Farewell to Reality (10 page)

^*
Physicists call this changing the
basis
of the description.

^*
Actually, the probability is related to the modulus-square of the amplitude. Amplitudes can be positive or negative or ‘imaginary' (i.e. they depend on
i
, the square root of -l), but, by definition, probabilities are always positive.

^*
This is only a high degree of certainty rather than absolute certainty as the polarizing film won't be perfect. It will allow some photons that aren't precisely vertically polarized to ‘leak' through.

^**
I'm sure you want to know what the other two laws are. The first law says that when a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is almost certainly wrong. The second law says that the only way to discover the limits of the possible is to venture a little way beyond them into the impossible.

^*
This is a variation of the original Einstein-Podolsky-Rosen thought experiment, but it is entirely consistent with their approach.

^*
Strictly speaking, it's not necessary to fix the polarization states at the moment the photons are produced. It's enough that the hidden variables are so fixed and determine how the photons interact with the polarizing film, such that if photon A is measured to be vertically polarized, photon B is, too.

^*
Here ‘polarizing films' is a shorthand for what was a complex bit of technical kit, including polarization analysers, photomultipliers, detectors and timing electronics that could identifty when the photons belonged to the same pair.

^**
Actually, quantum theory predicts the value 2√2.

^*
Again, I'm paraphrasing. The experiments were a lot more complicated than this.

3

The Construction of Mass

Matter, Force and the Standard Model of Particle Physics

A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability.

Albert Einstein
¹

Perhaps we would be more comfortable if the behaviour described in Chapter 2, which poses such bizarre philosophical conundrums, was in some way restricted to photons, those ghostly white ambassadors of morning. Alas, when in 1923 de Broglie speculated that there might be a connection between the wavelength of a quantum wave particle and its momentum, he was thinking not of photons, but of
electrons.
And, I can now admit, the two-slit interference pattern shown in Figure 1 on page 37 was produced not with a faint beam of light, admitting one photon after another, but with a faint beam of electrons.

It comes as something of a shock to realize that pictures such as Figure 1 relate to particles that we're more inclined to think of as tiny, but solid, bits of material substance. We then start to ask some really uncomfortable questions. If we thought it was spooky to lose sight of massless particles as they make their way (as waves) through a two-slit interference apparatus, then doing the same with electrons is surely downright embarrassing. As electrons pass — one after the other — through the apparatus, to be ‘constituted' only when the wavefunction collapses, we have to ask ourselves:
what happens to the electrons' mass?

Okay, okay. It's important to stay calm. Electrons are particles with mass, but this mass is nevertheless very, very small. The mass of an electron is about 0.9 thousandths of a billionth of a billionth of a
billionth (9 × 10
^-31
) of a kilogram. If we lost an electron, I guess we would hardly miss it. Perhaps we can still get away with the idea that, because of their small size, electrons are susceptible to phantom-like, non-local behaviour of the kind we associate with photons. Larger particles or more massive structures should surely be less susceptible.

But this won't do. Quantum wave interference effects have been demonstrated with large molecules containing 60 and 70 carbon
atoms.
Superconducting quantum interference devices (SQUIDs, for short) have been used to demonstrate interference in objects of millimetre dimensions. These are dimensions you can
see.
These experiments involved combining SQUID states in which a billion electrons move clockwise around a small superconducting ring and another billion electrons move anticlockwise around the ring. In such a quantum superposition, in what direction are the electrons actually supposed to be moving?

It gets worse. In the standard model of particle physics, we learn that the property of mass of all the elementary particles — the particles that make up everything we are and everything we experience — is not an intrinsic or primary property of the stuff of material substance. It results from the interaction of quantum particles that would otherwise be massless with a mysterious energy field called the Higgs field which pervades the entire universe, like a modern-day ether. These interactions slow down the particles that interact with it, to an extent determined by the magnitude of their coupling to the field. We interpret this slowing down as inertia. And, ever since Galileo, we interpret inertia as a property of objects possessing mass.

We are forced to conclude that this interaction with the Higgs field, this slowing down, is actually what mass
is.

We'd better take a closer look.

The forces of nature

When Einstein developed his theories of relativity and challenged Bohr over the interpretation of quantum theory in the 1920s, it was believed that there were just two forces of nature — electromagnetism and gravity. Early attempts to construct a unified theory capable in principle
of describing all the elementary particles and their interactions therefore involved reconciling just these two forces in a single framework.

But two forces of nature aren't enough to account for the properties of atoms as these came to be understood in the early 1930s.

In 1932, English physicist James Chadwick discovered the neutron, an electrically neutral particle which, together with the positively charged proton, forms the building blocks of all atomic nuclei. It was now understood that each chemical element listed in the periodic table consists of atoms. Each atom consists of a nucleus composed of varying numbers of protons and neutrons. Each element is characterized by the number of protons in the nuclei of its atoms. Hydrogen has one, helium two, lithium three, and so on to uranium, which has 92. It is possible to create elements heavier than uranium in a particle accelerator or a nuclear reactor, but they do not occur in nature.

This was all very well, but it posed something of a dilemma. We know that like charges repel each other, so how could all those positively charged protons be squeezed together and packed so tightly inside an atomic nucleus, and yet remain stable? Careful experimental studies revealed that the strengths of the interactions between protons and protons inside the nucleus are very similar in magnitude to those between protons and neutrons. None of this made any sense, unless the force governing these interactions is very different from electromagnetism. And very much stronger, able to overcome the force of electrostatic repulsion threatening to tear the nucleus apart.

