Physics Department, Trinity College Dublin.

WHAT IS QUANTUM THEORY ABOUT?

| Introduction | Energy Quantisation | The Uncertainty Principle | Particle-Wave Duality |
| Indeterminacy | Schrödinger's Cat |

Particle-Wave Duality

In 1900 Planck had suggested that atoms and molecules could only change their energy in discrete units. In 1905 Einstein went further and suggested that light itself could behave like little particles or quanta, with energy proportional to the frequency (the colour) of the light. These particles of light are what we now call photons. Einstein's suggestion went straight to the heart of Quantum Theory, and began to expose the fundamental conceptual difficulties associated with it. Indeed it was for this work that he was awarded the Nobel prize in 1921.

During the 19th century experimental and theoretical work on light had demonstrated - apparently conclusively - that light was a wave. The key experimental evidence for this is the observation of interference. If you drop a pebble into a still pond, you see circular wavelets spreading out. Drop another pebble in nearbye, and the two sets of waves will interfere where they overlap. Where the crest of one and the trough of another coincide, they cancel to leave the water undisturbed. At neighbouring places the cancellation is less perfect, and elsewhere the peaks or troughs of the two waves coincide and reinforce each other. Exactly this type of interference pattern can be observed with light, and it can only be explained by a wave theory.

If light behaves like little particles there is a difficulty in accounting for interference phenomena. But even worse, from the point of view of classical physics, streams of electrons, neutrons, and even atoms produce similar interference patterns. So particles show wave-like behaviour, and light, according to Einstein, shows particle-like behaviour. This is the famous problem of particle-wave duality.

The two-slit interference experiment

It is worth examining interference in more detail, and the simplest demonstartion of it is the two-slit interference experiment. Feynman said that this is
a phenomenon which has in it the heart of Quantum Mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by "explaining" how it works. We will just tell you how it works. In telling you how it works we will have told you about the basic peculiarities of all quantum mechanics.

Here a source of light shines on a screen in which have been cut two vertical slits, A and B. Light which passes through the slits is detected on a distant screen. We might expect the illumination on the detector screen to consist of two paler patches where light from only one slit falls, and a brighter panel in the centre (in the region between a and b in the diagram) where the two beams overlap:
In fact we see a pattern of light and dark vertical stripes in the central region. This is the 2-slit interference pattern:

The interference pattern is easily understood if we think of waves from the two slits reaching the same point on the detector and interfering. But it would not be expected for streams of particles. Each particle would go through one slit or the other, and we should expect an increased number of particles to arrive in the central area of the detector. But the detection of one particle cannot be cancelled out by the arrival of another. So the minima - the dark stripes - of the pattern cannot be explained in terms of particles.

Even worse, if we reduced the intensity of the source sufficiently we can arrive at a situation where only one particle at a time arrives on the detector. In this situation what we see on the detector is surprising: Each particle that arrives produces a spot on the screen. So the detector sees the arriving light as individual particles. When only a few particles have arrived it looks as though the pattern of arrival points is random, but eventually, when enough points have been collected, we see that the interference pattern appears. It is made up of a very large number of separate spots, each marking the arrival of a particle.

Since the pattern can be built up with particles going through the apparatus one at a time, the path of each individual particle must be constrained so that it avoids arriving at an interference minimum. If we close slit B, to try and establish which regions of the pattern are due to particles going through slit A, the pattern vanishes and particles begin to arrive at minima - points which they would be unable to reach if both slits were open. It seems that in some way the path of a particle passing through one slit - A say - is affected by whether or not the other slit - which it DOESN'T pass through - is open or not!

To explain the two-slit experiment we need a wave to be associated with each particle. This wave determines the interference pattern, and constrains the path of the particle so that it doesn't arrive at interference minima. The intensity of this quantum mechanical wave over a region on the detector determines the probability that the particle will arrive there - this should be zero at the minima.

There are good applets showing the two-slit interference experiment on the Physics 2000 web site . Select 'Applet Thumbnails' and then 'The Atomic Lab'. Choose:
  • 'Classic Two-Slit Exp.' for the classically expected interference pattern,
  • 'Electron Interference' to see the pattern build up from individual arrival points.

Uncertainty Looking at 2-slit interference in terms of particles introduces
indeterminacy .....