Particle accelerators as black hole factories?

The intriguing possibility that the next generation of particle accelerators might produce – and allow the detection of – miniature black holes

An article by Marco Cavaglià

One peculiar feature of string theory, one of the candidates for a theory of quantum gravity, is the presence of extra dimensions of space. Typically, string theory models, or models inspired by the theory, include some way of explaining why we do not notice those extra dimensions in everyday life – they are either “rolled up” (see the spotlight text Extra dimensions – and how to hide them), or our world occupies only a small part of the higher-dimensional universe (see the spotlight text The embedded universe).

Can the presence of such extra dimensions be detected? Depending on how well they are hidden away, the answer might be yes. Typically, the presence of extra dimensions influences the way that the strength of gravity increases as you get closer and closer to a given mass. Ordinarily, strength increases (or decreases) with the square of the distance. If you halve your distance to a massive body, the gravitational pull you feel will be four times as strong as at your original location. With extra dimensions in the game, gravity will typically grow stronger much faster – at least at very small distances! (More about the relation between extra dimensions and the strength of gravity can be found in the spotlight text Hunting for extra dimensions.)

However, for most realistic models with extra dimensions, the length scales at which this stronger-than-usual gravity becomes important are very small – far smaller than the size of an atom, or even an atomic nucleus! The proper tools to probe such small distance scales are the most powerful “microscopes” that experimental physics has to offer: particle accelerators!

Particle accelerators, length scales, and gravity

In particle accelerators, physicists routinely accelerate elementary particles and bring them to collision. The particle energy is a direct measure of the length scales being probed – roughly, the higher the energy, the closer the colliding particles approach each other as they interact. If the length scales reached are those where gravity becomes significantly stronger through the presence of extra dimensions, then the result of such particle collisions, which are monitored using sophisticated detectors, should be influenced by gravitational effects.

For some of the models with extra dimensions, this critical threshold would be reached by particle accelerators of the next generation, namely with the Large Hadron Collider (LHC) that is currently under construction at the European particle physics laboratory CERN near Geneva. This illustration shows a view of the tunnel in which the LHC is currently being installed. The blue tubes are the covers of the magnets which keep the particles on track:

[Image: CERN]

The most striking gravitational events that could be observed in particle colliders would be the formation of minuscule black holes.

Black holes in particle accelerators?

According to general relativity, a black hole should form whenever some mass is squeezed into a very small region of space. The precise meaning of “very small” is defined by a length scale called the Schwarzschild radius. This radius depends on the mass, but also on the properties of whatever hidden extra dimensions there might be. For certain kinds of extra dimensions, the Schwarzschild radius of a given mass will be significantly larger than otherwise. Consequently, in order to form a black hole, you wouldn’t need to compress matter nearly as much as in a space without extra dimensions. Under those favourable conditions, collisions of protons with other protons at the LHC should result in the formation of miniature black holes.

More concretely: Protons consist of subcomponents called quarks. When two quarks in collision do not just fly past each other, but collide nearly head-on, then, at the energies achievable with the LHC, a sufficiently high concentration of mass would result, and a mini-black hole would form. In the following animation, the relevant portion of our three-dimensional world is represented by a plane, embedded in a higher-dimensional (in the image: three-dimensional) space. Ordinary elementary particles are confined to the world-plane – they cannot ever move out into the extra dimensions. When the two particles moving in that plane have almost reached each other, a black hole forms, its horizon represented by the black sphere:

Particles in the plane in near collision, resulting in the formation of a black hole

Black holes with a mass that is extremely small are extremely unstable. The intensity of Hawking radiation, a hypothetical quantum process by which black holes emit elementary particles, depends on the black hole’s mass – the smaller the mass of a black hole, the greater the amount of energy emitted in this way. By this process, the mini-black holes formed in particle accelerators would evaporate nearly as soon as they are created – typically, such black holes would only exist for a few tenth of a trillionth of a trillionth (10^-25, in exponential notation) seconds. Their decay would result in a sudden blast of a few energetic particles. Possibly, some exotic remnant object might survive as well (however, what such an object could be, and whether or not there really are exotic remnants, is not at all clear to present physics):

Minuscule black hole decaying into particles and into gravitational energy leaving the brane

With respect to the numbers, types and energies of the resulting particles a decaying black hole would look different from other particle collisions. Some of its characteristics are directly related to the existence of the extra dimensions: For instance, in the animation above, you can see that some energy associated with gravity (shown as yellow, wiggly arrows) is carried off into the extra dimensions – from the point of view of a physicist in our three-dimensional universe, this energy would simply vanish!

