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Imaginary time is a mathematical representation of time that appears in some approaches to special relativity and quantum mechanics. It finds uses in certain cosmological theories. Mathematically, imaginary time is real time which has undergone a Wick rotation so that its coordinates are multiplied by the imaginary unit i .
Like other complex number variables, complex time is two-dimensional, comprising one real time dimension and one imaginary time dimension, changing time from a real number line into a complex plane. [3] Introducing it into Minkowski spacetime allows a generalization of Kaluza–Klein theory. [7]
The line element ds 2 is complex-valued, so that the real part corresponds to mass and gravitation, while the imaginary part with charge and electromagnetism. The usual space x , y , z and time t coordinates themselves are real and spacetime is not complex, but tangent spaces are allowed to be.
In 1958 J. Frank Adams published a further generalization in terms of Hopf invariants on H-spaces which still limits the dimension to 1, 2, 4, or 8. [2] It was matrix algebra that harnessed the hypercomplex systems. For instance, 2 x 2 real matrices were found isomorphic to coquaternions. Soon the matrix paradigm began to explain several others ...
Hermann Minkowski (1864–1909) found that the theory of special relativity could be best understood as a four-dimensional space, since known as the Minkowski spacetime.. In physics, Minkowski space (or Minkowski spacetime) (/ m ɪ ŋ ˈ k ɔː f s k i,-ˈ k ɒ f-/ [1]) is the main mathematical description of spacetime in the absence of gravitation.
The growing block universe, or the growing block view, is a theory of time arguing that the past and present both exist, and the future as yet does not. The present is an objective property, to be compared with a moving spotlight. By the passage of time more of the world comes into being; therefore, the block universe is said to be growing.
In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal x-axis, called the real axis, is formed by the real numbers, and the vertical y-axis, called the imaginary axis, is formed by the imaginary numbers.
More precisely, the Hartle-Hawking state is a hypothetical vector in the Hilbert space of a theory of quantum gravity that describes the wave function of the universe.. It is a functional of the metric tensor defined at a (D − 1)-dimensional compact surface, the universe, where D is the spacetime dimension.