on the smallest scales, what is a particle? A particle is a wave packet. Consider the graph shown below where two sine waves of slightly different frequency are superposed, creating a periodic variation in amplitude. What is most remarkable about this simple combination is that, if the waves are set in motion, frequencies and wavelengths can be selected that will make the bulges move at a different speed than the advancing waves that compose them. They can even go in opposite directions. If a larger number of sine waves are superposed, it is even possible to select a set of parameters such that the combination has a significant amplitude at essentially one location only. The form below was created by taking the sum of the first ten cosine waves of the form y = cos(Nx)where Nis a positive integer. If more waves were summed, the isolation of the pulse at the center would become more and more perfect. If the wave
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