Everything about Scalar Physics totally explained
In
physics, a
scalar is a simple
physical quantity that isn't changed by
coordinate system rotations or translations (in Newtonian mechanics), or by
Lorentz transformations or space-time translations (in relativity). (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. On the other hand, the
electric field at a point isn't a scalar in this sense, since to specify it one must give three real numbers that depend on the coordinate system chosen. The
speed of an object is a scalar (for example 180 km/h), while its
velocity isn't (for example 180 km/h
north). The
gravitational
force acting on a particle isn't a scalar, but its
magnitude is.
Examples of scalar quantities in Newtonian mechanics:
A physical
quantity is expressed as the
product of a
numerical value and a
physical unit, not just a number. It doesn't depend on the unit distance (1 km is the same as 1000 m), although the number depends on the unit. Thus distance doesn't 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 in not being just a real number; however it satisfies all other properties. 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. 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. Similarly,
energy density must be combined with momentum density and
pressure into the
stress-energy tensor.
Examples of scalar quantities in relativity:
electric charge
spacetime interval (for example, 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. One example is the scalar triple product (see vector), and thus the signed volume. Another example is magnetic charge (as it's mathematically defined, regardless of whether it actually exists physically).
Further Information
Get more info on 'Scalar Physics'.
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