The paper presents a very simple and straight forward yet pure mathematical derivation of the structure of actual spacetime from quantum set theory. This is achieved by utilizing elements of the topological theory of ...The paper presents a very simple and straight forward yet pure mathematical derivation of the structure of actual spacetime from quantum set theory. This is achieved by utilizing elements of the topological theory of cobordism and the Menger-Urysohn dimensional theory in conjunction with von Neumann-Connes dimensional function of Klein-Penrose modular holographic boundary of the E8E8 exceptional Lie group bulk of our universe. The final result is a lucid sharp mental picture, namely that the quantum wave is an empty set representing the surface, i.e. boundary of the zero set quantum particle and in turn quantum spacetime is simply the boundary or the surface of the quantum wave empty set. The essential difference of the quantum wave and quantum spacetime is that the wave is a simple empty set while spacetime is a multi-fractal type of infinitely many empty sets with increasing degrees of emptiness.展开更多
Recently, considerable progress has been made in understanding the early universe by loop quantum cosmology. Modesto et al. investigated the loop quantum black hole （LQBH）using improved semiclassical analysis and th...Recently, considerable progress has been made in understanding the early universe by loop quantum cosmology. Modesto et al. investigated the loop quantum black hole （LQBH）using improved semiclassical analysis and they found that the LQBH has two horizons, an event horizon and a Cauchy horizon, just like the Reissner-NordstrSm black hole. This paper focuses on the dynamical evolution of a massless scalar wave in the LQBH background. By investigating the relation between the complex frequencies of the massless scalar field and the LQBH parameters using the numerical method, we find that the polymeric parameter P makes the massless scalar field decay more quickly and makes the ground scalar wave oscillate slowly. However, the polymeric parameter P causes the frequency of the high harmonic massless scalar wave to shift according to its value. We also find that the loop quantum gravity area gap parameter a0 causes the massless scalar field to decay more slowly and makes the period of the massless scalar field wave become longer. In the complex ω plane, the frequency curves move counterclockwise when the polymeric parameter P increases and this spiral effect is more obvious for a higher harmonic scalar wave.展开更多
In this article we hypothesized that the arrow of time and space evolve in a discontinuous way in the form of quanta (<i>t</i>=<i>nt<sub>p</sub></i>, <i>s=ml<sub>p</s...In this article we hypothesized that the arrow of time and space evolve in a discontinuous way in the form of quanta (<i>t</i>=<i>nt<sub>p</sub></i>, <i>s=ml<sub>p</sub></i>). We applied this reasoning to the light geodesics of Schwarzschild’s metric (d<i>s</i><sub>min</sub>=<i>l<sub>p</sub></i>) and obtained different characteristics of the BH. Indeed, quantum light geodesics show that inside the BH a WH is formed and the mass (energy) is not directing towards the singularity <i>r</i>→0 but rather around the BH near the EH as a thick skin (tickness <img src="Edit_ff6adb16-d005-4998-8a9c-badd521800d3.png" width="18" height="25" alt="" />). The total relativistic energy invariant is satisfied for the entire route of the photons. Subsequently, as mass (energy) is found directly at the EH, we applied the quantum tunnel effect in simple semi-classical analysis, and we obtained that particles like protons can leave the EH and that the energy associated with them is in the order of magnitude of Hawking’s radiation. However, the energy of the protons is not necessarily identified with that of the black body (photonic or electromagnetic). Finally, it would be interesting to see the impacts of this quantum light geodesics (d<i>s</i><sub>min</sub>=<i>l<sub>p</sub></i>) on other cases like Kerr’s metric.展开更多
This paper proposes a novel approach and simplified model of Quantum Gravity based on the unification framework of Generalized Thermodynamics which suggests cross-related terms and modified equations of General Relati...This paper proposes a novel approach and simplified model of Quantum Gravity based on the unification framework of Generalized Thermodynamics which suggests cross-related terms and modified equations of General Relativity and Quantum Mechanics. To address the “background problem”, a metric tensor is introduced into stationary Schrödinger equations via curved coordinates yielding quantum spacetime variation term. Then quantum Lagrangian is added to Einstein-Hilbert functional yielding quantum stress-energy tensor. Obtained from one variational principle, two theories are linked by a common quantum spacetime field. The theory offers some interpretations of the quantum vacuum spacetime fluctuations, zero-point-fields, quantum fields shifting towards high spacetime densities, the quantum nature of spacetime, and black hole singularity.展开更多
