A very important concept in physics is the symmetry or invariance of the equations describing a physical system under an operation – which might be, for example, a translation or rotation in space. Intimately connected with such invariance properties are conservation laws – in the above cases, conservation of linear and angular momentum. Such conservation laws and the invariance principles and symmetries underlying them are the very backbone of particle physics. However, one must remember that their credibility rests entirely on experimental verification. A conservation law can be assumed to be absolute if there is no observational evidence to the contrary, but this assumption has to be accompanied by a limit set on possible violations by experiment.

The transformations to be considered can be either continuous or discrete. A translation or rotation in space is an example of a continuous transformation, while spatial reflection through the origin of coordinates (the parity operation) is a discrete transformation. The associated conservation laws are additive and multiplicative, respectively.

Translation and rotation operators

In an isolated physical system, free of any external forces, the total energy must be invariant under translations of the whole system in space. Since there are no external forces, the rate of change of momentum is zero and the momentum is constant. So invariance of the energy of a system under space translations corresponds to conservation of linear momentum. Similarly, invariance of the energy of a system under spatial rotations corresponds to conservation of angular momentum.

1897 Discovery of electron

1900 α, β and γ radioactivity

1905 Photon identified as quantum of electromagnetic field

1911 Discovery of atomic nucleus

1912 Discovery of cosmic rays

Invention of cloud chamber

1913 Bohr model of atom

1919 Discovery of proton

1923 de Broglie wave–particle duality

1925 Introduction of electron spin

1926 Wave mechanics

1927 Uncertainty Principle

1928 Dirac wave equation

1930 Neutrino hypothesis

1931 Operation of first cyclotron and of Van der Graaff accelerator

1932 Discovery of positron

Discovery of neutron

1933 Discovery of electromagnetic showers

1934 Theory of beta decay

Discovery of Čerenkov effect

1935 Yukawa theory of nuclear forces

1936 Breit–Wigner resonance formula

1937 First evidence for mesotron (= muon)

1939 Observation of mesotron (= muon) decay

1940 Spin-statistics theorem

1945 Phase stability in accelerators (synchrotron principle)

Classification

The weak interactions between quarks and leptons are those mediated by the socalled intermediate bosons W± and Z0, with a coupling which we generically label g. As indicated in Figure 7.1, there is a strong similarity between the Feynman diagrams for electromagnetic interactions mediated by photon exchange and weak interactions mediated by the intermediate bosons.

A familiar interaction is that between two straight wires hanging close together when electric currents – i.e. a flow of electrons and ions – pass through them. So, we can view the interaction of Figure 7.1(a) as that of two conserved electric currents jem, carried in this case by the electron e and the quark Q. Similarly, the interactions shown in Figures 7.1(b) and (c) can be viewed as between weak currents jweak. The difference is that these currents consist of a flow of conserved weak charge g rather than electric charge, e. In either case, these currents will contain the product of the (normalised) wavefunctions of the ‘in’ and ‘out’ particles that occur in the matrix element (2.16) for the interaction. Thus j ∝ ψ* ψ, where ψ* denotes an incoming and ψ an outgoing amplitude.

In Figure 7.1(b) one sees that the electric charges associated with the weak current actually change in the interaction, while in Figure 7.1(c) they do not. Rather inaccurately, these two are referred to as charged-current weak interactions (those in which the electric charge of each weak current changes) and neutral-current weak interactions (those in which the electric charges do not change).

Classical and quantum pictures of interactions

Classically, interaction at a distance, e.g. in electromagnetism, is described in terms of a potential or field due to one charged particle acting on another, the field permeating the whole of space around the source charge. A conceptually more appealing idea, perhaps, is that of an exchange interaction, where the object exchanged carries momentum from one charge to the other, the rate of exchange of momentum providing the force. A frequently quoted everyday example is of two ice-skaters travelling side by side, initially moving parallel, who start to diverge as they repel one another by throwing a ball back and forth.

In quantum theory, action at a distance is indeed viewed in terms of an exchange interaction, the exchange being of a specific quantum (a boson) associated with the particular type of interaction. Since the quantum carries momentum and energy, say ΔE, the conservation laws can only be satisfied if the process takes place within a timescale Δt limited by the Uncertainty Principle, i.e. ΔE Δt ≃ ħ. Such transient quanta are said to be virtual.

The quantum concept of an electromagnetic interaction is of the continual exchange (emission and absorption) of virtual photons by the charges, which is no more or less fictitious than the classical concept of an all-pervading field surrounding a source charge. Neither the field nor the virtual quanta are directly observable; it is the force that is the measured quantity.

ORIGIN OF LIFE ON EARTH

How did life originate on Earth? There are various theories, most of which fall into the four classes: special creation theories, spontaneous creation theories, panspermia theories, and biochemical theories.

