The Experts below are selected from a list of 3936 Experts worldwide ranked by ideXlab platform
Coddens Gerrit - One of the best experts on this subject based on the ideXlab platform.
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Exact theory of the Stern-Gerlach experiment - extended version
HAL CCSD, 2021Co-Authors: Coddens GerritAbstract:Version élargie de l'article accepté pour publication dans Symmetry.The Stern-Gerlach experiment is notoriously counter-intuitive. The official theory is that the spin of a fermion remains always aligned with the magnetic field. Its directions are thus quantized: It can only be spin-up or spin-down. But that theory is based on mathematical errors in the way it (mis)treats spinors and group theory.We present here a mathematically rigorous theory for a fermion in a magnetic field, which is no longer counter-intuitive. It is based on an understanding of spinors in SU(2) which is only Euclidean geometry.Contrary to what Pauli has been reading into the Stern-Gerlach experiment,the spin directions are not quantized. The new corrected paradigm, which solves all conceptual problems, is that the fermions precess around the magnetic-field just as Einstein and Ehrenfest had conjectured.Surprizingly this leads to only two energy states, which should be qualified as precession-up and precession-down rather thanspin-up and spin down.Indeed, despite the presence of the many different possible angles $\theta$ betweenthe spin axis ${\mathbf{s}}$ and the magnetic field ${\mathbf{B}}$, the fermions can only have two possible energies $m_{0}c^{2}\pm\mu B$. The values $\pm\mu B$ do thus not correspond to the continuum of values $-{\boldsymbol{\mu\cdot}}{\mathbf{B}}$ Einstein and Ehrenfest had conjectured. The energy term $V= -{\boldsymbol{\mu\cdot}}{\mathbf{B}}$ is a Macroscopic Quantity. It is a statistical average over a large ensemble of fermions distributed over the two microscopic states with energies $\pm\mu B$, and as such not valid for individual fermions. The two fermion states with energy $\pm\mu B$ are not potential-energy states. We also explain themathematically rigorous meaning of the up and down spinors. They represent left-handed and right-handed reference frames, such that now everything is intuitively clearand understandable in simple geometrical terms. The paradigm shift does not affect the Pauli principle
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The exact theory of the Stern-Gerlach experiment and why it does not imply that a fermion can only have its spin up or down
HAL CCSD, 2020Co-Authors: Coddens GerritAbstract:Example of spin echo method added. Small improvements. Explanation added why pointing errors is necessary.The Stern-Gerlach experiment is notoriously counter-intuitive. The official theory is that the spin of a fermion remains always aligned with the magnetic field. Its directions are thus quantized: It can only be spin up or down. But that theory is based on mathematical errors in the way it (mis)treats spinors and group theory.We present here a mathematically rigorous theory for a fermion in a magnetic field, which is no longer counter-intuitive. It is based on an understanding of spinors in SU(2) which is only Euclidean geometry.Contrary to what Pauli has been reading into the Stern-Gerlach experiment,the spin directions are not quantized. The new corrected paradigm, which solves all conceptual problems, is that the fermions precess around the magnetic-field just like Einstein and Ehrenfest had conjectured.Surprizingly this leads to only two energy states, which should be qualified as precession-up and precession-down rather thanspin-up and spin down.Indeed, despite the presence of the many different possible angles $\theta$ betweenthe spin axis ${\mathbf{s}}$ and the magnetic field ${\mathbf{B}}$, the fermions can only have two possible energies $m_{0}c^{2}\pm\mu B$. The values $\pm\mu B$ do thus not correspond to the continuum of values $-{\boldsymbol{\mu\cdot}}{\mathbf{B}}$ Einstein and Ehrenfest had conjectured. The energy term $V= -{\boldsymbol{\mu\cdot}}{\mathbf{B}}$ is a Macroscopic Quantity. It is a statistical average over a large ensemble of fermions distributed over the two microscopic energy states $\pm\mu B$, and as such not valid for individual fermions. The two fermion states $\pm\mu B$ are not potential-energy states. We also explain themathematically rigorous meaning of the up and down spinors. They represent left-handed and right-handed reference frames, such that now everything is intuitively clearand understandable in simple geometrical terms. The paradigm shift does not affect the Pauli principle
