Chronology

a chronology

of events, insights, and discoveries

1687  Newton publishes his Principia, in which are formulated his concepts of absolute space and time, and his laws of motion and laws of gravity. [Ch. 1]
1783&1795  Michell and Laplace, using Newton’s laws of motion, gravity, and light, formulate the concept of a Newtonian black hole. [Ch. 3]
1864  Maxwell formulates his unified laws of electromagnetism. [Ch. 1]
1887  Michelson and Morley show, experimentally, that the speed of light is independent of the velocity of the Earth through absolute space. [Ch. 1]
1905  Einstein shows that space and time are relative rather than absolute, and formulates the special relativistic laws of physics. [Ch. 1]
 Einstein shows that electromagnetic waves behave under some circumstances like particles, thereby initiating the concept of wave/particle duality that underlies quantum mechanics. [Ch. 4]
1907  Einstein, taking his first steps toward general relativity, formulates the concept of a local inertial frame and the equivalence principle, and deduces the gravitational dilation of time. [Ch. 2]
1908  Hermann Minkowski unifies space and time into an absolute four-dimensional spacetime. [Ch. 2]
1912  Einstein realizes that spacetime is curved, and that tidal gravity is a manifestation of that curvature. [Ch. 2]
1915   Einstein and Hilbert independently formulate the Einstein field equation (which describes how mass curves spacetime), thereby completing the laws of general relativity. [Ch. 2]
1916  Karl Schwarzschild discovers the Schwarzschild solution of the Einstein field equation, which later will turn out to describe nonspinning, uncharged black holes. [Ch. 3]
 Flamm discovers that, with an appropriate choice of topology, the Schwarzschild solution of the Einstein equation can describe a wormhole. [Ch. 14]
1916&1918  Reissner and Nordstrom discover their solution of the Einstein field equation, which later will describe nonspinning, charged black holes. [Ch. 7]
1926  Eddington poses the mystery of the white dwarfs and attacks the reality of black holes. [Ch. 4]
 Schrödinger and Heisenberg, building on others’ work, complete the formulation of the quantum mechanical laws of physics. [Ch. 4]
 Fowler uses the quantum mechanical laws to show how electron degeneracy resolves the mystery of the white dwarfs. [Ch. 4]
1930  Chandrasekhar discovers that there is a maximum mass for white dwarfs. [Ch. 4]
1932  Chadwick discovers the neutron. [Ch. 5]
1933  Jansky discovers cosmic radio waves. [Ch. 9]
1934  Landau creates his research group in the V.S.S.R. and begins to transfuse theoretical physics there from Western Europe. [Ch. 5, 13]
 Baade and Zwicky identify supernovae, propose the concept of a neutron star, and suggest that supernovae are powered by the implosion of a stellar core to form a neutron star. [Ch. 5]
1935  Chandrasekhar makes more complete his demonstration of the maximum mass for white-dwarf stars, and Eddington attacks his work. [Ch. 4]
1935–1939  The Great Terror in the V.S.S.R. [Ch. 5, 6]
1957  Greenstein and Whipple demonstrate that Jansky’s cosmic radio waves cannot be explained by then-known astrophysical processes. [Ch. 9]
 Landau, in a desperate attempt to avoid prison and death, proposes that stars are kept hot by energy released when matter flows onto neutron cores at their centers. [Ch. 5]
1958  Landau is imprisoned in Moscow on charges of spying for Germany. [Ch. 5]
 Oppenheimer and Serber disprove Landau’s neutron core method for keeping stars hot; Oppenheimer and Volkoff show that there is a maximum mass for neutron stars. [Ch. 5]
 Bethe and Critchfield show that the Sun and other stars are kept hot by burning nuclear fuel. [Ch.5]
1939   Landau, near death, is released from prison. [Ch. 5]
 Einstein argues that black holes cannot exist in the real Universe. [Ch. 4]
 Oppenheimer and Snyder, in a highly idealized calculation, show that an imploding star forms a black hole, and (paradoxically) that the implosion appears to freeze at the horizon as seen from the outside but not as seen from the star’s surface. [Ch. 6]
 Reber discovers cosmic radio waves from distant galaxies, but does not know that is what he is seeing. [Ch. 9]
 Bohr and Wheeler develop the theory of nuclear fission. [Ch. 6]
 Khariton and Zel’dovich develop the theory of a chain reaction of nuclear fissions. [Ch. 6]
 The German army invades Poland, setting off World War 11.
1942  The U.S. launches a crash program to develop the atomic bomb, led by Oppenheimer. [Ch. 6]
1943  The U.S.S.R. launches a low-level effort to design nuclear reactors and atomic bombs, with Zel’dovich as a lead theorist. [Ch. 6]
1945  The U.S. drops atomic bombs on Hiroshima and Nagasaki. World War 11 ends. A low-level U.S. effort to develop the superbomb is begun. [Ch. 6]
 The U.S.S.R. launches a crash program to develop the atomic bomb, with Zel’dovich as a lead theorist. [Ch. 6]
1946  Friedman and his team launch the first astronomical instrument above the Earth’s atmosphere, on a captured German V-2 rocket. [Ch. 8]
 Experimental physicists in England and Australia begin constructing radio telescopes and radio interferometers. [Ch. 9]
1948  Zel’dovich” Sakharov, Ginzburg, and others in the U.S.S.R. initiate design work for a superbomb (hydrogen bomb); Ginzburg invents the LiD fuel, Sakharov the layered-cake design. [Ch. 6]
1949  The U.S.S.R. explodes its first atomic bomb, setting off a debate in the U.S. about a crash program to develop the superbomb. The D.S.S.R. proceeds directly into a crash program for the superbomb, without debate. [Ch. 6]
1950  The V.S. launches a crash superbomb effort. [Ch. 6]
 Kiepenheuer and Ginzburg realize that cosmic radio waves are produced by cosmic-ray electrons spiraling in interstellar magnetic fields. [Ch. 9]
 Alexandrov and Pimenov initiate an ill-fated attempt to introduce topological tools into mathematical studies of curved spacetime. [Ch. 13]
1951  Teller and Vlam in the U.S. invent the idea for a “real” superbomb, one that can be arbitrarily powerful; Wheeler puts together a team to design a bomb based on the idea and simulate its explosion on computers. [Ch. 6]
  Graham Smith provides Baade with a 1-arc-minute error box for the cosmic radio source Cyg A, and Baade discovers with an optical telescope that Cyg A is a distant galaxy—a “radio galaxy.” [Ch. 9]
1952  The U.S. explodes its first superbomb device, one too massive to be delivered by an airplane or rocket, but using the Teller–Vlam invention and based on the Wheeler team’s design work. [Ch. 6]
1953  Wheeler launches into research on general relativity. [Ch. 6]
 Jennison and Das Gupta discover that the radio waves from galaxies are produced by two giant lobes on opposite sides of the galaxy. [Ch. 9]
 Stalin dies. [Ch. 6]
 The U.S.S.R. explodes its first hydrogen bomb, based on the Ginzburg and Sakharov ideas. It is claimed by U.S. scientists not to be a “real” superbomb because the design does not permit the bomb to be arbitrarily powerful. [Ch.6]
1954  Sakharov and Zel’dovich invent the Teller–Ulam idea for a “real” superbomb. [Ch. 6]
