The Book of Nothing Read online

As an illustration, consider a rather corrugated terrain of valleys and hills of different depths and heights, like that in Figure 7.5. The valley bottoms are the different minima of the system. They have different heights and are characterised locally by the simple fact that if you move slightly away from them in any direction you must travel uphill. One of these minima is lower than the others and is called the global minimum. The others are merely local minima. In the study of energies of systems of elementary particles of matter, such minima are called vacua to emphasise the characterisation of the vacuum by a minimum energy state. This example also illustrates something that will prove to have enormous importance for our understanding of the Universe and the structures within it: it is possible for there to be many different minimum energy states, and hence different vacua, in a given system of matter.

  Indirect evidence for the physical reality of the zero-point energy appears every time a successful prediction emerges from quantum theories of the behaviour of radiation and matter. However, it is important to have a direct probe of its existence. The simplest way to do this was suggested by the Dutch physicist Hendrik Casimir in 1948 and has been known ever since as the Casimir Effect.

  Figure 7.5 An undulating terrain displaying several local peaks and valleys.

  Casimir wanted to instigate a way for the sea of zero-point fluctuations to manifest themselves in an experiment. He came up with several ideas to achieve this, of which the simplest was to place two parallel, electrically conducting metal plates in the quantum vacuum. Ideally, the experiment should be performed at absolute zero temperature (or at least as close to it as it is possible to achieve). The plates are set up to reflect any black-body radiation that falls on them.

  Before the plates are added to it we can think of the vacuum as a sea of zero-point waves of all wavelengths. The addition of the plates to the vacuum has an unusual effect upon the distribution of the zero-point waves. Only rather particular waves can exist between the two plates. These are waves which can fit in a whole number of undulations between the plates. The wave has to begin with a zero amplitude at the plate and end in the same way on the other plate. It is like attaching an elastic band between the two plates and setting it vibrating. It will be fixed at each end and the vibrations will undergo one, or two, or three, or four, or more, complete vibrations before the other plate is reached (see Figure 7.6).

  The simple consequence of this is that those zero-point waves which do not fit an exact number of wavelengths between the plates cannot reside there, but there is nothing stopping them from inhabiting the region of space outside the plates. This means that there must be more zero-point fluctuations outside the plates than between them. Therefore the plates get hit by more waves on their outside than they do on the inside-facing surfaces. The plates will therefore be pushed towards one another. The magnitude of the pressure (force per unit area) pushing the plates together is πhc/480d4, where d is the distance between the plates, c is the speed of light, and h is Planck’s constant. This is called the Casimir Effect.15 As you might expect, it is very small. The closer the plates can be placed (the smaller d) so the bigger will be the pressure pushing them together. This is to be expected since the effect arises because some wavelengths have been excluded from the collection between the plates as they don’t fit in. If we separate the plates a little further then more waves will be able to fit in and the disparity between the number of waves present between and outside the plates will get smaller. If the plates are separated by one half of one thousandth of a millimetre then the attractive pressure will be the same as that created by the weight of a fifth of a milligram16 sitting on your finger tip, similar to that of a fly’s wing.

  Figure 7.6 In the presence of a pair of parallel plates those vacuum energy waves that can fit a whole number of wavelengths between the plate will be present there. All possible wavelengths can still exist outside the plates.

  Casimir had hoped that a spherical version of this model might provide a viable picture of the electron but unfortunately it was not possible to balance the repulsive electrostatic force against an attractive Casimir force as he expected. In fact, when one replaces the parallel plates in the zero-point sea by a spherical shell, or by other shapes, the calculations become very different (and very difficult) and the overall effect need not even have an attractive effect. The shape of the region placed in the vacuum is critically important in determining the magnitude and sense of the resulting vacuum effect.17

  Casimir’s beautifully simple idea has been observed in experiments. The first claim to see the effect was made by Marcus Sparnaay18 in 1958, using two plates one centimetre square made of steel and chromium. However, the uncertainties in the final results were large enough to be consistent with no attractive effect being present, and it was not until 1996 that a completely unambiguous detection of the effect was made by Steve Lamoreaux19 in Seattle with the help of his student Dev Sen. One of the greatest difficulties in performing these experiments is ensuring that the two plates are very accurately aligned parallel. In order to see an attractive effect between the plates which is as small as Casimir predicts, one must be able to control their separations to an accuracy of 1 micron over a distance of 1 centimetre. This job can be made easier by replacing one of the plates by a spherical surface so that it does not matter how it is orientated with respect to the flat plate – it always sees the same curvature. So long as the spherical surface is almost flat (or, at least, is not significantly curved over a distance equal to the distance between its surface and the flat plate – in Lamoreaux’s experiment the separation was varied between 0.6 and 11 microns, whilst the radius of curvature of the curved surface was two metres) the expected attractive force can be recalculated to high accuracy. In the experiment, the force is measured by attaching one of the surfaces to the end of one arm of a torsion pendulum. Both surfaces are made of gold-coated quartz to maximise conductivity and robustness. The other end of the pendulum arm is placed between two conducting plates across which there is a voltage difference. A precise measurement of this voltage difference enables one to determine the electric force needed to overcome the attractive Casimir force between the plates and keep them at a fixed separation. The separation is measured with a laser interferometer20 which is able to detect twisting of the pendulum to an accuracy of 0.01 of a micron (see Figure 7.7). The measured attraction of about 100 microdynes agrees with Casimir’s prediction to an accuracy of five per cent.

