Astronomical unit of distance:
1 parsec = 3.26 light-years
= 200 000 astronomical units
= 20 trillion miles
= 30 trillion kilometres.
Abbreviation: pc. Parsec is an acronym for “parallax second”.
The most important experimental technique of particle physics: accelerating electrically charged particles with the help of electric forces, make them collide with each other and, from the result of the collision, draw conclusions about the properties of elementary particles and their interactions.
It is an intriguing possibility, suggested by models based on the ideas of string theory, that particle accelerators such as the LHC might actually produce miniature black holes (for more about this, see the spotlight text Particle accelerators as black hole factories?).
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.
Synonym: Sum over histories. A technique for performing calculations in quantum theory. Roughly speaking, the probability for a certain outcome (for instance, a particle reaching location A at time t) is calculated by performing a sum over all possible ways in which this particular outcome can come about.
A description of the path integral formulation of quantum theory can be found in the spotlight text The sum over all possibilities.
Pauli exclusion principle
Basic principle of quantum theory stating that no two fermions can be in exactly the same state – for instance: no two fermions with identical properties can be at the same location. Formulated by the physicist Wolfgang Pauli.
Electrons are fermions, and the Pauli exclusion principle plays a crucial role in bringing about the properties of matter as we know them: It is responsible for the fact that the electrons of atoms do not all cluster together in the lowest-energy state close to the atomic nucleus, but instead spread out, occupying different states. This is what gives atoms their shell structure, responsible for different atoms’ different chemical properties.
For a planet or other heavenly body orbiting the sun on an elliptic orbit, that point of the orbit closest to the sun. In the context of general relativity, the perihelion is of great interest as that theory predicts a slight motion of this point around the sun, cf. (relativistic) perihelion shift.
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.
Synonyms: perihelion shift, relativistic
Perimeter Institute for Theoretical Physics
Privately funded institute for basic research in theoretical physics, located in Waterloo, Canada. Currently, the main areas of research are quantum computing, the foundations of quantum theory, and quantum gravity.
When light shines onto a metal, it can knock electrons out of the metal’s atoms. This is the photoelectric effect, and its properties – how does the number and energy of the electrons depend on the frequency and intensity of the light? – can only be explained if one accepts that light is no mere electromagnetic wave, but somehow made up of some kind of light particles. With this postulate, Einstein, in 1905, paved the way for the later development of quantum mechanics.
Synonyms: photoelectric effect
Synonym: light particle, light quantum. In quantum theory, light is not a continuous electromagnetic wave, but a steady stream of tiny energy packets – photons.
In a certain distance from a spherically symmetric black hole, the deflection of light because of the black hole’s gravity is so great that light can move on closed circular orbits – photons (light particles) can, at this distance, orbit the black hole like a planet the sun. This particular distance is called the photon radius.
An observer at rest at this distance can see the back of his or her own head (or at least a small region thereof), as the photons emitted by the back of the head travel once around the black hole and fly directly into his or her eyes.
Pierre Auger Observatory
An observatory in western Argentina built to study high energy cosmic rays. From the viewpoint of relativity, one interesting aspect of this is the possibility that such cosmic rays might produce miniature black holes (see the spotlight text Particle accelerators as black hole factories?).
Natural unit of energy that can be obtained by combining the fundamental natural constants that govern spacetime, the strength of gravity and the quantum world: the gravitational constant, Planck’s constant and the speed of light. Whenever elementary particles reach this kind of energy, in addition to the effects of quantum theory, the effects of general relativity should become important, in short: such situations could only be described adequately using a theory of quantum gravity.
Compare: Planck length, Planck time, Planck mass.
Natural length that can be obtained by combining the fundamental natural constants that govern spacetime, the strength of gravity and the quantum world: the gravitational constant, Planck’s constant and the speed of light. It amounts to roughly 1.6·10-35 meters [see exponential notation].
At such length scales, both the effects of quantum theory and those of general relativity should become important, in short: whatever concerns such scales can only be described adequately using a theory of quantum gravity.
Compare Planck time, Planck energy, Planck mass.
Natural unit of mass that can be obtained by combining the fundamental natural constants that govern spacetime, the strength of gravity and the quantum world: the gravitational constant, Planck’s constant and the speed of light. Compared with the masses we’re used to in everyday life, the Planck mass is rather small, a mere 2 hundredth of a thousandth of a gram. However, if this mass is concentrated in a single elementary particle then, in addition to the effects of quantum theory, the effects of general relativity should become important, in short: such a particle could only be described adequately using a theory of quantum gravity.
Compare Planck length, Planck time, Planck energy.
Natural interval of time that can be obtained by combining the fundamental natural constants that govern spacetime, the strength of gravity and the quantum world: the gravitational constant, Planck’s constant and the speed of light. It amounts to about 5·10-44 seconds [see exponential notation] and is the time it takes light to traverse one Planck length’s worth of distance.
