The End of Time: The Next Revolution in Physics

Heisenberg’s scheme, or picture, is based on abstract algebra and is often regarded as giving a truer picture. In the form in which quantum theory currently exists, it is more flexible and general. Unfortunately, it is rooted in abstract algebra, making it very difficult to describe in intuitive terms. I shall therefore use the Schrödinger picture. Luckily, this will not detract from what I want to say. In fact, one of the main ideas I want to develop is that the Schrödinger picture is actually more fundamental than the Heisenberg picture, and is the only one that can be used to describe the universe quantum-mechanically. Many physicists will be sceptical about this, but perhaps this is because they study phenomena in an environment and do not consider how local physics might arise from the behaviour of the universe as a whole.

Schrödinger’s work developed out of yet another revolutionary idea, put forward by the Frenchman Louis de Broglie in 1924. It finally overthrew the dualistic picture of particles and fields that had crystallized at the end of the nineteenth century. Einstein had already shown that the electromagnetic field possessed not only wave but also particle attributes. De Broglie wondered whether, since light can behave both as wave and particle, might not electrons do the same? Together with its position, the most fundamental property of a particle of mass m and velocity v is its momentum, mv. De Broglie assumed that particles are invariably associated with waves with wavelength λ related by Planck’s constant to their momentum: λ = h/mv.

He applied this idea to Bohr’s model. At each energy level, the electron has a definite momentum and hence a wavelength. We can imagine moving round an orbit, watching the wave oscillations. In general, if we start from a wave crest, the wave will not have returned to a crest after one circuit. De Broglie showed that crest-to-crest matching, or resonance, would happen only for the orbits with quantized angular momentum that figured so prominently in the Bohr model.

Although he had not, strictly, made any new discovery, his proposal was suggestive. It restored a semblance of unity to the world – both electrons and the electromagnetic field exhibited wave and particle properties. De Broglie’s thesis was sent to Einstein, who was impressed and drew attention to its promise. Schrödinger got the hint, and, as they say, the rest is history. During the winter of 1925/6 and the following months he created wave mechanics. This will be the subject of the following chapters.

In 1927 de Broglie’s conjecture was brilliantly confirmed for electrons first in an experiment by the Englishman George Thomson, and then in a particularly famous experiment by the Americans Clinton Davisson and Lester Germer. These experiments paralleled those made about a decade and a half earlier by the German physicist Max von Laue, in which he had directed X-rays onto crystals and observed very characteristic diffraction patterns, from which the structure of the crystals could be deduced. The patterns were explained in terms of the interaction of waves with the regular lattice of the atoms forming the crystals. They demonstrated graphically the wave-like behaviour of the electromagnetic field (X-rays are, of course, electromagnetic waves, like light, but with much higher frequency and shorter wavelength). In the 1927 experiments, electrons were directed onto crystals, and diffraction patterns identical in nature to those produced by X-rays were seen. Thus, the particle nature of electrons was observed long before their wave nature was suspected. With light it was the other way round – wave interference was observed a century before Einstein suspected that light could have a particle aspect too.