When physicists study collisions in particle accelerators, they use sensitive detectors to keep track of the different types of resulting particles and their energies, which enables painstaking reconstructions of each collision. The following image, based on a simulation, shows what physicists might see in their detector when a mini-black hole decays:

Simulated particle traces for black hole decay

The image shows a sideways cut-away view of the particle detector CMS currently under construction at the LHC accelerator. The colliding particles move at right angles to the image, either directly towards the observer or directly away. The lines represent traces of particles produced by the black hole decay. The violet line is the trace of an electron, while the red lines are traces of particles called muons, which are similar to electrons but more massive. The blue and cyan lines denote particles consisting of quarks, and are thus distant kin to protons and neutrons – so-called Kaons in blue, pions in cyan.

The detector contains a powerful magnet which produces a strong magnetic field. This field deflects all moving particles which carry electric charge – in the illustration, their traces are curved. The degree of curvature, combined with other data, is used to infer each particle’s momentum and mass.

By studying collision products, physicists at LHC would be able to identify and study the decay of mini-black holes. In this way, they might be able to prove the existence of extra dimensions, and even gain some insight into their properties.

How often would black holes be produced? The answer depends on what model of the extra dimensions one uses for the calculation. According to some models, black holes should be produced at the LHC at a rate of one per second!

If particle collisions at high-energy may indeed create black holes, we should also expect creation of other gravitational objects which are predicted by string theory, such as higher-dimensional spatially extended solutions of the gravitational equations called branes – cousins of the three-dimensional extended subdomain that is our world.

Artificial mini-black holes – should we worry?

Do we need to worry? Might these mini black holes start growing and, eventually, devour the whole earth? We should not worry about this. Even if you do not trust the calculations predicting a quick demise for such minuscule black holes, there is solid data to go by.

If black holes really form in high-energy particle collisions, they are also continuously created in the earth’s atmosphere by the collision of Ultra High-Energy Cosmic Rays (UHECRs) with nuclei of oxygen, carbon, nitrogen and other elements present in the atmosphere.

UHECRs are particles of unknown origin and identity (protons? light atomic nuclei?) reaching the earth from outer space. In such collisions with atmospheric nuclei, a shower of new particles is produced (consisting mostly of electrons, their slightly more massive cousins called muons, and photons). These particles can be detected by specialized observatories on earth or in space, as sketched in the following illustration:

Incoming cosmic ray colliding with atmospheric nucleus, producing a shower of particles, some of which are detected by a detector array on Earth

The collision energies for UHECRs can be enormous – some observations show energies of hundreds of TeV (hundreds of trillions of electron volts), which is much larger than the collision energies in particle collider experiments. And while the events with very high energy are exceedingly rare, this type of collision has been going on for literally billions of years, so an inordinate number of mini black holes would have formed. Since the earth has not (yet!) disappeared into one of these black holes, the much less massive man-made mini black holes should be quite safe.

The rarity of ultra-high energy collisions is also one of the reasons that physicists have not been able to confirm or disprove the formation of mini-black holes in this way. Still, this could change over the next few years, as the Pierre Auger Cosmic Ray Observatory in Argentina, which has just started taking data, becomes fully operational.

So will we actually find these tiny black holes? Hard to tell – at the moment, we have no direct evidence that the models predicting the existence of extra dimensions are on the right track, and if they are, that among all the many possible shapes and sizes for the extra dimensions, those realized in our universe allow the production of miniature black holes at a detectable rate. Our search is akin to playing the lottery – we will need to get very, very lucky to find what we seek, but if we did, the payoff would be enormous: We would have the first direct evidence that space has extra dimensions!

Further Information

The relativistic background of this spotlight topic is explained in Elementary Einstein, in particular in the chapter Relativity and the quantum.

For more information about extra dimensions, check out the spotlight topics Extra dimensions – and how to hide them, The embedded universe, Hunting for extra dimensions and Simplicity in higher dimensions. Related spotlight topics can be found in the section Relativity and the quantum.

Colophon

Marco Cavaglià

is a professor of physics at the Missouri University of Science & Technology. His research interests are quantum gravity and cosmology.

Citation

Cite this article as:
Marco Cavaglià, “Particle accelerators as black hole factories?” in: Einstein Online Band 04 (2010), 03-1010

Definitioner

TeV

Siehe Elektronenvolt.

