of the universe would seem to be within our grasp. Could this result be accomplished, a momentous discovery would have been made, since all the laws of the physical world would be comprised in the expression
The application of the principle of action, expressed in the preceding formula, would enable us to derive all the laws of the physical universe. We should understand many things that are still mysterious; the elusive reason for the existence of two types of electricity in nature would be revealed, and the strange tendency of matter and energy to congregate into atoms and quanta would be explained. Unfortunately we are far from being able to determine the “function of action” of the universe, for there may be physical elements entering into its constitution whose nature we as yet ignore. (Furthermore, we might mention that the very validity of the principle of action is called into question by the quantum phenomena.) The following passage quoted from Weyl gives an idea of what is at stake:
“Whereas, in mechanics, however, a definite function
of action corresponds to every given mechanical system and has to be deduced from the constitution of the system, we are here concerned with a single system, the world. This is where the real problem of matter takes its beginning: we have to determine the ‘function of action,’ the world-function
, belonging to the world. For the present it leaves us in perplexity. If we choose an arbitrary
, we get a ‘possible’ world governed by this function of action, which will be perfectly intelligible to us—more so than the actual world—provided that our mathematical analysis does not fail us. We are, of course, then concerned in discovering the only existing world, the real world for us. Judging from what we know of physical laws, we may expect the