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In
theoretical physicsTheoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
, a
local reference frame (
local frame) refers to a
coordinate systemIn geometry, a coordinate system is a system which uses one or more 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...
or
frame of referenceA frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer.It may also refer to both an...
that is only expected to function over a small region or a restricted region of space or
spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being threedimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
.
The term is most often used in the context of the application of
local inertial frames to small regions of a
gravitational fieldThe gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...
. Although gravitational tidal forces will cause the background geometry to become noticeably nonEuclidean over larger regions, if we restrict ourselves to a sufficiently small region containing a cluster of objects falling together in an
effectively uniform gravitational field, their physics can be described as the physics of that cluster in a space free from explicit background gravitational effects.
Einstein and general relativity
When constructing his general theory of relativity,
EinsteinAlbert Einstein was a Germanborn theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
took the result that an accelerated body feels an apparent gravitational field (
geeforceThe gforce associated with an object is its acceleration relative to freefall. This acceleration experienced by an object is due to the vector sum of nongravitational forces acting on an object free to move. The accelerations that are not produced by gravity are termed proper accelerations, and...
s), and inverted it: an object in a gravitational field, if it is
not accelerated, will
not be able to detect the existence of the field by making local measurements ("a falling man feels no gravity"). Einstein was then able to complete his general theory by arguing that the physics of curved spacetime must reduce over small regions to the physics of simple inertial mechanics (in this case
special relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
) for small freefalling regions.
Einstein referred to this as "the happiest idea of my life".
See also
 Equivalence principle
In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body is actually...
 Inertial frame of reference
In physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a timeindependent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...
 Local coordinates
Local coordinates are measurement indices into a local coordinate system or a local coordinate space. A simple example is using house numbers to locate a house on a street; the street is a local coordinate system within a larger system composed of city townships, states, countries, etc.Local...
 Local spacetime structure
Local spacetime structure refers to the structure of spacetime on a local level, i.e. only considering those points in an open region of a point. This notion is useful in many areas of physics, most notably in Einstein's theory of general relativity....
 Local Lorentz covariance
 Minkowski space
In physics and mathematics, Minkowski space or Minkowski spacetime is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated...
 Normal coordinates
In differential geometry, normal coordinates at a point p in a differentiable manifold equipped with a symmetric affine connection are a local coordinate system in a neighborhood of p obtained by applying the exponential map to the tangent space at p...
