Julian Barbour - The End of Time - The Next Revolution in Physics

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.

Although it was now clear that both light and electrons exhibited wave-particle duality, there were important differences between them. A brief description of the picture as it now appears will help. All particles are associated with fields, and can be described as excitations of those fields. To get some idea of what this means, we can liken the particles to water waves, which are excitations of undisturbed water. However, the analogy is only partial. The classic example of a particle associated with a wave is the photon, which is an excitation of the Maxwell field. Fields and associated particles of different kinds exist. There are fields described by a single number at each point, called scalar fields, and vector fields, which are described by three numbers. Scalar fields represent a simple intensity, while the vector fields – such as Maxwell’s field – are a kind of ‘directed’ intensity. In general relativity we also encountered tensors. Mathematically, scalar, vector and tensor fields belong to one family and obey the same kind of rule under rotations of the coordinate system. In particular, after one rotation they return to the values they had before. However, in 1927 yet another sensational quantum discovery was made, this one by Dirac. He found a quite different family of fields, called spinor fields , which are associated with electrons and protons (as well as many other particles). In their case, one rotation of the coordinate system brings them back to minus the value they had before, and two rotations are needed to restore their original value. Dirac found spinors by trying to make the newly discovered quantum principles compatible with relativity, and achieved a spectacular success even though it was subsequently found that his arguments were not totally compelling. However, the main point is that electrons are associated with a spinor field, photons with a vector field.

Both electrons and photons can, depending on the circumstances, exhibit wave or particle behaviour. Otherwise they behave very differently. Many photons can be present simultaneously in the same state (a state being a characteristic set of properties of particles, such as position and direction of motion), but for electrons this is impossible – there can be at most one in any given state. The two kinds of particle have different statistical behaviour, so-called Fermi-Dirac statistics for electrons and Bose-Einstein statistics for photons. In fact, there are now known to be many different particles, each with an associated field. They satisfy either Fermi-Dirac statistics, and are thus called fermions , or Bose-Einstein statistics, in which case they are called bosons . In addition, nearly all particles have an antiparticle. An antiparticle is identical to the original particle in some respects, but opposite to it in others; in particular, a particle and its antiparticle always have opposite charges.

In many ways, the story of fundamental physics during the last seventy years has been the discovery of particles and the understanding of the manner in which they interact. All particles that have so far been discovered – there is a whole ‘zoo’ of them – are either spinor or vector particles. Ironically, particles corresponding to the simplest scalar fields have not yet been discovered, though it is confidently believed that they will be soon, mainly on the grounds of indirect but rather persuasive theoretical arguments. Currently, an immense amount of work is being done in the attempt to unify the two broad categories of particles – fermions and bosons – by means of an idea called supersymmetry . In the last two or three years, there has been another great surge of excitement in the field of superstring theory. This combines the idea of supersymmetry with the idea that the complete ‘zoo’ of particles known at present are simply different manifestations of the vibrations of a string, much as a violin string can vibrate at its different harmonics. This is the dream of the theory of everything (TOE). Some readers may be familiar with these ideas, originally embodied in the acronym GUT – grand unified theory. This was the aim of physicists who wished to describe within a single, unified theoretical framework all the forces of nature except gravity (long recognized as especially difficult to include). More recent, and more ambitious since it aims to include gravity, is the quest for the big TOE.

I am not going to make any attempt to discuss this work, nor will I try to explain the connection between a particle and its associated field. If a theory of everything is found, it may well change the framework of physics. We may find ourselves in a quite new arena and have to change our ideas about space and time yet again. However, as of now I believe we can glimpse the outlines of an arena large enough to accommodate not only the present ‘zoo’ but also whatever entities some putative theory of everything will come up with. The arena I have in mind is vast and timeless. I see it not as a rival to the theory of everything, but as a general framework in which such a theory can be formulated.