Physics is the science of matter – the stuff of the Universe around us, and of energy – the capacity of matter to act in different ways. Physics is the systematic study of how this matter and energy behave, the explanation of what this reveals, and the understanding it brings. A magnificent allegory of what a physicist does can be found in the Old Testament, the Book of Job, Chapter 28.

If our surroundings are seen as being built up of matter, much of Nature is ultimately physics, so physics underpins many other branches of science. It is difficult to be more ambitious than that. But as though such boldness were not enough of a challenge, new physics has gone on to reveal that matter and energy can exist in forms and behave in ways very different from those we know in everyday life. The goal becomes even more ambitious. Nature, and therefore physics, has become much wider than what we normally see around us.

Introduction

All scientists reading this would agree that scientific research in general, and Physics in particular, deserves to be pursued if only for the sake of understanding and enjoying the world in which we live. They share Albert Einstein’s opinion: “Why do we devise theories at all? The answer is simply: because we enjoy ‘comprehending’ . . . There exists a passion for comprehending, just as there exists a passion for music” [1]. At the same time, all scientists also believe that new basic knowledge will continue to bring concrete benefits to Society.

However, this intimate conviction, well-founded on past experience, is no longer sufficient. For about twenty years, politicians and the public have increasingly been asking scientists, and in particular physicists, to

1. better describe what they do and what they learn;

2. explain what advantages Society has gained and can expect to receive in the future from the funds allocated to fundamental research; and

3. organize the production and dissemination of fundamental research in such a way as to maximize its benefits to Society.

It is my opinion that in such an enterprise other scientists perform better than physicists, possibly (but not only) because the subject of their research helps them: advances in medicine and, more recently, in molecular biology are naturally close to human life and are thus easily perceived as “useful.”

Introduction

In the course of the twentieth century fundamental notions concerning the physical world were radically altered by a succession of unifying insights. In the early part of the century quantum theory provided the framework for understanding the structure of the atom, its nucleus, and the “elementary” particles of which it is made. This understanding, combined with the special theory of relativity, led, by the early 1970s, to a comprehensive account of three of the fundamental forces – the weak, strong, and electromagnetic forces – in the “Standard Model.” Meanwhile, Einstein’s 1915 general theory of relativity replaced Newton’s theory of gravity, leading to a unification of the force of gravity with spacetime geometry, and explanations of the evolution of the Universe from the time of the Big Bang and of weird astrophysical phenomena, such as black holes. Yet, with each advance ever-deeper questions were posed and remained unanswered. What determines the species of observed elementary particles, such as the electron, neutrinos, quarks, etc., and what principle leads to a unified description of all of them? How can quantum theory be consistent with general relativity? What is the meaning of space and time at extremely small distances, where quantum theory plays a dominant role? How did the Universe begin and how will it end?

An optimist should regard such unresolved puzzles as the seeds from which further insights will arise. This spirit of incompleteness is a distinguishing feature of this chapter. Here we will see that many, if not all, of these deep questions might be resolved by string theory. Although there is no single mathematical equation that summarizes string theory – indeed, it is not yet a complete theory – it has many intriguing interrelations with some of the most modern areas of mathematics. Its compelling qualities suggest that string theory has the potential to overcome key problems present in previous physical theories and to overcome them in a manner that is surprisingly simple and at the same time very novel.

Introduction

Cosmology is the study of the origin, evolution, composition, and structure of the Universe. As a scientific discipline cosmology began only in the twentieth century. Among the fundamental theoretical and observational developments that established the Big-Bang model were the general theory of relativity proposed by Albert Einstein in 1915, the development of the theory of an expanding relativistic cosmology by Alexander Friedmann in 1922 and Georges LemaÎtre in 1927, the observation of the expansion of the Universe by Edwin Hubble in 1929, the development of the theory of Big-Bang nucleosynthesis by Ralph Alpher, George Gamow, and Robert Herman in the early 1950s, and the discovery of the cosmic background radiation by Arno Penzias and Robert Wilson in 1964.

Traditionally, cosmology has been a data-starved science, but cosmology today is experiencing a fertile interplay between observation and theory. Precision measurements of the expansion rate of the Universe, the large-scale homogeneity and isotropy of the distribution of galaxies, the existence and high degree of isotropy of the 3-K cosmic microwave background radiation, and the abundances of the light elements support the basic picture of an expanding hot-Big-Bang Universe.

