2.4 Consequences of Falsification

When the scientific knowledge grows within a field, the theories of that field are sometimes affected. New insights are not always compatible with current theory. There are, in principle, three possible scenarios in such cases. The theory may be modified to explain more aspects of the world, it may be completely replaced, or, sometimes, it is not affected at all. We will continue to use the laws of planetary motion as examples to illustrate these scenarios.

Today, few physics undergraduates learn about Ptolemy's theory for planetary motion. This is because it has been proven wrong and has been successively replaced with better theories. Ptolemy lived in the second century of the Common Era (CE) and his theory was based on Aristotle's cosmology, stating that the earth was situated at the center of the universe with the sun and planets revolving around it. The planets moved in perfect circles with uniform motion, since nothing in heaven could deviate from perfection.

Readers who have studied the motions of the planets in the night sky may have noticed a curious effect called retrograde motion. Looking night after night at the planet Mars, for example, it seems to move westward relative to the backdrop of the stars. At some point it suddenly makes a halt and starts to move backwards. Later, the backwards motion ceases and the planet continues in the westward direction. This motion makes perfect sense in a heliocentric system, where the earth revolves with the other planets around the sun. From our point of view it looks as if Mars moves backwards, because the earth “overtakes” it in its inner orbit. In the Ptolemaic system this motion was, of course, more difficult to explain. Ptolemy attempted to do so by letting the planets move in smaller circular orbits, called epicycles. These, in turn, revolved in larger, circular orbits around the earth. This solved the problem at the cost of immense complexity. Instead of one circular orbit for each planet the Ptolemaic universe consisted of several dozens of cycles and epicycles rotating upon and about each other. There were equants, eccentrics, deferents, but still this system could only approximately match the observations. By the sixteenth century the calendar and the seasons diverged by weeks, and predictions of eclipses and conjunctions could miss their mark by a month [6]. In the hypothetico-deductive account of science the Ptolemaic system had been falsified since the observations did not match its predictions.

Copernicus realized that a heliocentric system was a more accurate model of the universe. He placed the planets and the earth in orbit around the sun and the moon in orbit around the earth, but held on to the assumption of circular orbits. His system was both more accurate and mathematically simpler than the Ptolemaic one, though it still made use of epicycles to better match astronomical observations. Although modern astronomers do not accept the details of the Copernican system, the heliocentric theory of the solar system has certainly replaced the geocentric one. This is an example of how a theory that fails to describe reality may eventually be replaced.

In the hypothetico-deductive approach, a falsified theory should be discarded and replaced with a new and better theory. The new theory should account for more phenomena than old theory did. Besides explaining the phenomena that falsified the old theory, it should also account for everything that the old theory explained. Then, how can it be that some theories survive falsification? Consider, for instance, Newton's laws of motion. At the beginning of the last century physicists found that these laws, which had been believed to be universal laws of motion, did not apply to the motion of the tiny constituents of atoms. On the scale of the very small, the established theories describing our everyday world broke down completely. This became the starting point of a new theory called quantum mechanics, developed to describe the microscopic world of atoms and elementary particles. Newton's theory had been falsified since it had been shown not to be as general as previously believed. An area had been found in which it did not apply, but should it be discarded?

Completely replacing an established theory is a formidable task. At the beginning of the twentieth century Newton's theory had been supported by a plethora of various observational tests for more than two centuries. It had predicted new phenomena and had even been used to predict the existence of the previously unknown planet Neptune. With such merits it would be preposterous to suggest that the theory was completely false. It had obviously been brought to its limit when it was confronted with the mysteries of the quantum world, but it still applied to the macroscopic world.

The new theory of quantum mechanics is indeed more falsifiable, since it includes Newton's mechanics as a special case, and this is an important aspect of the growth of science. But although quantum mechanics may be a more general theory, there is no doubt that Newtonian mechanics are still used extensively by scientists and engineers to solve problems on the macroscopic scale. It is an example of a theory that has been falsified without being replaced. It is still valid and useful but we are more conscious of its limitations.

As previously mentioned, there is another alternative to replacing a whole theory that is in trouble. A smaller modification might save it from being falsified. Newton's laws have previously been described as an improvement over Kepler's laws. These, in turn, were an improvement on Copernicus’ heliocentric theory. Johannes Kepler had access to the best astronomical data available before the invention of the telescope and struggled to find a mathematical representation that fitted with them. After years of calculations he overthrew the last two fundamental assumptions of the Aristotelian cosmology – that planets move in circles and that the motion is uniform. His system can be described as an addition to the heliocentric theory. The planets were ordered around the sun as in the Copernican system but they moved in elliptic orbits with the sun in one focus and they moved faster when they were closer to the sun. Since this addition removed the discrepancy between the data and the heliocentric theory, the theory was saved from falsification. Most readers will probably agree that his addition was a legitimate one but the following example illustrates that not all modifications of theories are.

A central assumption in Aristotle's cosmology was that nothing in the heavens could deviate from perfection. As a result, it was long believed that all celestial objects were perfect spheres. When Galileo Galilei pointed his telescope towards the moon in 1609 he was intrigued to find that it was far from a perfect sphere. It was scattered with mountains, some of which he estimated were more than 6000 meters high [7]. One of his Aristotelian adversaries agreed that it looked that way in the telescope but cunningly suggested that there was an invisible substance filling the valleys and covering the mountains in such a way that the moon was still a perfect sphere. When Galileo asked how this invisible substance could be detected, the answer was that it couldn’t. The only purpose of this additional theory was to save the original one. It was an ad hoc modification. The moon was still spherical, it just did not look that way. Any modification of a theory must of course be testable. It must also be testable independently of the theory that is saved from falsification. Galileo went right to the core of this problem in his brilliant response to his adversary. He agreed that there was an invisible and undetectable substance on the moon but instead of filling out the valleys he suggested that it was piled on top of the mountains, so that the surface was even less smooth than it appeared in his telescope [3].