In this paper I have shown that squeezed modified quantum vacua have an effect on the background geometry by solving the semi-classical Einstein Field Equations in modified vacuum. The resultant geometry is similar to...In this paper I have shown that squeezed modified quantum vacua have an effect on the background geometry by solving the semi-classical Einstein Field Equations in modified vacuum. The resultant geometry is similar to (anti) de Sitter spacetime. This geometry could explain the change of causal structure—speed of light—in such vacua without violating diffeomorphism covariance or causality. The superluminal propagation of photons in Casimir vacuum is deduced from the effective electromagnetic action in the resultant curved geometry. Singling between different vacua is shown not to violate causality as well when the geometric effect on the null rays is considered, causing a refraction of those rays when traveling between unbounded and modified vacua.展开更多
Dark energy is explained using familiar notions and concepts used in quantum field theory, string theory and the exact mathematical theory of spacetime. The main result of the present work is first a new mathematical ...Dark energy is explained using familiar notions and concepts used in quantum field theory, string theory and the exact mathematical theory of spacetime. The main result of the present work is first a new mathematical definition of pre-quantum spacetime (QST) as a multiset made of infinitely many empty Cantor sets connected to pre-quantum wave empty set (QW) and the pre-quantum particle (QP) zero set via the cobordism equation ∂(QW) = (QP)U(QST). Second, and in turn, this new path of reasoning is used to validate the quantum splitting of Einstein’s E = mc<sup>2</sup> into the sum of the ordinary energy E = mc<sup>2</sup>/22 of the quantum particle and the dark energy E = mc<sup>2</sup>(21/22) of the quantum wave, used predominantly to explain the observed accelerated expansion of the universe.展开更多
We study spontaneous excitation of both a static detector （modelled by a two-level atom） immersed in a thermal bath and a uniformly accelerated one in the Minkowski vacuum interacting with a real massive scalar fiel...We study spontaneous excitation of both a static detector （modelled by a two-level atom） immersed in a thermal bath and a uniformly accelerated one in the Minkowski vacuum interacting with a real massive scalar field. Our results show that the mass of the scalar field manifests itself in the spontaneous excitation rate of the static detector in a thermal bath （and in vacuum） in the form of a selection rule for transitions among states of the detector. However, this selection rule disappears for the accelerated ones, demonstrating that an accelerated detector does not necessarily behave the same as an inertial one in a thermal bath. We lind the imprint left by the mass is the appearance of a grey-body factor in the spontaneous excitation and de-excitation rates, which maintains the detailed balance condition between them and thus ensures a thermal equilibrium at the Unruh temperature the same as that of the massless case. We also analyze quantitatively the effect of the mass on the rate of change of the detector＇s energy and find that when the mass is very small, it only induces a small negative correction. However, when it is very large, it then exponentially damps the rate, thus essentially forbidding any transitions among states of the detector.展开更多
In this paper, a new complex variable defined as “precursive time” able to correlate general relativity (GR) and quantum field theory (QFT) in a single principle was characterized. The thesis was elaborated accordin...In this paper, a new complex variable defined as “precursive time” able to correlate general relativity (GR) and quantum field theory (QFT) in a single principle was characterized. The thesis was elaborated according to a hypothesis coherent with the “Einstein’s General Theory of Relativity”, making use of a new mathematical-topological variety called “time-space” developed on the properties of the hypersphere and explained mathematically through the quaternion of Hurwitz-Lipschitz algebra. In this publication we pay attention to the interaction between the weak nuclear force theory (EWT) and the nuclear mass of the Standard Model.展开更多
In this paper,we study the Hawking radiation of Dirac particles via tunneling formalism from linearly supertranslated Schwarzschild black holes.We find that the radiation spectrum and the Hawking temperature remain th...In this paper,we study the Hawking radiation of Dirac particles via tunneling formalism from linearly supertranslated Schwarzschild black holes.We find that the radiation spectrum and the Hawking temperature remain the same as the one without soft hair.展开更多
We study adiabatic regularization of a coupling massless scalar field in general spatially flat Robertson-Walker(RW)spacetimes.For the conformal coupling,the 2nd-order regularized power spectrum and 4th-order regulari...We study adiabatic regularization of a coupling massless scalar field in general spatially flat Robertson-Walker(RW)spacetimes.For the conformal coupling,the 2nd-order regularized power spectrum and 4th-order regularized stress tensor are zero,and no trace anomaly exists in general RW spacetimes.This is a new result that exceeds those found in de Sitter space.For the minimal coupling,the regularized spectra are also zero in the radiationdominant and matter-dominant stages,as well as in de Sitter space.The vanishing of these adiabatically regularized spectra is further confirmed by direct regularization of the Green's function.For a general coupling and general RW spacetimes,the regularized spectra can be negative under the conventional prescription.At a higher order of regularization,the spectra will generally become positive,but will also acquire IR divergence,which is inevitable for a massless field.To avoid the IR divergence,the inside-horizon regularization is applied.Through these procedures,nonnegative UV-and IR-convergent power spectrum and spectral energy density will eventually be achieved.展开更多
