In physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations (in Newtonian mechanics), or by Lorentz transformations or space-time translations (in relativity). Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. A physical Quantity is a physical property that can be quantified In Mathematics and its applications a coordinate system is a system for assigning an n - Tuple of Numbers or scalars to each point In Physics, the Lorentz transformation converts between two different observers' measurements of space and time where one observer is in constant motion with respect to (Contrast to vector. )

Examples

For example, the distance between two points in space is a scalar, as are the mass, charge, and kinetic energy of an object, or the temperature and electric potential at a point inside a medium. Distance is a numerical description of how far apart objects are Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object In Physics, a charge may refer to one of many different quantities such as the Electric charge in Electromagnetism or the Color charge in The kinetic energy of an object is the extra Energy which it possesses due to its motion Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature At a point in space the electric potential is the Potential energy per unit of charge that is associated with a static (time-invariant Electric field On the other hand, the electric field at a point is not a scalar in this sense, since to specify it one must give three real numbers that depend on the coordinate system chosen. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can The speed of an object is a scalar (e. Speed is the rate of motion, or equivalently the rate of change in position often expressed as Distance d traveled per unit of g. 180 km/h), while its velocity is not (i. In Physics, velocity is defined as the rate of change of Position. e. 180 km/h north). The gravitational force acting on a particle is not a scalar, but its magnitude is. Gravitation is a natural Phenomenon by which objects with Mass attract one another In Physics, a force is whatever can cause an object with Mass to Accelerate. The magnitude of a mathematical object is its size a property by which it can be larger or smaller than other objects of the same kind in technical terms an Ordering

Examples of scalar quantities in Newtonian mechanics:

• electric charge and charge density
• mass and mass density
• speed, but not velocity or momentum
• temperature
• energy and energy density
• time
• pressure
• entropy
• negentropy

A physical quantity is expressed as the product of a numerical value and a physical unit, not just a number. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. The linear surface or volume charge density is the amount of Electric charge in a line, Surface, or Volume. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different Speed is the rate of motion, or equivalently the rate of change in position often expressed as Distance d traveled per unit of In Physics, velocity is defined as the rate of change of Position. In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός Energy density is the amount of Energy stored in a given system or region of space per unit Volume, or per unit Mass, depending on the context although For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy Negative Entropy or negentropy or syntropy of a living system is the entropy that it exports to maintain its own entropy low (see Entropy and life Quantity is a kind of property which exists as magnitude or multitude In Mathematics, a product is the Result of multiplying, or an expression that identifies factors to be multiplied A number is an Abstract object, tokens of which are Symbols used in Counting and measuring. It does not depend on the unit distance (1 km is the same as 1000 m), although the number depends on the unit. Thus distance does not depend on the length of the base vectors of the coordinate system. Also, other changes of the coordinate system may affect the formula for computing the scalar (for example, the Euclidean formula for distance in terms of coordinates relies on the basis being orthonormal), but not the scalar itself. In Linear algebra, two vectors in an Inner product space are orthonormal if they are orthogonal and both of unit length In this sense, physical distance deviates from the definition of metric in not being just a real number; however it satisfies all other properties. In Mathematics, a metric or distance function is a function which defines a Distance between elements of a set. The same applies for other physical quantities which are not dimensionless.

Scalars in relativity theory

In the theory of relativity, one considers changes of coordinate systems that trade space for time. This page is about the scientific concept of relativity for philosophical or sociological theories about relativity see Relativism. As a consequence, several physical quantities that are scalars in "classical" (non-relativistic) physics need to be combined with other quantities and treated as four-dimensional vectors or tensors. For example, the charge density at a point in a medium, which is a scalar in classical physics, must be combined with the local current density (a 3-vector) to comprise a relativistic 4-vector. The linear surface or volume charge density is the amount of Electric charge in a line, Surface, or Volume. Current density is a measure of the Density of flow of a conserved charge. Similarly, energy density must be combined with momentum density and pressure into the stress-energy tensor. Energy density is the amount of Energy stored in a given system or region of space per unit Volume, or per unit Mass, depending on the context although Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface The stress-energy tensor (sometimes stress-energy-momentum tensor is a Tensor quantity in Physics that describes the Density and Flux

Examples of scalar quantities in relativity:

• electric charge
• spacetime interval (e. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS g. , proper time and proper length)
• invariant mass

A related concept is a pseudoscalar, which is invariant under proper rotations but (like a pseudovector) flips sign under improper rotations. In relativity, proper time is Time measured by a single Clock between events that occur at the same place as the clock In relativistic Physics, proper Length is an invariant quantity which is the rod Distance between Spacelike In Physics, a pseudoscalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion such as Improper rotations In 3D Geometry, an improper rotation, also called rotoreflection or rotary reflection is depending on context a Linear transformation or In Physics and Mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under a proper rotation but gains an In 3D Geometry, an improper rotation, also called rotoreflection or rotary reflection is depending on context a Linear transformation or One example is the scalar triple product (see vector), and thus the signed volume. This article is about mathematics See Lawson criterion for the use of the term triple product in relation to Nuclear fusion. Another example is magnetic charge (as it is mathematically defined, regardless of whether it actually exists physically). In Physics, a magnetic monopole is a hypothetical particle that is a Magnet with only one pole (see Maxwell's equations for more on magnetic

See also

• Scalar field
• Scalar field theory
• Pseudoscalar (physics)
• Scalar (mathematics)
• Lorentz scalar