Heuristic Value?
Section Fourteen
What is the point of this short Section? Einstein seems to be saying two different things: First, (1) he points out the mathematical property, called the covariance with respect to Lorentz transformatins. Once we obtain the Lorentz transformation, one of the essential properties the special theory of relativity attained can be expressed as: every general law of nature has the same form, either in K or in K'; in other words, the law is covariant under the Lorentz transformation.
Second, Einstein wishes to say that (2) physics should aim at a theory which captures the most general law of nature; we want a law of nature which holds not only in an inertial system but also in any system. This is an expression of Einstein's ideal for doing physics, and hence this may be called a norm for physics. And Einstein seems to want to say that the special relativity is valuable because it suggested this norm, thereby showing the direction into which we should go, in order to obtain a better theory. In fact, Einstein soon began a new effort for incorporating gravity into his theory of relativity, and he pursued this line of quest for general covariance (not limited to the Lorentz transformation).
However, we will later see that we have to distinguish a mathematical property such as covariance, from a physical requirement such as the principle of (special) relativity. The former is essentially concerned with formulations of a physical theory, whereas the latter is concerned with the physical content of such a theory. Many physicists and philosophers of science were misled by Einstein's words.
Last modified, April 30, 2002. (c) Soshichi Uchii
suchii@bun.kyoto-u.ac.jp