  What these beautiful experiments show is that there really is a base level of electromagnetic oscillation in space after everything removable has been removed. Moreover, this base level changes as the plate separations are changed and it exists between the plates and outside the plates at different levels. The energy in a given volume of the space between the plates is greater when the plates are closer than when they are far apart. This is understandable. If the plates attract one another you need to expend energy to separate them, after which the vacuum energy between them will be lower than before.

  Figure 7.7 The experimental set-up used to measure the Casimir force of attraction between two plates in a quantum vacuum.

  Even more ingenious experiments have been devised to probe the quantum fluctuations between the Casimir plates.21 Atoms can be perturbed so that their electrons will change from one quantum orbital to another. When this happens they will emit light with a particular wavelength determined by the quantum of energy equal to the difference between the two energy levels. Allow this process to occur between a pair of Casimir plates and the normal decay will not be able to occur if the emitted light has a wavelength that does not fit between the plates. The atom will not decay as expected. Instead, it will remain in its perturbed state. If the wavelength of the emitted radiation fits nicely into the distance between the plates then the atom will decay more rapidly than it otherwise would in a space without the plates present.

  There are many other experimentally observed effects of the zero-point energy. One of the earlie
st to be discovered was by Paul Debeye in 1914, who found that significant scattering of X-rays still occurred from the lattice of atoms making up a chunk of solid material even when the temperature started to approach absolute zero. This scattering is produced by the zero-point energy of the vibrations in the solid.

  In the last few years a public controversy has arisen as to whether it is possible to extract and utilise the zero-point vacuum energy as a source of energy. A small group of physicists, led by American physicist Harold Puthoff,22 have claimed that we can tap into the infinite sea of zero-point fluctuations. They have so far failed to convince others that the zero-point energy is available to us in any sense. This is a modern version of the old quest for a perpetual motion machine: a source of potentially unlimited, clean energy, at no cost.

  While this more speculative programme was being argued about, wider interest in the vacuum was aroused by a phenomenon called ‘sonoluminescence’, which displays the spectacular conversion of sound-wave energy into light. If water is bombarded with intense sound waves, under the right conditions, then air bubbles can form which quickly contract and then suddenly disappear in a flash of light. The conventional explanation of what is being seen here is that a shock wave, a little sonic boom, is created inside the bubble, which dumps its energy, causing the interior to be quickly heated to flash point. But a more dramatic possibility, first suggested by the Nobel prize-winner Julian Schwinger,23 has been entertained. Suppose the surface of the bubble is acting like a Casimir plate so that, as the bubble shrinks, it excludes more and more wavelengths of the zero-point fluctuations from existing within it. They can’t simply disappear into nothing; energy must be conserved, so they deposit their energy into light. At present, experimenters are still unconvinced that this is what is really happening,24 but it is remarkable that so fundamental a question about a highly visible phenomenon is still unresolved.

  Puthoff (see note 22) has claimed far more speculative uses for vacuum energy, arguing that by manipulating zero-point energies we could reduce the inertia of masses in quantum experiments and open the way for huge improvements in rocket performance. The consensus is that things are far less spectacular. It is hard to see how we could usefully extract zero-point energy. It defines the minimum energy that an atom could possess. If we were able to extract some of it the atom would need to end up in an even lower energy state, which is simply not available.

  ALL AT SEA IN THE VACUUM

  “I must go down to the sea again, to the lonely sea and the sky,

  And all I ask is a tall ship and a star to steer her by,

  And the wheel’s kick and the wind’s song and the white sail’s shaking,

  And a grey mist on the sea’s face and a grey dawn breaking.”

  John Masefield25

  During the first half of the nineteenth century, an illustrated nautical book appeared in France26 containing advice to mariners on how to deal with a host of dangerous situations encountered at sea. Some involved coping with adverse weather conditions and natural hazards, whilst others dealt with close encounters with other vessels. The Dutch physicist Sipko Boersma noticed that this handbook contained a peculiar warning to sailors of something that is reminiscent of the Casimir effect that we have just described.27

  Sailors are warned that when there is no wind and a strong swell building, then two large sailing ships will start to roll. If they come close together and lie parallel to one another then they are at risk. An attractive force (‘une certaine force attractive’) will draw the two ships together and there will be a disaster if their riggings collide and become entangled. The sailors are advised to put a small boat in the water and tow one of the ships out of the range of the attractive influence of the other. This sounds like a strange warning. Is there any truth to it? Remarkably, it turns out that there is. The attractive force between the ships arises in an analogous way to the force of attraction between the Casimir plates although there is no quantum physics or zero-point fluctuations of the vacuum involved – ships are too large for those effects to be big enough to worry about. Instead of waves of zero-point energy, the ships feel the pressure of the water waves.