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Exact theory of the Stern-Gerlach experiment - extended version
HAL CCSD, 2020Co-Authors: Coddens GerritAbstract:première version soumis au journal le 21 novembreThe Stern-Gerlach experiment is notoriously counter-intuitive. The official theory is that the spin of a fermion remains always aligned with the magnetic field. Its directions are thus quantized: It can only be spin-up or spin-down. But that theory is based on mathematical errors in the way it (mis)treats spinors and group theory.We present here a mathematically rigorous theory for a fermion in a magnetic field, which is no longer counter-intuitive. It is based on an understanding of spinors in SU(2) which is only Euclidean geometry.Contrary to what Pauli has been reading into the Stern-Gerlach experiment,the spin directions are not quantized. The new corrected paradigm, which solves all conceptual problems, is that the fermions precess around the magnetic-field just like Einstein and Ehrenfest had conjectured.Surprizingly this leads to only two energy states, which should be qualified as precession-up and precession-down rather thanspin-up and spin down.Indeed, despite the presence of the many different possible angles $\theta$ betweenthe spin axis ${\mathbf{s}}$ and the magnetic field ${\mathbf{B}}$, the fermions can only have two possible energies $m_{0}c^{2}\pm\mu B$. The values $\pm\mu B$ do thus not correspond to the continuum of values $-{\boldsymbol{\mu\cdot}}{\mathbf{B}}$ Einstein and Ehrenfest had conjectured. The energy term $V= -{\boldsymbol{\mu\cdot}}{\mathbf{B}}$ is a Macroscopic Quantity. It is a statistical average over a large ensemble of fermions distributed over the two microscopic energy states $\pm\mu B$, and as such not valid for individual fermions. The two fermion states $\pm\mu B$ are not potential-energy states. We also explain themathematically rigorous meaning of the up and down spinors. They represent left-handed and right-handed reference frames, such that now everything is intuitively clearand understandable in simple geometrical terms. The paradigm shift does not affect the Pauli principle
Miao Yan-gang - One of the best experts on this subject based on the ideXlab platform.
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Connections between entropy surface density and microscopic property in black holes
2021Co-Authors: Cai Xin-chang, Miao Yan-gangAbstract:We introduce a new microscopic Quantity $\varepsilon $ that describes the contribution of a single black hole molecule to black hole entropy and give a key relation that this microscopic Quantity is proportional to the Macroscopic Quantity -- entropy surface density $\sigma_{S}$, thus connecting a microscopic Quantity to a Macroscopic Quantity of black holes. Such a connection provides a new probe for understanding the black hole microstructure from the Macroscopic perspective. We also classify black holes in terms of entropy surface density. When its entropy surface density is larger (smaller) than $1/4$, this type of black holes is defined as strong (weak) Bekenstein-Hawking black holes, where the black holes with $1/4$-entropy surface density are regarded as Bekenstein-Hawking black holes. We compute the entropy surface density for four models, where three of them are regular black holes -- the Bardeen black hole, the Ay\'{o}n-Beato-Garc\'{\i}a black hole, and the Hayward black hole, and one of them is a singular black hole -- the five-dimensional neutral Gauss-Bonnet black hole. Under this scheme of classification, the Bardeen black hole, the Ay\'{o}n-Beato-Garc\'{\i}a black hole, and the five-dimensional neutral Gauss-Bonnet black hole belong to the type of strong Bekenstein-Hawking black holes, but the Hayward black hole belongs to the type of weak Bekenstein-Hawking black holes, and the four black holes approach to the Bekenstein-Hawking black hole if their event horizon radii go to infinity. In addition, we find interesting properties in phase transitions from the viewpoint of entropy surface density, or equivalently from the viewpoint of a single black hole molecule entropy, for the five-dimensional neutral Gauss-Bonnet AdS black hole.Comment: v1: 16 pages, 7 figures; v2: clarifications added and typos correcte
Yangang Miao - One of the best experts on this subject based on the ideXlab platform.
