Fear of Physics Read Free Page B

revolution):
    Every gear, every pulley, every nut, every bolt, is in exactly the same place! Nothing has shifted, nothing has “fallen,” nothing has evaporated. If the large flywheel were standing still at the beginning of the cycle, how can it be moving at the end?
    The problem with trying to perform an “engineering” analysis of the device is that if there are many components, it may be extremely difficult to determine exactly where and when the forces on any specific component cause the motion to cease. A “physics” analysis instead involves concentrating on the fundamentals and not the details. Put the whole thing in a black box, for example (a spherical one if you wish!), and consider only the simple requirement: If something, such as energy, is to be produced, it must come from inside; but if nothing changes inside, nothing can come out. If you try instead to keep track of everything, you can easily lose the forest for the trees.
    How do you know in advance what is essential from what you can safely throw out? Often you don’t. The only way to find out is to go ahead as best you can and see if the results make sense. In
the words of Richard Feynman, “Damn the torpedoes, full speed ahead!” a
     
     
    Consider, for example, trying to understand the structure of the sun. To produce the observed energy being emitted from the solar surface, the equivalent of a hundred billion hydrogen bombs must be exploding every second in its unfathomably hot, dense core! On the face of it, one could not imagine a more turbulent and complex environment. Luckily for the human species, the solar furnace has nevertheless been pretty consistent over the past few billion years, so it is reasonable to assume that things inside the sun are pretty much under control. The simplest alternative and, more important, perhaps the only one that lends itself even to the possibility of an analytical treatment, is to assume the inside of the sun is in “hydrostatic equilibrium.” This means that the nuclear reactions going on inside the sun heat it up until just enough pressure is created to hold up the outside, which otherwise would collapse inward due to gravity. If the outside of the sun were to begin to collapse inward, the pressure and temperature inside the sun would increase, causing the nuclear reactions to happen more quickly, which in turn would cause the pressure to increase still more and push the outside back out. Similarly, if the sun were to expand in size, the core would get cooler, the nuclear reactions would proceed more slowly, the pressure would drop, and the outside would fall in a little. So the sun keeps burning at the same rate over long time intervals. In this sense, the
sun works just like the piston in the engine of your car as you cruise along at a constant speed.
    Even this explanation would be too difficult to handle numerically if we didn’t make some further simplifications. First, we assume the sun is a sphere! Namely, we assume that the density of the sun changes in exactly the same way as we travel out from its center in any direction—we assume the density, pressure, and temperature are the same everywhere on the surface of any sphere inside the sun. Next, we assume that lots of other things that could dramatically complicate the dynamics of the sun, such as huge magnetic fields in its core, aren’t there.
    Unlike the assumption of hydrostatic equilibrium, these assumptions aren’t made primarily on physical grounds. After all, we know from observation that the sun rotates, and this causes observable spatial variations as one moves around the solar surface. Similarly, the existence of sunspots tells us that the conditions on the solar surface are variable—its period of activity varies regularly on an eleven-year cycle at the surface. We ignore these complications both because for the most part they are too difficult to deal with, at least initially, and because it is quite plausible that the amount of