Introduction

Physics ultimately rules the processes in living organisms and thus is in that sense fundamental for understanding medicine. To cite some examples involving different branches of physics:

• the dynamics of forces in joints, e.g. the dependence of stress in an articulation → mechanics

• the microstructure of bones and the role of compounds with high elasticity and high tensile strength → solid-state physics of articulations

• control of blood circulation and the variable viscosity of blood and blood plasma → hydrodynamics

• passive molecular transport through membranes via osmosis → thermodynamics

• signal conduction in nerve cells → electrodynamics

• image formation on the retina → optics and

• hearing → acoustics and mechanics.

Many physical properties of tissues, substances, cells, and molecules and of their mechanisms of operation are exploited for diagnostics and therapy (e.g. ultrasonic imaging, electro- or magneto-encephalography, high-frequency electromagnetic-radiation therapy). Rather than these manifold relationships between physics and the phenomena of medicine and biology, medical physics today covers that part of physics in which new phenomema are exploited and new techniques developed explicitly for use in diagnostics and treatment. The largest area has to do with diagnostic methods, the most prominent being transmission radiography with X-rays, which was introduced soon after the discovery of X-rays by Röntgen in 1895. Many sections of this chapter cover the principles and recent developments of diagnostic tools, weighing their virtues as well as possible disadvantages (e.g. adverse side effects). The various techniques also provide complementary information.

Introduction

We all observe phase transitions in our daily lives, with hardly a second thought. When we boil water for a cup of tea, we observe that the water is quiescent until it reaches a certain temperature (100 ℃), and then bubbles appear vigorously until all the water has turned to steam. Or after an overnight snowfall, we have watched the snow melt away when temperatures rise during the day. The more adventurous among us may have heated an iron magnet above about 760 ℃ and noted the disappearance of its magnetism.

Familiar and ubiquitous as these and many related phenomena are, a little reflection shows that they are quite mysterious and not easy to understand: indeed, the outlines of a theory did not emerge until the middle of the twentieth century, and, although much has been understood since then, active research continues. Ice and water both consist of molecules of H2O, and we can look up all the physical parameters of a single molecule, and of the interaction between a pair of molecules, in standard reference texts. However, no detailed study of this information prepares us for the dramatic change that occurs at 0 ℃. Below 0 ℃, the H2O molecules of ice are arranged in a regular crystalline lattice, and each H2O molecule hardly strays from its own lattice site. Above 0 ℃, we obtain liquid water, in which all the molecules are moving freely throughout the liquid container at high speeds. Why do 1023 H2O molecules cooperatively “decide” to become mobile at a certain temperature, leading to the phase transition from ice to water?

Introduction

It is a universally acknowledged truth that any useful artifact is made of materials. A material is a substance, or combination of substances, which has achieved utility. To convert a mere substance into a material requires the imposition of appropriate structure, which is one of the subtlest of scientific concepts; indeed, the control of structure is a central skill of the materials scientist, and that skill makes new artifacts feasible.

Any structure involves two constituents: building blocks and laws of assembly. Crystal structure will serve as the key example, with wide ramifications. Any solid element, pure chemical compound, or solid solution ideally consists of a crystal, or an assembly of crystals that are internally identical. (The qualification “ideally” is necessary because some liquids are kinetically unable to crystallize and turn instead into glasses, which are simply congealed liquids.) Every crystal has a structure, which is defined when (1) the size and shape of the repeating unit, or unit cell, and (2) the position and species of each atom located in the unit cell have all been specified. At one level, the unit cells are the building blocks; at another level, the individual atoms are. The laws of assembly are implicit in the laws of interatomic force: once we know how the strength of attraction or repulsion between two atoms depends on their separation and what angles between covalent bonds issuing from the same atom are stable then, in principle, we can predict the entire arrangement of the atoms in the unit cell. Once the crystal structure has been established, many physical properties, such as the cleavage plane, melting temperature, and thermal expansion coefficient, are thereby rendered determinate. In the fullest sense, structure determines behavior.

Origins of particle physics

Within the lifetime of my grandparents, there lived distinguished scientists who did not believe in atoms. Within the lifetime of my children, there lived distinguished scientists who did not believe in quarks. Although we can trace the notion of fundamental constituents of matter – minimal parts – to the ancients, the experimental reality of the atom is a profoundly modern achievement. The experimental reality of the quark is more modern still.

