Higgs:The invention and discovery of the 'God Particle' Read online

  FIGURE 3 A cube of ice measuring 2.7 centimetres in length will weigh about 18 grams (a). It consists of a lattice structure containing a little over six hundred billion trillion molecules of water, H2O (b). Each atom of oxygen contains eight protons and eight neutrons and each hydrogen atom contains one proton (c). The cube of ice therefore contains about 10,800 billion trillion protons and neutrons.

  Substantial, but not immutable. Einstein showed that matter (mass) is not conserved – it can be converted to energy. When an atom of uranium-235 is fissioned by bombardment with a fast neutron, about one-fifth of the mass of a single proton is converted into energy in the resulting nuclear reaction. When scaled up to a 56-kilogram bomb core of 90 per cent pure uranium-235, the amount of mass-energy released was sufficient to destroy utterly the Japanese city of Hiroshima in August 1945.

  But Einstein was actually chasing a deeper truth. There was a clue in the title of his 1905 paper: ‘Does the inertia of a body depend on its energy content?’1 Einstein had understood that E = mc2 really means that m = E/c2: all inertial mass is just another form of energy.* The profound implications of this observation would not become apparent for another sixty years.

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  By the mid-1930s, fundamental building blocks of protons, neutrons, and electrons seemed to provide a comprehensive answer to our opening question. But there was a problem. It had been known since the late nineteenth century that isotopes of certain elements are unstable. They are radioactive: their nuclei disintegrate spontaneously in a series of nuclear reactions.

  There are different kinds of radioactivity. One kind, which was called beta-radioactivity by Rutherford in 1899, involves the transformation of a neutron in a nucleus into a proton, accompanied by the ejection of a high-speed electron (a ‘betaparticle’). This is a natural form of alchemy: changing the number of protons in the nucleus necessarily changes its chemical identity.*

  Beta-radioactivity implied that the neutron is an unstable, composite particle, and so not really ‘fundamental’ at all. There was also a problem with the balance of energy in this process. The theoretical energy released by the transformation of a proton inside the nucleus could not all be accounted for by the energy of the emitted electron. In 1930 Pauli had felt that he had no choice but to propose that the energy ‘missing’ in the reaction was being carried away by an as yet unobserved, light, electrically neutral particle which eventually came to be called a neutrino (‘small neutral one’). At the time it was judged that it would be impossible to detect such a particle, but it was first discovered in 1956.

  It was time to take stock. This much was clear. Matter relies on force to hold it together. Aside from the force of gravity, which acts universally on all matter, there were now judged to be three other kinds of force at play within the atom itself.

  The interactions between electrically charged particles are derived from the force of electromagnetism, well known from the pioneering work of nineteenth century physicists which, among many notable achievements, laid the foundations for the power industry. A fully relativistic quantum theory of the electromagnetic field, called quantum electrodynamics (QED), was worked out in 1948 by American physicists Richard Feynman and Julian Schwinger, and Japanese physicist Sin-Itiro Tomonaga. In QED, the forces of attraction and repulsion between electrically charged particles are ‘carried’ by so-called force particles.

  For example, as two electrons approach each other, they exchange a force particle which causes them to be repelled (see Figure 4). The force carrier of the electromagnetic field is the photon, the quantum particle which makes up ordinary light. QED was quickly established as a theory of unprecedented predictive power.

  FIGURE 4 Representation of the interaction between two electrons as described by quantum electrodynamics. The electromagnetic force of repulsion between the two negatively charged electrons involves the exchange of a virtual photon at the point of closest approach. The photon is ‘virtual’ as it is not visible during the interaction.

  There were yet another two forces to contend with. Electromagnetism could not explain how protons and neutrons bind together inside atomic nuclei, nor could it explain the interactions associated with beta-radioactive decay. These interactions work at such different energy scales that no single force can accommodate both. It was recognized that two forces were needed, a ‘strong’ nuclear force responsible for holding atomic nuclei together and a ‘weak’ nuclear force governing certain nuclear transformations.

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  This brings us to the period in the history of physics to be described in this book. A further 60 years of theoretical and experimental particle physics have brought us to the Standard Model, a collection of fundamental quantum field theories which describe all matter and all the forces between material particles with the exception of gravity. The easiest way to appreciate what the Standard Model is and what it means for our understanding of the material world is to take a quick tour through its history.

  Our journey begins in 1915, in the quiet German university town of Göttingen.

  PART I

  Invention

  1

  The Poetry of Logical Ideas

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  In which German mathematician Emmy Noether discovers the relationship between conservation laws and the deep symmetries of nature

  Perhaps we might agree that one of the aims of science is to explain what the world is made of and why it is the way it is. It seeks to do this by elucidating the fundamental constituents of matter and the laws of nature that govern its behaviour.