 The U.S. explodes its first real superbomb, based on the Teller–Ulam/Sakharov–Zel’dovich idea. [Ch. 6]
 Teller testifies against Oppenheimer, and Oppenheimer’s security clearance is revoked. [Ch. 6]
1955  The U.S.S.R. explodes its first real superbomb, based on the Teller–Ulam/Sakharov–Zel’dovich idea. [Ch. 6]
 Wheeler formulates the concept of gravitational vacuum fluctuations, identifies the Planck–Wheeler length as the scale on which they become huge, and suggests that on this scale the concept of spacetime gets replaced by quantum foam. [Ch. 12, 13, 14]
1957  Wheeler, Harrison, and Wakano formulate the concept of cold, dead matter and make a catalog of all possible cold, dead stars. Their catalog firms up the conclusion that massive stars must implode when they die. [Ch. 5]
 Wheeler’s group studies wormholes; Regge and Wheeler invent perturbation methods for analyzing small perturbations of wormholes; their formalism later will be used to study perturbations of black holes. [Ch. 7, 14]
 Wheeler poses the issue of the final state of stellar implosion as a holy grail for research and, in a confrontation with Oppenheimer, opposes the idea that the final state will be hidden inside a black hole. [Ch. 6, 13J
1958  Finkelstein discovers a new reference frame for the Schwarzschild geometry, and it resolves the 1939 Oppenheimer–Snyder paradox of why an imploding star freezes at the critical circumference as seen from outside but implodes through the critical circumference as seen from inside. [Ch. 6]
1958 – 1960  Wheeler gradually embraces the concept of a black hole and becomes its leading proponent. [Ch. 6]
1959   Wheeler argues that spacetime singularities formed in the big crunch or inside a black hole are governed by the laws of quantum gravity, and may consist of quantum foam. [Ch. 13]
 Burbidge shows that the giant lobes of radio galaxies contain magnetic and kinetic energy equivalent to that obtained by a perfect conversion of 10 million Suns into pure energy. [Ch. 9]
1960  Weber initiates construction of bar detectors for gravitational waves. [Ch. 10]
 Kruskal shows that, if it is not threaded by any material, a spherical worm-hole will pinch off so quickly that it cannot be traversed. [Ch. 14]
 Graves and Brill discover that the Reissner–Nordstrom solution of Einstein’s equation describes a spherical, electrically charged black hole and also a wormhole. [Ch. 7] Their work suggests (incorrectly) that it might be possible to travel from the interior of a black hole in our Universe through hyperspace and into some other universe. [Ch. 13]
1961  Khalatnikov and Lifshitz argue (incorrectly) that Einstein’s field equation does not permit the existence of singularities with randomly deformed curvature, and therefore singularities cannot form inside real black holes or in the Universe’s big crunch. [Ch. 13]
1961–1962  Zel’dovich begins research on astrophysics and general relativity, recruits Novikov, and begins to build his research team. [Ch. 6]
1962  Thorne begins research under Wheeler’s guidance and initiates research that will lead to the hoop conjecture. [Ch. 7]
 Giacconi and his team discover cosmic X-rays, using a Geiger counter flown above the Earth’s atmosphere on an Aerobee rocket. [Ch. 8]
1963  Kerr discovers his solution of Einstein’s field equation. [Ch. 7]
 Schmidt, Greenstein, and Sandage discover quasars. [Ch. 9]
1964  The golden age of theoretical black-hole research begins. [Ch. 7]
 Penrose introduces topology as a tool in relativity research, and uses it to prove that singularities must reside inside all black holes. [Ch. 13]
 Ginzburg and then Doroshkevich, Novikov, and Zel’dovich discover the first evidence that a black hole has no “hair.” [Ch. 7]
 Colgate, May, and White in the U.S., and Podurets, Imshennik, and Nadezhin in the U.S.S.R., adapt bomb design computer codes to simulate realistic implosions of stellar cores; they confirm Zwicky’s 1934 speculation that implosions with low mass will form a neutron star and trigger a supernova, and confirm the 1939 Oppenheimer–Snyder conclusion that implosions with larger mass will create a black hole. [Ch. 6]
 Zel’dovich, Guseinov, and Salpeter make the first proposals for how to search for black holes in the real Universe. [Ch. 8]
 Salpeter and Zel’dovich speculate (correctly) that supermassive black holes power quasars and radio galaxies. [Ch. 9]
  Herbert Friedman and his team discover Cygnus X-1, using a Geiger counter flown on a rocket. [Ch. 8]
1965  Boyer and Lindquist, Carter, and Penrose discover that Kerr’s solution of Einstein’s field equation describes a spinning black hole. [Ch. 7]
1966  Zel’dovich and Novikov propose searching for black holes in binaries where one object emits X-rays and the other light; this method will succeed in the 1970s (probably). [Ch. 8]
 Geroch shows that the topology of space can change (for example, a worm-hole can form) non–quantum mechanically only if a time machine is created in the process, at least momentarily. [Ch. 14]
1967  Wheeler coins the name black hole. [Ch. 7]
 Israel proves rigorously the first piece of the black-hole, no-hair conjecture: A nonspinning black hole must be precisely spherical. [Ch. 7]
1968  Penrose argues that it is impossible to travel from the interior of a black hole in our Universe through hyperspace and into some other universe; others, in the 1970s, will confirm that his argument is correct. [Ch. 13]
 Carter discovers the nature of the swirl of space around a spinning black hole and its influence on infalling particles. [Ch. 7]
 Misner and independently Belinsky, Khalatnikov, and Lifshitz discover the oscillatory “mixmaster” singularity as a solution of Einstein’s equation. [Ch. 13]
1969  Hawking and Penrose prove that our Universe must have had a singularity at the beginning of its big bang expansion. [Ch. 13]
 Belinsky, Khalatnikov, and Lifshitz discover the oscillatory BKL singularity as a solution of Einstein’s equation; they show that it has random deformations of its spacetime curvature and argue that therefore it is the type of singularity that forms inside black holes and in the big crunch. [Ch. 13]
 Penrose discovers that a spinning black hole stores enormous energy in the swirling motion of space around it, and that this rotational energy can be extracted. [Ch. 7]
 Penrose proposes his cosmic censorship conjecture, that the laws of physics prevent naked singularities from forming. [Ch. 13]
 Lynden-Bell proposes that gigantic black holes reside in the nuclei of galaxies and are surrounded by accretion disks. [Ch. 9]
 Christodoulou notices a similarity between the evolution of a black hole when it slowly accretes matter and the laws of thermodynamics. [Ch. 12]
 Weber announces tentative observational evidence for the existence of gravitational waves, triggering many other experimenters to start constructing bar detectors. By 1975 it will be clear he was not seeing waves. [Ch. 10]
 Braginsky discovers evidence that there will be a quantum limit on the sensitivities of gravitational-wave detectors. [Ch. 10]
1970   Bardeen shows that the accretion of gas is likely to make typical black holes in our Universe spin very rapidly. [Ch. 9]