This suggested the existence of another force, which became known as the
strong nuclear force,
binding protons and neutrons together in atomic nuclei.

This was not quite the end of the story. It had been known since the late nineteenth century that certain isotopes of certain elements — atoms with the same numbers of protons in their nuclei but different numbers of neutrons — are unstable. For example, the isotope caesium-137 contains 55 protons and 82 neutrons. It is radioactive, with a half-life (the time taken for half the radioactive caesium-137 to disintegrate) of about thirty years. The caesium-137 nuclei disintegrate spontaneously through one or more nuclear reactions.

There are different kinds of radioactivity. One kind, which was called beta-radioactivity by New Zealand physicist Ernest Rutherford
in 1899, involves the transformation of a neutron in a nucleus into a proton, accompanied by the ejection of a high-speed electron (also known as a ‘beta particle'). This is a natural form of alchemy: changing the number of protons in the nucleus changes its chemical identity. In fact, caesium-137 decays by emission of a high-speed electron to produce barium-137, which contains 56 protons and 81 neutrons. This implies that the neutron is an unstable, composite particle, and so not really elementary at all. Left to its own devices, an isolated neutron will decay spontaneously in about 15 minutes.

The origin of beta-radioactivity was a bit of a puzzle. What was an
electron
supposed to be doing inside the nucleus? But it posed an even bigger problem. It could be expected that in this process of radioactive decay, energy and momentum should be conserved, just as they are conserved in every chemical and physical change that has ever been studied. But a careful accounting of the energies and momenta involved in beta-radioactivity showed that the numbers just didn't add up. The theoretical energy and momentum released by the transformation of a neutron inside the nucleus could not all be accounted for by the energy and momentum of the ejected electron.

In 1930, Wolfgang Pauli reluctantly suggested that the energy and momentum ‘missing' in the reaction were being carried away by an as yet unobserved, light, electrically neutral particle which interacts with virtually nothing. It came to be called a
neutrino
(Italian for ‘small neutral one'). At the time it was judged that it would be impossible to detect, but it was first discovered experimentally in 1956.

The strong nuclear force was judged to be about a hundred times stronger than electromagnetism. But the force governing beta-radioactive decay was found to be much weaker, about ten billionths of the strength of the electromagnetic force. It was also clear that this weak force acted on nuclear particles — protons and neutrons — although electrons, too, were somehow involved. There was no choice but to conclude that this was evidence for yet another force of nature, which became known as the
weak nuclear force.

Instead of two fundamental forces there were now four: the strong and weak nuclear forces, electromagnetism and gravity. Constructing a quantum theory that could accommodate three of these forces (the exception being gravity) took another forty years. It is called the
standard model of particle physics, and it is one of the most successful theories of physics ever devised.

Spinning electrons and anti-matter

Two versions of quantum theory were developed in the 1920s and were applied principally to the study of the properties and behaviour of electrons. These were
matrix mechanics,
devised in 1925 by Heisenberg, and
wave mechanics,
devised in late 1925/early 1926 by Austrian physicist Erwin Schrödinger. Although these were rival theories, Schrödinger himself demonstrated that they are, in fact, equivalent; one and the same theory expressed in two different mathematical ‘languages'.

These early quantum theories were further developed and elaborated, and cast into other mathematical forms that have since proved to be useful (or, at least, they avoid some of the metaphysical baggage that the early theories tended to carry). Quantum theory is still very much a theory of contemporary physics.

But the equations of quantum theory describe individual quantum particles or systems. They describe how the energies associated with various motions of the particles or systems are ‘quantized', able to admit or remove energy only in discrete lumps, or quanta. Adding quanta therefore involves increasing the energy, promoting the particles or systems to higher-energy quantum states. Taking quanta away likewise involves removing energy, often in the form of emitted photons, demoting the particles or systems to lower-energy states.

To describe correctly such ‘dynamics' of quantum systems, the theory must in principle conform to the stringent requirements of Einstein's special theory of relativity. This ensures that the laws of nature that we can observe or measure are guaranteed to be the same independently of how fast the observer or measuring device might happen to be moving in relation to the object under study.
^*
It also
ensures that the speed of light retains its privileged status as an ultimate speed that cannot be exceeded.
^*

Einstein himself identified one important consequence of the special theory. This was a deep connection between energy and mass reflected in the world's most famous scientific equation, E = mc
²
, or energy equals mass multiplied by the speed of light squared. This is interpreted to mean that mass is a form of energy, and from energy can spring mass.

Now this might already cause us to pause for a moment's quiet reflection on what it may mean for our interpretation of mass. I confess that, as a young student, the notion that mass represents a vast reservoir of energy somehow made it seem even more tangible, and ‘solid'. It didn't shake my naïve conviction that mass must surely be an intrinsic property or primary quality of material substance.

In essence, producing a so-called ‘relativistic' theory — one that meets the requirements of the special theory of relativity — is all about ensuring that the theory treats
time
as a kind of fourth dimension, on an equal footing with the three dimensions of space. In late 1927, Paul Dirac extended the early version of quantum theory and made it conform to the special theory of relativity.

The resulting theory predicted that the electron should possess a spin quantum number s equal to ½ and two different spin orientations, labelled spin-up and spin-down.
²
This was something of a revelation. That electrons possess an intrinsic spin angular momentum had been shown experimentally some years previously, but neither matrix nor wave mechanics had predicted this behaviour.