In Search of Divine Reality: Science as a Source of Inspiration

Appendix 6. Some Properties of Waves and Particles

Appendix 6 SOME PROPERTIES OF WAVES AND PARTICLES waves Waves are characterized by phenomena that only waves can produce, because waves can add in a characteristic way. When two waves coming from different sources and directions meet at the same spot in space, they become components of a single wave whose amplitude (the height of a crest) is either larger or smaller than the amplitudes of the components, depending on whether a crest of one wave adds to the crest or a trough of the other. Wave addition of this kind is called the interference of waves. It is a characteristic aspect of wave interference that two waves which at one time interpenetrate, interfere, and superpose into a single wave, can reemerge as individual waves unharmed at a later time, resuming their individuality as though nothing had happened and continuing along the original line of propagation. There is a principle called Huygens’ principle after its discoverer , the Dutch physicist Christiaan Huygens. It states that every point in a wave can be considered the source of elementary wavelets that spread out equally in all directions. In a train of waves that propagates in space, the individual wavelets are not seen because they interfere, superimpose , and merge. But when a wave train strikes a barrier with a hole, a single wavelet can be seen to emerge behind it. Since it spreads out equally in all directions, waves bend around the edges of objects that obstruct their paths. This phenomenon is called diffraction.  1SCHÄFER_PAGES:SCHÄFER PAGES 4/29/10 11:14 AM Page 152 FIGURE  The Generation of a Diffraction Pattern by Two Slits: When a barrier with a single slit is struck by a wave train (left side of the Figure) it becomes the source of elementary wavelets which spread out in all directions behind the barrier. Here a planar wave train— one whose wave front is a plane—is shown striking a single slit S0. When the wavelets emanating at S0 strike a second barrier, but with two slits in it, S1 and S2, each of the latter becomes a new point source of elementary wavelets which spread out as shown. In this process wavelets sent out from S1 will interfere with those sent out from S2, constructively in some places— where hills of one get to lie on top of hills of the other. If the waves used in the experiment are lightwaves, bright regions— constructive interference—will be seen on the screen to alternate with dark regions—destructive interference. The pattern of fringes of alternating bright and dark regions is a diffraction pattern. FIGURE  A typical interference pattern obtained by the diffraction of lightwaves by a system of slits. The intensity distribution in the pattern is a function of the number of slits.  1SCHÄFER_PAGES:SCHÄFER PAGES 4/29/10 11:14 AM Page 153 YOUNG’S DOUBLE-SLIT EXPERIMENT At the beginning of the nineteenth century, Thomas Young performed diffraction experiments with light, allowing lightwaves to diffract and interfere after they passed an array of slits. For example, when a light beam encounters a barrier with two slits, each of them becomes the source of elementary wavelets which can be seen to emerge behind the screen, superimposing and interfering. Along certain lines from the center of the slits, the waves are exactly in phase (crests are on top of crests, troughs on top of troughs) and reinforce . Along other lines they cancel because they are out of step in such a way that crests of waves from one slit coincide with troughs of waves coming from the other. In the first case, constructive interference enhances brightness. In the second case, destructive interference leads to darkness. Therefore, on a screen behind the two slits a diffraction pattern is observed, a pattern of fringes in which regions of darkness alternate with brightness. From the way this pattern is engendered it is clear that its intensity distribution— that is, the variation of darkness and brightness—is the result of the interference of waves that originate in both slits, not just in one of them. Specifically, if the number of slits is changed, a different number of wavelets will interfere, and the diffraction pattern is changed. The example shows how waves are extended in space, not localized. Waves are characterized by their wavelength (the distance between the two...