 Price, building on work of Penrose, Novikov, and Chase, de la Cruz, and Israel, shows that black holes lose their hair by radiating it away, and he proves that anything which can be radiated will be radiated away completely. [Ch. 7]
 Hawking formulates the concept of a black hole’s absolute horizon and proves that the surface areas of absolute horizons always increase. [Ch. 12]
 Giacconi’s team constructs Uhuru, the first X-ray detector on a satellite; it is launched into orbit. [Ch. 8]
1971  Combined X-ray, radio-wave, and optical observations begin to bring strong evidence that Cygnus X-1 is a black hole orbiting a normal star. [Ch. 8]
 Weiss at MIT and Forward at Hughes pioneer interferometric detectors for gravitational waves. [Ch. 10]
 Rees proposes that a radio galaxy’s giant lobes are powered by jets that shoot out of the galaxy’s core. [Ch. 9]
 Hanni and Ruffini formulate the concept of surface charge on a horizon, a foundation for the membrane paradigm. [Ch. 11]
 Press discovers that black holes can pulsate. [Ch. 7]
 Zel’dovich speculates that spinning black holes radiate, and Zel’dovich and Starobinsky use the laws of quantum fields in curved spacetime to justify Zel’dovich’s speculation. [Ch. 12]
 Hawking points out that tiny “primordial” black holes might have been created in the big bang. [Ch. 12]
1972  Carter, building on work by Hawking and Israel, proves the no-hair conjecture for spinning, uncharged black holes (except for some technical details filled in later by Robinson). He shows that such a black hole is always described by Kerr’s solution of Einstein’s equation. [Ch. 7]
 Thorne proposes the hoop conjecture as a criterion for when black holes form. [Ch. 7]
 Bekenstein conjectures that a black hole’s surface area is its entropy in disguise, and conjectures that the hole’s entropy is the logarithm of the number of ways the hole could have been made. Hawking argues vigorously against this conjecture. [Ch. 12]
 Bardeen, Carter, and Hawking formulate the laws of evolution of black holes in a form that is identical to the laws of thermodynamics, but maintain that the horizon’s surface area cannot be the hole’s entropy in disguise. [Ch. 12]
 Teukolsky develops perturbation methods to describe the pulsations of spinning black holes. [Ch. 7]
1973  Press and Teukolsky prove that the pulsations of a spinning black hole are stable; they do not grow by feeding off the hole’s rotational energy. [Ch. 7]
1974   Hawking shows that all black holes, spinning or nonspinning, radiate precisely as though they had a temperature that is proportional to their surface gravity, and they thereby evaporate. He then recants his claim that the laws of black-hole mechanics are not the laws of thermodynamics in disguise and recants his critique of Bekenstein’s conjecture that a hole’s surface area is its entropy in disguise. [Ch. 12]
1974–1978  Blandford, Rees, and Lynden-Bell identify several methods by which supermassive black holes in the nuclei of galaxies and quasars can create jets. [Ch. 9]
1975  Bardeen and Petterson show that the swirl of space around a spinning black hole can act as a gyroscope to maintain the directions of jets. [Ch. 9]
 Chandrasekhar embarks on a five-year quest to develop a complete mathematical description of perturbations of black holes. [Ch. 7]
 Unruh and Davies infer that, as seen by accelerating observers just above a black hole’s horizon, the hole is surrounded by a hot atmosphere of particles, whose gradual escape accounts for the hole’s evaporation. [Ch. 12]
 Page computes the spectrum of particles radiated by black holes. Hawking and Page, from observational data on cosmic gamma rays, infer that there can be no more than 300 tiny, primordial, evaporating black holes in each cubic light-year of space. [Ch. 12]
 The golden age of theoretical black-hole research is declared finished by youthful researchers. [Ch. 7]
1977  Gibbons and Hawking verify Bekenstein’s conjecture that a black hole’s entropy is the logarithm of the number of ways it might have been made. [Ch. 12]
 Radio astronomers use interferometers to discover the jets that feed power from a galaxy’s central black-hole engine to its giant radio-emitting lobes. [Ch. 9]
 Blandford and Znajek show that magnetic fields, threading the horizon of a spinning black hole, can extract the hole’s spin energy, and that the extracted energy can power quasars and radio galaxies. [Ch. 9]
 Znajek and Damour formulate the membrane description of a black-hole horizon. [Ch. 11]
 Braginsky and colleagues, and Caves, Thorne, and colleagues, devise quantum nondemolition sensors for circumventing the quantum limit on bar detectors of gravitational waves. [Ch. 10]
1978  Giacconi’s group completes construction of the first high-resolution X-ray telescope, called “Einstein,” and it is launched into orbit. [Ch. 8]1
1979  Townes and others discover evidence for a 3-million-solar-mass black hole at the center of our galaxy. [Ch. 9]
 Drever initiates an interferometric gravitational-wave detection project at Caltech.[Ch. 10]
1982   Bunting and Mazur prove the no-hair conjecture for spinning, electrically charged black holes. [Ch. 7]
1983–1988  Phinney and others develop comprehensive black-hole-based models to explain the full details of quasars and radio galaxies. [Ch. 9]
1984  The National Science Foundation forges a shotgun marriage between the Caltech and MIT gravitational-wave detection efforts, giving rise to the LIGO Project. [Ch. 10]
 Redmount (building on earlier work by Eardley) shows that radiation falling into an empty, spherical wormhole gets accelerated to high energy and greatly speeds up the wormhole’s pinch-off. [Ch. 14]
1985–1993  Thorne, Morris, Yurtsever, Friedman, Novikov, and others probe the laws of physics by asking whether they permit traversable wormholes and time machines. [Ch. 14]
1987  Vogt becomes director of the LIGO Project, and it then begins to move forward vigorously. [Ch. 10]
1990  Kim and Thorne show that, whenever one tries to create a time machine, by any method whatsoever, an intense beam of vacuum fluctuations circulates through the machine at the moment it is first created. [Ch. 14]
1991  Hawking proposes the chronology protection conjecture (that the laws of physics forbid time machines) and argues that it will be enforced by the circulating beam of vacuum fluctuations destroying any time machine at its moment of formation. [Ch. 14]
 Israel, Poisson, and Ori, building on work by Doroshkevich and Novikov, show that the singularity inside a black hole ages; Ori shows that when the hole is old and quiescent, infalling objects do not get strongly deformed by the singularity’s tidal gravity until the moment they hit its quantum gravity core. [Ch. 13]
 Shapiro and Teukolsky discover evidence, in supercomputer simulations, that the cosmic censorship conjecture might be wrong: Naked singularities might be able to form when highly nonspherical stars implode. [Ch. 13]
1993  Hulse and Taylor are awarded the Nobel Prize for demonstrating, by measurements of a binary pulsar, that gravitational waves exist. [Ch. 10]