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connections between entropy surface density and microscopic property in black holes
arXiv: General Relativity and Quantum Cosmology, 2021Co-Authors: Xinchang Cai, Yangang MiaoAbstract:We introduce a new microscopic Quantity $\varepsilon $ that describes the contribution of a single black hole molecule to black hole entropy and give a key relation that this microscopic Quantity is proportional to the Macroscopic Quantity -- entropy surface density $\sigma_{S}$, thus connecting a microscopic Quantity to a Macroscopic Quantity of black holes. Such a connection provides a new probe for understanding the black hole microstructure from the Macroscopic perspective. We also classify black holes in terms of entropy surface density. When its entropy surface density is larger (smaller) than $1/4$, this type of black holes is defined as strong (weak) Bekenstein-Hawking black holes, where the black holes with $1/4$-entropy surface density are regarded as Bekenstein-Hawking black holes. We compute the entropy surface density for four models, where three of them are regular black holes -- the Bardeen black hole, the Ayon-Beato-Garc\'ia black hole, and the Hayward black hole, and one of them is a singular black hole -- the five-dimensional neutral Gauss-Bonnet black hole. Under this scheme of classification, the Bardeen black hole, the Ayon-Beato-Garc\'ia black hole, and the five-dimensional neutral Gauss-Bonnet black hole belong to the type of strong Bekenstein-Hawking black holes, but the Hayward black hole belongs to the type of weak Bekenstein-Hawking black holes, and the four black holes approach to the Bekenstein-Hawking black hole if their event horizon radii go to infinity. In addition, we find interesting properties in phase transitions from the viewpoint of entropy surface density, or equivalently from the viewpoint of a single black hole molecule entropy, for the five-dimensional neutral Gauss-Bonnet AdS black hole.
Andrei V Naumov - One of the best experts on this subject based on the ideXlab platform.
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micro refractometry and local field mapping with single molecules
Nano Letters, 2018Co-Authors: Andrei V Naumov, A A Gorshelev, M G Gladush, T A Anikushina, A V Golovanova, Jurgen KohlerAbstract:The refractive index n is one of the most important materials parameters of solids and, in recent years, has become the subject of significant interdisciplinary interest, especially in nanostructures and meta-materials. It is, in principle, a Macroscopic Quantity, so its meaning on a length scale of a few nanometers, i.e., well below the wavelength of light, is not clear a priori and is related to methods of its measurement on this length scale. Here we introduce a novel experimental approach for mapping the effective local value n∼ of the refractive index in solid films and the analysis of related local-field enhancement effects. The approach is based on the imaging and spectroscopy of single chromophore molecules at cryogenic temperatures. Since the fluorescence lifetime T1 of dye molecules in a transparent matrix depends on the refractive index due to the local density of the electromagnetic field (i.e., of the photon states), one can obtain the local n∼ values in the surroundings of individual chromop...
Cai Xin-chang - One of the best experts on this subject based on the ideXlab platform.
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Connections between entropy surface density and microscopic property in black holes
2021Co-Authors: Cai Xin-chang, Miao Yan-gangAbstract:We introduce a new microscopic Quantity $\varepsilon $ that describes the contribution of a single black hole molecule to black hole entropy and give a key relation that this microscopic Quantity is proportional to the Macroscopic Quantity -- entropy surface density $\sigma_{S}$, thus connecting a microscopic Quantity to a Macroscopic Quantity of black holes. Such a connection provides a new probe for understanding the black hole microstructure from the Macroscopic perspective. We also classify black holes in terms of entropy surface density. When its entropy surface density is larger (smaller) than $1/4$, this type of black holes is defined as strong (weak) Bekenstein-Hawking black holes, where the black holes with $1/4$-entropy surface density are regarded as Bekenstein-Hawking black holes. We compute the entropy surface density for four models, where three of them are regular black holes -- the Bardeen black hole, the Ay\'{o}n-Beato-Garc\'{\i}a black hole, and the Hayward black hole, and one of them is a singular black hole -- the five-dimensional neutral Gauss-Bonnet black hole. Under this scheme of classification, the Bardeen black hole, the Ay\'{o}n-Beato-Garc\'{\i}a black hole, and the five-dimensional neutral Gauss-Bonnet black hole belong to the type of strong Bekenstein-Hawking black holes, but the Hayward black hole belongs to the type of weak Bekenstein-Hawking black holes, and the four black holes approach to the Bekenstein-Hawking black hole if their event horizon radii go to infinity. In addition, we find interesting properties in phase transitions from the viewpoint of entropy surface density, or equivalently from the viewpoint of a single black hole molecule entropy, for the five-dimensional neutral Gauss-Bonnet AdS black hole.Comment: v1: 16 pages, 7 figures; v2: clarifications added and typos correcte