At such time scales – for instance: at cosmic time comparable to the Planck time in the big bang models – both the effects of quantum theory and those of general relativity should become important, in short: such time intervals and what happens in them can only be described adequately using a theory of quantum gravity.
Compare: Planck length, Planck energy, Planck mass.
Natural units for length, time, energy and mass, obtained by combining the fundamental natural constants that govern spacetime, the strength of gravity and the quantum world: the gravitational constant, Planck’s constant and the speed of light.
See: Planck length, Planck time, Planck energy, Planck mass.
Fundamental constant of quantum theory; of the dimension energy times time. For instance, the energy of a single photon is equal to Planck’s constant times the photon’s frequency. Abbreviated as h in formulae.
Planck’s radiation law
The fundamental law governing the properties of the simplest form of thermal radiation – that emitted by a blackbody. It describes the spectrum of such radiation in terms of universal constants and a single parameter – the body’s temperature. The result is also called a blackbody spectrum.
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.
Planets are not-too-small companions of a star that are not stars themselves (nor ever were stars). In our solar system, the planets are, listed from the one closest to the sun to the one farthest: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune. As of August 2006, Pluto, which used to be a proper planet, is officially a “dwarf planet”. In the night sky, the distinguishing characteristic of planets is that they move around relative to the unchanging background of stars – which gave them their name, loosely translated from Greek as “wanderers”.
State of matter in which the atoms are largely or even completely separated into electrons and atomic nuclei, which fly around in a highly energetic mixture.
Compare the other states of matter: solid state, gas, liquid.
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.
Waves that are especially simple can be completely described by stating the direction in which they propagate, their speed of propagation, frequency, and amplitude. But there are also simple waves where these quantities are not sufficient for a complete description – for these waves, the oscillation has an orientation in space. This orientation, which is called polarization, needs to be specified as well.
For example, for electromagnetic waves, the polarization describes the directions of the electric and the magnetic fields. For gravitational waves, the polarization describes the orientation of the two orthogonal directions in which distances are maximally stretched and squeezed as the gravitational wave passes.
Positrons are the anti-particles of electrons: light elementary particles with positive electric charge.
For situations in which gravity is very weak, general relativity and Newton’s theory of gravity lead to very similar predictions for the motion of bodies (e.g. the planets in our solar system) and the propagation of light. Such situations can be described by starting out with the Newtonian description and then, step by step, adding correction terms that take into account the effects of general relativity. The post-Newtonian formalism is a method for performing those step-by-step corrections. As the correction terms are ordered in a systematic way (the largest effects are called “of first post-Newtonian order, 1pN”, the next smallest ones of second order, and so on), the progression of ever smaller corrections is also called the post-Newtonian expansion.
The post-Newtonian formalism is also crucial to describe relativistic effects in binary systems (binary neutron stars or black holes). It therefore plays a key role in the direct detection of gravitational waves: Based on the post-Newtonian formalism, various possible gravitational waveforms are modeled and used for searching the detector data for signals. The post-Newtonian formalism is a vital ingredient for all waveform models, but is particularly important for binary neutron stars. For those systems, most of the observed signal is in the regime where post-Newtonian terms are dominant. It was thanks to a post-Newtonian model that gravitational waves from the merger of two orbiting neutron stars were detected for the first time in 2017.
Synonyms: post-Newtonian expansions
When an object is being acted upon by a force like the electric or gravitational force, then it can be assigned an energy that depends only on its location relative to the source of the force. This energy is called the potential energy – “potential” as it can easily be transformed into kinetic energy, energy associated with the object’s motion: As the object yields to the pull or push of the force, its potential energy decreases while the energy associated with its motion increases.
A measure for the strength of the resistance with which matter (for instance a gas) resists attempts to decrease the volume it occupies.
In cosmology: At, from, or relating to the beginning (or at least the early phases) of the universe. For example, the primordial abundances of the chemical elements are the abundances right after Big Bang Nucleosynthesis, at a cosmic time of a few minutes.
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.
A specific binary system consisting of two orbiting neutron stars, one of which is a pulsar from which we here on Earth receive regularly spaced radio pulses. From the point of view of general relativity, the system is interesting not only because, using the pulses, one can measure effects such as Shapiro delay with impressive precision, but because it has given us the first indirect proof for the existence of gravitational waves: the orbital period of the two stars becomes slightly shorter with each orbit, exactly in the way predicted by general relativity due to the energy the system radiates away in the form of gravitational waves.
Rotating neutron star from which regular pulses of radiation reach the Earth. Behind those pulses is the fact that the pulsar sends out narrowly focussed beams of radiation that, due to the pulsar’s rotation, sweep through space like the beam of a light-house. An animation illustrating this effect can be found on the page Neutron stars and pulsars in the chapter Black holes & Co. of Elementary Einstein.
For a triangle in the plane (or in a more general flat space), two of whose sides form an angle of 90 degrees, the following holds: The lengths a and b of the two sides that form the 90 degrees angle and the length c of the third side are related by the formula