Glossary

definitions of exotic terms

absolute. Independent of one’s reference frame; the same as measured in each and every reference frame.

absolute horizon. The surface of a black hole. See horizon.

absolute space. Newton’s conception of the three-dimensional space in which we live as having a notion of absolute rest, and as having the property that the lengths of objects are independent of the motion of the reference frame in which they are measured.

absolute time. Newton’s conception of time as being universal, with a unique, universally agreed upon notion of simultaneity of events and a unique, universally agreed upon time interval between any two events.

accelerated observer. An observer who does not fall freely.

accretion disk. A disk of gas that surrounds a black hole or neutron star. Friction in the disk makes the gas gradually spiral inward and accrete onto the hole or star.

adiabatic index. Same as resistance to compression.

aether. The hypothetical medium which (according to, nineteenth-century thinking) oscillates when electromagnetic waves go by, and by its oscillations, makes the waves possible. The aether was believed to be at rest in absolute space.

angular momentum. A measure of the amount of rotation that a body has. In this book the word spin is often used in place of “angular momentum.”

antimatter. A form of material that is “anathema” to ordinary matter. To each type of particle of ordinary matter (for example, an electron or proton or neutron) there corresponds an almost identical antiparticle of antimatter (the positron or antiproton or antineutron). When a particle of matter meets its corresponding antiparticle of antimatter, they annihilate each other.

apparent horizon. The outermost location around a black hole, where photons, trying to escape, get pulled inward by gravity. This is the same as the (absolute) horizon only when the hole is in a quiescent, unchanging state.

astronomer. A scientist who specializes in observing cosmic objects using telescopes.

astrophysicist. A physicist (usually a theoretical physicist) who specializes in using the laws of physics to try to understand how cosmic objects behave.

astrophysics. The branch of physics that deals with cosmic objects and the laws of physics that govern them.

atom. The basic building block of matter. Each atom consists of a nucleus with positive electric charge and a surrounding cloud of electrons with negative charge. Electric forces bind the electron cloud to the nucleus.

atomic bomb. A bomb whose explosive energy comes from a chain reaction of fissions of uranium-235 or plutonium-239 nuclei.

band. A range of frequencies.

bandwidth. The range of frequencies over which an instrument can detect a wave.

bar detector. A gravitational-wave detector in which the waves squeeze and stretch a large metal bar, and a sensor monitors the bar’s vibrations.

beam splitter. A device used to split a light beam into two parts going in different directions, and to combine two light beams that come from different directions.

big bang. The explosion in which the Universe began.

big crunch. The final stage of recollapse of the Universe (assuming the Universe does ultimately recollapse; we don’t know whether it will or not).

binary system. Two objects in orbit around each other; the objects may be stars or black holes or a star and a black hole.

BKL singularity. A singularity near which tidal gravity oscillates chaotically both in time and space. This is the type of singularity that probably forms at the centers of black holes and in the big crunch of our Universe.

black hole. An object (created by the implosion of a star) down which things can fall but out of which nothing can ever escape.

black-hole binary. A binary system made of two black holes.

Blandford–Znajek process. The extraction of rotational energy from a spinning black hole by magnetic fields that thread through the hole.

boosted atomic bomb. An atomic bomb whose explosive power is increased by one or more layers of fusion fuel.

chain reaction. A sequence of fissions of atomic nuclei in which neutrons from one fission trigger additional fissions, and neutrons from those trigger still more fissions, and so on.

Chandrasekhar limit. The maximum mass that a white-dwarf star can have.

chronology protection conjecture. Hawking’s conjecture that the laws of physics do not allow time machines.

classical. Subject to the laws of physics that govern macroscopic objects; non–quantum mechanical.

cold, dead matter. Cold matter in which all nuclear reactions have gone to completion, expelling from the matter all the nuclear energy that can possibly be removed.

collapsed star. The name used for a black hole in the West in the 1960s.

conservation law. Any law of physics that says some specific quantity can never change. Examples are conservation of mass and energy (taken together as a single entity via Einstein’s E = Mc 2 ), conservation of total electric charge, and conservation of angular momentum (total amount of spin).

corpuscle. The name used for a particle of light in the seventeenth and eighteenth centuries.

cosmic censorship conjecture. The conjecture that the laws of physics prevent naked singularities from forming when an object implodes.

cosmic ray. A particle of matter or antimatter that bombards the Earth from space. Some cosmic rays are produced by the Sun, but most are created in distant regions of our Milky Way galaxy, perhaps in hot clouds of gas that are ejected into interstellar space by supernovae.

cosmic string. A hypothetical one-dimensional, string-like object that is made from a warpage of space. The string has no ends (either it is closed on itself like a rubber band or it extends on and on forever), and its space warpage causes any circle around it to have a circumference divided by diameter slightly less than π.

critical circumference. The circumference of the horizon of a black hole; the circumference inside which an object must shrink in order for it to form a black hole around itself. The value of the critical circumference is 18.5 kilometers times the mass of the hole or object in units of the mass of the Sun.

curvature of space or spacetime. The property of space or spacetime that makes it violate Euclid’s or Minkowski’s notions of geometry; that is, the property that enables straight lines that are initially parallel to cross.