LHC

Der Large Hadron Collider, zu deutsch etwa die große Maschine, um Kernteilchen zusammenstoßen zu lassen, ist ein Teilchenbeschleuniger am Teilchenforschungszentrum CERN. Aus Sicht der Relativitätstheorie ist er nicht nur interessant, weil die in ihm beschleunigten Protonen so hohe Energien erreichen wie nie zuvor und so neue Tests der relativistischen Quantenfeldtheorien ermöglichen, auf denen die moderne Elementarteilchenphysik beruht, sondern auch, weil sich bei so hohen Energien erste Spuren einer bislang noch nicht experimentell nachgewiesenen Symmetrie der Natur zeigen sollten, der so genannten Supersymmetrie, die eine wichtige Rolle im Zusammenhang mit der Stringtheorie spielt, einem der Ansätze, Allgemeine Relativitätstheorie und Quantentheorie zu einer Theorie der Quantengravitation zu verbinden. Außerdem gibt Physik bei so hohen Energien Aufschluss über die Eigenschaften der Materie des frühen, heißen Universums, die für die Urknallmodelle wichtig sind.

Webseiten des CERN

CERN

Europäisches Forschungszentrum für Kern- und Teilchenphysik (Centre Européen pour la Récherche Nucleaire), angesiedelt nahe Genf beidseits der französisch-schweizerischen Grenze, gegründet 1954.

CERN ist nicht nur für seine Teilchenbeschleuniger wie den Large Hadron Collider (LHC) bekannt, sondern auch als Geburtsort des World Wide Web.

Webseiten des CERN

TeV

See electron volt

string theory

Candidate for a theory of quantum gravity; a quantum theory, where the fundamental building blocks are tiny, one-dimensional, oscillating entities, called strings. A brief description can be found on the page String theory in the chapter Relativity and the quantum of Elementary Einstein.

string (string theory)

sphere

A spherical surface is a simple example for a curved surface. It is easily pictured as a surface embedded in three-dimensional space: a spherical surface is the set of all points at a certain fixed distance from a given point (the point being the centre of the sphere). Mathematically, a spherical surface can be described without recourse to three-dimensional space - when mathematicians talk of the geometry of such a surface, they (almost) always mean the "inner geometry": Those properties of the surface noticeable to two-dimensional beings, living and working in that surface, capable of measuring distances and angles in it. Sphere is regularly used as a synonym for spherical surface (instead of describing a solid, three-dimensional ball). And not only for the two-dimensional spherical surface described above, but also for its analogues in lower and higher dimensions. A one-sphere, for instance, is the same as a circle, a two-sphere is the spherical surface defined above, a three-sphere its three-dimensional analogue.

space

In a strict sense: Space as we know it from everyday life: the totality of all locations in which objects can sit, with three dimensions. In a more general sense used by mathematicians, all kinds of sets of points are spaces - a line for instance, which has but a single dimension, or a two-dimensional surface, but also higher-dimensional spaces. Also, in such more general spaces, geometry can be different from the standard Euclidean geometry taught in high schools - such spaces can be curved.

second

In the International System of units: the basic unit of time. Defined as a certain multiple of the oscillation period of electromagnetic radiation set free in a certain transition within the electron shell of atoms of the type Cesium-133.

Schwarzschild radius

A measure for the size of a spherically symmetric black hole. It is defined using the area of the black hole's horizon: In usual high school geometry (the geometry of flat space), radius and area of a spherical surface are related as

area = 4 times pi times radius².

The Schwarzschild radius is defined indirectly by the formula

Area of the black hole's horizon = 4 times pi times (Schwarzschild radius)².

It is directly proportional to the black hole's mass. The Schwarzschild radius for an object the mass of the earth is 9 millimetres, for an object with the mass of the sun, 2.95 kilometres. There is a quite general result that says: If a sphere of matter is compressed further and further, a black hole forms as soon as the sphere's radius gets smaller than the Schwarzschild radius corresponding to the matter's mass.

relativistic

Models, effects or phenomena in which special relativity or general relativity play a crucial role are called relativistic. Examples are relativistic quantum field theories as theories based on special relativity, or the relativistic perihelion shift as a consequence of general relativity. In addition, conditions under which the difference between relativistic physics and ordinary, classical physics are especially pronounced, are also called relativistic. For instance, when material objects reach speeds close to speed of light, one talks of relativistic speeds, while speeds that are so small compared to light as to make relativistic effects undetectably small are non-relativistic.

