Scalar (physics)

	Email		Print
	Bookmark		Link

Scalar (physics)

In physics

Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, a scalar is a simple physical quantity

Physical quantity

A physical quantity is a physical property that can be Quantitative. This means it can be measured and/or calculated and expressed in numbers. For example, "weight" is a physical quantity that can be expressed by stating a number of some basic measurement unit such as pound or kilograms, while "beauty" is a property that is difficult to desc...
that is not changed by coordinate system

Coordinate system

In mathematics and its applications, a coordinate system is a system for assigning an n-tuple of numbers or scalar to each Point in an n-dimensional space....
rotations or translations (in Newtonian mechanics), or by Lorentz transformation

Lorentz transformation

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 the other....
s or space-time translations (in relativity). (Contrast to vector.)

ysical quantity

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....
is not quite expressed as the product

Product (mathematics)

In the a mathematics, a product is the result of Multiplication, or an expression that identifies divisors to be multiplied. The order in real number or complex number numbers are multiplied has no bearing on the product; this is known as the Commutativity of multiplication....
of a numerical value

Number

Discussion

Ask a question about 'Scalar (physics)'

Start a new discussion about 'Scalar (physics)'

Answer questions from other users

Full Discussion Forum

Encyclopedia

In physics

Physics

Physical quantity

Coordinate system

Lorentz transformation

Physical quantity

A physical quantity

Quantity

Product (mathematics)

Number

A number is a mathematical object used in counting and measurement. A notational symbol which represents a number is called a Numeral system, but in common usage the word number is used for both the abstract object and the symbol, as well as for the numeral for the number....
and a physical unit, not just 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), but not the scalar itself. In this sense, physical distance deviates from the definition of metric

Metric (mathematics)

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....
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

Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
, charge

Charge (physics)

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....
, or kinetic energy

Kinetic energy

The kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the mechanical work needed to accelerate a body of a given mass from rest to its current velocity....
of an object, or the temperature

Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
, or electric potential

Electric potential

At a point in space, the electric potential is the potential energy per unit of electric charge that is associated with a static electric field....
at a point inside a medium. The distance

Distance

Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria ....
between two points in three-dimensional space is a scalar, but the direction

Direction (geometry, geography)

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 direction to some indicated reference , or absolute according to some previously agreed upon frame of reference ....
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

Force

In physics, a force is that which can cause an object with mass to change its velocity. Force has both Euclidean_vector#Length of a vector and Direction , making it a Vector quantity....
cannot be described using a scalar, since force is composed of direction and magnitude

Magnitude (mathematics)

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 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 gravitation

Gravitation

Gravitation is a natural phenomenon that gives weight to objects. In everyday life, attraction due to gravity is the result of the presence of relatively large bodies, such as the Earth and the Moon....
al force

Force

In physics, a force is that which can cause an object with mass to change its velocity. Force has both Euclidean_vector#Length of a vector and Direction , making it a Vector quantity....
acting on a particle is not a scalar, but its magnitude is. The speed

Speed

Speed is the rate of Motion , or equivalently the rate of change of distance.Speed is a Scalar quantity with dimensions length/time; the equivalent Vector quantity to speed is velocity....
of an object is a scalar (e.g. 180 km/h), while its velocity

Velocity

In physics, velocity is defined as the Derivative of Position vector. It is a vector physical quantity; both speed and direction are required to define it....
is not (i.e. 180 km/h north).

Examples of scalar quantities in Newtonian mechanics:

electric charge
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....
and charge density
Charge density

The linear, surface, or volume charge density is the amount of electric charge in a line , surface, or volume. It is measured in coulombs per metre , square metre , or cubic metre , respectively....
mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
and mass density
speed
Speed

Speed is the rate of Motion , or equivalently the rate of change of distance.Speed is a Scalar quantity with dimensions length/time; the equivalent Vector quantity to speed is velocity....
, but not velocity
Velocity

In physics, velocity is defined as the Derivative of Position vector. It is a vector physical quantity; both speed and direction are required to define it....
or momentum
Momentum

In classical mechanics, momentum is the product of the mass and velocity of an object . For more accurate measures of momentum, see the section Momentum#Modern definitions of momentum on this page....
temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
energy
Energy

In physics, energy is a scalar physical quantity that describes the amount of Work_ that can be performed by a force. Energy is an attribute of objects and systems that is subject to a conservation law....
and energy density
Energy density

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 the latter is more formally specific energy ....
time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
pressure
Pressure

Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
entropy
Entropy

In many branches of science, entropy is a measure of the disorder of a system. The concept of entropy is particularly notable as it is applied across physics, information theory and mathematics....
negentropy
Negentropy

The negentropy, also negative entropy or syntropy, of a living system is the entropy that it exports to keep its own entropy low; it lies at the intersection of entropy and life....

Scalars in relativity theory

In the theory of relativity

Theory of relativity

File:spacetime curvature.pngThe theory of relativity, or simply relativity, generally refers specifically to two theories of Albert Einstein: special relativity and general relativity....
, 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

Charge density

The linear, surface, or volume charge density is the amount of electric charge in a line , surface, or volume. It is measured in coulombs per metre , square metre , or cubic metre , respectively....
at a point in a medium, which is a scalar in classical physics, must be combined with the local current density

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....
(a 3-vector) to comprise a relativistic 4-vector. Similarly, energy density

Energy density

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 the latter is more formally specific energy ....
must be combined with momentum density and pressure

Pressure

Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
into the stress-energy tensor

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 of Newtonian physics....
.

Examples of scalar quantities in relativity:

electric charge
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....
spacetime interval
Spacetime

In physics, spacetime is any mathematical model that combines space and Time in physics into a single continuum . Spacetime is usually interpreted with space being Three-dimensional space and time playing the role of a fourth dimension that is of a different sort than the spatial dimensions....
(e.g., proper time
Proper time

In theory of 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....
and proper length
Proper length

In theory of relativity physics, proper length is an invariant quantity which is the ruler distance between spacelike-separated Spacetime#Basic conceptss in a frame of reference in which the events are simultaneous....
)
invariant mass
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 Invariant ....

A related concept is a pseudoscalar, which is invariant under proper rotations but (like a pseudovector

Pseudovector

In physics and mathematics, a pseudovector is a quantity that transforms like a vector under a proper Rotation , i.e. a transformation that rotates vectors and pseudovectors by an arbitrary angle about an arbitrary axis, but gains an additional sign flip under an improper rotation: a transformation that can be expressed as a proper rotation...
) flips sign under improper rotation

Improper rotation

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....
s. One example is the scalar triple product

Triple product

In vector calculus, there are two ways of multiplying three vector together, to make a triple product of vectors.Scalar triple product ...
(see vector), and thus the signed volume. Another example is magnetic charge (as it is mathematically defined, regardless of whether it actually exists physically).

Scalar (physics)

Physical quantity

Examples

Scalars in relativity theory

See also