Through the end of the nineteenth century, controversy seethed over whether atoms were real material bodies or merely convenient computational fictions. The law of multiple proportions, the indivisibility of the elements, and the kinetic theory of gases supported the notion of real atoms, but a reasonable person could resist because no one had ever seen an atom. One of the founders of physical chemistry, Wilhelm Ostwald, wrote influential chemistry textbooks that made no use of atoms. The physicist, philosopher, and psychologist Ernst Mach likened “artificial and hypothetical atoms and molecules” to algebraic symbols – tokens, devoid of physical reality – that could be manipulated to answer questions about Nature.

What is a superfluid?

The word “superfluid” was coined to describe a qualitatively different state of a fluid that can occur at low temperatures, in which the resistance to flow is identically zero, so that flow round a closed path lasts for ever – a persistent current. Superfluidity can occur either for uncharged particles such as helium atoms or for charged particles such as the electrons in a metal. In the latter case the flow constitutes an electric current and we have a superconductor. Since an electric current is accompanied by a magnetic field, it is much easier to demonstrate the presence of a persistent current in a superconductor than in a neutral superfluid.

In this chapter I shall describe the properties of superfluids, starting with the simplest and working up to more complicated examples. But in this introductory section I shall depart from the historical order even further by turning to the last page of the detective story so as to catch a glimpse of the conclusion from almost a century of experimental and theoretical research; we shall then have an idea of where we are heading.

The conclusion is that superfluidity is more than just flow without resistance. It is an example of a transition to a more ordered state as the temperature is lowered, like the transition to ferromagnetism. At such a transition new macroscopically measurable quantities appear: in the case of a ferromagnet, the spontaneous magnetization. Such new measurable quantities are known as the order parameter of the low-temperature phase. The new quantities in the case of a superfluid are more subtle and more surprising: the amplitude and phase of the de Broglie wave associated with the motion of the superfluid particles. A superfluid can therefore exhibit quantummechanical effects on a macroscopic scale.

Introduction

This chapter describes remarkable new experiments that have been made possible through recent advances in laser cooling of atoms. Cooling of atoms in a gas by laser light is in itself surprising and this technique is important in a range of applications. In particular the experiments described here take atoms that have been laser cooled and then use other methods to reach even lower temperatures, at which wonderful and fascinating quantum effects occur. As well as revealing new phenomena, these experiments explore the deep analogies between the roles played by light waves in lasers and matter waves. These techniques are widely accessible and enable skilled researchers in laboratories all over the world to explore exciting new physics. The key physics and techniques of laser cooling are described in depth in Chapter 6.

What is “temperature”?

We use the words “cold” and “hot” every day; for example to refer to the temperature of the air outside. But what do “cold” and “hot” mean for the air’s molecules? Broadly speaking, we can say that atoms in a hot gas move faster than those in a cold gas and that cooling, by taking energy out of the gas, slows the atoms down. In this description of the gas as a collection of atoms behaving like billiard balls, or little hard spheres, the lowest possible temperature occurs when the atoms stop moving but, as we shall see, this picture does not give an accurate description at very low energies, for which quantum effects become important. In this chapter we will look at the fascinating properties of atomic gases cooled to temperatures within one millionth of a degree Kelvin from absolute zero. We shall use the term “ultra-cold” to refer to such extremely low temperatures that have only recently been achieved in experiments on atomic gases. The techniques used to cool liquids and solids have a longer history and have made available a different set of possibilities (see Chapter 8). Note that most of this chapter refers to gases in which the individual particles are atoms, but the general statements about temperature scales apply equally well to gases of molecules, e.g. air, whose major constituents, oxygen and nitrogen, exist as diatomic molecules.

The attraction of gravity

Gravity attracts. It attracts every body in the Universe to every other, and it has attracted the interest of physicists for centuries. It was the first fundamental force to be understood mathematically in Isaac Newton’s action-at-a-distance theory, it is a center of current attention in Albert Einstein’s general relativity theory, and it promises to be the last force to be fully understood and integrated with the rest of physics.