quarks (quark)

Elementary particle that is subject to the strong interaction. Quarks come in six species: up, down, strange, charme, bottom and top (with the last two sometimes called beauty and truth). Quarks are the constituents of protons and neutrons, and thus the material atomic nuclei are made of.

quantum gravity

Theory based both on the effects, concepts and laws of quantum theory and on those of general relativity. To date, no complete such theory exists; the best-known candidate theories are string theory and loop quantum gravity. Some information on the question of quantum gravity can be found in the chapter Relativity and the quantum of Elementary Einstein, starting with the page Border regions of gravity. Selected aspects of quantum gravity are described in the category Relativity and the quantum of our Spotlights on relativity.

protons (proton)

Particle that carries positive electric charge and is comparatively massive; the atomic nuclei consist of protons and neutrons. Protons are not elementary particles, they are compound particles consisting of quarks that are bound together through the strong nuclear interaction . Collectively, protons, neutrons and a number of similar particles are called baryons.

point

Elementary "building block" of geometrical entities such as surfaces or more general spaces. For instance, a surface is the set of all its points, of all possible locations on the surface, and all geometrical objects in that surface are defined by the points that belong to them - for instance, a line on the surface is the set of (infinitely many) points.

plane

A surface within which the axioms of Euclidean geometry (synonym: plane geometry) hold - the rules of geometry as they are taught in high school, with well-known formulae such as Pythagoras's theorem and "the perimeter of a circle is 2 times pi times its radius" hold.

relativistic (perihelion advance, relativistic)

For planetary orbits, there is a small difference between the predictions of Newtonian gravity and general relativity. For instance, in Newton's theory, the orbital curve of a lonely planet orbiting a star is an ellipse. In general relativity, it is a kind of rose or rhodonea curve. Such a curve is similar to an ellipse curve, which shifts a bit with each additional orbit. The shift can be defined by looking at the point which is closest to the sun (perihelion) on each orbit. The additional relativistic shift is, hence, called relativistic perihelion shift or relativistic perihelion advance. A picture can be seen on the page A planet goes astray in the chapter General relativity of Elementary Einstein.

particle physics

The branch of physics that deals with particles that are, to the best of today's knowledge, not made up of more fundamental sub-units, for instance with electrons, quarks or neutrinos. Also included is the study of some species of particles that do have more elementary constitutents, such as protons or neutrons, but not of larger systems such as atomic nuclei (that would be nuclear physics) or, even worse, whole atoms. Questions such as, whether the particles nowadays thought to be elementary really are elementary, or are, for instance, different manifestations of one and the same species of string, fall within the scope of particle physics. The theoretical tools of particle physics are the so-called quantum field theories which allow the description of elementary particles on the basis of both quantum theory and special relativity, while the main experimental tools are particle accelerators in which particles are accelerated and then brought to collision.

oxygen

Chemical element whose atoms have eight protons each in their nuclei. In the context of relativity, more concretely: cosmology, oxygen is interesting as an indicator of chemical evolution: Oxygen nuclei are not produced during Big Bang Nucleosynthesis, but they are produced by nuclear fusion reactions in the interior of stars. The presence of oxygen in an astronomical object is an indicator that stellar fusion has taken place, and that the abundances of the different elements thus do not reflect the element abundances in the early universe.

observer

In the context of relativity, "observer" can mean two different things. Often, observer is synonymous with reference frame or (spacetime-)coordinate system: An observer in this sense is someone who assigns coordinates to everything that happens around him. In particular, all events are assigned space coordinate values and a time coordinate value. In the context of special relativity, it is often the case that when one talks about an observer, what is really meant is an inertial observer, corresponding to a special type of reference frame. On other occasions, the term is used in a more narrow sense - in those cases, an observer is someone sitting at a certain point in space and using the light signals reaching that location to construct an image of his surroundings. In the context of optical effects in relativity, for instance gravitational lensing, observer is usually meant in this way.

nucleus

Extremely dense central region of an atom, consisting of protons and neutrons held together by nuclear forces. The number of protons determines what chemical element a nucleus represents. Typical diameter for atomic nuclei are in the region of a quadrillionth of a metre= 10^-15 metres. This makes nuclei about a hundredth of a thousandth as large as atoms.

