Small, Smaller, Smallest – How the Components of Matter Were Found

Abstract

Alhough we are not always aware of it, our experience makes us classify all phenomena into two categories, discrete and continuous. Those which are not discrete must be continuous. Being discrete means being countable, and undoubtedly we see around us a world of objects which we could begin to count. Besides this discrete world, we also experience a continuous world, for the flow of time, the motion through space and the changes of temperature or daylight are perceived as continuous processes without any granularity. In mathematics, the discrete world is captured by the natural numbers which are used for counting, while the continuous world is captured by the real numbers which are used for measuring. While philosophers never questioned the existence of the discrete world of countable objects, there were philosophers, even at the time of Socrates, who speculated that the continuous world does not really exist, but is only a mental construction as a consequence of the restricted resolution of human perception. In Chapter 7 on mechanics, I mentioned the Greek philosopher Protagoras (490-411 BC) who said, “Man is the measure of all things.” In today’s language of science, this means that the restricted resolution of our sense organs determines our world view. But in spite of that, we are able to talk and write about magnitudes which are far beyond our capability of perception. We just express extremely great or small numbers by using powers of ten as shown in Fig. 10.1. Nobody can really imagine how short a picosecond is, but of course we can define it as the millionth part of the millionth part of a second. Using these powers of ten, we can enter into the world of extremely long distances and time durations which become relevant when considering the universe. But we can also enter into the world of extremely short distances and time durations which are typical in the areas of electronics and nuclear processes. This is the world which we shall now consider.