# Glossary

Major research university located in Pasadena, California. Areas of research include general relativity, particle physics, quantum gravity and cosmology; in addition, Caltech is one of the main sites for the researchers (although not the detectors!) of the LIGO project, which operates the most sensitive gravitational wave detectors to date. Also, the Einstein Papers Project, which is working on an edition of Einstein’s collected papers, is based at Caltech.

> Caltech webpages

> Webpages of the Theoretical Astrophysics and Relativity group at Caltech

carrier particle

In the framework of relativistic quantum field theories (which form the theoretical basis of the physics of elementary particles, the forces by which matter particles interact are transmitted by so-called carrier particles travelling back and forth between them. For instance, the electric force between two electrons would come about through the exchange of photons, the carrier particles of the electromagnetic interaction. Carrier particles always have integer spin, such as spin 1 or 2 (which means they belong to the class of particles called bosons). Synonym: force particles.

causal

In the context of relativity: causality concerns the question of which events cause which other events (Latin *causa*, the reason, the cause) or, more generally, can influence them. In special relativity, nothing, no moving object, no information, no influence can move faster than light. Thus, in principle, an event can only influence another event if the hypothetical influence (such as a signal or a force) would not have to be transmitted faster than light. In other words, light propagation determines the causal structure of spacetime (cf. light-cone). Models and theories that take this structure into account are called causal – for example the relativistic quantum field theories.

In general relativity, the cosmic speed limit, the speed of light is only defined locally: In a side-by-side race, no object, no influence can overtake a light signal. Also from this a causal structure can be derived and determines which events can influence which other events. As gravity deflects and delays light signals, the matter is more complicated in general relativity than in special relativity. Although this makes the analysis somewhat more complicated, the following still applies: the propagation of light determines the causal structure.

Synonyms: causality causal structure

causal sets

Approach to the problem of finding a theory of quantum gravity: In causet models, spacetime is composed of elementary building blocks that represent elementary events.

More information about causal sets can be found in the spotlight topic From order to Geometry: causal sets.

Synonyms: causets

celestial mechanics

That discipline in physics (and astronomy) dealing with the laws that govern the motions of heavenly bodies. Originally seen as distinct from the motions of bodies on earth (see Kepler’s laws of motion), it has been a sub-discipline of mechanics ever since Newton derived the cosmic laws of motions from more general mechanical laws.

For most astronomical applications, Newtonian, classical mechanics works perfectly well, however, as soon as high-precision measurements or strong gravitational fields come into play, celestial mechanics is governed by laws of relativistic mechanics derived from Einstein’s theory of general relativity.

Celsius

Most European countries use the Celsius temperature scale in everyday life. Temperatures are given in “degrees Celsius” (abbreviated as °C). By definition, the zero point of this scale (0°C) is the melting point of water, while the temperature 100°C corresponds to its boiling point (both parts of the definition assume the same standard value for air pressure).

Relation to the Fahrenheit scale: X degrees Celsius correspond to (9/5 times X) +32 Fahrenheit, Y Fahrenheit are (Y-32)*5/9 degrees Celsius.

Relation to the Kelvin temperature scale used in physics: X degree Celsius are X plus 273.15 Kelvin, Y Kelvin are Y minus 273.15 degrees Celsius. In particular, differences in temperature are the same in Kelvin and in degrees Celsius; the only difference between the two scales is their choice of zero point.

censorship

See cosmic censorship.

centrifugal force

An inertial force which an observer in a rotating reference frame needs to introduce in order to explain why nearly all objects in the vicinity appear to undergo acceleration away from the axis of rotation.

CERN

European research centre for nuclear and particle physics (Centre Européen pour la Récherche Nucleaire – pardon my French), located near Geneva on both sides of the franco-swiss border, founded 1954.

CERN isn’t famous just because of particle accelerators like its proton synchrotron, the Large Electron Positron Collider (LEP) and the Large Hadron Collider (LHC), but also as the birthplace of the World Wide Web.

Chandrasekhar mass

Upper bound for the masses of white dwarfs, in other words: for what low-mass stars become when they have used up their nuclear fuel. The first to calculate this upper bound was the Indian-American astrophysicist Subramanian Chandrasekhar.

The Chandrasekhar mass is 1.4 times as large as the solar_mass. The reason that no white dwarf can have more mass follows from its need to maintain equilibrium between the gravitational force working towards further collapse and the interior pressure of the star acting to prevent collapse. For larger masses, the degeneracy pressure on which a white dwarf’s stability depends is overcome by the gravitational force, and further collapse ensues.