Cyg A. Cygnus A; a radio galaxy that looks like (but is not) two colliding galaxies. The first radio galaxy to be firmly identified.

Cyg X-1. Cygnus X-1; a massive object in our galaxy that is probably a black hole. Hot gas falling toward the object emits X-rays observed on Earth.

dark star. A phrase used in the late eighteenth and early nineteenth centuries to describe what we now call a black hole.

degeneracy pressure. Pressure inside high-density matter, produced by erratic, high-speed, wave/particle-duality-induced motions of electrons or neutrons. This type of pressure remains strong when matter is cooled to absolute zero temperature.

deuterium nuclei, or deuterons. Atomic nuclei made from a single proton and a single neutron held together by the nuclear force. Also called “heavy hydrogen” because atoms of deuterium have almost the same chemical properties as hydrogen.

differential equation. An equation that combines in a single formula various functions and their rates of change; that is, the functions and their “derivatives.” By “solve a differential equation” is meant “compute the functions themselves from the differential equation.”

Doppler shift. The shift of a wave to a higher frequency (shorter wavelength, higher energy) when its source is moving toward a receiver, and to a lower frequency (longer wavelength, lower energy) when the source is moving away from the receiver.

electric charge. The property of a particle or matter by which it produces and feels electric forces.

electric field. The force field around an electric charge, which pulls and pushes on other electric charges.

electric field lines. Lines that point in the direction of the force that an electric field exerts on charged particles. Electric analogue of magnetic field lines.

electromagnetic waves. Waves of electric and magnetic forces. These include, depending on the wavelength, radio waves, microwaves, infrared radiation, light, ultraviolet radiation, X-rays, and gamma rays.

electron. A fundamental particle of matter, with negative electric charge, which populates the outer regions of atoms.

electron degeneracy. The behavior of electrons at high densities, in which they move erratically with high speeds as a result of quantum mechanical wave/ particle duality.

elementary particle. A subatomic particle of matter or antimatter. Among the elementary particles are electrons, protons, neutrons, positrons, antiprotons, and antineutrons.

embedding diagram. A diagram in which one visualizes the curvature of a two-dimensional surface by embedding it in a flat, three-dimensional space.

entropy. A measure of the amount of randomness in large collections of atoms, molecules, and other particles; equal to the logarithm of the number of ways that the particles could be distributed without changing their macroscopic appearance.

equation of state. The manner in which the pressure of matter (or matter’s resistance to compression) depends on its density.

equivalence principle. See principle of equivalence.

error box. The region of the sky in which observations suggest that a specific star or other object is located. It is called an error box because the larger are the uncertainties (errors) of the observations, the larger will be this region.

escape velocity. The speed with which an object must be launched from the surface of a gravitating body in order for it to escape the body’s gravitational pull.

event. A point in spacetime; that is, a location in space at a specific moment of time. Alternatively, something that happens at a point in spacetime, for example, the explosion of a firecracker.

exotic material. Material that has a negative average energy density, as measured by someone moving through it at nearly the speed of light.

field. Something that is distributed continuously and smoothly in space. Examples are the electric field, the magnetic field, the curvature of spacetime, and a gravitational wave.

fission, nuclear. The breakup of a large atomic nucleus to form several smaller ones. The fission of uranium or plutonium nuclei is the source of the energy that drives the explosion of an atomic bomb, and fission is the energy source in nuclear reactors.

freely falling object. An object on which no forces act except gravity.

free particle. A particle on which no forces act; that is, a particle that moves solely under the influence of its own inertia. When gravity is present: A particle on which no forces act except gravity.

frequency. The rate at which a wave oscillates; that is, its number of cycles of oscillation per second.

frozen star. The name used for a black hole in the U.S.S.R. during the 1960s.

function. A mathematical expression that tells how one quantity, for example, the circumference of a black hole’s horizon, depends on some other quantity, for example, the black hole’s mass; in this example, the function is C = 4π GM /c 2 , where C is the circumference, M is the mass, G is Newton’s gravitation constant, and c is the speed of light.

fusion, nuclear. The merger of two small atomic nuclei to form a larger one. The Sun is kept hot and hydrogen bombs are driven by the fusion of hydrogen, deuterium, and tritium nuclei to form helium nuclei.

galaxy. A collection of between 1 billion and 1 trillion stars that all orbit around a common center. Galaxies are typically about 100,000 light-years in diameter.

gamma rays. Electromagnetic waves with extremely short wavelengths; see Figure P.2 on page 25 .

Geiger counter. A simple instrument for detecting X-rays; also called a “proportional counter.”

general relativity. Einstein’s laws of physics in which gravity is described by a curvature of spacetime

geodesic. A straight line in a curved space or curved spacetime. On the Earth’s surface the geodesics are the great circles.

gigantic black hole. A black hole that weighs as much as a million Suns, or more. Such holes are thought to inhabit the cores of galaxies and quasars.

global methods. Mathematical techniques, based on a combination of topology and geometry, for analyzing the structure of spacetime.

gravitational cutoff. Oppenheimer’s phrase for the formation of a black hole around an imploding star.

gravitational lens. The role of a gravitating body, such as a black hole or a galaxy, to focus light from a distant source by deflecting the light rays; see light deflection

gravitational redshift of light. The lengthening of the wavelength of light (the reddening of its color) as it propagates upward through a gravitational field.

gravitational time dilation. The slowing of the flow of time near a gravitating body.

gravitational wave. A ripple of spacetime curvature that travels with the speed of light.

graviton. The particle which, according to wave/particle duality, is associated with gravitational waves.

gyroscope. A rapidly spinning object which holds its spin axis steadily fixed for a very long time.