  If we can agree on this point, we would then have to admit that not all ‘laws’ are the same. Not all laws are truly fundamental. In the seventeenth century, Johannes Kepler toiled for many years with Tycho Brahe’s painstakingly wrought astronomical data and eventually devised three laws that govern the motions of the planets around the sun. These laws are very powerful, but they belie a more fundamental explanation, a reason why the planets orbit the sun in the way they do. Isaac Newton’s law of universal gravitation provided just such an explanation. Newton’s law stood firm for another two hundred years before it was eventually replaced by the interplay of matter and curved space-time in Einstein’s general theory of relativity.

  So, what are the ‘fundamental’ laws? This is perhaps not so difficult to answer. Much of what we understand about the nature of our world is founded on some deceptively simple laws of conservation. The Ancient Greeks believed that matter is conserved. They were almost right. Einstein later taught that matter can be reduced to energy, and from energy can spring matter.

  Matter (in the form of material substance) is not conserved, but mass-energy is. No matter how hard we try, we cannot make or destroy energy. We can only convert it from one kind to another. In every physical interaction of every conceivable description, energy is conserved.

  So too is linear momentum, the mass of an object multiplied by its velocity in a straight line. At first, this does not seem to be consistent with common experience. A popular theme-park ride shoots thrill-seekers at high velocity horizontally along a track.* The track loops-the-loop. The car carrying the passengers then climbs a steep ramp, losing its momentum before slowing to a halt. Gravity pulls it back down the ramp. The car picks up momentum and loops-the-loop backwards before finally coming to rest. Now, it seems quite clear that linear momentum is not conserved as the car climbs the ramp and comes to a stop.

  But there is a bigger picture here. As the car loses momentum, the rest of the world beneath it and to which it is attached imperceptibly gains momentum, such that momentum is conserved.

  So too is angular momentum, the momentum of rotating bodies, calculated as the linear momentum multiplied by the distance from the centre of the rotation. A figure-skater enters a spin with arms and one leg outstretched. As she draws her arms and leg back towards her centre of mass, she reduces the distance from her centre of rotation, and she spins faster. This is the conservation of a
ngular momentum in action.

  As the example of linear momentum shows, these laws are hardly intuitive. They were hinted at for many centuries but, to articulate a law of conservation, it is first necessary to be clear about the quantity that is being conserved. And the concept of energy was not properly formalized and understood until the nineteenth century.

  The conservation laws as they are presented today represent the culmination of centuries of hit-and-miss experimentation and theorizing. Though fundamental, there is a sense in which these laws are nevertheless empirical – they derive from observations and experiments rather than from some deep, underlying theoretical model of the world. Could there be some deeper principle from which the conservation of energy and momentum would automatically result?

  In 1915, German mathematician Amalie Emmy Noether certainly thought so.

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  Noether was born in Erlangen, in Bavaria, in March 1882. Her father, Max, was a mathematician at the University of Erlangen and in 1900 Emmy became one of only two female students to attend the university. Like all academic institutions in Germany at that time, the university did not wish to encourage female students and Emmy was obliged first to seek permission from her lecturers before attending their classes.

  After graduating in the summer of 1903, she spent the winter months at the University of Göttingen. Here she was exposed to lectures delivered by some of Germany’s leading mathematicians, including David Hilbert and Felix Klein. She then returned to Erlangen to work on her dissertation, and in 1908 she became an unpaid lecturer at the university.

  She developed an interest in Hilbert’s work and published several papers extending some of his methods in abstract algebra. Both Hilbert and Klein were impressed, and in early 1915 they sought to bring her back to Göttingen to join the faculty.

  They met with stubborn resistance.

  ‘What will our soldiers think when they return to the university and find they are required to learn at the feet of a woman?’ argued the conservatives on the faculty.

  ‘I do not see that the sex of the candidate is an argument against her admission as a Privatdozent [an assistant professor],’ countered Hilbert. ‘After all, we are a university, not a bath house.’1

  Hilbert prevailed, and Noether moved to Göttingen in April 1915.

  It was shortly after arriving in Göttingen that Noether formulated what was to become one of the most famous theorems in physics.

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  Noether deduced that the principles of the conservation of physical quantities such as energy and momentum can be traced to the behaviour of the laws describing them in relation to the operation of certain continuous symmetry transformations. The conservation laws are manifestations of the deep symmetries of nature.

  We tend to think of symmetry in terms of mirror reflections: left–right, top–bottom, front–back. We say something is symmetrical if it looks the same on either side of some centre or axis of symmetry. In this case, a symmetry ‘transformation’ is the act of reflecting an object as though in a mirror. If the object is unchanged (or ‘invariant’) following such an act we say it is symmetrical.

