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# Spacetime

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. [1]

## Aberration of light

The aberration of light (also referred to as astronomical aberration, stellar aberration, or velocity aberration) is an astronomical phenomenon which produces an apparent motion of celestial objects about their true positions, dependent on the velocity of the observer.

## Aether drag hypothesis

In the 19th century, the theory of the luminiferous aether as the hypothetical medium for the propagation of light was widely discussed.

## Albert Einstein

Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics).

## Angular momentum

In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of linear momentum.

## Apollo 11

Apollo 11 was the spaceflight that landed the first two humans on the Moon.

## Arago spot

In optics, the Arago spot, Poisson spot, or Fresnel bright spot, is a bright point that appears at the center of a circular object's shadow due to Fresnel diffraction.

## Astrometry

Astrometry is the branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies.

## Astrophysical jet

An astrophysical jet is an astronomical phenomenon where outflows of ionised matter are emitted as an extended beam along the axis of rotation.

## Atlas (topology)

In mathematics, particularly topology, one describes a manifold using an atlas.

Bell's spaceship paradox is a thought experiment in special relativity.

## Black hole

A black hole is a region of spacetime exhibiting such strong gravitational effects that nothing—not even particles and electromagnetic radiation such as light—can escape from inside it.

## Blueshift

A blueshift is any decrease in wavelength, with a corresponding increase in frequency, of an electromagnetic wave; the opposite effect is referred to as redshift.

## Boca Raton, Florida

Boca Raton (lit) is the southernmost city in Palm Beach County, Florida, United States, first incorporated on August 2, 1924 as "Bocaratone," and then incorporated as "Boca Raton" in 1925.

## Bohr–Einstein debates

The Bohr–Einstein debates were a series of public disputes about quantum mechanics between Albert Einstein and Niels Bohr.

## Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

## Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

## Causality

Causality (also referred to as causation, or cause and effect) is what connects one process (the cause) with another process or state (the effect), where the first is partly responsible for the second, and the second is partly dependent on the first.

## Cavendish experiment

The Cavendish experiment, performed in 1797&ndash;1798 by British scientist Henry Cavendish, was the first experiment to measure the force of gravity between masses in the laboratory and the first to yield accurate values for the gravitational constant.

## Center of mass

In physics, the center of mass of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero, or the point where if a force is applied it moves in the direction of the force without rotating.

## Center-of-momentum frame

In physics, the center-of-momentum frame (also zero-momentum frame or COM frame) of a system is the unique (up to velocity but not origin) inertial frame in which the total momentum of the system vanishes.

## Classical mechanics

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.

## Closed system

A closed system is a physical system that does not allow certain types of transfers (such as transfer of mass and energy transfer) in or out of the system.

## Cone

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.

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## Conformal geometry

In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space.

## Conservation of energy

In physics, the law of conservation of energy states that the total energy of an isolated system remains constant, it is said to be ''conserved'' over time.

## Continuum (measurement)

Continuum theories or models explain variation as involving gradual quantitative transitions without abrupt changes or discontinuities.

## Conventionalism

Conventionalism is the philosophical attitude that fundamental principles of a certain kind are grounded on (explicit or implicit) agreements in society, rather than on external reality.

## Corpuscular theory of light

In optics, the corpuscular theory of light, arguably set forward by Descartes (1637) states that light is made up of small discrete particles called "corpuscles" (little particles) which travel in a straight line with a finite velocity and possess impetus.

## Data reduction

Data reduction is the transformation of numerical or alphabetical digital information derived empirically or experimentally into a corrected, ordered, and simplified form.

## David Hilbert

David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.

## Derivations of the Lorentz transformations

There are many ways to derive the Lorentz transformations utilizing a variety of physical principles, ranging from Maxwell's equations to Einstein's postulates of special relativity, and mathematical tools, spanning from elementary algebra and hyperbolic functions, to linear algebra and group theory.

## Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

## Doppler effect

The Doppler effect (or the Doppler shift) is the change in frequency or wavelength of a wave in relation to observer who is moving relative to the wave source.

## Dynamics (mechanics)

Dynamics is the branch of applied mathematics (specifically classical mechanics) concerned with the study of forces and torques and their effect on motion, as opposed to kinematics, which studies the motion of objects without reference to these forces.