Synonyms: Chandrasekhar limit

charge

On the one hand: a measure of the strength of a force (action-at-a-distance) originating from a body, and of how susceptible it is to being influenced by other bodies via the same force. The most famous example is electric charge: Electrically charged bodies act on other electrically charged bodies via an electric force whose strength is proportional to the electric charges of the bodies involved.

It is a characteristic property of charges that they are conserved; they can neither be created from nothing nor simply disappear. For instance, when a positron with electric charge +1 (in suitable units) and an electron with electric charge -1 annihilate to give electromagnetic radiation, overall charge conservation is satisfied: Before the annihilation, the sum of the electric charges was 1+(-1)=0, and afterwards, when there is only uncharged electromagnetic radiation left, it is also zero.

In the context of particle physics, there are more abstract charges not directly connected with forces and interaction, but subject to similar conservation laws.

chemical element

See element

chemical evolution

The changes in the abundances of the different chemical elements that have taken place throughout the history of the universe, mainly in the very early universe during the phase called Big Bang Nucleosynthesis and, from a couple of hundred million years later until today, in the interior of stars (stellar nucleosynthesis).

classical

In physics, the word is used with two meanings. First of all, it denotes physical models or theories that take into account neither the effects of Einstein’s theories of relativity nor those of quantum physics, for example classical mechanics. However, it is also used to denote models or theories that are not formulated in the framework of quantum physics; in that sense, general relativity is an example for a classical theory.

classical mechanics

classical tests of general relativity

Compton Gamma Ray Observatory

A satellite observatory for astronomical observations of gamma rays operated by NASA from 1991 to 2000. Scientific aims included the study of gamma ray bursts, pulsars, supernovae, and accretion processes around black holes.

conic singularity

A particular type of spacetime singularity (i.e. a boundary where spacetime ends) that is not associated with curvature, but instead is the analogue of the pointed tip of a cone.

More information about the different types of singularity can be found in the spotlight text Spacetime singularities.

conservation laws

Some of the most important quantities in physics are *conserved *: What they measure can neither be created nor destroyed, and their total sum is constant over time. Such statements of constancy over time are called *conservation laws*.

The most important conserved quantity is energy. Energy can neither be created from nothing nor simply vanish. If the energy contained in a system increases, it must be because energy has been transported into the system (and there is now less energy outside the system); if the energy decreases, it must be because energy has been transferred from the system (and there is now more energy outside).

Another important class of conserved quantities are charges, for instance electric charge. A further conserved quantity in mechanics is angular momentum; a quantity associated with a body’s rotation.

Synonyms: conserved quantities

constancy of the speed of light

One of the basic postulates of special relativity: The speed of light in a vacuum is the same for all observers drifting through gravity-free space (more precisely: for all inertial observers. In particular, its value is independent of an observer’s motion relative to the source of the light.

continuous

Space as we are used to thinking about it is a continuum or, equivalently, continuous space: Between every two points, there always exists an infinity of other points, and every volume can be divided into smaller and smaller parts without ever reaching a limit.

Synonyms: continuum

coordinates

A rule for assigning to each point of a general space (that is to say: of a line segment, a surface, three-dimensional space or higher-dimensional analogues) or spacetime a set of numbers for purposes of identification.

Many readers will know two examples from school: In the case of the line of real numbers, every point on the line corresponds to a real number which can be seen as its coordinate. What’s important is that these coordinates reflect neighbourly relations: The number 1 lies between the number 0 and the number 2, and so does the point corresponding to it lie between the two points corresponding to 0 and 2. The second example is the usual X-Y-coordinate system (sometimes called Cartesian coordinates), by which every point in a plane can be characterized by two numbers: the first its X coordinate value, the second its Y coordinate value.

The examples reflect an important property of coordinates: To uniquely identify a point in space, one needs as many coordinate values as the space has dimensions.

Of the four coordinates defining an event in spacetime, three serve to fix its location in three-dimensional space, while the fourth gives the point in time for the event.

Synonyms: coordinate system

Coriolis force

An inertial force which an observer in a rotating reference frame needs to introduce in order to explain why certain moving objects appear to undergo acceleration at right angles to their direction of motion.

The Coriolis force plays an important role in meteorology – from the point of view of an observer at rest on the surface of the earth, it explains the deflection of certain wind flows.

cosmic background radiation

“Electromagnetic echo” of the early universe; first predicted by the big bang models in the context of general relativity; later, from the 1960s on, observed with radio telescopes.

The cosmic microwave background contains important information about the properties and the earliest history of the universe. For instance, it can be used to deduce whether space is curved or Euclidean; more information about this can be found in the spotlight text Cosmic sound.

cosmic censorship

Possibly the most disturbing feature of Einstein’s general theory of relativity is the existence of singularities – most commonly, regions of spacetime in which density and curvature go to infinity.