  To take one example, it seems that facial symmetry is deeply woven into our human perception of beauty and attractiveness, serving as a subliminal indicator of genetic quality. Those exalted as beautiful people tend to have more symmetrical faces and, generally speaking, we tend to want to mate with those we regard as beautiful (see Figure 5).*

  These examples of symmetry transformations are said to be ‘discrete’. They require an instantaneous ‘flipping’ from one perspective to another, such as left-to-right. The kinds of symmetry transformations involved in Noether’s theorem are very different. They involve continuous, gradual changes, such as a continuous rotation in a circle. It seems blindingly obvious that if we rotate a circle through an infinitesimally small angle measured from its centre, then the circle appears unchanged. The circle is symmetric to continuous rotational transformations. A square is not symmetric in this same sense. It is rather symmetric to discrete rotations through 90° (Figure 6).

  FIGURE 5 We tend to think of symmetry in terms of mirror reflections, and say that something is symmetrical if it looks the same on either side of some centre or axis of symmetry. Elizabeth Hurley demonstrates the relationship between facial symmetry and classical beauty.

  Source: ©Peter Steffen/dpa/Corbis

  Noether’s theorem connects each conservation law with a continuous symmetry transformation. She found that the laws governing energy are invariant to continuous changes or ‘translations’ in time. In other words, the mathematical relationships which describe the dynamics of energy in a physical system at some time t are exactly the same an infinitesimally short time later.

  FIGURE 6 Continuous symmetry transformations involve small, incremental changes to a continuous variable, such as a distance or an angle. (a) When we rotate a circle through a small angle (δ), the circle appears unchanged (or ‘invariant’) and we say that it is symmetric to such transformations. (b) In contrast, a square is not symmetric in this same sense. A square is, instead, symmetric to discrete rotations through 90°.

  This means that these laws do not change with time, which is precisely what we might expect from relationships between physical quantities that we wish to elevate to the status of fundamental ‘laws’. These laws are the same yesterday, today, and tomorrow, which is immensely reassuring. If the laws describing energy do not change with time, then energy must be conserved.

  For linear momentum, Noether found the laws to be invariant to continuous translations in space. The laws governing conservation of linear momentum do not depend on any specific location in space. They are the same here, there, and everywhere. For angular momentum, the laws are invariant to rotational symmetry transformations, as in the example of a circle described above. They are the same irrespective of the angle of direction measured from the centre of the rotation.

  The logic by which Noether arrived at her theorem goes something like this. In physics, there are certain quantities that appear from careful observation and experiment to be conserved. After much effort, physicists deduced the laws governing these quantities. These laws are found to be invariant to certain continuous symmetry transformations. Such invariance means that the quantities so governed are required to be conserved.

  This logic could now be turned on its head. Suppose there is a physical quantity which appears to be conserved but for which the laws governing its behaviour have yet to be properly elucidated. If the physical quantity is indeed conserved, then the laws – whatever they are – must be invariant to a particular continuous symmetry transformation. If we can discover what this symmetry is, then we are well on the way to identifying the laws.

  Inverting Noether’s logic offers a way of avoiding considerable hit-and-miss theorizing. Physicists were presented with an approach to identifying laws that helped to rule out whole varieties of possible mathematical structures. Finding the symmetry underlying the physical quantity offers a shortcut to the answer.

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  There was indeed a physical quantity that appeared to be rigorously conserved but for which the appropriate laws had yet to be deduced. This was electric charge.

  The phenomenon of static electricity was known to the philosophers of Ancient Greece. They found that they could generate electric charges and even sparks by rubbing substances such as amber with fur. The scientific study of electricity has a long and illustrious history, with many participants. But it was English physicist Michael Faraday, working at the Royal Institution in London, who synthesized the multitude of observations and experiments into a single, coherent understanding of the nature of electric charge. The result of much experimentation led to the inescapable conclusion that electric change cannot be created or destroyed in any physical or chemical change. Charge is conserved.

  There was no shortage of laws or rules governing electric charge and its rather mysterious
connection with magnetism – Coulomb’s law, Gauss’s law, Ampère’s law, Biot-Savart’s rule, Faraday’s law, and so on. In the early 1860s, Scottish physicist James Clerk Maxwell did for electromagnetism what Newton had done for the theory of planetary motion. He provided a bold theoretical synthesis to parallel Faraday’s experimental unification. Maxwell’s beautiful equations tied in an intimate embrace the electric and magnetic fields generated by a moving electric charge.*

  The equations also demonstrated that all electromagnetic radiation – including light – can be described as a wave motion with a speed that can be calculated from known physical constants. These are the permittivity of free space, which is a measure of the ability of empty space to transmit or ‘permit’ an electric field generated by an electric charge, and the permeability of free space, a measure of the ability of empty space to develop a magnetic field surrounding a moving electric charge. When Maxwell combined these constants in the way dictated by his new electromagnetic theory, the result he obtained for the speed of his ‘waves of electromagnetism’ was precisely the speed of light.

  But Maxwell’s equations deal with the fields generated by electric charge, not the charge itself. These are intimately related, but the equations give no basis in principle for understanding the origin of charge conservation. In the light of Noether’s theorem, the search for the laws governing electric charge became a search for the underlying continuous symmetry transformation to which the laws are invariant.

  The search was picked up by German mathematician Hermann Weyl.