The End of Time: The Next Revolution in Physics

In those days, alpha particles were observed in devices called Wilson cloud chambers through their interaction with atoms, which they ionize by dislodging electrons, leaving the previously neutral atoms positively charged. The alpha particles invariably ionize atoms that lie more or less along a straight line emanating from the radioactive source. The excess positive charge of the ionized atoms stimulates vapour condensation around them, making the tracks visible. If we take Gamow’s theory literally, there is something deeply mysterious about these tracks. If there really is a blue probability mist spreading out spherically all round the radium atom, why are atoms not ionized at random all over the chamber, wherever the blue mist permeates? How come they are ionized only along one line?

Standard quantum mechanics gives two answers, one much cruder than the other. In the crude answer (which is nevertheless very interesting, so I shall take a few pages to discuss it), only the alpha particle is treated in quantum-mechanical terms: the atoms of the cloud chamber are treated as classical external measuring instruments. They are used to ‘measure the position’ of the alpha particle, this being done by the ionization of an atom at some position. In accordance with the standard rules, any position measurement yields a unique position, after which the wave function will be concentrated at that position. The rest of the wave function will be instantaneously destroyed.

Now, atoms actually have a finite diameter, of about 10^–8 centimetres. So the ionization of an atom is not a perfect position measurement, and this has important consequences for the alpha-particle tracks. It is helpful to think in terms of the blue mist. Before the measuring ionization happens, the blue mist is expanding outwards uniformly in all directions. When the first ionization occurs, it is as if a spherical shell has suddenly been placed round the atom. At one point on the shell there is a small hole through which the wave function can pass. This is the point at which the ionized atom is situated. It is only here that the wave function is not totally destroyed and can continue streaming on outwards. In fact, it does so in the form of a jet, which can be very narrow and accurately directed, especially if the alpha particle has a high energy.

At this point it is worth saying something about the diffraction of light. If monochromatic light (light of one wavelength) encounters an opaque screen with an opening, the result depends on its size. If the opening is large compared with the wavelength of the light, the screen cuts off all the light except at the opening and a more or less perfect ‘pencil’ of light – a beam – passes through. The width of the luminous pencil is equal to the width of the opening. However, if the opening is made smaller, diffraction comes into play and the beam of light spreads out, becoming very diffuse for a tiny opening. Diffraction effects are more pronounced for red light, with its longer wavelength, than violet light. Like light, alpha particles have an associated wavelength, which is very short for the ones produced in radioactive decay. Although ionization of the atom creates effectively a very small ‘opening’, the ‘jet of wave function’ that survives the wave-function collapse is narrow and concentrated in a cone with a very small opening angle (much less than a degree). The wave-function jet continues through the cloud chamber like a searchlight beam.

To simplify things, imagine that the cloud-chamber atoms are concentrated on uniformly spaced, spherical concentric shells surrounding the radium atom. The first ionization (quantum measurement and collapse) happens when the alpha particle’s spherical waves reach the first shell. On the second shell, the alpha particle can ionize atoms only where its wave function has non-vanishing value. The atoms that can be ionized are located in the small spot that is ‘lit up’ by the ‘beam’ and hence lie rather accurately on the line joining the radium atom to the ‘opening’ in the first shell. The spot still contains many hundreds or thousands of atoms, any one of which can now be ionized. A second position ‘measurement’ of the alpha particle is about to be made.

The quantum measurement laws now tell us that one and only one of the atoms will be ionized. It is selected by pure chance – it can be anywhere in the spot. Once again, the entire wave function that ‘bathes’ the other atoms is instantly destroyed, and a new narrow beam continues outward from the second ionized atom. The same process of ionization, collapse and ‘jet formation’ is repeated at each successive shell. For an alpha particle with sufficient energy, this may happen hundreds or even thousands of times. A track is formed. It has some important features.