How Hertz changed the world

We said in a previous post that when Maxwell’s equations made him think that there were waves related to electricity and magnetism, nobody had yet observed these waves. That would change some twenty-five years after the equations were discovered and, incidentally, those waves changed the world.

In 1878, Heinrich Hertz (1857-1894) had arrived in Berlin. In his early twenties, Hertz was a promising physics student with an excellent mathematical background. From 1884 he began to study Maxwell’s theory in depth, although, as he later admitted, he had great difficulty in understanding the Scotsman’s text. Despite this, he simplified Maxwell’s equations and reduced them to four – as opposed to the eight used by Maxwell – which also showed perfect symmetry between the electric and magnetic fields. According to Hertz, these equations contained everything that was certain in Maxwell’s theory, to the point of writing: “Maxwell’s theory is Maxwell’s equations”. So he proposed to take them not as something to be deduced from physical postulates, but as the starting point for the development of electromagnetism. Hertz’s work on Maxwell’s equations led the German physicist Arnold Sommerfeld to say: “the blindfold has fallen from my eyes”, and he was certainly not the only one who thought so.

However, Hertz’s greatest contribution to electromagnetism came in 1888. Hertz was then a professor in Karlsruhe and had decided to investigate the problem posed by the Berlin Academy for its 1879 prize. His experiments, however, were of far greater significance than anyone could have imagined. As William Berkson wrote in his book The Theories of Force Fields: “It is no exaggeration to say that Hertz’s experiments constituted one of the critical points, socially and intellectually, in the history of mankind. Socially, these experiments have made possible the development of mass communication by means of radio and television. Intellectually, the outcome of the experiments showed that the Newtonian world view, which had been in some ways the modern gospel, needed to be changed”.

Hertz’s experiments began in 1886 and culminated in 1888. They did not start well, because Hertz thought he had disproved Maxwell’s theory several times, until he realised the disturbances in his experiments caused by the huge iron cooker and the metal pillars in his laboratory. But they concluded impeccably: he managed to generate electromagnetic waves of various frequencies, from radio to microwaves; he managed to observe both those corresponding to the electric and magnetic fields, and found that they oscillated in perpendicular directions and were transmitted in the direction perpendicular to the direction of oscillation; he managed to prove that the waves reflected, diffracted, refracted, interfered and could be polarised just like light, which they became more and more similar to as their wavelength was reduced. He also measured the speed of propagation using standing waves and found it to be that of light.

Hertz died very young, aged 36, after a painful illness that began with severe toothache while he was conducting his crucial experiments on electromagnetic waves; within a year he had lost all his teeth, and the pain then spread to the rest of his face. After his death, Hertz received various honours. In Hamburg, his hometown, a street was named after him, and a bas-relief of his face was placed in the town hall. The portrait was removed by the Nazis – replaced again in 1949 – because although Hertz was a Lutheran, his father was a Jew.

Electromagnetic waves form a very broad spectrum, ranging from ELF waves, with wavelengths that can reach thousands of kilometres – thus carrying a tiny amount of energy – to gamma rays, with wavelengths as short as a trillionth of a millimetre – and carrying an enormous amount of energy – to radio waves – a few hundred metres for the medium wave and only a few metres for the modulated frequency. This range of possibilities is known as the electromagnetic spectrum. Electromagnetic radiation is produced when a charged particle changes its speed; the energy it carries comes from the particle, which loses energy with the radiation. Thus, a radio antenna is part of an electrical resonance circuit in which a charge is made to oscillate at a certain frequency; the wave generated can be received by an antenna connected to a similar circuit tuned to the same frequency. The waves thus produced have lengths of the order of centimetres or more; if one wants to decrease the order of length, or, in other words, increase the frequency, up to X-rays for example, another type of technology is needed, since the oscillation of the charges required already takes place at the molecular and atomic levels.

Of the entire electromagnetic spectrum, a tiny slit corresponds to the light we can see with our eyes, and is therefore called the visible spectrum: it ranges from the 75 nanometres of red light – a nanometre is one billionth of a metre – to the 40 nanometres of violet light, through the 60 nanometres of yellow or the 45 nanometres of blue. Our eyes, like the eyes of most animals, have been made by evolution to take advantage of the most abundant part of the sun’s electromagnetic radiation. Our skin – that is, our sense of touch – also detects, for example, ultraviolet radiation, but in what a painful way: these waves, more energetic than the visible ones, burn our skin. And we are still lucky that the atmosphere and the magnetic field neutralise the higher-frequency ones.

No one, until Maxwell’s equations revealed it, had ever imagined that there could be so much information in the form of waves swarming around – with the exception of astronomer William Herschel, who managed to detect the invisible-to-the-eye infrared radiation from the Sun in 1800. Thus we learned of the abundance and variety of electromagnetic waves, not because we saw or heard them, not through our senses, but illuminated by a mathematical construct. Mathematics are a kind of glasses that the human mind needs to see better: with them we were able to see all the richness and variety of electromagnetic waves, and what could be achieved with them: radio, television, mobile communications, exploration of the interior of the human body for medical diagnosis… The reasonable handling we have achieved of this type of waves – most of which are absolutely beyond the reach of our senses – owes almost everything to the theoretical physics of Maxwell, to the experimental physics of Hertz, and to engineering, but mathematics also has its share of responsibility in this collective success of science and technology.