Relativity Lite

82 | Relativity Lite magnetic moment vectors of the bar’s electrons are equally likely to be aligned toward the left as toward the right. Actually, the ball in the bowl would be equally content to roll in the forward and back- ward directions as left and right. If we were to start its motion at any point around the rim, nothing changes in its oscillatory motion since the bowl is rotationally symmetrical. Given a bit of friction, the ball will eventually come to rest at the lowest potential energy position, in the center. In the case of electrons, the point of zero magnetization corresponds to what we call the ground state or vacuum state. The potential energy curve for the bar magnet at high temperatures is likewise rotation- ally symmetrical; the magnetic moment vectors of the bar’s electrons could point in any direction. But as the temperature drops below 770° C, the potential energy curve for the bar magnet slumps to the left and the right of the central vacuum state, as in figure 6 of the present chapter. A ball rolling in this shape of a bowl would come to rest in the newly created trough at some point away from the central peak. It might be to the right or to the left or to the front or the back of the central peak, but it will be in a definite direction. There is no one who chooses this final position so we say that the rotational symmetry is “spontaneously broken,” replaced with a lesser symmetry called parity , in which the ball’s po- sition relative to the central peak in figure 6 will look the same to us if we see it reflected in a mirror lying in the same plane as this page. The magnetic moment vectors of the bar’s electrons will point to one position—for instance, to the right in figure 6.The bar magnet will, in this case, have its north magnetic pole to the right and its south magnetic pole to the left. 1 0 –1 0.5 0.0 –1 0 1 Figure 6. Below the 770° CCurie temperature, the potential energy curve for the bar magnet slumps to the left and the right of the central vacuum state that had been the low energy point of the high-temperature bowl shape. The resulting parity symmetry is less rich than the fully rotational symmetry we have at high temperatures.