Big Bang term facetiously coined by Cambridge physicist Fred Hoyle around 1950 to designate an initial violent event at the beginning of the universe.
blackbody idealized object assumed to be in perfect equilibrium with electromagnetic radiation. The spectrum of its emitted radiation depends only on the temperature and is independent of the object’s material composition.
Boltzmann’s principle name given by Einstein to Boltzmann’s result holding that the entropy of a thermodynamic (macroscopic) state is directly proportional to the probability of occurrence of that state.
Bose-Einstein condensate unusual state of matter at very low temperatures in which all the constituent atoms or particles have the same energy.
Bose-Einstein quantum statistics quantum statistics obeyed by particles of integer spin (bosons). Bosons are indistinguishable, differing only by differing energies.
Brownian motion a consequence of the kinetic theory of fluids, the random motion of small but observable granules due to thermal motions of the fluid’s molecules.
cosmological constant term added to Einstein’s field equations representing a repulsive pressure in the vacuum of space.
cosmological principle at very large distance scales (> 3 × 106 light years, approximately 3 × 1024 meters), the universe is homogeneous and appears the same in all directions from any point.
curvature in the general theory of relativity, a property of space-time derivable from the metric tensor determining whether straight lines initially parallel remain so when extended indefinitely.
De Sitter’s universe a 1917 solution to the matter-free Einstein field equations (supplemented by the cosmological constant) describing a universe infinite in extent, and expanding.
determinism a property of laws of nature, such that with exact knowledge of the initial conditions of a system, the laws precisely predict the state of the system at any other time.
Einstein field equations the gravitational field equations of general relativity. On one side is a tensor expression for the curvature of space-time; on the other, a tensor expression for matter-energy sources of curvature. In all, there are ten equations to be solved for the ten independent components of the metric tensor gμν.
Einstein universe a solution to his field equations derived by Einstein in 1917 describing a spatially closed static universe with a uniform distribution of matter. By closing the universe spatially, the problem of specifying boundary conditions was circumvented, but to render the universe stable against gravitational collapse, the cosmological constant was required. The solution was later shown to be non-static.
energy principle in Newtonian physics and in special relativity, the total energy of any isolated system is constant in time. In general relativity, the conservation of energy holds rigorously only for time-independent space-time geometries.
entropy a measure of the disorder of a system, inversely related to the amount of structure of the system. The second law of thermodynamics holds that the total entropy of any closed system cannot decrease with time.
EPR acronym for the 1935 Einstein-Rosen-Podolsky paper arguing that quantum mechanics is either incomplete or it allows intervention on one part of a separated system to influence the other distant part.
equipartition theorem the prediction of the kinetic theory that at thermal equilibrium, the energy available to a system will be distributed equally among all possible degrees of freedom (varieties of motion) of the system.
event a physical occurrence, or possible occurrence, with a definite spatio-temporal location relative to other occurrences. Events can be considered points of space-time, with the proviso that events are occurrences, not mathematical points.
fluctuation theory a statistical theory developed by Einstein in 1902–1904 showing that systems at thermal equilibrium will fluctuate around the average values considered by thermodynamics.
frame of reference a system of coordinates that an observer constructs to locate events and determine spatial and temporal relations between them.
hole argument a faulty argument persuading Einstein for two years (1913–1915) that generally covariant field equations were incompatible with the requirement that a field theory be deterministic.
inertial frame a frame of reference (reference system or observer plus coordinate system) in which a body on which no accelerative forces act maintains its state of motion. The laws of Newtonian mechanics require the existence of such homogenous frames, as do the laws in special relativity. In the general theory of relativity, space-time curvature allows only local inertial frames, a limited region surrounding a freely falling test body in which the laws of special relativity obtain.
kinetic theory a classical theory of the (Newtonian) motions of atoms or molecules that averages over vast numbers of such particles to explain physical properties of gases, liquids, or solids.
length contraction a core prediction of special relativity that bodies in motion, with respect to the observer measuring them, are shortened in the direction of their motion by a factor that depends upon v2/c2, the ratio of the square of the body’s velocity to the square of the speed of light in a vacuum.
light principle the principle that the velocity of light in a vacuum is a constant and independent of the velocity of the emitter of light.
linear in mathematics, linear relations between two variables x and y are described by an equation of the form y = ax + b for constants a and b. Physically, a linear relation between two quantities means that the change of one is directly proportional to the change of the other.
Mach’s principle a principle adopted by Einstein in recognition of Mach’s criticism of Newton’s invocation of absolute space and time in explaining the effects of inertia. Mach’s proposal that inertial effects result from accelerations with respect to distant cosmic masses (and not absolute space) was used by Einstein to argue for the relativity of acceleration, i.e., a principle of general relativity. In Einstein’s hands, the principle states that inertio-gravitational effects are fully determined by matter-energy. Einstein adopted a closed universe cosmology in an attempt to satisfy Mach’s principle, but de Sitter’s empty universe model clearly violates it.
metric tensor the fundamental mathematical quantity of Einstein’s field equations, a tensor gμν that is a 4 × 4 matrix with 10 independent components. Its primary role lies in the determination of the space-time interval between two nearby points, ds2= gμνdxμdxν (see Box 6.2). Other quantities pertaining to curvature of space-time are derivable from it.
