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Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world.
The Einstein–de Sitter universe is a model of the universe proposed by Albert Einstein and Willem de Sitter in 1932. [1] On first learning of Edwin Hubble's discovery of a linear relation between the redshift of the galaxies and their distance, [2] Einstein set the cosmological constant to zero in the Friedmann equations, resulting in a model of the expanding universe known as the Friedmann ...
The structures are listed based on their longest dimension. This list refers only to coupling of matter with defined limits, and not the coupling of matter in general (such as, for example, the cosmic microwave background, which fills the entire universe). All structures in this list are defined as to whether their presiding limits have been ...
Hence, it is unclear whether the observable universe matches the entire universe or is significantly smaller, though it is generally accepted that the universe is larger than the observable universe. The universe may be compact in some dimensions and not in others, similar to how a cuboid [citation needed] is longer in one dimension than the ...
According to Mach, Newton's examples simply illustrate relative rotation of spheres and the bulk of the universe. [8] When, accordingly, we say that a body preserves unchanged its direction and velocity in space, our assertion is nothing more or less than an abbreviated reference to the entire universe. —Ernst Mach [9]
Linear operations, given in a linear space by definition, lead to such notions as straight lines (and planes, and other linear subspaces); parallel lines; ellipses (and ellipsoids). However, it is impossible to define orthogonal (perpendicular) lines, or to single out circles among ellipses, because in a linear space there is no structure like ...
The second equation states that both the energy density and the pressure cause the expansion rate of the universe ˙ to decrease, i.e., both cause a deceleration in the expansion of the universe. This is a consequence of gravitation , with pressure playing a similar role to that of energy (or mass) density, according to the principles of ...
The dimension of a vector space is the number of vectors in any basis for the space, i.e. the number of coordinates necessary to specify any vector. This notion of dimension (the cardinality of a basis) is often referred to as the Hamel dimension or algebraic dimension to distinguish it from other notions of dimension.