## Einstein field equations

The Einstein field equations (EFE; also known as Einstein's equations) comprise the set of 10 equations in Albert Einstein's general theory of relativity that describe the fundamental interaction of gravitation as a result of spacetime being curved by mass and energy.

## Einstein synchronisation

Einstein synchronisation (or Poincaré&ndash;Einstein synchronisation) is a convention for synchronising clocks at different places by means of signal exchanges.

## Einstein's thought experiments

A hallmark of Albert Einstein's career was his use of visualized thought experiments (Gedankenexperiment) as a fundamental tool for understanding physical issues and for elucidating his concepts to others.

## Electromagnetic induction

Electromagnetic or magnetic induction is the production of an electromotive force (i.e., voltage) across an electrical conductor in a changing magnetic field.

## Electromagnetic mass

Electromagnetic mass was initially a concept of classical mechanics, denoting as to how much the electromagnetic field, or the self-energy, is contributing to the mass of charged particles.

## Electromagnetic tensor

In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime.

## Elementary particle

In particle physics, an elementary particle or fundamental particle is a particle with no substructure, thus not composed of other particles.

## Emmy Noether

Amalie Emmy NoetherEmmy is the Rufname, the second of two official given names, intended for daily use.

## Encyclopædia Britannica

The Encyclopædia Britannica (Latin for "British Encyclopaedia"), published by Encyclopædia Britannica, Inc., is a general knowledge English-language encyclopaedia.

## Equivalence principle

In the theory of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.

## Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.

## Event (relativity)

In physics, and in particular relativity, an event is the instantaneous physical situation or occurrence associated with a point in spacetime (that is, a specific place and time).

## Event horizon

In general relativity, an event horizon is a region in spacetime beyond which events cannot affect an outside observer.

## Fizeau experiment

The Fizeau experiment was carried out by Hippolyte Fizeau in 1851 to measure the relative speeds of light in moving water.

## Fizeau–Foucault apparatus

Fizeau–Foucault apparatus is a term sometimes used to refer to two types of instrument historically used to measure the speed of light.

## Four-dimensional space

A four-dimensional space or 4D space is a mathematical extension of the concept of three-dimensional or 3D space.

## Four-force

In the special theory of relativity, four-force is a four-vector that replaces the classical force.

## Four-momentum

In special relativity, four-momentum is the generalization of the classical three-dimensional momentum to four-dimensional spacetime.

## Four-vector

In special relativity, a four-vector (also known as a 4-vector) is an object with four components, which transform in a specific way under Lorentz transformation.

## Four-velocity

In physics, in particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetimeTechnically, the four-vector should be thought of as residing in the tangent space of a point in spacetime, spacetime itself being modeled as a smooth manifold.

## Frame of reference

In physics, a frame of reference (or reference frame) consists of an abstract coordinate system and the set of physical reference points that uniquely fix (locate and orient) the coordinate system and standardize measurements.

## Frame-dragging

Frame-dragging is an effect on spacetime, predicted by Einstein's general theory of relativity, that is due to non-static stationary distributions of mass–energy.

## General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

## Geodesic

In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".

## Geodesics in general relativity

In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime.

## Geodetic effect

The geodetic effect (also known as geodetic precession, de Sitter precession or de Sitter effect) represents the effect of the curvature of spacetime, predicted by general relativity, on a vector carried along with an orbiting body.

## George F. Ellis

George F. Ellis was a cattleman, pioneer in the field of beef cattle production, and a published author.

## George Francis FitzGerald

Prof George Francis FitzGerald FRS FRSE (3 August 1851 – 22 February 1901) was an Irish professor of "natural and experimental philosophy" (i.e., physics) at Trinity College in Dublin, Ireland, during the last quarter of the 19th century.

## Gravitational energy

Gravitational energy is the potential energy a body with mass has in relation to another massive object due to gravity.

## Gravitational field

In physics, a gravitational field is a model used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body.

## Gravitational time dilation

Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events as measured by observers situated at varying distances from a gravitating mass.

## Gravitational wave

Gravitational waves are the disturbance in the fabric ("curvature") of spacetime generated by accelerated masses and propagate as waves outward from their source at the speed of light.

## Gravitoelectromagnetism

Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity.

## Gravity Probe B

Gravity Probe B (GP-B) was a satellite-based mission which launched on 20 April 2004 on a Delta II rocket.