nuclei (nucleus)

nitrogen

Chemical element whose atoms have seven protons each in their nuclei. In the context of relativity, more concretely: cosmology, nitrogen is interesting as an indicator of chemical evolution: Its nuclei are not produced during Big Bang Nucleosynthesis, but they are produced by nuclear fusion reactions in the interior of stars. The presence of nitrogen (or, for that matter, of other elements such as oxygen or iron) in an astronomical object is an indicator that stellar fusion has taken place, and hence that the abundances of the different elements do not reflect the element abundances in the early universe.

neutrons (neutron)

Particle that is electrically neutral and comparatively massive; the atomic nuclei consist of neutrons and protons. Neutrons are not elementary particles, they are compound particles consisting of quarks that are bound together through the strong nuclear interaction . Collectively, neutrons, protons and a number of similar particles are called baryons. Neutron stars are mainly made of neutrons.

momentum

Physical quantity that is equal to a body's mass times its velocity (in special relativity: its relativistic mass times its velocity). What makes momentum a useful quantity is that it is conserved - if several bodies interact, the sum of their momenta before and after the interaction is the same. Momentum is neither created nor destroyed, merely passed on from one body to another. In general relativity, momentum is one of a number of quantities (like mass and energy) that acts as a source of gravity.

matter

In general relativity: All contents of spacetime that contribute to its curvature: particles, dust, gases, fluids, electromagnetic and other fields. In particle physics: All elementary particles with half-integer spin, such as electrons and quarks, as well as their composites such as protons and neutrons, in contrast with force particles.

mass

In classical physics, mass plays a triple role. First of all, it is a measure for how easy it is to influence the motion of a body. Imagine that you're drifting in emtpy space. Drifting by are an elephant and a mouse, and you give each of them a push of equal strength. The fact that the mouse abruptly changes its path, while the elephant's course is as good as unaltered, is a sure sign that the mass (or, in the language of physics, the inertia or inertial mass) of the elephant is much greater than that of the mouse. Secondly, mass is a measure of how many atoms there are in a body, and of what type they are. All atoms of one and the same type have the same mass, and adding up all those tiny component masses, the total mass of the body results. Thirdly, in Newton's theory of gravity, mass determines how strongly a body attracts other bodies via the gravitational force, and how strongly these bodies attract it (in this sense, mass is the charge associated with the gravitational force). In special relativity, one can also define a mass that is a measure for a bodies resistance to changing its motion. However, the value of this relativistic mass depends on the relative motion of the body and the observer. The relativistic mass is the "m" in Einstein's famous E=mc² (cf. equivalence of mass and energy). The relativistic mass has a minimum for an observer that is at rest relative to the body in question. This value is the so-called rest mass of the body, and when particle physicists talk of mass, this is usually what they mean. Just as in classical physics, the rest mass is a kind of measure for how much matter the body is made up of - with one caveat: For composite bodies, the energies associated with the forces holding the body together contribute to the total mass, as well (another consequence of the equivalence of mass and energy). In general relativity, mass still plays a role as a source of gravity; however, it has been joined by physical quantities such as energy, momentum and pressure.

magnetic field

The magnetic force is a force by which electric currents (i.e. moving electric charges) act on each other; the magnetic field is the associated field. All phenomena related to the magnetic force or magnetic field are subsumed under the heading of magnetism. Magnetic fields cannot be understood separate from electric fields - their complete description is possible only within the more general context of electromagnetism.

line

Geometric object with a single dimension. A line can either be an independent one-dimensional space (in the abstract mathematical space where a space does not need to have three dimensions), or it can be embedded into a more general space, like a line drawn onto a piece of paper (i.e. a surface).

light

Light in the strict sense of the word is electromagnetic radiation the human eye can detect, with wave-lengths between 400 and 700 nano metres. In relativity theory and in astronomy, the word is often used in a more general sense, encompassing all kinds of electromagnetic radiation. For instance, astronomers might talk about "infrared light" or "gamma light"; in this context, light in the stricter sense is referred to as "visible light". Within classical physics, the properties of light are governed by Maxwell's equations; in quantum physics, it turns out that light is a stream of energy packets called light quanta or photons. In the context of relativistic physics, light is of great interest, and for a number of reasons. First of all, the speed of light plays a central role in both special and general relativity. Also, there are a number of interesting effects in general relativity which are associated with the propagation of light, namely deflection, the Shapiro effect and the gravitational redshift.

