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An observational frame of reference, often referred to as a physical frame of reference, a frame of reference, or simply a frame, is a physical concept related to an observer and the observer's state of motion. Here we adopt the view expressed by Kumar and Barve: an observational frame of reference is characterized only by its state of motion. [19]
An accelerated frame of reference is often delineated as being the "primed" frame, and all variables that are dependent on that frame are notated with primes, e.g. x′, y′, a′. The vector from the origin of an inertial reference frame to the origin of an accelerated reference frame is commonly notated as R.
In an n-dimensional Riemannian manifold or pseudo-Riemannian manifold, a frame field is a set of orthonormal vector fields which forms a basis for the tangent space at each point in the manifold. This is possible globally in a continuous fashion if and only if the manifold is parallelizable .
The description of physical phenomena should not depend upon who does the measuring — one reference frame should be as good as any other. Special relativity demonstrated that no inertial reference frame was preferential to any other inertial reference frame, but preferred inertial reference frames over noninertial reference frames. General ...
In an inertial reference frame a free particle has a straight world line. In a non-inertial reference frame the world line of a free particle is curved. Take the example of the fall of an object dropped without initial velocity from a rocket. The rocket has a uniformly accelerated motion with respect to an inertial reference frame.
If n ≥ 2, n-dimensional Minkowski space is a vector space of real dimension n on which there is a constant Minkowski metric of signature (n − 1, 1) or (1, n − 1). These generalizations are used in theories where spacetime is assumed to have more or less than 4 dimensions. String theory and M-theory are two examples where n > 4.
A projective frame on n-dimensional projective space is an ordered collection of n+2 points such that any subset of n+1 points is linearly independent. Frame fields in general relativity are four-dimensional frames, or vierbeins, in German. In each of these examples, the collection of all frames is homogeneous in a certain sense.
where x' is the position as seen by a reference frame that is moving at speed, v, in the "unprimed" (x) reference frame. [ note 3 ] Taking the differential of the first of the two equations above, we have, d x ′ = d x − v d t {\displaystyle dx'=dx-v\,dt} , and what may seem like the obvious [ note 4 ] statement that d t ′ = d t ...