“hair.” Any property that a black hole can radiate away and thus cannot hold on to; for example, a magnetic field or a mountain on its horizon.

hoop conjecture. The conjecture that a black hole forms when and only when a body gets compressed so small that a hoop with the critical circumference can be placed around it and twisted in all directions.

horizon. The surface of a black hole; the point of no return, out of which nothing can emerge. Also called the absolute horizon to distinguish it from the apparent horizon.

hydrogen bomb. A bomb whose explosive energy comes from the fusion of hydrogen, deuterium, and tritium nuclei to form helium nuclei. See also superbomb.

hyperspace. A fictitious flat space in which one imagines pieces of our Universe’s curved space as embedded.

implosion. The high-speed shrinkage of a star produced by the pull of its own gravity.

inertia. A body’s resistance to being accelerated by forces that act on it.

inertial reference frame. A reference frame that does not rotate and on which no external forces push or pull. The motion of such a reference frame is driven solely by its own inertia. See also local inertial reference frame.

infrared radiation. Electromagnetic waves with wavelength a little longer than light; see Figure P.2 on page 25 .

interference. The manner in which two waves, superimposing on each other and adding linearly, reinforce each other when their crests match with crests and troughs with troughs (constructive interference), and cancel each other when crests match up with troughs (destructive interference).

interferometer. A device based on the interference of waves. See radio interferometer and interferometric detector.

interferometric detector. A detector of gravitational waves in which the waves’ tidal forces wiggle masses that hang from wires, and the interference of laser beams is used to monitor the masses’ motions. Also called interferometer.

interferometry. The process of interfering two or more waves with each other.

intergalactic space. The space between the galaxies.

interstellar space. The space between the stars of our Milky Way galaxy.

inverse square law of gravity. Newton’s law of gravity, which says that between every pair of objects in the Universe there acts a gravitational force that pulls the objects toward each other, and the force is proportional to the product of the objects’ masses and inversely proportional to the square of the distance between them.

ion. An atom that has lost some of its orbital electrons and therefore has a net positive charge.

ionized gas. Gas in which a large fraction of the atoms have lost orbital electrons.

jet. A beam of gas that carries power from the central engine of a radio galaxy or quasar to a distant, radio-emitting lobe.

laws of physics. Fundamental principles from which one can deduce, by logical and mathematical calculations, how our Universe behaves.

length contraction. The contraction of an object’s length as a result of its motion past the person who measures the length. The contraction occurs only along the direction of motion.

light. The type of electromagnetic waves that can be seen by the human eye; see Figure P.2 on page 25 .

light deflection. The deflection of the direction of propagation of light and other electromagnetic waves, as they pass near the Sun or any other gravitating body. This deflection is produced by the curvature of spacetime around the body.

LIGO. The Laser Interferometer Gravitational-Wave Observatory.

linear. The property of combining together by simple addition.

lobe. A huge radio-emitting cloud of gas outside a galaxy or quasar.

local inertial reference frame. A reference frame on which no forces except gravity act, that falls freely in response to gravity’s pull, and that is small enough for tidal gravitational accelerations to be negligible inside it.

magnetic field. The field that produces magnetic forces.

magnetic field lines. Lines that point along the direction of a magnetic field (that is, along the direction that a compass needle would point if it were placed in the magnetic field). These field lines can be made evident around a bar magnet by placing a sheet of paper above the magnet and scattering bits of iron on the paper.

mass. A measure of the amount of matter in an object. (The object’s inertia is proportional to its mass, and Einstein showed that mass is actually a very compact form of energy.) The word “mass” is also used to mean “an object made of mass,” in contexts where the inertia of the object is important.

Maxwell’s laws of electromagnetism. The set of laws of physics by which James Clerk Maxwell unified all electromagnetic phenomena. From these laws one can predict, by mathematical calculations, the behaviors of electricity, magnetism, and electromagnetic waves.

metaprinciple. A principle that all physical laws should obey. The principle of relativity is an example of a metaprinciple.

microsecond. One-millionth of a second.

microwaves. Electromagnetic radiation with wavelength a little shorter than radio waves; see Figure P.2 on page 25 .

Milky Way. The galaxy in which we live.

mixmaster singularity. A singularity near which tidal gravity oscillates chaotically with time, but does not necessarily vary in space. See also BKL singularity.

molecule. An entity made of several atoms that share their electron clouds with each other. Water is a molecule made in this way from two hydrogen atoms and one oxygen.

mouth. An entrance to a wormhole. There is a mouth at each of the two ends of the wormhole.

naked singularity. A singularity that is not inside a black hole (not surrounded by a black-hole horizon), and that therefore can be seen and studied by someone outside it. See cosmic censorship conjecture.

National Science Foundation (NSF). The agency of the United States government charged with the support of basic scientific research.

natural philosopher. A phrase widely used in the seventeenth, eighteenth, and nineteenth centuries to describe what we now call a scientist.

nebula. A cloud of brightly shining gas in interstellar space. Before the 1930s, galaxies were widely, but not universally, mistaken for nebulas.

neutrino. A very light particle that resembles the photon, except that it interacts hardly at all with matter. Neutrinos produced in the Sun’s center, for example, fly out through the Sun’s surrounding matter without being absorbed or scattered hardly at all.

neutron. A subatomic particle. Neutrons and protons, held together by the nuclear force, make up the nuclei of atoms.

neutron core. Oppenheimer’s name for a neutron star. Also a neutron star at the center of a normal star.

neutron star. A star, about as massive as the Sun but only 50 to 1000 kilometers in circumference, and made from neutrons packed tightly together by the force of gravity.

new quantum mechanics. The final version of the laws of quantum mechanics, formulated in 1926.

Newtonian laws of physics. The laws of physics, built on Newton’s conception of space and time as absolute, which were the centerpiece of nineteenth-century thinking about the Universe.

Newton’s law of gravity. See inverse square law of gravity.

no-hair conjecture. The conjecture in the 1960s and 1970s (which was proved to be true in the 1970s and 1980s) that all the properties of a black hole are determined uniquely by its mass, electric charge, and spin.

nonlinear. The property of combining together in a more complicated way than simple addition.

nova. A brilliant outburst of light from an old star, now known to be caused by a nuclear explosion in the star’s outer layers.

nuclear burning. Nuclear fusion reactions that keep stars hot and power hydrogen bombs.

nuclear force. Also called the “strong interaction.” The force between protons and protons, protons and neutrons, and neutrons and neutrons, which holds atomic nuclei together. When the particles are somewhat far from each other, the nuclear force is attractive; when they are closer it becomes repulsive. The nuclear force is responsible for much of the pressure near the center of a neutron star.

nuclear reaction. The merging of several atomic nuclei to form a larger one (fusion), or the breakup of a larger one to form several smaller ones (fission).

nuclear reactor. A device in which a chain reaction of nuclear fissions is used to generate energy, produce plutonium, and in some cases produce electricity.

nucleon. Neutron or proton.

nucleus, atomic. The dense core of an atom. Atomic nuclei have positive electric charge, are made of neutrons and protons, and are held together by the nuclear force.

observer. A (usually hypothetical) person or being who makes a measurement.

old quantum mechanics. The early version of the laws of quantum mechanics, developed in the first two decades of the twentieth century.

optical astronomer. An astronomer who observes the Universe using visible light (light that can be seen by the human eye).

orbital period. The time it takes for one object, in orbit around another, to encircle its companion once.

paradigm. A set of tools that a community of scientists uses in its research on a given topic, and in communicating the results of its research to others.

particle. A tiny object; one of the building blocks of matter (such as an electron, proton, photon, or graviton).

perihelion. The location, on a planet’s orbit around the Sun, at which it is closest to the Sun.

perihelion shift of Mercury. The tiny failure of Mercury’s elliptical orbit to close on itself, which results in its perihelion shifting in position each time Mercury passes through the perihelion.

perturbation. A small distortion (from its normal shape) of an object or of the spacetime curvature around an object.

perturbation methods. Methods of analyzing, mathematically, the behaviors of small perturbations of an object, for example, a black hole.

photon. A particle of light or of any other type of electromagnetic radiation (radio, microwave, infrared, ultraviolet, X-ray, gamma ray); the particle which, according to wave/particle duality, is associated with electromagnetic waves.

piezoelectric crystal. A crystal that produces a voltage when squeezed or stretched.

