In
theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...
, a local reference frame (local frame) refers to a
coordinate system or
frame of reference that is only expected to function over a small region or a restricted region of space or
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...
.
The term is most often used in the context of the application of local inertial frames to small regions of a
gravitational field. Although gravitational
tidal forces
The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomen ...
will cause the background geometry to become noticeably
non-Euclidean 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.
Equivalence principle
When constructing his
general theory of relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current descr ...
,
Einstein made the following observation: a freely falling object in a gravitational field 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 relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws ...
) for small freefalling regions.
Einstein referred to this as "the happiest idea of my life".
Laboratory frame
In physics, the laboratory frame of reference, or lab frame for short, is a
frame of reference centered on the
laboratory
A laboratory (; ; colloquially lab) is a facility that provides controlled conditions in which scientific or technological research, experiments, and measurement may be performed. Laboratory services are provided in a variety of settings: physic ...
in which the
experiment
An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into Causality, cause-and-effect by demonstrating what outcome oc ...
(either real or thought experiment) is done. This is the reference frame in which the laboratory is at rest. Also, this is usually the frame of reference in which
measurements are made, since they are presumed (unless stated otherwise) to be made by laboratory instruments. An example of instruments in a lab frame, would be the
particle detector
In experimental and applied particle physics, nuclear physics, and nuclear engineering, a particle detector, also known as a radiation detector, is a device used to detect, track, and/or identify ionizing particles, such as those produced by nu ...
s at the detection facility of a
particle accelerator
A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams.
Large accelerators are used for fundamental research in particle ...
.
See also
*
Breit frame In particle physics, the Breit frame (also known as infinite-momentum frame or IMF) is a frame of reference used to describe scattering experiments of the form A + B \rightarrow A + \sum C_i, that is experiments in which particle A scatters off part ...
*
Center-of-mass frame
In physics, the center-of-momentum frame (also zero-momentum frame or COM frame) of a system is the unique (up to velocity but not origin) inertial frame in which the total momentum of the system vanishes. The ''center of momentum'' of a system is ...
*
Frame bundle
In mathematics, a frame bundle is a principal fiber bundle F(''E'') associated to any vector bundle ''E''. The fiber of F(''E'') over a point ''x'' is the set of all ordered bases, or ''frames'', for ''E'x''. The general linear group acts nat ...
*
Inertial frame of reference
In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration. ...
*
Local coordinates
Local coordinates are the ones used in a ''local coordinate system'' or a ''local coordinate space''. Simple examples:
* Houses. In order to work in a house construction, the measurements are referred to a control arbitrary point that will allow ...
*
Local spacetime structure
*
Lorentz covariance
In relativistic physics, Lorentz symmetry or Lorentz invariance, named after the Dutch physicist Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same ...
*
Minkowski space
In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the iner ...
*
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 tang ...
Frames of reference
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