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Dimensions
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.[1][2] Thus a line has a dimension of one because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces. In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism
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Size
Size
Size
is the magnitude or dimensions of a thing, or how big something is. Size
Size
can be measured as length, width, height, diameter, perimeter, area, volume, or mass.Play mediaThis animation gives a sense of the awe-inspiring scale of some of the known objects in our universe.In mathematical terms, "size is a concept abstracted from the process of measuring by comparing a longer to a shorter".[1] Size
Size
is determined by the process of comparing or measuring objects, which results in the determination of the magnitude of a quantity, such as length or mass, relative to a unit of measurement. Such a magnitude is usually expressed as a numerical value of units on a previously established spatial scale, such as meters or inches. The sizes with which humans tend to be most familiar are body dimensions (measures of anthropometry), which include measures such as human height, and human body weight
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Pseudo-Riemannian Manifold
In differential geometry, a pseudo-Riemannian manifold[1][2] (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. Every tangent space of a pseudo- Riemannian manifold is a pseudo- Euclidean space
Euclidean space
described by a quadratic form, which may be isotropic. A special case of great importance to general relativity is a Lorentzian manifold, in which one dimension has a sign opposite to that of the rest. This allows tangent vectors to be classified into timelike, null, and spacelike. In relativity, this sign convention is crucial to the invariance of the speed of light (which is achieved via length contraction and time dilation)
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Classical Mechanics
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. If the present state of an object is known it is possible to predict by the laws of classical mechanics how it will move in the future (determinism) and how it has moved in the past (reversibility) The earliest development of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts employed by and the mathematical methods invented by Isaac Newton
Isaac Newton
and Gottfried Wilhelm Leibniz and others in the 17th century to describe the motion of bodies under the influence of a system of forces. Later, more abstract methods were developed, leading to the reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics
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Space
Space
Space
is the boundless three-dimensional extent in which objects and events have relative position and direction.[1] Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework. Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the Timaeus of Plato, or Socrates
Socrates
in his reflections on what the Greeks called khôra (i.e
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TIME
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.[1][2][3] Time
Time
is a component quantity of various measurements used to sequence events, to compare the duration of events or the intervals
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Absolute Space And Time
Absolute space and time
Absolute space and time
is a concept in physics and philosophy about the properties of the universe
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Electromagnetism
Electromagnetism
Electromagnetism
is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force usually exhibits electromagnetic fields such as electric fields, magnetic fields and light, and is one of the four fundamental interactions (commonly called forces) in nature. The other three fundamental interactions are the strong interaction, the weak interaction and gravitation.[1] Lightning
Lightning
is an electrostatic discharge that travels between two charged regions.The word electromagnetism is a compound form of two Greek terms, ἤλεκτρον ēlektron, "amber", and μαγνῆτις λίθος magnētis lithos,[2] which means "Μagnesian stone",[3] a type of iron ore
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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). For example, a glass breaking on the floor is an event; it occurs at a unique place and a unique time.[1] Strictly speaking, the notion of an event is an idealization, in the sense that it specifies a definite time and place, whereas any actual event is bound to have a finite extent, both in time and in space.[2][3] Upon choosing a frame of reference, one can assign coordinates to the event: three spatial coordinates x → = ( x , y , z ) displaystyle vec x =(x,y,z) to describe the location and one time coordinate t displaystyle t to specify the moment at which the event occurs
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Observer (special Relativity)
In special relativity, an observer is a frame of reference from which a set of objects or events are being measured. Usually this is an inertial reference frame or "inertial observer". Less often an observer may be an arbitrary non-inertial reference frame such as a Rindler frame which may be called an "accelerating observer". The special relativity usage differs significantly from the ordinary English meaning of "observer". Reference frames are inherently nonlocal constructs, covering all of space and time or a nontrivial part of it; thus it does not make sense to speak of an observer (in the special relativistic sense) having a location. Also, an inertial observer cannot accelerate at a later time, nor can an accelerating observer stop accelerating. Physicists use the term "observer" as shorthand for a specific reference frame from which a set of objects or events is being measured
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Minkowski Space
In mathematical physics, Minkowski space
Minkowski space
(or Minkowski spacetime) is a combining of three-dimensional Euclidean space
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. Although initially developed by mathematician Hermann Minkowski for Maxwell's equations
Maxwell's equations
of electromagnetism, the mathematical structure of Minkowski spacetime was shown to be an immediate consequence of the postulates of special relativity.[1] Minkowski space
Minkowski space
is closely associated with Einstein's theory of special relativity, and is the most common mathematical structure on which special relativity is formulated
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Quantum Mechanics
Quantum mechanics (QM; also known as quantum physics or quantum theory), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.[2] Classical physics
Classical physics
(the physics existing before quantum mechanics) is a set of fundamental theories which describes nature at ordinary (macroscopic) scale
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Latitude
In geography, latitude is a geographic coordinate that specifies the north–south position of a point on the Earth's surface. Latitude
Latitude
is an angle (defined below) which ranges from 0° at the Equator
Equator
to 90° ( North
North
or South) at the poles. Lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude
Latitude
is used together with longitude to specify the precise location of features on the surface of the Earth. Without qualification the term latitude should be taken to be the geodetic latitude as defined in the following sections
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Function Space
In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is inherited by the function space. For example, the set of functions from any set X into a vector space have a natural vector space structure given by pointwise addition and scalar multiplication. In other scenarios, the function space might inherit a topological or metric structure, hence the name function space.Contents1 In linear algebra 2 Examples 3 Functional analysis 4 Norm 5 Bibliography 6 See also 7 FootnotesIn linear algebra[edit] See also: Vector space
Vector space
§ Function spacesThis section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (November 2017) (Learn how and when to remove this template message)Let V be a vector space over a field F and let X be any set
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Parameter Space
In science, a parameter space is the set of all possible combinations of values for all the different parameters contained in a particular mathematical model. The ranges of values of the parameters may form the axes of a plot, and particular outcomes of the model may be plotted against these axes to illustrate how different regions of the parameter space produce different types of behaviour in the model. Often the parameters are inputs of a function, in which case the technical term for the parameter space is domain of a function. Parameter
Parameter
spaces are particularly useful for describing families of probability distributions that depend on parameters. More generally in science, the term parameter space is used to describe experimental variables
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Configuration Space (mathematics)
In mathematics a configuration space (also known as Fadell's configuration space[1]) is any of several constructions closely related to the state space notion in physics. In physics, these are used to describe the state of a whole system as a single point in a high-dimensional space. In mathematics, they are used to describe assignments of a collection of points to positions in a topological space
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