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The diagonal boundary lines of a Penrose diagram correspond to the region called "null infinity", or to singularities where light rays must end. Thus, Penrose diagrams are also useful in the study of asymptotic properties of spacetimes and singularities.
The Penrose diagram for Minkowski spacetime. Radial position is on the horizontal axis and time is on the vertical axis. Null infinity is the diagonal boundary of the diagram, designated with script 'I'. The metric for a flat Minkowski spacetime in spherical coordinates is = + +.
In particular, categorical quantum mechanics (which includes ZX-calculus) is a fully comprehensive reformulation of quantum theory in terms of Penrose diagrams. The notation has been studied extensively by Predrag Cvitanović , who used it, along with Feynman's diagrams and other related notations in developing "birdtracks", a group-theoretical ...
The pattern represented by every finite patch of tiles in a Penrose tiling occurs infinitely many times throughout the tiling. They are quasicrystals : implemented as a physical structure a Penrose tiling will produce diffraction patterns with Bragg peaks and five-fold symmetry, revealing the repeated patterns and fixed orientations of its ...
Conformal cyclic cosmology (CCC) is a cosmological model in the framework of general relativity and proposed by theoretical physicist Roger Penrose. [1] [2] [3] In CCC, the universe iterates through infinite cycles, with the future timelike infinity (i.e. the latest end of any possible timescale evaluated for any point in space) of each previous iteration being identified with the Big Bang ...
The use of the word "tiling" is problematic as well, despite its straightforward definition. There is no single Penrose tiling, for example: the Penrose rhombs admit infinitely many tilings (which cannot be distinguished locally). A common solution is to try to use the terms carefully in technical writing, but recognize the widespread use of ...
Carathéodory's theorem – A conformal map extends continuously to the boundary; Penrose diagram; Schwarz–Christoffel mapping – a conformal transformation of the upper half-plane onto the interior of a simple polygon; Special linear group – transformations that preserve volume (as opposed to angles) and orientation
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