Phase transitions

A most important field of investigation concerns what are known as phase transitions – the critical point where matter changes from solid to liquid or from liquid to vapour; or the change from nonmagnet to magnet; or from conductor to superconductor. All these processes are different, yet it has now been established beyond doubt that they are similar, so much so that the mathematics applied to one of these experiments can be applied to many others. This is a very clear example of a qualitative leap, as the following passage from James Gleick (1954-) shows:

Like so much of chaos itself, phase transitions involve a kind of macroscopic behaviour that seems hard to predict by looking at the microscopic details. When a solid is heated, its molecules vibrate with the added energy. They push outward against their bonds and force the substance to expand. The more heat, the more expansion. Yet at a certain temperature and pressure, the change becomes sudden and discontinuous. A rope has been stretching; now it breaks. Crystalline form dissolves, and the molecules slide away from one another. They obey fluid laws that could not have been inferred from any aspect of the solid. The average atomic energy has barely changed, but the material – now a liquid, or a magnet, or a superconductor – has entered a new realm.^[28]

Newton’s dynamics were quite sufficient to explain large-scale phenomena but broke down for systems of atomic dimensions. Indeed, classical mechanics are still valid for most operations that do not involve very high speeds or the processes that take place at the subatomic level. Quantum mechanics will be dealt with in detail in another section. It represented a qualitative leap in science. Its relation to classical mechanics is similar to that between higher and lower mathematics and that between dialectics and formal logic. It can explain facts which classical mechanics could not, such as radioactive transformation, the transformation of matter into energy. It gave rise to new branches of science – theoretical chemistry, capable of solving previously insoluble problems. The theory of metallic magnetism underwent a fundamental change, making possible brilliant discoveries in the flow of electricity through metals. A whole series of theoretical difficulties were eliminated, once the new standpoint was accepted. But for a long time it met with a stubborn resistance, precisely because its results clashed head-on with the traditional mode of thinking and the laws of formal logic.

Modern physics furnishes a wealth of examples of the laws of dialectics, starting with quantity and quality. Take, for instance, the relation between the different kinds of electromagnetic wave and their frequencies, that is, the speed with which they pulsate. The work of Scottish physicist James Clerk Maxwell (1831-79), which Engels was very interested in, showed that electromagnetic waves and light waves were of the same kind. Quantum mechanics later showed that the situation is much more complex and contradictory, but at lower frequencies, the wave theory holds good.

The properties of different waves are determined by the number of oscillations per second. The difference is in the frequency of the waves, the speed with which they pulsate, the number of vibrations per second. That is to say, quantitative changes give rise to different kinds of wave signals. Translated into colours, red light indicates light waves of low frequency. An increased rate of vibration turns the colour to orange-yellow, then to violet, then to the invisible ultraviolet and X-rays and finally to gamma rays. If we reverse the process, at the lower end, we go from infrared and heat rays to radio waves. Thus, the same phenomenon manifests itself differently, in accordance with a higher or lower frequency. Quantity changes into quality.

Source: RP Feynman, Lectures on Physics, chapter 2, p. 7, Table 2-1.

1. Gleick, J. Chaos, Making a New Science, p. 127.