In physics Physics is a natural science that involves the study of matter and its motion through space-time, as well as all applicable concepts, such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves, a scalar is a simple physical quantity Physical quantity is the numerical value of a measurable property that describes a physical system's state at a moment in time. For that reason, the changes in the physical quantities of a system describe its transformation that is not changed by coordinate system In geometry, a coordinate system is a system which uses a set of numbers, or coordinates, to uniquely determine the position of a point or other geometric element. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in 'the x-coordinate'. In elementary rotations or translations (in Newtonian mechanics), or by Lorentz transformations In physics, the Lorentz transformation, named after the Dutch physicist Hendrik Lorentz, describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frames of reference. It reflects the surprising fact that observers moving at different velocities may or space-time translations (in relativity). (Contrast to vector In elementary mathematics, physics, and engineering, a Euclidean vector is a geometric object that has both a magnitude (or length) and direction. A Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B, and denoted by.)
Contents |
Physical quantity
A physical quantity Quantity is a kind of property which exists as magnitude or multitude. It is among the basic classes of things along with quality, substance, change, and relation. Quantity was first introduced as quantum, an entity having quantity. Being a fundamental term, quantity is used to refer to any type of quantitative properties or attributes of things is expressed as the product In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied. The order in real or complex numbers are multiplied has no bearing on the product; this is known as the commutative law of multiplication. When matrices or members of various other associative algebras are multiplied the product of a numerical value A number is a mathematical object used in counting and measuring. A notational symbol which represents a number is called a numeral, but in common usage the word number is used for both the abstract object and the symbol, as well as for the word for the number. In addition to their use in counting and measuring, numerals are often used for labels , and a physical unit A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of measurement, not merely a number. 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 In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal and both of unit length. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal and all of unit length. An orthonormal set which forms a basis is called an orthonormal basis), but not the scalar itself. In this sense, physical distance deviates from the definition of metric In mathematics, a metric or distance function is a function which defines a distance between elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set but not all topologies can be generated by a metric. When a topological space has a topology that can be described by a metric, we say that the in not being just a real number; however it satisfies all other properties. The same applies for other physical quantities which are not dimensionless.
Examples
Some examples of scalars include the mass In physics, mass commonly refers to any of three properties of matter, which have been shown experimentally to be equivalent: Inertial mass, active gravitational mass and passive gravitational mass. In everyday usage, mass is often taken to mean weight, but in scientific use, they refer to different properties, charge In physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges are associated with conserved quantum numbers, or the temperature Historically, two equivalent concepts of temperature have developed, the thermodynamic description and a microscopic explanation based on statistical physics. Since thermodynamics deals entirely with macroscopic measurements, the thermodynamic definition of temperature, first stated by Lord Kelvin, is stated entirely in empirical, measurable, or electric potential In classical electromagnetism, the electric potential at a point in space is electrical potential energy divided by charge that is associated with a static (time-invariant) electric field. It is a scalar quantity, typically measured in volts at a point inside a medium. The distance Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance. A metric is a function that behaves according to a specific between two points in three-dimensional space is a scalar, but the direction Direction is the information contained in the relative position of one point with respect to another point without the distance information. Directions may be either relative to some indicated reference , or absolute according to some previously agreed upon frame of reference (New York City lies due west of Madrid). Direction is often indicated from one of those points to the other is not, since describing a direction requires two physical quantities such as the angle on the horizontal plane and the angle away from that plane. Force In physics, a force is any influence that causes a free body to undergo an acceleration. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform. A force has both magnitude and direction, making it a cannot be described using a scalar, since force is composed of direction and magnitude The magnitude of a mathematical object is its size: a property by which it can be compared as larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs, however, the magnitude of a force alone can be described with a scalar, for instance the gravitational Gravitation, or gravity, is one of the four fundamental interactions of nature , in which objects with mass attract one another. In everyday life, gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped. Gravitation causes dispersed matter to coalesce, thus accounting for force In physics, a force is any influence that causes a free body to undergo an acceleration. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform. A force has both magnitude and direction, making it a acting on a particle is not a scalar, but its magnitude is. The speed In kinematics, the instantaneous speed of an object is the magnitude of its instantaneous velocity (the rate of change of its position); it is thus the scalar equivalent of velocity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the of an object is a scalar (e.g. 180 km/h), while its velocity In physics, velocity is the rate of change of position. It is a vector physical quantity; both magnitude and direction are required to define it. The scalar absolute value of velocity is speed, a quantity that is measured in meters per second (m/s or ms−1) when using the SI (metric) system is not (i.e. 180 km/h north).