## Hendrik Lorentz

Hendrik Antoon Lorentz (18 July 1853 – 4 February 1928) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect.

## Henri Bergson

Henri-Louis Bergson (18 October 1859 – 4 January 1941) was a French-Jewish philosopher who was influential in the tradition of continental philosophy, especially during the first half of the 20th century until World War II.

## Henri Poincaré

Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.

## Hermann Minkowski

Hermann Minkowski (22 June 1864 – 12 January 1909) was a German mathematician and professor at Königsberg, Zürich and Göttingen.

## Hermann Weyl

Hermann Klaus Hugo Weyl, (9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher.

## History of Lorentz transformations

The history of Lorentz transformations comprises the development of linear transformations forming the Lorentz group or Poincaré group preserving the Lorentz interval -x_0^2+\cdots+x_n^2 and the Minkowski inner product -x_0^2 y_0^2+\cdots+x_n^2 y_n^2.

## Hyperbolic angle

In mathematics, a hyperbolic angle is a geometric figure that divides a hyperbola. The science of hyperbolic angle parallels the relation of an ordinary angle to a circle. The hyperbolic angle is first defined for a "standard position", and subsequently as a measure of an interval on a branch of a hyperbola. A hyperbolic angle in standard position is the angle at (0, 0) between the ray to (1, 1) and the ray to (x, 1/x) where x > 1. The magnitude of the hyperbolic angle is the area of the corresponding hyperbolic sector which is ln x. Note that unlike circular angle, hyperbolic angle is unbounded, as is the function ln x, a fact related to the unbounded nature of the harmonic series. The hyperbolic angle in standard position is considered to be negative when 0 a > 1 so that (a, b) and (c, d) determine an interval on the hyperbola xy.

## Hyperbolic function

In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.

## Hyperbolic geometry

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.

## Hyperbolic manifold

In mathematics, a hyperbolic manifold is a space where every point looks locally like hyperbolic space of some dimension.

## Hyperbolic space

In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.

## Hyperboloid

In geometry, a hyperboloid of revolution, sometimes called circular hyperboloid, is a surface that may be generated by rotating a hyperbola around one of its principal axes.

## Hyperboloid model

In geometry, the hyperboloid model, also known as the Minkowski model or the Lorentz model (after Hermann Minkowski and Hendrik Lorentz), is a model of n-dimensional hyperbolic geometry in which points are represented by the points on the forward sheet S+ of a two-sheeted hyperboloid in (n+1)-dimensional Minkowski space and m-planes are represented by the intersections of the (m+1)-planes in Minkowski space with S+.

## Inertial frame of reference

An inertial frame of reference in classical physics and special relativity is a frame of reference in which a body with zero net force acting upon it is not accelerating; that is, such a body is at rest or it is moving at a constant speed in a straight line.

## Introduction to general relativity

General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915.

## Introduction to the mathematics of general relativity

The mathematics of general relativity is complex.

## Invariant (physics)

In mathematics and theoretical physics, an invariant is a property of a system which remains unchanged under some transformation.

## Invariant mass

The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system.

## John Lucas (philosopher)

John Randolph Lucas FBA (born 18 June 1929) is a British philosopher.

## Kinematics

Kinematics is a branch of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the mass of each or the forces that caused the motion.

## LAGEOS

LAGEOS, Laser Geodynamics Satellite or Laser Geometric Environmental Observation Survey, are a series of two scientific research satellites designed to provide an orbiting laser ranging benchmark for geodynamical studies of the Earth.

## LARES (satellite)

LARES (acronym for Laser Relativity Satellite) (COSPAR ID) is an Italian Space Agency scientific satellite launched from the ESA Guiana Space Centre of Kourou, French Guiana, by the maiden flight of the European launch vehicle Vega on 13 February 2012.

## Length contraction

Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame.

## Lense–Thirring precession

In general relativity, Lense–Thirring precession or the Lense–Thirring effect (named after Josef Lense and Hans Thirring) is a relativistic correction to the precession of a gyroscope near a large rotating mass such as the Earth.

## Lie algebra

In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.

## Lie sphere geometry

Lie sphere geometry is a geometrical theory of planar or spatial geometry in which the fundamental concept is the circle or sphere.