Some aspects of atom-field interactions in curved spacetime are reviewed.Of great interest are quantum radiative and entanglement processes arising out of Rindler and black hole spacetimes,which involve the role of Ha...Some aspects of atom-field interactions in curved spacetime are reviewed.Of great interest are quantum radiative and entanglement processes arising out of Rindler and black hole spacetimes,which involve the role of Hawking-Unruh and dynamical Casimir effects.Most of the discussion surrounds the radiative part of interactions.For this,we specifically reassess the conventional understandings of atomic radiative transitions and energy level shifts in curved spacetime.We also briefly outline the status quo of entanglement dynamics study in curved spacetime,and highlight literature related to some novel insights,like entanglement harvesting.On one hand,the study of the role played by spacetime curvature in quantum radiative and informational phenomena has implications for fundamental physics,notably the gravity-quantum interface.In particular,one examines the viability of the Equivalence Principle,which is at the heart of Einstein’s general theory of relativity.On the other hand,it can be instructive for manipulating quantum information and light propagation in arbitrary geometries.Some issues related to nonthermal effects of acceleration are also discussed.展开更多
We develop a covariant kinetic theory for massive fermions in a curved spacetime and an external electromagnetic field based on quantum field theory.We derive four coupled semi-classical kinetic equations accurate to ...We develop a covariant kinetic theory for massive fermions in a curved spacetime and an external electromagnetic field based on quantum field theory.We derive four coupled semi-classical kinetic equations accurate to O(ℏ),which describe the transports of particle number and spin degrees of freedom.The relationship with chiral kinetic theory is discussed.As an application,we study spin polarization in the presence of finite Riemann curvature and an electromagnetic field in both local and global equilibrium states.展开更多
文摘The paper presents a very simple and straight forward yet pure mathematical derivation of the structure of actual spacetime from quantum set theory. This is achieved by utilizing elements of the topological theory of cobordism and the Menger-Urysohn dimensional theory in conjunction with von Neumann-Connes dimensional function of Klein-Penrose modular holographic boundary of the E8E8 exceptional Lie group bulk of our universe. The final result is a lucid sharp mental picture, namely that the quantum wave is an empty set representing the surface, i.e. boundary of the zero set quantum particle and in turn quantum spacetime is simply the boundary or the surface of the quantum wave empty set. The essential difference of the quantum wave and quantum spacetime is that the wave is a simple empty set while spacetime is a multi-fractal type of infinitely many empty sets with increasing degrees of emptiness.
基金supported Project supported by the National Natural Science Foundation of China (Grant No. 10873004)the Program for Excellent Talents at Hunan Normal University,China+4 种基金the National Basic Research Program of China (Grant No. 2010CB832803)the Key Program of the National Natural Science Foundation of China (Grant No. 10935013)the Construct Program of the National Key Disciplinethe Program for Changjiang Scholarsthe Innovative Research Team in University,China(Grant No. IRT0964)
文摘Recently, considerable progress has been made in understanding the early universe by loop quantum cosmology. Modesto et al. investigated the loop quantum black hole （LQBH）using improved semiclassical analysis and they found that the LQBH has two horizons, an event horizon and a Cauchy horizon, just like the Reissner-NordstrSm black hole. This paper focuses on the dynamical evolution of a massless scalar wave in the LQBH background. By investigating the relation between the complex frequencies of the massless scalar field and the LQBH parameters using the numerical method, we find that the polymeric parameter P makes the massless scalar field decay more quickly and makes the ground scalar wave oscillate slowly. However, the polymeric parameter P causes the frequency of the high harmonic massless scalar wave to shift according to its value. We also find that the loop quantum gravity area gap parameter a0 causes the massless scalar field to decay more slowly and makes the period of the massless scalar field wave become longer. In the complex ω plane, the frequency curves move counterclockwise when the polymeric parameter P increases and this spiral effect is more obvious for a higher harmonic scalar wave.
