Farewell to Reality (6 page)

This is a particularly pleasant metaphor for photons, the elementary particles that constitute all electromagnetic radiation, including light. However, on a bright morning there are rather more than a million of them streaming through the window. And photons are no ordinary particles. For one thing, they have no mass. They have
spin —
an intrinsic angular momentum — which we perceive as polarisation. They also have something called
phase,
which means that they are particles that can also behave like waves.

Let's look at them a bit more closely.

Einstein's light quantum hypothesis

In fact, photons were the first ‘quantum particles', suggested by Einstein in a paper he published in 1905. At that time, light was thought to consist of a series of wave disturbances, with peaks and troughs moving much like the ripples that spread out on the surface of a pond where a stone has been thrown.

The evidence for wave behaviour was very compelling. Light can be diffracted. When forced to squeeze through a narrow aperture or slit in a metal plate, it spreads out (diffracts) in much the same way that ocean waves will spread if forced through a narrow gap in a harbour wall. This is behaviour that's hard to explain if light is presumed to be composed of particles obeying Newton's laws of motion and moving in straight lines.

Light also exhibits interference. Shine light on two narrow apertures or slits side by side and it will diffract through both. The wave spreading out beyond each aperture acts as though it comes from a ‘secondary' source of light, and the two sets of waves run into each other. Where the peak of one wave meets the peak of the other, the result is constructive interference — the waves mutually reinforce to produce a bigger peak. Where trough meets trough the result is a deeper trough. But where peak meets trough the result is destructive interference: the waves cancel each other out.

The result is a pattern of alternating brightness and darkness called
interference fringes,
which can be observed using photographic film. The bright bands are produced by constructive interference and the dark bands by destructive interference. This is called two-slit interference.

The wave model of light was given a compelling theoretical foundation in a series of papers published in the 1860s by Scottish physicist James Clerk Maxwell. He devised an elaborate model which combined the forces of electricity and magnetism into a single theory of electromagnetism. Maxwell's theory consists of a complex set of interconnecting differential equations, but can be greatly simplified for the case of electromagnetic radiation in a vacuum. When recast, these equations look exactly like the equations of wave motion. Maxwell himself discovered that the speed of these ‘waves of electromagnetism' is predicted to be precisely the speed of light.

But waves are disturbances
in
something, and it was not at all clear what light waves were meant to be disturbances in. Some physicists
(including Maxwell) argued that these were waves in a tenuous form of matter called the ether, which was supposed to pervade the entire universe. But subsequent experimental searches for evidence of the ether came up empty.

Einstein didn't believe that the ether existed, and argued that earlier work in 1900 by German physicist Max Planck hinted at an altogether different interpretation. He boldly suggested that Planck's result should be taken as evidence that light consists instead of independent, self-contained ‘bundles' of energy, called
quanta.

According to the assumption considered here, in the propagation of a light ray emitted from a point source, the energy is not distributed continuously over ever-increasing volumes of space, but consists of a finite number of energy quanta localized at points of space that move without dividing, and can be absorbed or generated only as complete units.
³

This was Einstein's ‘light quantum hypothesis'. He went on in the same paper to predict the outcomes of experiments on something called the photoelectric effect. This effect results from shining light on to the surfaces of certain metals. Light with wave frequencies above a threshold characteristic of the metal will cause negatively charged electrons to be kicked out from the surface. This was a bit of a challenge for the wave theory of light, as the energy in a classical wave depends on its intensity (related to the wave amplitude, the height of its peaks and depth of its troughs), not its frequency. The bigger the wave, the higher its energy.
^*

Einstein figured that if light actually consists of self-contained bundles of energy, with the energy of each bundle proportional to the frequency of the light, then the puzzle is solved.
⁴
Light quanta with low frequencies don't have enough energy to dislodge the electrons. As the frequency is increased, a threshold is reached above which the absorption of a light quantum knocks an electron out of the lattice of metal ions at the surface. Increasing the intensity of the light simply
increases the number (but not the energies) of the light quanta incident on the surface. He went on to make some simple predictions that could be tested in future experiments.

These were highly speculative ideas, and physicists did not rush to embrace them. Fortunately for Einstein, his work on the special theory of relativity, published in the same year, was better regarded. It was greeted as a work of genius.

When in 1913 Einstein was recommended for membership of the prestigious Prussian Academy of Sciences, its leading members — Planck among them — acknowledged his remarkable contributions to physics. They were prepared to forgive his lapse of judgement over light quanta:

That he may sometimes have missed the target in his speculations, as, for example, in his hypothesis of light-quanta, cannot be really held against him, for it is not possible to introduce really new ideas even in the most exact sciences without sometimes taking a risk.
⁵

The risk was partly rewarded just two years later. When American physicist Robert Millikan reported the results of further experiments on the photoelectric effect, Einstein's predictions were all borne out. The results were declared to be supportive of the predictive ability of Einstein's equation connecting photoelectricity and light frequency, but the light quantum hypothesis remained controversial.

Einstein was awarded the 1921 Nobel Prize for physics for his work on the photoelectric effect (but not the light quantum). Two years later, American physicist Arthur Compton and Dutch theorist Pieter Debye showed that light could be ‘bounced' off electrons, with a predictable change in light frequency. These experiments appear to demonstrate that light does indeed consist of particles moving in trajectories, like small projectiles. Gradually, the light quantum became less controversial and more acceptable. In 1926, the American chemist Gilbert Lewis coined the name ‘photon' for it.