Planck’s constant. A fundamental constant, denoted , that enters into the laws of quantum mechanics; the ratio of the energy of a photon to its angular frequency (that is, to 2π times its frequency); 1.055 × 10 -27 erg-second.

Planck-Wheeler length, area, and time . Quantities associated with the laws of quantum gravity. The Planck—Wheeler length, = 1.62 × 10 −33 centimeter, is the length scale below which space as we know it ceases to exist and becomes quantum foam. The Planck—Wheeler time (lie times the Planck-Wheeler length or about 10 −43 second) is the shortest time interval that can exist; if two events are separated by less than this, one cannot say which comes before and which after. The Planck–Wheeler area (the square of the Planck–Wheeler length, that is, 2.61 × 10 −66 square centimeter) plays a key role in black-hole entropy. In the above formulas, G = 6.670 × 10 −8 dyne-centimeter 2 /gram 2 is Newton’s gravitation constant, ħ = 1.055 × 10 −27 erg-second is Planck’s quantum mechanical constant, and c = 2.998 × 10 10 centimeter/second is the speed of light.

plasma . Hot, ionized, electrically conducting gas.

plutonium-239. A specific type of plutonium atomic nucleus which contains 239 protons and neutrons (94 protons and 145 neutrons).

polarization. The property that electromagnetic and gravitational waves have of consisting of two components, one that oscillates in one direction or set of directions, and the other in a different direction or set of directions. The two components are called the waves’ two polarizations.

polarized body. A body with negative electric charge concentrated in one region and positive charge concentrated in another region.

polarized light; polarized gravitational waves. Light or gravitational waves in which one of the two polarizations is completely absent (vanishes).

postdoc. Postdoctoral fellow; a person who has recently received the Ph.D. degree and is continuing his or her training in how to do research, usually under the guidance of a more senior researcher.

pressure. The amount of outward force that matter produces when it is squeezed.

Price’s theorem. The theorem that all properties of a black hole that can be converted into radiation will be converted into radiation and will be radiated away completely, thereby making the hole “hairless.”

primordial black hole. A black hole typically far less massive than the Sun that was created in the big bang.

principle of absoluteness of the speed of light. Einstein’s principle that the speed of light is a universal constant, the same in all directions and the same in every inertial reference frame, independent of the frame’s motion.

principle of equivalence. The principle that in a local inertial reference frame in the presence of gravity, all the laws of physics should take the same form as they do in an inertial reference frame in the absence of gravity.

principle of relativity. Einstein’s principle that the laws of physics should not be able to distinguish one inertial reference frame from another; that is, that they should take on the same form in every inertial reference frame. When gravity is present: this same principle, but with local inertial reference frames playing the role of the inertial reference frames.

pulsar. A magnetized, spinning neutron star that emits a beam of radiation (radio waves and sometimes also light and X-rays). As the star spins, its beam sweeps around like the beam of a turning spotlight; each time the beam sweeps past Earth, astronomers receive a pulse of radiation.

pulsation. The vibration or oscillation of an object, for example, a black hole or a star or a bell.

quantum field. A field that is governed by the laws of quantum mechanics. All fields, when measured with sufficient accuracy, turn out to be quantum fields; but when measured with modest accuracy, they may behave classically (that is, they do not exhibit wave/particle duality or vacuum fluctuations).

quantum fields in curved spacetime, the laws of. A partial marriage of general relativity (curved spacetime) with the laws of quantum fields, in which gravitational waves and nongravitational fields are regarded as quantum mechanical, while the curved spacetime in which they reside is regarded as classical.

quantum foam. A probabilistic foamlike structure of space that probably makes up the cores of singularities, and that probably occurs in ordinary space on scales of the Planck—Wheeler length and less.

quantum gravity. The laws of physics that are obtained by merging (“marrying”) general relativity with quantum mechanics.

quantum mechanics. The laws of physics that govern the realm of the small (atoms, molecules, electron, protons), and that also underlie the realm of the large, but rarely show themselves there. Among the phenomena that quantum mechanics predicts are the uncertainty principle, wave/particle duality, and vacuum fluctuations.

quantum nondemolition. A method of measurement that circumvents the standard quantum limit.

quantum theory. The same as quantum mechanics.

quasar. A compact, highly luminous object in the distant Universe, believed to be powered by a gigantic black hole.

radiation. Any form of high-speed particles or waves.

radio astronomer. An astronomer who studies the Universe using radio waves.

radio galaxy. A galaxy that emits strong radio waves.

radio interferometer. A device consisting of several radio telescopes linked together, which simulates a single much larger radio telescope.

radio source. Any astronomical object that emits radio waves.

radio telescope. A telescope that observes the Universe using radio waves.

radio waves. Electromagnetic waves of very low frequency, used by humans to transmit radio signals and used by astronomers to study distant astronomical objects; see Figure P.2 on page 25 .

redshift. A shifting of electromagnetic waves to longer wavelengths, that is, a “reddening” of the waves.

reference frame. A (possibly imaginary) laboratory for making physical measurements, which moves through the Universe in some particular manner.

relative. Dependent on one’s reference frame; different, as measured in one frame which moves through the Universe in one manner, than as measured in another frame which moves in another manner.

resistance to compression, or simply resistance. Also called adiabatic index. The percentage by which the pressure inside matter increases when the density is increased by 1 percent.

rigor; rigorous. A high degree of precision, exactness, and reliability (a term applied to mathematical calculations and arguments).

rotational energy. The energy associated with the spin of a black hole or a star or some other object.

Schwarzschild geometry. The geometry of spacetime around and inside a spherical, nonspinning hole.

Schwarzschild singularity. The phrase used between 1916 and about 1958 to describe what we now call a black hole.