  The analogy is quite clear. Although we were dealing with radiation pressure between Casimir’s plates, the same ideas apply to other waves as well, including water waves. In Figure 7.8, we see the situation of two ships, oscillating from side to side in the swell. The rolling ship absorbs energy from the waves and then re-emits this by creating a train of outgoing water waves. If the principal wavelength of these waves is much bigger than the distance between the two ships then they will rock together in time like a pair of copy-cat dancers. However, the waves that they radiate towards each other will be exactly out of phase. The peaks of one ship’s waves will coincide with the troughs of the other ship’s waves. The net result is that they will cancel each other out. As a result, there is virtually no radiated waterwave energy in between the two ships, and the pushing together of the ships, caused by the outgoing waves from the other sides of the ships, is not balanced. Thus, rolling ships will approach one another, just like atoms in a sea of vacuum fluctuations.

  Figure 7.8 Two nearby ships rolling in a swell of ocean waves. Some waves are excluded from the region between the ships and the ships are forced together by the higher wave pressure on their outer sides.

  The calculations28 show that two 700-ton clipper ships should attract one another with a force equal to the weight of a 2000-kilogram mass. This is a reasonable answer. It is a force that a large boat of rowers could overcome by concerted effort. If the force were ten times bigger then all such efforts would be hopeless, whereas if it were ten times smaller the attraction would be negligible and no action would be needed to avert a collision. Boersma also discovered that the attractive force between the boats is proportional to the square of the maximum angle that they swing back and forth in the swell. In breezy conditions these oscillations will die out fairly quickly as the sails take up their energy. Thus we see the reason for the warning about the naufragous effects of coming too close to another ship in fairly calm conditions.

  THE LAMB SHIFT

  “I used to be Snow White … but I drifted.”

  Mae West29

  One of the greatest successes of the quantum theory was to explain in exquisite detail the structure of atoms and the characteristic frequencies of the light waves that they emit when their electrons change from one quantum energy level to another. The first calculations of these levels got very accurate answers, in line with all observations, without realising that the vacuum energy might have an effect on the levels. Fortunately, the effect is very small and requires very sensitive measurements to detect it. It was not until 1947 that instruments were sensitive enough to detect these tiny changes. The electrons near the atomic nucleus feel tiny fluctuations created by the zero-point motions around them. These slight jigglings should result in a slight change in the path of the electron’s orbit and a tiny shift of the energy level of the electron compared to its expected value if we ignore the vacuum fluctuations. In particular, in the hydrogen atom, two energy levels which would otherwise have the same level are split by a tiny amount, four millionths of an electron volt – more than three million times smaller than the energy needed to remove an electron from the atom. This tiny energy difference, now called the ‘Lamb Shift’, was first measured by the Americans Willis Lamb and Robert Retherford,30 in 1947, using some of the techniques developed for the use of radar during the Second World War. Lamb received the Nobel prize for physics for this discovery in 1955.

  FORCES OF THE WORLD UNITE

  “God is in the atoms… A superposition, if you like. Or whether you don’t like actually, that’s what it’s called. A superposition is like God in that the quantum object occupying a number of different states simultaneously can be everywhere at once. A superposition is a kind of immanence. Without these superpositions, quantum objects would simply crash into each other and solid matter could not possibl
y exist.”

  Philip Kerr31

  The quantum vacuum with its seething mass of activity has ultimately proved to be the foundation of all our detailed understanding of the most elementary particles of matter. We have found only four distinct forces of Nature acting in the relatively low-energy world in which we live. Their properties are summarised in Figure 7.9. The action of each of these forces is sufficient to understand almost all the things that we see around us.32 The quartet of forces includes gravity and electromagnetism, which are both familiar to us in everyday life, but they are joined by two microscopic forces which have only been explicitly isolated during the twentieth century. The ‘weak’ force lies at the root of radioactivity whilst the ‘strong’ force is responsible for nuclear reactions and the binding together of atomic nuclei. Each of these forces is described by the exchange of a ‘carrier’ particle which conveys the force. The quantum wavelength of this particle determines the range of influence of the force. The force of gravity is carried by the exchange of a massless particle, the graviton, and so has an infinite range.33 Gravity is unique in that it acts on every particle. The force of electromagnetism also has an infinite range because it is carried by the exchange of another massless particle, the photon of light. It acts on every particle that possesses electric charge. The weak interaction is different. It acts upon a class of elementary particles called leptons (Greek for light ones), like electrons, muons, tauons, and their associated neutrinos, and is carried by three very massive particles, the so-called intermediate vector bosons (W+, W− and Z0). These particles are about 90 times heavier than the proton and the weak force they mediate has a finite range 100 times less than the radius of an atomic nucleus.