Introductory remarks

What distinguishes modem physics from classical physics is the recognition of the role of fundamental (or universal) constants. Mathematical physics must be formulated so as to admit such constants; that is what distinguishes it from other applied mathematics. It is the particular values actually possessed by the constants that make our Universe what it is. Some analysis of this whole situation is the theme of this Discussion. We contemplate essentially dimensionless constants, or, equivalently, constants expressed in natural units which exist because the constants exist. Naturally, however, values expressed in ' practical ' units are an indispensable convenience. The domain is one in which observation and theory are inseparable. For instance, had general relativity come without newtonian theory having been thought of, we should not have heard of the gravitational constant G . In this Discussion we learn about observations designed to test whether G varies with time. Now exactly the same observational procedures could be performed by astronomers who had never heard of G . They would express the purpose of the observations in other language. But this language would depend again on whether they had heard of cosmic time or not. Actually, however, in practice a different theoretical approach would probably have led to somewhat differently designed observations. Anyhow, the contemplation of such an example serves to illustrate how theory and observation interact. At any point in our deliberation, it therefore seems inevitable that we should speak in terms of some definite theoretical model of the world of experience. There appears, however, to be no meaning in supposing there to exist a unique final model that we are trying to discover. We construct a model, we do not discover it.