文摘In this article we hypothesized that the arrow of time and space evolve in a discontinuous way in the form of quanta (<i>t</i>=<i>nt<sub>p</sub></i>, <i>s=ml<sub>p</sub></i>). We applied this reasoning to the light geodesics of Schwarzschild’s metric (d<i>s</i><sub>min</sub>=<i>l<sub>p</sub></i>) and obtained different characteristics of the BH. Indeed, quantum light geodesics show that inside the BH a WH is formed and the mass (energy) is not directing towards the singularity <i>r</i>→0 but rather around the BH near the EH as a thick skin (tickness <img src="Edit_ff6adb16-d005-4998-8a9c-badd521800d3.png" width="18" height="25" alt="" />). The total relativistic energy invariant is satisfied for the entire route of the photons. Subsequently, as mass (energy) is found directly at the EH, we applied the quantum tunnel effect in simple semi-classical analysis, and we obtained that particles like protons can leave the EH and that the energy associated with them is in the order of magnitude of Hawking’s radiation. However, the energy of the protons is not necessarily identified with that of the black body (photonic or electromagnetic). Finally, it would be interesting to see the impacts of this quantum light geodesics (d<i>s</i><sub>min</sub>=<i>l<sub>p</sub></i>) on other cases like Kerr’s metric.
文摘This paper proposes a novel approach and simplified model of Quantum Gravity based on the unification framework of Generalized Thermodynamics which suggests cross-related terms and modified equations of General Relativity and Quantum Mechanics. To address the “background problem”, a metric tensor is introduced into stationary Schrödinger equations via curved coordinates yielding quantum spacetime variation term. Then quantum Lagrangian is added to Einstein-Hilbert functional yielding quantum stress-energy tensor. Obtained from one variational principle, two theories are linked by a common quantum spacetime field. The theory offers some interpretations of the quantum vacuum spacetime fluctuations, zero-point-fields, quantum fields shifting towards high spacetime densities, the quantum nature of spacetime, and black hole singularity.
文摘In this paper I have shown that squeezed modified quantum vacua have an effect on the background geometry by solving the semi-classical Einstein Field Equations in modified vacuum. The resultant geometry is similar to (anti) de Sitter spacetime. This geometry could explain the change of causal structure—speed of light—in such vacua without violating diffeomorphism covariance or causality. The superluminal propagation of photons in Casimir vacuum is deduced from the effective electromagnetic action in the resultant curved geometry. Singling between different vacua is shown not to violate causality as well when the geometric effect on the null rays is considered, causing a refraction of those rays when traveling between unbounded and modified vacua.
文摘Dark energy is explained using familiar notions and concepts used in quantum field theory, string theory and the exact mathematical theory of spacetime. The main result of the present work is first a new mathematical definition of pre-quantum spacetime (QST) as a multiset made of infinitely many empty Cantor sets connected to pre-quantum wave empty set (QW) and the pre-quantum particle (QP) zero set via the cobordism equation ∂(QW) = (QP)U(QST). Second, and in turn, this new path of reasoning is used to validate the quantum splitting of Einstein’s E = mc<sup>2</sup> into the sum of the ordinary energy E = mc<sup>2</sup>/22 of the quantum particle and the dark energy E = mc<sup>2</sup>(21/22) of the quantum wave, used predominantly to explain the observed accelerated expansion of the universe.
