Three Roads to Quantum Gravity (32 page)

A scientific model or theory often describes only part of the universe. Some features of the rest of the universe may be included as necessary to define the properties of that part of the universe that is studied. These features are called the background. For example, in Newtonian physics space and time are part of the background because they are taken to be absolute.

A theory, such as Newtonian physics, that makes use of a background.

A theory that does not make use of a division of the universe into a part that is modelled and the rest, which is taken to be part of the background. General relativity is said to be background independent because the geometry of space and time is not fixed, but evolves in time just as any other field, such as the electromagnetic field.

The relationship between the area of a surface and the maximum amount of information about the universe on one side of it that can pass through it to an observer on the other side. The relationship states that the number of bits of information the observer can gain
cannot be greater than one-quarter the area of the surface in Planck units.

A region of space and time that cannot send signals to the outside world because all light emitted comes back. Among the ways a black hole may be formed is by the collapse of a very massive star when it runs out of its nuclear fuel.

The surface surrounding a black hole, within which is the region from which light signals cannot escape.

A particle whose angular momentum comes in integer multiples of Planck’s constant. Bosons do not obey the Pauli exclusion principle.

A possible feature of geometry, as described in string theory, which consists of a surface of some dimensions embedded in space, which evolves in time. For example, strings are one-dimensional branes.

The principle that events are influenced by those in their past. In relativity theory one event can have a causal influence on another only if energy or information sent from the first reaches the second.

Because there is a maximum speed at which energy and information can be transmitted, the events in the history of the universe can be organized in terms of their possible causal relations. To do this one indicates, for every pair of events, whether the first is in the causal future of the second, or vice versa, or whether there is no possible causal relation between them because no signal could have travelled between them. Such a complete description defines the causal structure of the universe.

Any physical theory that shares certain features with Newtonian physics, including the assumption that the future is completely determined by the present and that the act of observation has no effect on the system studied. The term is used mainly to label any theory that is not part of quantum theory. Einstein’s general theory of relativity is considered to be a classical theory.

The collection of classical theories.

An approach to the interpretation of quantum theory which asserts that the theory makes predictions about the probabilities for sets of alternative histories, when these can be done consistently.

Describing a smooth and unbroken space which has the property of the number line, which is that it can be quantified in terms of coordinates expressed in real numbers. Any region of continuous space having a finite volume contains an infinitely uncountable number of points.

Any space that is continuous.

The basic mathematical object in Einstein’s general theory of relativity. It determines how the tipping of light cones changes from time to time and place to place in the history of the universe.

Any variable in a physical theory that may be specified independently of the other variables, which once specifies evolves in time according to a dynamical law. Examples are the positions of particles and the values of the electric and magnetic fields.

An operation that moves the points of space around, preserving only those relationships between them that are used to define which points are near to one another.

Describing a space that is made of a finite number of points.

The principle of duality applies when two descriptions are different ways of looking at the same thing. In particle physics it usually refers to a description in terms of strings and a description in terms of the flux of the electric field or some generalization of it.

The basic equations of the general theory of relativity. They determine how light cones tip and how they are related to the distribution of matter in the universe.

The theory of electricity and magnetism, including light, developed by Michael Faraday and James Clerk Maxwell in the nineteenth century.

A measure of the disorder of a physical system. It is defined as the amount of information about the microscopic motion of the atoms making up the system which is not determined by a description of the macroscopic state of that system.

A system is defined to be in equilibrium, or thermodynamic equilibrium, when it has the maximum possible amount of entropy.

In relativity theory, something that happens at a particular point of space and moment of time.

see Pauli exclusion principle.

A particle whose angular momentum comes in integer multiples of one-half of Planck’s constant. Fermions satisfy the Pauli exclusion principle.

A depiction of a possible process in the interaction of several elementary particles. Quantum theory assigns to each diagram the probability amplitude for that process to occur. The total probability is proportional to the square of the sum of the amplitudes of the possible processes, each of which is depicted by a Feynman diagram.

