All Is Not Well with Classical Mechanics
It was mentioned in the Prelude that as we keep expanding our domain of observations we must constantly check to see if the existing laws of physics continue to explain the new phenomena, and that, if they do not, we must try to find new laws that do.
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explain the new phenomena, and that, if they do not, we must try to find new laws that do. In this chapter you will get acquainted with experiments that betray the inadequacy of the classical scheme. The experiments to be described were never performed exactly as described here, but they contain the essential features of the actual experiments that were performed (in the first quarter of this century) with none of their inessential complications.
3.1. Particles and Waves in Classical Physics There exist in classical physics two distinct entities: particles and waves. We have studied the particles in some detail in the last chapter and may summarize their essential features as follows. Particles are localized bundles of energy and momentum. They are described at any instant by the state parameters q and q (or q and p ). These parameters evolve in time according to some equations of motion. Given the initial values q(ti) and q(td at time ti, the trajectory q(t) may be deduced for all future times from the equations of motion. A wave, in contrast. is a disturbance spread over space. Jt is described by a wave function tp(r, t) which characterizes the disturbance at the point r at time t. In the case of sound waves, tp is the excess air pressure above the normal, while in the case of electromagnetic waves, tp can be any component of the electric field vector E. The analogs of q and q for a wave are tp and 1jr at each point r, assuming tp obeys a second-order wave equation in time, such as
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CHAPTER 3
Figure 3.1. (a) When a wave w=e''c.-wn is incident on the screen with either slit S 1 or S, open, the intensity patterns ! 1 and / 2 • respectively, are measured by the row of detectors on A B. (b) With both slits open, the pattern I, , 2 is observed. Note that /1 ~ 2 /o/1 +I,. This is called interference.
which describes waves propagating at the speed of light, c. Given 1/'(r, 0) and lfr(r, 0) one can get the wave function 1/'(r, t) for all future times by solving the wave equation. Of special interest to us are waves that are periodic in space and time, called plane waves. In one dimension, the plane wave may be written as
ljl(x,t)=Aexpl< 2; x- 2; r)}=Aexp[i
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