Wave particle duality and the Copenhagen interpretation

But this couldn't simply be a case of reverting to a purely particulate description of light. Nobody was denying all the evidence of
wave-like behaviour, such as diffraction and interference. Besides, Einstein had retained the central property of ‘frequency' in his description of the light quanta, and frequency is a property of waves.

So, how could particles of light also be waves? Particles are by definition localized bits of stuff — they are ‘here' or ‘there'. Waves are delocalized disturbances in a medium; they are ‘everywhere', spreading out beyond the point where the disturbance is caused. How could photons be here, there
and
everywhere?

Einstein believed that photons are first and foremost particles, following predetermined trajectories through space. In this scheme, the trajectories are determined by some other, unguessed property that leads to the
appearance
of wave behaviour as a result of statistical averaging. According to this interpretation, in the two-slit interference experiment each photon follows a precise and predetermined trajectory. It is only when we have observed a large number of photons that we see that the trajectories bunch together in some places and avoid other places, and we interpret this bunching as interference.

There was another view, however. Danish physicist Niels Bohr and German Werner Heisenberg argued that particles and waves are merely the shadowy projections of an unfathomable reality into our empirical world of measurement and perception. They claimed that it made no sense to speculate about what photons
really are.
Better to focus on how they
appear
— in this kind of experiment they appear as waves, in that kind of experiment they appear as particles.

Bohr is credited with the statement:

There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.
⁶

This approach to quantum theory became known as the
Copenhagen interpretation,
named for the city in which Bohr had established a physics institute where much of the debate about the interpretation of quantum theory took place. At the heart of this interpretation lies Bohr's notion of
complementarity,
a fundamental duality of wave and particle behaviour.

Photon spin and polarization

Before we continue with this exploration of the historical development of quantum theory, and what it tells us about the ways in which we try to understand light, it's important to take a short diversion to look more closely at the properties of photons.

Photons are massless particles which in a vacuum travel at the speed of light. The Particle Data Group, an international collaboration of some 170 physicists that reviews data on elementary particles and produces an annual ‘bible' of recommended data for practitioners, suggests that photons cannot possess a so-called ‘rest mass' greater than about two millionths of a billionth of a billionth (2 × 10
^-24
) of the rest mass of the electron.
^*
If the photon does have a rest mass, it is indeed very,
very
small.

Photons are also electrically neutral — they carry no electrical charge. They are instead characterized by their energies, which are directly related to their frequencies or inversely to their wavelengths. This reference to wave-like behaviour, with properties of frequency and wavelength, belies a property called
phase
that all photons (and in fact all types of quantum particle) possess.

In one sense, the phase of a wave is simply related to the position it has in its peak and trough cycle. However, in practical terms, the phase of a quantum particle can never be observed directly. Measurements reveal properties that are affected by the phase, but not the phase itself. According to the Copenhagen interpretation, we should deal only with what we can measure. Whatever the origin of phase, it results in the observation of behaviour that we interpret in terms of waves, and we must leave it at that.

Photons are also characterized by their intrinsic angular momentum, or what physicists call
spin.
In classical Newtonian mechanics, we associate angular momentum with objects that spin around some central axis. For a solid body spinning on its axis, such as a spinning top or the earth, the angular momentum is calculated from its moment of
inertia (a measure of the body's resistance to rotational motion) multiplied by the speed of the rotation.

This obviously can't be applicable for photons. For one thing, photons are massless: they have no central axis they can spin around. They can't be made to spin faster or slower. The term ‘spin' is actually quite misleading. It is a hangover from an early stage in the development of quantum theory, when it was thought that this property could be traced to an intrinsic ‘self-rotation', literally quantum particles spinning like tops. This was quickly dismissed as impossible, but the term ‘spin' was retained.

As with phase, it doesn't help to look too closely at the property of spin and ask what a photon is really doing. We do know that the property of spin is manifested as angular momentum. The interactions between photons and matter are governed by the conservation of angular momentum, and experiments performed over many years have demonstrated this. When we create an intense beam of photons (such as a laser beam), selected so that the spins of the photons are aligned, the angular momentum of all the individual photons adds up and the beam imparts a measurable torque. A target placed in the path of the beam will be visibly twisted in the direction of the beam's rotation.

Physicists characterize the spin properties of quantum particles according to a
spin quantum number,
which provides a measure of the particles' intrinsic angular momentum.
⁷
This quantum number can take half-integral or integral values. Quantum particles with half-integral spins are called
fermions,
named for Italian physicist Enrico Fermi. If we persist in pushing the spinning top analogy, we find that fermions would have to spin twice around their axes in order to get back to where they started (which shows that persisting with classical analogies in the quantum world usually leads only to headaches).

The most important thing to know about fermions is that they are forbidden from occupying the same quantum ‘state'. In this context the state of a quantum particle is defined in terms of the various properties the particle possesses, such as energy and angular momentum. These properties are characterized by their quantum numbers, so a quantum state is defined in terms of its particular set of quantum numbers. Thus when we say that fermions are forbidden from occupying the same quantum state, we mean that no two fermions can have the same set of quantum numbers.

This is called the Pauli exclusion principle, first devised by Austrian physicist Wolfgang Pauli in 1925, and it explains the existence of all material substance and the structure of the periodic table of the elements.