Examples of scalar quantities in Newtonian mechanics:
- electric charge Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields. The interaction between a moving charge and an electromagnetic field is the source of the electromagnetic force, which is one of the and charge density The linear, surface, or volume charge density is the amount of electric charge in a line, surface, or volume respectively. It is measured in coulombs per metre , square metre (C/m²), or cubic metre (C/m³), respectively. Since there are positive as well as negative charges, the charge density can take on negative values. Like any density it can
Scalars in relativity theory
In the theory of relativity The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word "relativity" is sometimes used in reference to Galilean invariance, one considers changes of coordinate systems that trade space for time. 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 The linear, surface, or volume charge density is the amount of electric charge in a line, surface, or volume respectively. It is measured in coulombs per metre , square metre (C/m²), or cubic metre (C/m³), respectively. Since there are positive as well as negative charges, the charge density can take on negative values. Like any density it can at a point in a medium, which is a scalar in classical physics, must be combined with the local current density Current density is a measure of the density of flow of a conserved charge. Usually the charge is the electric charge, in which case the associated current density is the electric current per unit area of cross section, but the term current density can also be applied to other conserved quantities. It is defined as a vector whose magnitude is the (a 3-vector) to comprise a relativistic 4-vector. Similarly, energy density Energy density is a term used for the amount of useful energy stored in a given system or region of space per unit volume.[clarification needed] must be combined with momentum density and pressure Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure into the stress-energy tensor The stress-energy 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. It is an attribute of matter, radiation, and non-gravitational force fields. The stress-energy tensor is the source of the gravitational field in the Einstein field.
Examples of scalar quantities in relativity:
- electric charge Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields. The interaction between a moving charge and an electromagnetic field is the source of the electromagnetic force, which is one of the
- spacetime interval In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions. According to certain Euclidean space perceptions, the universe has three (e.g., proper time In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. It depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a proper time between two events that is shorter than the coordinate time measured by a non-accelerated and proper length In relativistic physics, proper length is an invariant measure of the distance between two spacelike-separated events, or of the length of a spacelike path within a spacetime)
- invariant mass The invariant mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference. When the system as a whole is at rest, the invariant mass is equal to the total energy of the system divided by c2, which is equal to the mass of the
A related concept is a pseudoscalar 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 while a true scalar does not, which is invariant under proper rotations In 3D geometry, an improper rotation, also called rotoreflection or rotary reflection is, depending on context, a linear transformation or affine transformation which is the combination of a rotation about an axis and a reflection in a plane perpendicular to the axis but (like a pseudovector In physics and mathematics, a pseudovector is a quantity that transforms like a vector under a proper rotation (that is, a rotation by an arbitrary angle about an arbitrary axis), but gains an additional sign flip under an improper rotation (that is, a transformation that can be expressed as a proper rotation of a mirror image, or equivalently as) flips sign under improper rotations In 3D geometry, an improper rotation, also called rotoreflection or rotary reflection is, depending on context, a linear transformation or affine transformation which is the combination of a rotation about an axis and a reflection in a plane perpendicular to the axis. One example is the scalar triple product In vector calculus, there are two ways of multiplying three vectors together, to make a triple product of vectors (see vector In elementary mathematics, physics, and engineering, a Euclidean vector is a geometric object that has both a magnitude (or length) and direction. A Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B, and denoted by), and thus the signed volume. Another example is magnetic charge A magnetic monopole is a hypothetical particle in physics that is a magnet with only one pole . In more technical terms, it would have a net "magnetic charge." Modern interest in the concept stems from particle theories, notably the grand unification theory and superstring theories, which predict their existence (as it is mathematically defined, regardless of whether it actually exists physically).
See also
- Scalar field In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the value of the scalar field at the same point in space
- Scalar field theory In theoretical physics, scalar field theory can refer to a classical or quantum theory of scalar fields. Such a field is distinguished by its invariance under a Lorentz transformation, hence the name "scalar," in contrast to a vector or tensor field. The quanta of the quantized scalar field are spin-zero particles, and as such are bosons
- Pseudoscalar (physics) 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 while a true scalar does not
- Scalar (mathematics) In linear algebra, real numbers are called scalars and relate to vectors in a vector space through the operation of scalar multiplication, in which a vector can be multiplied by a number to produce another vector
- Lorentz scalar In physics a Lorentz scalar is a scalar which is invariant under a Lorentz transformation. A Lorentz scalar is generated from vectors and tensors. While the vectors and tensors are altered by Lorentz transformations, scalars are unchanged
- vector In elementary mathematics, physics, and engineering, a Euclidean vector is a geometric object that has both a magnitude (or length) and direction. A Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B, and denoted by
Categories: Introductory physics This category includes topics in physics that are commonly taught in middle school or high school, or may be in the curriculum for college freshmen. See also the list of basic physics topics | Fundamental physics concepts
|
Physics
The minimal standard model [4] requires in addition a massive scalar boson, the Higgs boson, to allow the W and Z to be massive, as described by the Higgs ...
and more »
343px x 428px | 109.50kB
[source page]
References S M de Bruyn Kops and J J Riley 2000 Re examining the thermal mixing layer with numerical simulations Physics of Fluids 12 1 pp 185 192 S M de Bruyn Kops and J J
Michael Welcome
Mon, 14 Aug 2006 22:09:00 GM
3566::2948::3095 Cells Communication . Physics. Small/Companion Animal Medicine Architecture Performance Characteristics of an Adaptive Mesh Re nement Calculation on . Scalar. and Vector Platforms Michael Welcome, Charles Rendleman, ...
Q. Im gonna have to leave this one to voting - all three of you had great answers. Thank you.
Asked by DontWorryBeHappy - Tue Nov 6 18:20:19 2007 - - 3 Answers - 0 Comments
A. scalar is the magnitude, the number example: - speed - the car is traveling 60 m/h vector is not only the number but also the direction of the movement and is expressed geometrically example - velocity - it is the movement of the car 60m/h in north direction
Answered by slunickosd - Tue Nov 6 18:28:59 2007