## Lilliput and Blefuscu

Lilliput and Blefuscu are two fictional island nations that appear in the first part of the 1726 novel Gulliver's Travels by Jonathan Swift.

## Line integral

In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve.

## Lorentz transformation

In physics, the Lorentz transformations (or transformation) are coordinate transformations between two coordinate frames that move at constant velocity relative to each other.

## Luminiferous aether

In the late 19th century, luminiferous aether or ether ("luminiferous", meaning "light-bearing"), was the postulated medium for the propagation of light.

## Lunar Laser Ranging experiment

The ongoing Lunar Laser Ranging experiment measures the distance between Earth and the Moon using laser ranging.

## Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

## Mass

Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied.

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## Mass in special relativity

Mass in special relativity incorporates the general understandings from the laws of motion of special relativity along with its concept of mass–energy equivalence.

## Mass–energy equivalence

In physics, mass–energy equivalence states that anything having mass has an equivalent amount of energy and vice versa, with these fundamental quantities directly relating to one another by Albert Einstein's famous formula: E.

## Massless particle

In particle physics, a massless particle is an elementary particle whose invariant mass is zero.

## Mathematical model

A mathematical model is a description of a system using mathematical concepts and language.

## Max Born

Max Born (11 December 1882 – 5 January 1970) was a German physicist and mathematician who was instrumental in the development of quantum mechanics.

## Maxwell's equations

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.

## Möbius transformation

In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0.

## Mercator projection

The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569.

## Mercury (planet)

Mercury is the smallest and innermost planet in the Solar System.

## Metric signature

The signature of a metric tensor g (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number (counted with multiplicity) of positive and zero eigenvalues of the real symmetric matrix of the metric tensor with respect to a basis.

## Metric space

In mathematics, a metric space is a set for which distances between all members of the set are defined.

## Michelson–Morley experiment

The Michelson–Morley experiment was performed between April and July, 1887 by Albert A. Michelson and Edward W. Morley at what is now Case Western Reserve University in Cleveland, Ohio, and published in November of the same year.

## Minkowski diagram

The Minkowski diagram, also known as a spacetime diagram, was developed in 1908 by Hermann Minkowski and provides an illustration of the properties of space and time in the special theory of relativity.

## Minkowski space

In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.

## Minute and second of arc

A minute of arc, arcminute (arcmin), arc minute, or minute arc is a unit of angular measurement equal to of one degree.

## Momentum

In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object.

## Motion (physics)

In physics, motion is a change in position of an object over time.

## NASA

The National Aeronautics and Space Administration (NASA) is an independent agency of the executive branch of the United States federal government responsible for the civilian space program, as well as aeronautics and aerospace research.

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## Neutron star

A neutron star is the collapsed core of a large star which before collapse had a total of between 10 and 29 solar masses.

## Newton's law of universal gravitation

Newton's law of universal gravitation states that a particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

## Newtonian limit

In physics, the Newtonian limit is a mathematical approximation applicable to physical systems exhibiting (1) weak gravitation, (2) objects moving slowly compared to the speed of light, and (3) slowly changing (or completely static) gravitational fields.

## Niels Bohr

Niels Henrik David Bohr (7 October 1885 – 18 November 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922.

## Nucleosynthesis

Nucleosynthesis is the process that creates new atomic nuclei from pre-existing nucleons, primarily protons and neutrons.

## Numerical relativity

Numerical relativity is one of the branches of general relativity that uses numerical methods and algorithms to solve and analyze problems.

## Observer (special relativity)

In special relativity, an observer is a frame of reference from which a set of objects or events are being measured.

## Perpetual motion

Perpetual motion is motion of bodies that continues indefinitely.

## Philosophy of space and time

Philosophy of space and time is the branch of philosophy concerned with the issues surrounding the ontology, epistemology, and character of space and time.

## Physics

Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

## Pound–Rebka experiment

The Pound–Rebka experiment is a well known experiment to test Albert Einstein's theory of general relativity.

## Pressure

Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

## Principle of locality

In physics, the principle of locality states that an object is only directly influenced by its immediate surroundings.

## Principle of relativity

In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference.

## Pseudo-Riemannian manifold

In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.

## Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

## Quantum entanglement

Quantum entanglement is a physical phenomenon which occurs when pairs or groups of particles are generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the other(s), even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole.

