Dictionary

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.

Definitioner

time

It is a fact of life that not all events in our universe happen concurrently - instead, there is a certain order. Defining a time coordinate or defining time, the way physicists do it, is to define a prescription to associate with each event a number so as to reflect that order - if event B happens after event A, then the number associated with B should be larger than that associated with A. The first step of this definition is to construct a clock: Choose a simple process that repeats regularly. (What is "regular"? Luckily, in our universe, all elementary processes such as a swinging pendulum, the oscillations of atoms or of electronic circuits lead to the same concept of regularity.) As a second step, install a counter: A mechanism that, with every repetition of the chosen process, raises the count by one. With this definition, one can at least assign a time (the numerical value of the counter) to events happening at location of the clock. For events at different locations, an additional definition is necessary: One needs to define simultaneity. After all, the statement that some far-away event A happens at 12 o'clock is the same as saying that event A and "our clock counter shows 12:00:00" are simultaneous. The how and why of defining simultaneity - a centre-piece of Einstein's special theory of relativity - are described in the spotlight topic Defining "now". With all these preparations, physicists can, in principle, assign a time coordinate value ("a time") to any possible events, and describes how fast or how slow processes happen, compared to that time coordinate.

singularity

Irregular boundary of spacetime in general relativity - region where spacetime simply comes to an end. Often, such boundaries are associated with spacetime curvature growing beyond all bounds and becoming infinitely large - so-called curvature singularities (notably Ricci singularities or Weyl singularities - but there are exceptions (for instance a conic singularities). According to general relativity, a singularity exists inside every black hole, and the starting point of any universe described by a big bang model is a singularity as well. The occurrence of singularities is a failure of general relativity - and a strong indication that the theory is incomplete. Instead, one could describe the earliest universe and the interior of black holes using a theory of quantum gravity. More information about singularities can be found in the spotlight texts Spacetime singularities and Of singularities and breadmaking.

quantum theory

The framework for formulating the physical laws that govern the world at microscopic length-scales - the physics of the micro-world, for instance of atoms, atomic nuclei or elementary particles, but also the physics of ultra-precise measurements such as those made by gravitational wave detectors.

The laws of quantum theory are fundamentally different from our everyday experience and from those of classical physics.

The first unusual feature is that, in many cases, quantum theory merely allows statements about probabilities. For instance, in classical physics, one can assign to every particle, at every point in time, a location and a velocity. Whosoever can measure those quantities precisely can, in principle, predict where the particle in question can be found at every point in the future. In quantum theory, all one can assign to a system of particles is an abstract quantum state from which can be derived no precise predictions, but merely the probabilities for detecting a specific particle at a given time in a given place. Whether or not one will really find the particle at that location is governed by chance.

The second unusual feature is a fundamental restriction placed on the exactness of certain measurements (Heisenberg uncertainty relation). For instance, the more precise one measures a particle's location, the less definite any statements one can make about its velocity.

The third feature is how quantum theory came by its name: A number of physical quantities in nature come in little packets, in quanta. For instance, according to quantum theory, electromagnetic radiation is made of tiny quanta of energy called photons.

Examples for quantum theories are quantum mechanics and relativistic quantum field theories such as Quantum electrodynamics or other parts of the standard model of particle physics.

general relativity (general theory of relativity)

Albert Einstein's theory of gravity; a generalization of his special theory of relativity. For information about the concepts and applications of this theory, we recommend the chapter general relativity of our introductory section Elementary Einstein. Further information about many different aspects of general relativity and its applications can be found in our section Spotlights on relativity.

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.

censorship

See cosmic censorship.

black hole

Region in space where a sufficient amount of mass is concentrated so that it forms a gravitational prison - a region into which matter or light can enter from the outside, but from which nothing that has once entered can ever leave. Basic information on this key phenomenon of Einstein's general theory of relativity can be found in the chapter Black holes & Co. of Elementary Einstein. Selected aspects of the physics of black holes and neutron stars are described in the category Black holes & Co. of our Spotlights on relativity. In Einstein's theory, black holes are truly black, due to the fact that no radiation or light can ever escape them. Once quantum theory is taken into account, this assumption no longer holds - on the contrary, it seems as if black holes should emit so-called Hawking radiation. However, for astrophysical black holes (that typically have more or even much more than one solar mass), that radiation would be undetectable, even if we could transport today's most sensitive sensors into the immediate vicinity of the black hole.

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cosmic censorship

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