LHC (Large Hadron Collider)

The Large Hadron Collider is a particle accelerator in the research centre CERN. From the point of view of relativity theory, it has several points of interest: First of all, it accelerates protons to higher energies than ever, allowing new tests of the relativistic quantum field theories that are at the core of modern particle physics. Secondly, at such high energies, there should be first traces of an as-yet unproven symmetry of nature called supersymmetry, which plays an important role in string theory, one of the candidates for a theory of quantum gravity (the quantum theory version of Einstein's general relativity). Finally, the high energies are interesting because they give information about the very early high temperature universe, and about the physics that should be included in the big bang models of relativistic cosmology. CERN website

horizon

In general relativity: A closed surface that is the boundary of a black hole. Whatever enters through this boundary from the outside can never again leave the inside.

Synonym: event horizon.

gravity

See gravitation

gravity (gravitation)

In classical physics: An action-at-a-distance force by which all bodies that possess mass attract each other (see Newtonian theory of gravity), synonym: gravitational force. In Einstein's general theory of relativity: The fact that matter that possesses mass, energy, pressure or similar properties distorts spacetime, and that this distortion in turn influences whatever matter might be present. An introduction to the basic ideas of general relativity is provided by the section General relativity of Elementary Einstein. More information about the nature of gravity in general relativity can be found in the spotlight text Gravity: From weightlessness to curvature.

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.

field

A field describes how a physical quantity is distributed in space and time. For instance, the area where electric forces act on a test particle is subject to an electric field. Or the gravitational forces which act on the mass of a test body define a gravitational field. In general a field contains energy, occupies space and can change over time.

extra dimensions (extra dimension)

According to some of the candidate models for a theory of quantum gravity, notably in string theory, our world should have extra dimensions - space dimensions in addition to the three we know from everday life. More information about extra dimensions, possibilities of observing their effects and their use for building physical models can be found in our section Spotlights on relativity, namely Extra dimensions and how to hide them, The hunt for extra dimensions and Simplicity in higher dimensions.

energy

Physical quantity with the special property that, in physical processes, energy is neither destroyed nor created, simply transformed from one form of energy to another. Some of the different forms of energy that are defined separately are kinetic energy, thermal energy and the energy carried by electromagnetic radiation. Processes that transform one form of energy into another take place in all machines we use in everyday life, from the engine of a subway train (electrical energy into kinetic energy of the train) to an electric blanket (electrical energy into thermal energy). One important consequence of special relativity is that energy and mass are completely equivalent - two different ways to define what is, on closer inspection, one and the same physical quantity. See the keyword equivalence between mass and energy.

elementary particles (elementary particle)

Within the commonly accepted models of physics, certain particles are not built of even more fundamental sub-particles - they are themselves elementary. Examples for elementary particles are electrons, quarks and neutrinos, while particles such as protons or neutrons consist of sub-units and are thus not elementary. The study of elementary particles is called particle physics, under which keyword some more information about the theoretical framework of elementary particles can be found.

electron

Low-mass elementary particle with negative electric charge. The atoms that are the constituents of everyday matter each consists of a nucleus surrounded by a shell of electrons.

electrons (electron)

Low-mass elementary particle with negative electric charge. The atoms that are the constituents of everyday matter each consists of a nucleus surrounded by a shell of electrons.

electric charge

The charge associated with electromagnetism: a property of objects that determines the strength of the electric force with which they act on other charged objects, and the strength of electric forces by which other such objects act on them. Moving electric charges produce a magnetic field, and are influenced by such 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.

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.

charge

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.

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. > CERN website

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.

black holes (black hole)

atomic nucleus

See nucleus.

atom

All matter we encounter in everyday life consists of smallest units called atoms - the air we breath consists of a wildly careening crowd of little groups of atoms, my computer's keyboard of a tangle of atom chains, the metal surface it rests on is a crystal lattice of atoms. All the variety of matter consists of less than hundred species of atoms (in other words: less than a hundred different chemical elements). Every atom consists of an nucleus surrounded by a cloud of electrons. Nearly all of the atom's mass is concentrated in its nucleus, while the structure of the electron cloud determines how the atom can bind to other atoms (in other words: its chemical properties). Every chemical element can be defined via a characteristic number of protons in its nucleus. Atoms that have lost some of their usual number of electrons are called ions. Atoms are extremely small (typical diametres are in the region of tenths of a billionth of a metre = 10^-10 metres), and to describe their properties and behaviour, one has to resort to quantum theory.