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Concept
Euclidean quantum gravity
Résumé
In theoretical physics, Euclidean quantum gravity is a version of quantum gravity. It seeks to use the Wick rotation to describe the force of gravity according to the principles of quantum mechanics.
In physics, a Wick rotation, named after Gian-Carlo Wick, is a method of finding a solution to dynamics problems in dimensions, by transposing their descriptions in dimensions, by trading one dimension of space for one dimension of time. More precisely, it substitutes a mathematical problem in Minkowski space into a related problem in Euclidean space by means of a transformation that substitutes an imaginary-number variable for a real-number variable.
It is called a rotation because when complex numbers are represented as a plane, the multiplication of a complex number by is equivalent to rotating the vector representing that number by an angle of radians about the origin.
For example, a Wick rotation could be used to relate a macroscopic event temperature diffusion (like in a bath) to the underlying thermal movements of molecules. If we attempt to model the bath volume with the different gradients of temperature we would have to subdivide this volume into infinitesimal volumes and see how they interact. We know such infinitesimal volumes are in fact water molecules. If we represent all molecules in the bath by only one molecule in an attempt to simplify the problem, this unique molecule should walk along all possible paths that the real molecules might follow. The path integral formulation is the conceptual tool used to describe the movements of this unique molecule, and Wick rotation is one of the mathematical tools that are very useful to analyse a path integral problem.
In a somewhat similar manner, the motion of a quantum object as described by quantum mechanics implies that it can exist simultaneously in different positions and have different speeds. It differs clearly to the movement of a classical object (e.g. a billiard ball), since in this case a single path with precise position and speed can be described.
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