The Problem of the Continuum


By Steve Humphrey


This column is the first of three or four leading up to a discussion of the second great revolution in Physics in the 20th century, the development of Quantum Mechanics. Nothing has ever challenged our ordinary intuitions about the way the world works quite as much as what we discovered about the micro-world, the world of the teeny-tiny. But before we can delve into this amazing subject, I need to do some stage setting, explaining some of the history that led to the discoveries of the first quarter of the last century.

Rutherford’s Planetary Model.

It was known by the Greeks that matter has a variety of properties. Some objects are denser than others, some dissolve in water while others do not, substances come in a variety of colors and smells. An early attempt to explain these differences involved the hypothesis that matter consisted of various amounts of the five basic elements; Earth, Air, Fire, Water and Quintessence. Aristotle believed that matter was continuous, and infinitely divisible. But no clear account of how relative abundances of these elements could explain the diversity of material substances. It was left to the Atomists, in particular Leucippus and his disciple Democritus, in the fifth century BCE, to move forward. The Atomists held that matter could not be divided into smaller and smaller parts, indefinitely, but was composed of finitely large, though very small, basic building blocks, whose relations determined the gross properties of matter. These atoms come in a variety of shapes. Some are convex, some concave, some have hooks, and they float in the Void. When they come into contact, they form larger structures, depending upon how they fit together. These different structures are what account for the macroscopic properties of substances. This was a nice picture, but a little short on details. If atoms come in different shapes, then surely they have parts. Recognizing that atoms had parts and could be further divided led to modern chemistry. Some of the simpler elements were discovered. For example, it was shown that water consisted of a combination of two elements, hydrogen and oxygen. So, the research program became, how do atoms of the different elements combine to form material substances? And what binds different kinds of atoms together to form stable entities with distinct properties?

Plum Pudding Model.

Another puzzle that was being investigated during the 17th, 18th and 19th centuries was the nature of light. Light, or radiation, is a very familiar phenomenon. But what is it? How fast does it move? What is it made of? Why does a beam of light that goes through a prism break up into different colors? Why does a rainbow take its particular form? (A mnemonic for remembering the colors of a rainbow is Roy G Biv. Red, orange, yellow, green, blue, indigo, violet.) Experiments with prisms led Newton to the view that light consisted of a stream of corpuscles, little things distinguished by their energies, that are generated by a source, like the Sun, and travel at infinite speed in a straight line. Others, like Young and Fresnel, believed that light was a wave phenomenon. A crucial experiment was performed by shining a light on a solid disc and examining the shadow cast on a piece of paper. If light consisted of corpuscles, we would expect to see a clear and distinct edge to the shadow, but if it was made of waves, we should see some diffraction, a vagueness to the edge. Sure enough, interference patterns were seen, but the authority of Newton prevailed for many years, and the work of Young and Fresnel was forgotten for a time. (The distinction between wave and particle is particularly important in the development of Quantum theory, so keep it in mind. We will come back to it.) The next great step was taken by James Clerk Maxwell who, working on ideas first introduced by Michael Faraday, developed the theory of Electromagnetism, which unified the theories of electricity and magnetism and formalized the notion of a Field. His theory showed that light is an electromagnetic wave phenomenon, created by the propagation of an electric and magnetic field.

But back to the structure of matter. By the end of the 19th century, it was understood that atoms had an internal structure, consisting of both positively and negatively charged parts. In 1904, J. J. Thomson theorized that while an atom is electrically neutral, it consists of equal amounts of positive and negative charge, a sphere of positive charge with negatively charged electrons embedded in it, like “plums in a pudding”. A test of the Plum Pudding Model was conducted by Ernest Rutherford in the early 1900’s. He directed a beam of positively charged alpha particles at a very thin sheet of gold foil and marked where the alpha particles ended up. As expected, most went straight through the foil and into a detector. But some were deflected, and a few were deflected by a huge amount. This was surprising, compared to firing cannonballs at a piece of tissue paper and finding a few being deflected back toward the cannon. Rutherford proposed that the atom’s structure was mostly empty space with a heavy, positively charged nucleus at the center surrounded by lighter negatively charged electrons in orbit around the nucleus. This became known as Rutherford’s Planetary Model of the atom, which suggested that atomic structure was very similar to the structure of the Solar System. A pretty picture, indeed. But wrong.

Steve Humphrey has a Ph.D. in the history and philosophy of science, with a specialty in the philosophy of physics. Questions? Comments? Suggestions? Email him at Steve@thevoicelouisville.com