It is quite likely that singularities are artefacts resulting from the fact that Einstein’s theory does not take quantum effects into account, and that they will be absent in a more complete theory of quantum gravity. Yet even if you leave aside quantum theory, and stay strictly within the framework of Einstein’s theory, it is likely that most singularities are, if not absent, then at least well-concealed:

The hypothesis of cosmic censorship states that, whenever a body collapses so completely as to result in the formation of a singularity, a black hole will be formed so that the singularity will be hidden behind the horizon, and thus completely unobservable for anyone outside the black hole.

At the present time, this hypothesis is unproven. Indeed, there are some counterexamples, but they describe idealized situations which are not likely to tell us anything about the real world. Finding a proof that, for all realistic collapse situations, there is indeed cosmic censorship, is one of the great open problems of general relativity research.

Cosmic Explorer

Cosmic Explorer is a proposed third generation gravitational wave detector, which, together with other third generation detectors like the Einstein telescope, is supposed to allow for gravitational wave detection with greater sensitivity than ever before. The detector will be built in the United States and is designed with an L-shaped geometry, each arm being 40 kilometers in length.

Cosmic microwave background radiation

See cosmic background radiation, above.

cosmic rays

Highly energetic particles reaching the earth from the depths of space, mainly consisting of protons and light atomic nuclei.

cosmic time

Measure for the progress of the evolution of an expanding universe such as that of the big bang models. It corresponds to time as measured by clocks that are at rest relative to the expanding space, and that have been set to zero at the very beginning, the time of the hypothetical big bang singularity. Synonym: Age of the universe.

The basic features of the cosmological models that use cosmic time are reviewed in the chapter Cosmology of Elementary Einstein.

cosmological constant

In the big bang models, an inherent tendency of space to accelerate or decelerate its expansion. From observations, it seems that our own cosmos has a cosmological constant that leads to a slight acceleration of its expansion.

cosmological redshift

Consequence of cosmic expansion in the big bang models: the farther away a galaxy, the more strongly shifted towards lower frequencies is the light we receive from it .

cosmology

That branch of physics and astronomy dealing with the structure and development of the universe as a whole. At the core of modern cosmology are the big bang models based on Einstein’s general theory of relativity. Their basic features are reviewed in the chapter Cosmology of Elementary Einstein. In order to describe the very early universe, it will be necessary to take the effects of quantum gravity into account – this gives rise to models of quantum cosmology.

current

Matter in coordinated, flowing motion – think of water flowing in a pipe. An important example is the electric current associated with moving electric charges. Electric currents are the sources of magnetic fields.

curvature

For a two-dimensional surface: criterion that allows us to decide whether that surface is a plane, or part of a plane (i.e. a surface on which the usual rules of high school geometry apply), or not. Two possibilities to define the curvature of a plane are the following:

Sum of the angles of a triangle. In a plane, the sum of the three angles in a triangle formed by three straight lines is always 180 degrees. In a more general surface, the sum of the angles of a more general triangle formed by three straightest-possible lines (i.e. geodesics) can be larger or smaller than 180 degrees. The difference (the surplus or deficit), divided by the area of the triangle, is a measure for the curvature of that region of the surface.

Second possibility: the circumference of a circle. In the plane, that circumference is equal to 2 times pi times the circle’s radius. On a more general surface, it can be larger or smaller. The difference, divided by the third power of the radius, leads to the same measure for the curvature as the first definition.

Simple examples for curved surfaces are the surface of a sphere (positive curvature, that is to say: sum of the angles in a triangle larger than 180 degrees, circumference of a circle smaller than 2 times pi times radius) and that of a saddle (negative curvature, that is to say: sum of the angles in a triangle smaller than 180 degrees, circumference of a circle larger than 2 times pi times radius).

Curvature cannot only be defined for surfaces, but also for higher-dimensional, more general spaces or spacetimes. However, the generalized definition is substantially more complicated, and curvature is defined not by a single number, but by a set of numbers (that, together, form the “curvature tensor”). It’s basic meaning, however, is the same: it measures the space’s deviation from a flat space of the same dimension.

For physics, an important aspect of curvature is its connection with gravity, as described in Einstein’s general theory of relativity. Basic information about this can be found in the spotlight text Gravity: From weightlessness to curvature.

curvature singularity

A type of spacetime singularity (i.e. a boundary where spacetime ends) that is associated with infinitely strong gravity and, hence, infinitely strong spacetime curvature.

Two different varieties of curvature singularity are Ricci- and Weyl singularities.

More information about the different types of singularities can be found in the spotlight text Spacetime singularities.