Special creation theories

The belief that life originated as a supernatural event is the metaphysical theory of special creation. It has numerous mythic variations. Most recorded myths distinguish between nonliving and living things. Often the nonliving world comes first, the living world follows, and creation is thus a twofold act. Catastrophe theories of the eighteenth and nineteenth centuries elaborated on such beliefs and proposed that many acts of creation had occurred in the past. After a catastrophe had destroyed the terrestrial environment, newly created life arose in more evolved forms, and evolution occurred supernaturally, not naturally. Organic life even in its rudest forms was thought to be composed of substances fundamentally different from those of nonliving things. To this day we speak of organic and inorganic chemistry, although this distinction is now a matter of convenience only, and organic chemistry deals mostly with the numerous compounds containing carbon atoms. It came as a shock when the chemist Friedrich Wöhler in 1828 first made urea (a simple organic substance) from inorganic chemicals. Subsequent developments showed that chemicals are interchangeable between inorganic and organic things, thereby unifying the living and nonliving worlds at the atomic and molecular levels.

OUR GALAXY

Milky Way

Our Galaxy, an enormous system of clouds of glowing gas and 100 billion stars, is also known as the Milky Way. Light takes 100 000 years to cross the Galaxy from side to side, and the center of the Galaxy lies in the constellation of Sagittarius, obscured from view by clouds of dusty gas that drift among the stars. Far from the center of the Galaxy is our own star the Sun.

The disk and halo

The Galaxy consists of two basic components: disk and halo (see Figures 6.1 and 6.2). The Milky Way is actually our panoramic view of the disk that has a diameter of about 100 000 light years and a thickness of about one-twentieth, or less, of the diameter. The disk is composed of stars and interstellar gas, and contains over half the visible mass of the Galaxy. The gas amounts to one-tenth of the matter in the disk, and the dust amounts to about 1 percent or more of the mass of the gas. The disk of stars, gas, and dust rotates about the center, or nucleus, of the Galaxy like a giant carousel.

STATIC NEWTONIAN UNIVERSE

Until the 20th century everybody believed that the universe is naturally static: not expanding and not contracting. Even Albert Einstein, after the discovery of general relativity, continued to hold this belief for several years.

In the late 17th century, belief in a static order remained unshaken when Newton advanced the theory of universal gravity. In response to a question in a letter from the young clergyman Richard Bentley (Chapter 3), Newton wrote in reply that in an infinite universe it would be impossible for all matter to fall together and form a single large mass, but “some of it would convene into one mass and some into another, so as to make an infinite number of great masses, scattered at great distances from one to another throughout all that infinite space.”

The Newtonian theory of universal gravity, in which all bodies attract one another, reinforced the growing belief that the universe must be edgeless and therefore infinite. For if the universe were finite and bounded by a cosmic edge, it would have a center of gravity, and the attraction between its parts would cause it, said Newton, to “fall down into the middle of the whole space, and there compose one great spherical mass.” This argument led him finally to abandon the finite Stoic cosmos in favor of the infinite Atomist universe.

STATIC UNIVERSES

Before the twentieth century most Europeans and people of European descent believed the universe was created only a few thousand years ago, or at most a few hundred thousand years. Some people in the 18th and 19th centuries, more radical in outlook, thought the static Newtonian universe was in a steady state – everything remaining eternally unchanged – and the stars would shine endlessly. The realization in the late 19th century that stars have finite energy resources brought to an end the idea of a perpetually unchanging cosmos.

Static Einstein universe

In 1917, Einstein contrived an ingenious static universe using his recently developed theory of general relativity. In this universe, as in all universes we discuss, all places are alike and matter is distributed with uniform density.

Space and time in the new theory of general relativity had at last been awakened from the dead and become active participants in the world at large. Einstein, believing the universe to be static, tranquilized spacetime with a counteracting agent. In his 1917 paper, “Cosmological considerations on the general theory of relativity,” he wrote, “I shall conduct the reader over the road I have myself traveled, rather a rough and winding road, because otherwise I cannot hope that he will take much interest in the result at the end of the journey. The conclusion that I shall arrive at is that the field equations of gravitation that I have championed hitherto still need a slight modification.”

After Newton, astronomical advances in observation and theory were at first slow. Better telescopes had yet to be developed, photography and spectroscopy introduced into astronomy, and the chemical compositions and radial velocities of stars and nebulae determined. The puzzling nature of the nebulae had yet to be resolved, nebulae in the Galaxy to be distinguished from extragalactic nebulae, distance indicators to be found and calibrated, globular clusters to be identified as systems of stars lying in and on the outskirts of the Galaxy, and the confusing obscuration of starlight caused by interstellar absorption to be recognized. All this would be accomplished and accompanied by continual debate over controversial issues from the time of Newton to the time of Einstein during the eighteenth, nineteenth, and early twentieth centuries.