Sco X-1. Scorpius X-1, the brightest X-ray star in the sky.

second law of thermodynamics. The law that entropy can never decrease and almost always increases.

sensitivity. The weakest signal that can be measured by some device. Alternatively, the ability of a device to measure signals.

sensor. A device for monitoring the vibrations of a bar or motions of a mass.

shocked gas. Gas that has been heated and compressed in a shock front.

shock front. A place, in flowing gas, where the density and temperature of the gas suddenly jump upward by a large amount.

simultaneity breakdown. The fact that events which are simultaneous as measured in one reference frame are not simultaneous as measured in another frame that moves relative to the first.

singularity. A region of spacetime where spacetime curvature becomes so strong that the general relativistic laws break down and the laws of quantum gravity take over. If one tries to describe a singularity using general relativity alone, one finds (incorrectly) that tidal gravity and spacetime curvature are infinitely strong there. Quantum gravity probably replaces these infinities by quantum foam.

Sirius B. The white-dwarf star that orbits around the star Sirius.

spacetime. The four-dimensional “fabric” that results when space and time are unified.

spacetime curvature. The property of spacetime that causes freely falling particles that are initially moving along parallel world lines to subsequently move together or apart. Spacetime curvature and tidal gravity are different names for the same thing.

spacetime diagram. A diagram with time plotted upward and space plotted horizontally.

special relativity. Einstein’s laws of physics in the absence of gravity.

spectral lines. Sharp features in the. spectrum of the light emitted by some source. These features are due to strong emission or absorption at specific wavelengths, produced by specific atoms or molecules.

spectograph. A sophisticated version of a prism, for separating the various colors (wavelengths) of light and thereby measuring the light’s spectrum.

spectrum. The range of wavelengths or frequencies over which electromagnetic waves can exist, running from extremely low-frequency radio waves up through light to extremely high-frequency gamma rays; see Figure P.2 in the prologue. Also, a picture of the distribution of light as a function of frequency (or wavelength), obtained by sending the light through a prism.

spin. Rotation. See angular momentum

stability. The issue of whether an object is unstable or not. See also unstable.

standard quantum limit. A limit, due to the uncertainty principle, on how accurately certain quantities can be measured using standard methods. This limit can be circumvented using quantum nondemolition methods.

stroboscopic measurement. A specific kind of quantum nondemolition measurement in which one makes a sequence of very quick measurements of a vibrating bar, each measurement separated by one vibration period.

structure of a star. The details of how a star’s pressure, density, temperature, and gravity change as one goes inward from its surface to its center.

superbomb. A hydrogen bomb that uses a principle by which one can produce an arbitrarily large explosion.

superconductor. A material that conducts electricity perfectly, without any resistance.

supermassive star. A hypothetical star that weighs as much as or more than 10,000 Suns.

supernova. A gigantic explosion of a dying star. The explosion of the star’s outer layers is powered by energy that is released when the star’s inner core implodes to form a neutron star.

surface gravity. Roughly speaking, the strength of the gravitational pull felt by an observer at rest just above a black hole’s horizon. (More precisely: that gravitational pull multiplied by the amount of gravitational time dilation at the observer’s location.)

synchrotron radiation. Electromagnetic waves emitted by high-speed electrons that are spiraling around and around magnetic field lines.

thermal pressure. Pressure created by the heat-induced, random motions of atoms, molecules, electrons, and/or other particles.

thermodynamics. The set of physical laws that govern the random, statistical behavior of large numbers of atoms and molecules, including their heat.

thermonuclear reactions. Heat-induced nuclear reactions.

tidal gravity. Gravitational accelerations that squeeze objects along some directions and stretch them along others. Tidal gravity produced by the Moon and Sun is responsible for the tides on the Earth’s oceans.

time dilation. A slowing of the flow of time.

time machine. A device for traveling backward in time. In physicists’ jargon, a “closed timelike curve.”

topology. The branch of mathematics that deals with the qualitative ways that objects are connected to each other or to themselves. For example, topology distinguishes a sphere (which has no hole) from a doughnut (which has one).

tritium. Atomic nuclei made of one proton and two neutrons bound together by the nuclear force.

ultraviolet radiation. Electromagnetic radiation with a wavelength a little shorter than light; see Figure P.2 on page 25 .

uncertainty principle. A quantum mechanical law which states that, if one measures the position of an object or the strength of a field with high precision, one’s measurement must necessarily perturb the object’s velocity or the field’s rate of change by an unpredictable amount.

universe. A region of space that is disconnected from all other regions of space, much as an island is disconnected from all other pieces of land.

Universe. Our universe.

unstable. The property of an object that if one perturbs it slightly, the perturbation will grow large, thereby changing the object greatly and perhaps even destroying it. Also called, in more complete terminology, “unstable against small perturbations.”

uranium-255. A specific type of uranium nucleus which contains 235 protons and neutrons (92 protons and 143 neutrons).

vacuum. A region of spacetime from which have been removed all the particles and fields and energy that one can remove; the only things left are the irremovable vacuum fluctuations.

vacuum fluctuations. Random, unpredictable, irremovable oscillations of a field (for example, an electromagnetic or gravitational field), which are caused by a tug-of-war in which small regions of space momentarily steal energy from adjacent regions and then give it back. See also vacuum and virtual particles.

virtual particles. Particles that are created in pairs using energy borrowed from a nearby region of space. The laws of quantum mechanics require that the energy be given back quickly, so the virtual particles annihilate quickly and cannot be captured. Virtual particles are the particle aspect of vacuum fluctuations, as seen by freely falling observers. Virtual photons and virtual gravitons are the particle aspects of electromagnetic vacuum fluctuations and gravitational vacuum fluctuations, respectively. See also wave/particle duality.

warpage of spacetime. Same as curvature of spacetime.

wave. An oscillation in some field (for example, the electromagnetic field or space-time curvature) that propagates through spacetime.

waveform. A curve showing the details of the oscillations of a wave.

wavelength. The distance between the crests of a wave.

wave/particle duality. The fact that all waves sometimes behave like particles, and all particles sometimes behave like waves.

white-dwarf star. A star with roughly the circumference of the Earth but the mass of the Sun, which has exhausted all its nuclear fuel and is gradually cooling off. It supports itself against the squeeze of its own gravity by means of electron degeneracy pressure.

world line. The path of an object through spacetime or through a spacetime diagram.

wormhole. A “handle” in the topology of space, connecting two widely separated locations in our Universe.

X-rays. Electromagnetic waves with wavelength between that of ultraviolet radiation and gamma rays; see Figure P.2 on page 25 .