基金Supported in part by the National Natural Science Foundation of China under Grant Nos. 11075083,10935013 and 11005013the Zhejiang Provincial Natural Science Foundation of China under Grant No. Z6100077+3 种基金the National Basic Research Program of China under Grant No. 2010CB832803the PCSIRT under Grant No. IRT0964the Research Foundation of Education Bureau of Hunan Province under Grant No. 10C0377Provincial Natural Science Foundation of China under Grant No. 11JJ700
文摘We study spontaneous excitation of both a static detector （modelled by a two-level atom） immersed in a thermal bath and a uniformly accelerated one in the Minkowski vacuum interacting with a real massive scalar field. Our results show that the mass of the scalar field manifests itself in the spontaneous excitation rate of the static detector in a thermal bath （and in vacuum） in the form of a selection rule for transitions among states of the detector. However, this selection rule disappears for the accelerated ones, demonstrating that an accelerated detector does not necessarily behave the same as an inertial one in a thermal bath. We lind the imprint left by the mass is the appearance of a grey-body factor in the spontaneous excitation and de-excitation rates, which maintains the detailed balance condition between them and thus ensures a thermal equilibrium at the Unruh temperature the same as that of the massless case. We also analyze quantitatively the effect of the mass on the rate of change of the detector＇s energy and find that when the mass is very small, it only induces a small negative correction. However, when it is very large, it then exponentially damps the rate, thus essentially forbidding any transitions among states of the detector.
文摘In this paper, a new complex variable defined as “precursive time” able to correlate general relativity (GR) and quantum field theory (QFT) in a single principle was characterized. The thesis was elaborated according to a hypothesis coherent with the “Einstein’s General Theory of Relativity”, making use of a new mathematical-topological variety called “time-space” developed on the properties of the hypersphere and explained mathematically through the quaternion of Hurwitz-Lipschitz algebra. In this publication we pay attention to the interaction between the weak nuclear force theory (EWT) and the nuclear mass of the Standard Model.
基金supported in part by the National Natural Science Foundation of China under Grant No.11905156,No.11975164,No.11935009Natural Science Foundation of Tianjin under Grant No.20JCYBJC00910。
文摘In this paper,we study the Hawking radiation of Dirac particles via tunneling formalism from linearly supertranslated Schwarzschild black holes.We find that the radiation spectrum and the Hawking temperature remain the same as the one without soft hair.
基金Supported by NSFC(11421303,11675165,11633001,11961131007)B.Wang is supported by CPSF(2019M662168)。
文摘We study adiabatic regularization of a coupling massless scalar field in general spatially flat Robertson-Walker(RW)spacetimes.For the conformal coupling,the 2nd-order regularized power spectrum and 4th-order regularized stress tensor are zero,and no trace anomaly exists in general RW spacetimes.This is a new result that exceeds those found in de Sitter space.For the minimal coupling,the regularized spectra are also zero in the radiationdominant and matter-dominant stages,as well as in de Sitter space.The vanishing of these adiabatically regularized spectra is further confirmed by direct regularization of the Green's function.For a general coupling and general RW spacetimes,the regularized spectra can be negative under the conventional prescription.At a higher order of regularization,the spectra will generally become positive,but will also acquire IR divergence,which is inevitable for a massless field.To avoid the IR divergence,the inside-horizon regularization is applied.Through these procedures,nonnegative UV-and IR-convergent power spectrum and spectral energy density will eventually be achieved.
基金supported by the National Natural Science Foundation of China(NSFC)(Grant No.11974309)SMASB acknowledges financial support from China Scholarship Council at Zhejiang University.
文摘Some aspects of atom-field interactions in curved spacetime are reviewed.Of great interest are quantum radiative and entanglement processes arising out of Rindler and black hole spacetimes,which involve the role of Hawking-Unruh and dynamical Casimir effects.Most of the discussion surrounds the radiative part of interactions.For this,we specifically reassess the conventional understandings of atomic radiative transitions and energy level shifts in curved spacetime.We also briefly outline the status quo of entanglement dynamics study in curved spacetime,and highlight literature related to some novel insights,like entanglement harvesting.On one hand,the study of the role played by spacetime curvature in quantum radiative and informational phenomena has implications for fundamental physics,notably the gravity-quantum interface.In particular,one examines the viability of the Equivalence Principle,which is at the heart of Einstein’s general theory of relativity.On the other hand,it can be instructive for manipulating quantum information and light propagation in arbitrary geometries.Some issues related to nonthermal effects of acceleration are also discussed.
基金X.-G.H.was supported by NSFC(11535012,11675041)K.M.was supported by the China Postdoctoral Science Foundation(2017M621345)。
文摘We develop a covariant kinetic theory for massive fermions in a curved spacetime and an external electromagnetic field based on quantum field theory.We derive four coupled semi-classical kinetic equations accurate to O(ℏ),which describe the transports of particle number and spin degrees of freedom.The relationship with chiral kinetic theory is discussed.As an application,we study spin polarization in the presence of finite Riemann curvature and an electromagnetic field in both local and global equilibrium states.