## Redshift

In physics, redshift happens when light or other electromagnetic radiation from an object is increased in wavelength, or shifted to the red end of the spectrum.

## Relativistic Doppler effect

The relativistic Doppler effect is the change in frequency (and wavelength) of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects described by the special theory of relativity.

## Relativity of simultaneity

In physics, the relativity of simultaneity is the concept that distant simultaneity – whether two spatially separated events occur at the same time – is not absolute, but depends on the observer's reference frame.

## Retroreflector

A retroreflector (sometimes called a retroflector or cataphote) is a device or surface that reflects light back to its source with a minimum of scattering.

## Riemann curvature tensor

In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common method used to express the curvature of Riemannian manifolds.

## Ring laser

Ring lasers are composed of two beams of light of the same polarization traveling in opposite directions ("counter-rotating") in a closed loop.

## Scholarpedia

Scholarpedia is an English-language online wiki-based encyclopedia with features commonly associated with open-access online academic journals, which aims to have quality content.

## Singular point of an algebraic variety

In the mathematical field of algebraic geometry, a singular point of an algebraic variety V is a point P that is 'special' (so, singular), in the geometric sense that at this point the tangent space at the variety may not be regularly defined.

## Spacetime topology

Spacetime topology is the topological structure of spacetime, a topic studied primarily in general relativity.

## Special relativity

In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.

## Speed of light

The speed of light in vacuum, commonly denoted, is a universal physical constant important in many areas of physics.

## Spherical wave transformation

Spherical wave transformations leave the form of spherical waves as well as the laws of optics and electrodynamics invariant in all inertial frames.

## Squeeze mapping

In linear algebra, a squeeze mapping is a type of linear map that preserves Euclidean area of regions in the Cartesian plane, but is not a rotation or shear mapping.

## Stanford Encyclopedia of Philosophy

The Stanford Encyclopedia of Philosophy (SEP) combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users.

## Stress (mechanics)

In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material.

## Stress–energy tensor

The stress–energy tensor (sometimes stress–energy–momentum tensor or energy–momentum tensor) is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics.

## Supermassive black hole

A supermassive black hole (SMBH or SBH) is the largest type of black hole, on the order of hundreds of thousands to billions of solar masses, and is found in the centre of almost all currently known massive galaxies.

## Tensor

In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.

## The New York Times

The New York Times (sometimes abbreviated as The NYT or The Times) is an American newspaper based in New York City with worldwide influence and readership.

The Road to Reality: A Complete Guide to the Laws of the Universe is a book on modern physics by the British mathematical physicist Roger Penrose, published in 2004.

## Thought experiment

A thought experiment (Gedankenexperiment, Gedanken-Experiment or Gedankenerfahrung) considers some hypothesis, theory, or principle for the purpose of thinking through its consequences.

## Three-dimensional space

Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).

## Time

Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future.

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## Time dilation

According to the theory of relativity, time dilation is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other, or by being differently situated relative to a gravitational field.

## Time translation symmetry

Time translation symmetry or temporal translation symmetry (TTS) is a mathematical transformation in physics that moves the times of events through a common interval.

## Tolman–Oppenheimer–Volkoff limit

The Tolman–Oppenheimer–Volkoff limit (or TOV limit) is an upper bound to the mass of cold, nonrotating neutron stars, analogous to the Chandrasekhar limit for white dwarf stars.

## Torsion spring

A torsion spring is a spring that works by torsion or twisting; that is, a flexible elastic object that stores mechanical energy when it is twisted.

## Translational symmetry

In geometry, a translation "slides" a thing by a: Ta(p).

## Tropical year

A tropical year (also known as a solar year) is the time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice.

In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more.

## Uncertainty principle

In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.

## Unit circle

In mathematics, a unit circle is a circle with a radius of one.

## Unit hyperbola

In geometry, the unit hyperbola is the set of points (x,y) in the Cartesian plane that satisfy the implicit equation x^2 - y^2.

## Urbain Le Verrier

Urbain Jean Joseph Le Verrier (11 March 1811 – 23 September 1877) was a French mathematician who specialized in celestial mechanics and is best known for predicting the existence and position of Neptune using only mathematics.

## Vacuum

Vacuum is space devoid of matter.

## Velocity

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.

## World line

The world line (or worldline) of an object is the path that object traces in -dimensional spacetime.

## References

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