2/2/2024 0 Comments Curved space starWhere it was considered, the non-commutativity can induce entanglement. Įmerging of the entanglement entropy concept and its application to black hole entropy issues, another exciting area has attracted many physicists: the relationship between the structure of space–time and entanglement. This idea was the motivation behind studying non-commutative space with cosmological models, where NC Seiberg Witten space–time has played an important role in studying many phenomena in particle physics and cosmology, where some authors have suggested some non-commutative models in classical cosmology to explain the accelerated expansion of our universe, and NC opened the door for a new explanation of dark matter and dark energy as well as the cosmic microwave background (C.M.B) and its anisotropies. The very early quantum space–time model based on non-commutative (NC) algebra was suggested by Snyder in 1949 to ameliorate short-distance singularities in quantum field theory. Also, the spin entanglement can be more powerful against changes brought about by motion in the singlet state than in the triplet state. Moreover, they showed that the spin entropy of particles in a circular motion is quickly incremented close to the event horizon of the Schwarzschild black hole. Because the local inertial frames of reference at different points are different in general. Considering that if the spin state of the particle is pure at one point in space–time, it becomes mixed at another point. On the other hand, in they showed when the spin entropy of a spin-1/2 particle moving in the gravitational field can be generated. By considering accelerated particles in the gravitational field (GF), they showed that the acceleration and the gravity deteriorate the perfect anti-correlation of a pair of EPR spins in the same direction. Furthermore, this study is extended to a curved space–time, where Terashima and Ueda studied the EPR (Einstein–Podolsky–Rosen) correlation and Bell’s inequality in the Schwarzschild space–time. This latter in special relativity is known as the product of two Lorentz boost in different directions. The entangled momentum of rotation in a flat space–time is discussed by Peres, Scudo and Terno, in the same year Gingrich and Adami showed that the entanglement between the spins is affected by the Wigner rotation. Recently, the effect of relativistic motion on the entanglement correlation of quantum spin states has been the focus of many physicists, where the spin entanglement of massive particles can change under Lorentz transformations. The spin quantum entanglement of a bipartite system plays an important role in most physical systems, such as condensed matter. During the last decade, great interest has been devoted to quantum entanglement and information theory.
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