A physical entity that is described by specifying the value of some quantity at every point of space and time; examples are the electric and magnetic fields.

The future, or causal future, of an event consists of all those events that it can influence by sending energy or information to it.

For a specific event, all other events that can be reached from it by a signal travelling at the speed of light. Since the speed of light is the maximum speed at which energy or information can travel, the future light cone of an event marks the limits of the causal future of that event. See also light cone.

Einstein’s theory of gravity, according to which gravity is related to the influence the distribution of matter has on the causal structure of spacetime.

A diagram consisting of a set of points, called vertices, connected by lines, called edges. See also lattice.

The thermal radiation black holes are predicted to give off, having a temperature which is inversely proportional to the black hole’s mass. Hawking radiation is caused by quantum effects.

Conjectured degrees of freedom which underlie the statistical uncertainties in quantum theory. If there are hidden variables, then it is possible that the uncertainties in quantum theory are just the result of
our ignorance about the values of the hidden variables and are not fundamental.

For each observer in a spacetime, the surface beyond which they cannot see, or receive any signals from. Examples are black hole horizons.

A measure of the organization of a signal. It is equal to the number of yes/no questions whose answers could be coded in the signal.

A branch of mathematics concerned with classifying the different ways of tying a knot.

A space consisting of a finite number of points, with nearby points connected by lines called edges. A lattice is often, but not always, distinguished from a graph in that a lattice is a graph with a regular structure. An example of a lattice is shown in
Figure 22
.

A theory in which space or spacetime is considered to be a lattice.

All the events that can be reached by light signals travelling to the future, or coming from the past, from a single event. We may therefore distinguish between the future light cone, which contains events that can be reached by light travelling into the future, and the past light cone, which contains events that can be reached by light travelling from the past.

Two curves link in three-dimensional space if they cannot be pulled apart without passing one through the other.

A circle drawn in space.

An approach to quantum gravity in which space is constructed from the relationships between loops, originally derived by applying quantum theory to the formulation of general relativity discovered by Sen and Ashtekar.

An interpretation of quantum theory according to which the different possible outcomes of an observation of a quantum system reside in different universes, all of which somehow coexist.

The conjectured theory which would unify the different string theories.

The fundamental constant that measures the strength of the gravitational force.

All physical theories formulated on the pattern of Newton’s laws of motion. See classical physics, which is a synonymous term.

A description of a space in which it is impossible to determine enough information to locate a point, but which can have many other properties of space including the fact that it can support a description of particles and fields evolving in time.

For a particular event, all other events that could have influenced it by sending energy or information to it.

The past light cone of an event consists of all those events that could have sent a light signal to it.

The principle that no two fermions can be put into exactly the same quantum state; named after Wolfgang Pauli.

An approach to making calculations in physics in which some phenomena are represented in terms of small deviations from or oscillations of some stable state, or the interactions among such oscillations.

The scale of distance, time and energy on which quantum gravity effects are important. It is defined roughly by the Planck units - processes on the Planck scale take around a Planck time, which is 10
^-43
of a second. To observe on the Planck scale, distances of around the Planck length must be probed. This is about 10
^-33
of a centimetre.

A fundamental constant that sets the scale of quantum effects; normally denoted by h.

The basic units of measure in a quantum theory of gravity. Each is given by a unique combination of three basic constants: Planck’s constant, Newton’s gravitational constant and the speed of light. Planck units include the Planck length, Planck energy, Planck mass, Planck time and Planck temperature.

The theory of the forces between quarks.

The marriage of quantum theory with electrodynamics. It describes light and the electric and magnetic forces in quantum terms.

The theory that attempts to describe the whole universe in the language of quantum theory.

The theory that unifies quantum theory with Einstein’s general theory of relativity.

The theory of physics that attempts to explain the observed behaviour of matter and radiation. It is based on the uncertainty principle and wave-particle duality.

The complete description of a system at one moment of time, according to the quantum theory.

An elementary particle which is a constituent of a proton or neutron.