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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.
Mathematically, a four-dimensional space is a space that needs four parameters to specify a point in it. For example, a general point might have position vector a, equal to. This can be written in terms of the four standard basis vectors (e1, e2, e3, e4), given by. so the general vector a is. Vectors add, subtract and scale as in three ...
In mathematics, the group of rotations about a fixed point in four-dimensional Euclidean space is denoted SO (4). The name comes from the fact that it is the special orthogonal group of order 4. In this article rotation means rotational displacement. For the sake of uniqueness, rotation angles are assumed to be in the segment [0, π] except ...
e. In physics, Kaluza–Klein theory (KK theory) is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the common 4D of space and time and considered an important precursor to string theory. In their setup, the vacuum has the usual 3 dimensions of space and one dimension of ...
t. e. The world line (or worldline) of an object is the path that an object traces in 4- dimensional spacetime. It is an important concept of modern physics, and particularly theoretical physics. The concept of a "world line" is distinguished from concepts such as an "orbit" or a "trajectory" (e.g., a planet's orbit in space or the trajectory ...
Four-gradient. In differential geometry, the four-gradient (or 4-gradient) is the four-vector analogue of the gradient from vector calculus. In special relativity and in quantum mechanics, the four-gradient is used to define the properties and relations between the various physical four-vectors and tensors.
Four-velocity. In physics, in particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetime [nb 1] that represents the relativistic counterpart of velocity, which is a three-dimensional vector in space. Physical events correspond to mathematical points in time and space, the set of all ...
Complex spacetime is a mathematical framework that combines the concepts of complex numbers and spacetime in physics. In this framework, the usual real-valued coordinates of spacetime are replaced with complex-valued coordinates. This allows for the inclusion of imaginary components in the description of spacetime, which can have interesting ...