nonlinear a mathematical relationship between two variables that does not plot as a straight line. Physically, a nonlinear relation between two quantities can mean that a small change in one can result in a disproportionate change in the other. The Einstein field equations are nonlinear partial differential equations; the nonlinearity arises essentially from the fact that the gravitational field carries energy and can act as its own source.
opalescence light passing through a very dense gas or mixture of two fluids is strongly scattered (deviated in all directions) giving off a luminous glow. The scattering has a maximum when the gas or fluid is near its critical point (the temperature of a phase transition).
principle of equivalence a heuristic assisting Einstein in going from the special to the general theory of relativity. In weak form, it asserts the equivalence of inertial and gravitational mass. Since a body’s inertial mass is the parameter for its resistance to acceleration by a given force, while a body’s gravitational mass is determined by the strength of a given gravitational field, acceleration (in a gravity-free region) can in special circumstances simulate freefall in a gravitational field. In mature form, the principle affirms that the effects of inertia and the effects of gravitation cannot be distinguished in any invariant way.
principle of general covariance narrowly construed, the Einstein field equations, and every other physically meaningful mathematical statement within the general theory of relativity, must retain the same form in all systems of coordinates; more expansively, it asserts that the only space-time quantities that can appear in general relativity are the metric tensor gμν and quantities derivable from it.
principle of relativity a statement that the laws of physics should be independent of the motion of an observer who performs experiments testing the laws. For the case of uniform motions, the principle was first enunciated by Galileo, recognized by Newton as a corollary to his laws of motion and elevated to an axiom by Einstein with special relativity in 1905. Despite its name, the general theory of relativity does not extend the principle to non-uniform motions. To Einstein, the principle of general relativity was best expressed by the principle of general covariance.
principle of superposition a quantum principle, arising from the linearity of the Schrödinger equation. In quantum mechanics, states are described by wave-like ψ-functions of which sums can be formed. Time evolution by the Schrödinger equation preserves these sums, but measurement always reveals a system to be in a definite quantum state (a definite eigenstate of the observable measured), not a sum of them. This is the so-called collapse of the wave function upon measurement.
relativity of simultaneity Einstein’s 1905 assertion that the physical meaning of the relative time of occurrence of two distant events is established only by resting clocks at both events synchronized with each other via light signaling. Since according to the principle of relativity, resting and uniformly moving clocks must be considered as equivalent, the relative time of occurrence of the events will differ for differently moving inertial observers. These differences become physically significant only when the observer’s motion is some significant fraction of the speed of light.
Riemannian geometry the geometry of curved spaces (more generally, manifolds) developed by Bernard Riemann (1821–1866) as a generalization of the theory of curved surfaces of Carl Friedrich Gauss (1777–1855). Riemannian manifolds include spaces with variable curvature (varying smoothly from point to point) and with more than three dimensions. Riemann represented the relation between coordinates and distances in curved spaces with the fundamental, or “metric” tensor. Around 1912, Einstein recognized Riemannian geometry as especially suitable for a relativistic theory of gravitation. The geometry of general relativity is “pseudo-Riemannian” since it is necessary to consider time distinctly from the three dimensions of space.
singularity a place where the equations of general relativity break down. According to the modern definition, a particle encountering a singularity in general relativity has no future (its trajectory is not extendible).
space-time the set of all events past, current, and future.
specific heat the heat capacity characteristic of every substance, given by a number that is the ratio of thermal energy (heat) supplied to a unit mass of the substance to its consequent rise in temperature by one degree centigrade.
statistical mechanics the application of statistical methods to the microscopic constituents of a system in order to predict the system’s macroscopic behavior. Classically, the microconstituents obey Newtonian laws of motion.
supersymmetry a hypothetical symmetry of elementary particles at very high energies in the early universe; the simplest supersymmetric theories postulate a fermion partner for every boson, and vice versa.
symmetry an invariance of a system under transformation of the laws governing the system’s behavior. In special relativity, the symmetry is Lorentz invariance: inertial systems are invariant under Lorentz transformation. In the general theory of relativity, since inertial frames obtain only locally, there are no non-trivial space-time symmetries.
thermodynamics the science of heat and other forms of energy developed in the 19th century, based upon two laws considered absolute. The first law states that heat is a form of energy, and that the energy of a closed system can only be converted from one form to another, but not lost. The second pertains to the flow of heat and the availability of energy to do work. In one form, the second law states the entropy (roughly, measure of disorganization) of a closed system almost always increases. To these two laws are now added a definitional zeroth law (two systems in thermodynamic equilibrium with a third system are in thermodynamic equilibrium with each other) and a third law (due to Walther Nernst) that the entropy of a system approaches a constant minimum as the temperature approaches absolute zero (on the Kelvin scale; −273.15 °C).
time dilation as explained in special relativity, the slowing rate of a clock accompanying a moving body in an amount inversely proportional to the speed of the body.
unified field theory in present parlance, a quantum theory comprehending all known fundamental interactions (gravitational, electro-weak, and strong). The leading contemporary proposal is based upon superstring theory, the basic objects of which are tiny (10-35m) one-dimensional strings with quantum properties. Einstein’s conception was rather different and much more restricted: a classical, not quantum, unification of gravitation and electromagnetism in a single mathematical framework, stemming from a generalization of the space-time geometry of general relativity.
wave-particle duality according to quantum mechanics, light and matter have both particle and wave properties, but (standardly) the determination of one by a given experiment precludes determination of the other. In 1909 Einstein first proposed that the theory of light of the future would be an amalgam of the corpuscular and wave theories of light.