connection between the laws of conservation and the symmetries of physical laws We can only state this at present, without any attempt at explanation The fact, for aple, that the lav when we add the principles of quantum mechanics, turns out to mean that mo- mentum is conserved That the laws are symmetrical under translation in time means, in quantum mechanics, that energy is conserved Invariance under rotation through a fixed angle in space corresponds to the conservation of angular momentum. These connections are very interesting and beautiful things, among the most beautiful and profound things in physics. Incidentally, there are a number of symmetries which appear in quantum mechanics which have no classical analog, which have no method of description in classical physics. One of these is as follows: If y is the amplitude for some process or other, we know that the absolute square of y is the probability that the process will occur. Now if someone else were to make his calculations, not with this 4, but with a y which differs merely by a change in phase (let a be some constant, and multiply e times the old y), the absolute square of y, which is the probability of he event, is then equal to the absolute square of y W2=W2 (521) Therefore the physical laws are unchanged if the phase of the wave function is shifted by an arbitrary constant, That is another symmetry. Physical laws must be of such a nature that a shift in the quantum-mechanical phase makes no differ- ence. As we have just mentioned, in quantum mechanics there is a conservation law for every symmetry. The conservation law which is connected with the quar um-mechanical phase seems to be the conservation of electrical charge. This is altogether a very interesting business 524 Mirror reflections Now the next question, which is going to concern us for most of the rest of his chapter, is the question of symmetry under reflection in space. The problem is this: Are the physical laws symmetrical under reflection We may put it this way: Suppose we build a piece of equipment, let us say a clock, with lots of wheels and hands and numbers; it ticks, it works, and it has things wound up inside We look at the clock in the mirror. How it looks in the mirror is not the question But let us actually build another clock which is exactly the same as the first clock looks in the mirror-every time there is a screw with a right-hand thread in one we use a screw with a left-hand thread in the corresponding place of the other where one is marked“2” on the face, we mark a“s” on the face of the other; each coiled spring is twisted one way in one clock and the other way in the mir image clock; when we are all finished, we have two clocks, both physical, which bear to each other the relation of an object and its mirror image, although they are both actual, material objects, we emphasize. Now the question is: If the two clocks are started in the same condition, the springs wound to corresponding tight- nesses, will the two clocks tick and go around forever after, as exact mirror images? (This is a physical question, not a philosophical question. Our intuition about the laws of physics would suggest that they would We would suspect that, at least in the case of these clocks, reflection in space is one of the symmetries of physical laws, that if we change everything from"right' to"left"and leave it otherwise erence, Let example, impossible to define a particular absolute velocity by a physical phe- nomenon. So it should be impossible, by any physical phenomenon, to define bsolutely what by‘ right” as opposed to"left may call "geography, "surely"right"can be desal.Forexample,using what Of course the world does not have to be symmetri d. For instance, we stand