After centuries of success, Newton’s theory was finally replaced by Einstein’s theory, which describes gravity at a deeper level as due to curvature of spacetime. General relativity is widely considered to be the most elegant physical theory and one of the most profound. It has allowed the study and understanding of gravitational phenomena ranging from laboratory scale to the cosmological scale – the entire Universe; but many mysteries remain, especially in cosmology.

An impressive understanding of the other fundamental forces of nature, electromagnetism and the weak and strong nuclear forces, is now embodied in the Standard Model of elementary particles. However, these other forces are understood in terms of quantum field theory and are not geometric in the manner of general relativity, so gravity remains apart. Many physicists believe that the final phase of understanding gravity will be to include quantum effects and form a union of general relativity and the Standard Model. We would then understand all the forces and spacetime on a fundamental quantum level. This is proving to be quite a task.

Introduction

Electromagnetic interactions play a central role in low-energy physics, chemistry, and biology. They are responsible for the cohesion of atoms and molecules and are at the origin of the emission and absorption of light by such systems. They can be described in terms of absorptions and emissions of photons by charged particles or by systems of charged particles like atoms and molecules. Photons are the energy quanta associated with a light beam. Since the discoveries of Planck and Einstein at the beginning of the last century, we know that a plane light wave with frequency ν, propagating along a direction defined by the unit vector u, can also be considered as a beam of photons with energy E = hν and linear momentum p = (hν/c)u. We shall see later on that these photons also have an angular momentum along u depending on the polarization of the associated light wave.

Conservation laws are very useful for understanding the consequences of atom–photon interactions. They express that the total energy, the total linear momentum, and the total angular momentum are conserved when the atom emits or absorbs a photon. Consider for example the conservation of the total energy. Quantum mechanics tells us that the energy of an atom cannot take any value. It is quantized, the possible values of the energy forming a discrete set Ea, Eb, Ec, . . . In an emission process, the atom goes from an upper energy level Eb to a lower one Ea and emits a photon with energy hν. Conservation of the total energy requires The energy lost by the atom on going from Eb to Ea is carried away by the photon.

Introduction

Ever since physics came into existence as a scientific discipline, it has been mainly concerned with identifying a minimal set of fundamental laws connecting a minimal number of different constituents, under the more or less implicit assumption that knowledge of these rules were a sufficient condition for explaining the world we live in. Such a program has had remarkable success, to the extent that processes occurring on scales that range from that of elementary particles up to those of stellar evolution can nowadays be satisfactorily described. Nevertheless, it has meanwhile become clear that the inverse approach is a source of unexpected richness and can hardly be included with the original microscopic equations. The existence of different phases of matter (gas, liquid, solid, and plasma, together with perhaps glasses, granular materials, and Bose–Einstein condensates) provides the most striking evidence that the adjustment of a parameter (e.g. temperature) can dramatically change the organization of the system.

Moreover, not only can the same set of microscopic laws give rise to different structures, but also the converse is true: different systems can, for example, converge toward the same crystalline configuration. One of the basic ingredients that makes the connection between different levels of description complex, though very intriguing, is the presence of nonlinearities. As long as each atom deviates slightly from its equilibrium position, the equations of motion can be linearized and the dynamics thereby decomposed into the sum of independent evolutions of so-called normal modes. In some cases, especially when disorder is present, such a decomposition cannot be easily performed (and very interesting physics can indeed arise, e.g. Anderson localization) but is, at least in principle, feasible.

Introduction

The atomic nature of matter is well documented and appreciated. Solids are made from regular (in the case of crystals) or irregular (for the example of glasses) arrangements of atoms. Nature finds a way to produce various materials by combining constituent atoms into a macroscopic substance.

Imagine the following hypothetical experiment. Suppose that one builds up, for example, a crystal of silicon by starting with a single atom and adding atoms to make a small number of unit cells, repeating the process until a large enough crystallite has formed. A fundamental question is the following: at what stage in this process, i.e. at what size of the crystallite, will it approximately acquire the “bulk” properties? The precise answer to this question may well depend on what exactly one intends to do with the crystal.

While this may sound like a purely thought experiment, remarkable modern fabrication methods are close to being able to achieve this, using at least two independent approaches. Molecular-beam epitaxy (Figure 12.1) is able to grow high-quality crystalline layers one by one with remarkable control. Atomic-resolution methods are already able to deposit atoms selectively on some surfaces (Figure 12.2).