e real earth, and then we know it is stable. Then we should take the larger cathe- dral and take a bigger earth. But then it is even worse, because the gravitation is increased still more Today, of course, we understand the fact that phenomena depend on the scale on the grounds that matter is atomic in nature, and certainly if we built an appara tus that was so small there were only five atoms in it, it would clearly be something we could not scale up and down arbitrarily. The scale of an individual atom is not at all arbitrary-it is quite definite. The fact that the laws of physics are not unchanged under a change of scale was discovered by Galileo. He realized that the strengths of materials were not in exactly the right proportion to their sizes, and he illustrated this property that we were just discussing, about the cathedral of matchsticks, by drawing two bones the bone of one dog, in the right proportion for holding up his weight, and the maginary bone of a"super dog"that would be, say, ten or a hundred times bigger-that bone was a big, solid thing with quite different proportions. We do not know whether he ever carried the argument quite to the conclusion that the laws of nature must have a definite scale, but he was so impressed with this dis motion, because he published them both in the same volume, called"On Two New Sciences Another example in which the laws are not symmetrical, that we know quite well, is this: a system in rotation at a uniform angular velocity does not give the same apparent laws as one that is not rotating. If we make an experiment and hen put everything in a space ship and have the space ship spinning in empty space, all alone at a constant angular velocity, the apparatus will not work the same way because, as we know, things inside the equipment will be thrown to the outside, and so on, by the centrifugal or coriolis forces, etc. In fact, we can tell that the earth is rotating by using a so-called Foucault pendulum, without looking outside Next we mention a very interesting symmetry which is obviously false, i.e. reversibility in time. The physical laws apparently cannot be reversible in time because, as we know, all obvious phenomena are irreversible on a large scale he moving finger writes, and having writ, moves on. So far as we can tell, irreversibility is due to the very large number of particles involved, and if we could see the individual molecules, we would not be able to discern whether the machinery was working forward or backwards. To make it more precise: we build a small apparatus in which we know what all the atoms are doing, in which we can watch them jiggling. Now we build another apparatus but which starts its motion in the final condition of the other one, with all the velocities precisely reversed It will then go through the same motions, but exactly in reverse. Putting it another way: if we take a motion picture, with sufficient detail, of all the inner works of a piece of material and shine it on a screen and run it backwards, no physicist will be able to say, That is against the laws of physics, that is doing something wrong! If we do not see all the details, of course the situation will be perfectly clear, If we see the egg splattering on the sidewalk and the shell cracking open, and so on then we will surely say, " That is irreversible, because if we run the moving picture backwards the egg will all collect together and the shell will go back together, and that is obviously ridiculous! But if we look at the individual atoms themselves the laws look completely reversible. This is, of course, a much harder discovery to have made, but apparently it is true that the fundamental physical laws, on a microscopic and fundamental level, are completely reversible in time 52-3 Symmetry and conservation laws The symmetries of the physical laws are very interesting at this level, but they turn out, in the end, to be even more interesting and exciting when we come to quantum mechanics. For a reason which we cannot make clear at the level of the present discussion-a fact that most physicists still find somewhat staggering, a most profound and beautiful thing, is that, in quantum mechanics, for each of the rules of symmetry there is a corresponding conservation law; there is a definite