The Standard Model of Particle Physics treats four fields—the gravitational, electromagnetic, weak and strong fields. These fields are assumed to converge to a single field at the big bang, but the theory has failed ...The Standard Model of Particle Physics treats four fields—the gravitational, electromagnetic, weak and strong fields. These fields are assumed to converge to a single field at the big bang, but the theory has failed to produce this convergence. Our theory proposes<em> one </em>primordial field and analyzes the evolution of this field. The key assumption is that <em>only</em> the primordial field exists—if any change is to occur, it must be based upon self-interaction, as there is nothing other than the field itself to interact with. This can be formalized as the <em>Principle</em> <em>of </em><em>Self-interaction</em> and the consequences explored. I show that this leads to the linearized Einstein field equations and discuss the key ontological implications of the theory.展开更多
Effects of temperature on self-interaction of human-like collagen （HLC） were investigated by hydrophobic in- teraction chromatography, calorimetric measurement, and sodium dodecyl sulphate-polyacrylamide gel electro...Effects of temperature on self-interaction of human-like collagen （HLC） were investigated by hydrophobic in- teraction chromatography, calorimetric measurement, and sodium dodecyl sulphate-polyacrylamide gel electropho- resis （SDS-PAGE） analysis. Results show that three types of interaction roles may exist between ttLC molecules at 3--50 ℃, which were divided into three narrower temperature ranges. In temperature range from 3--22 ℃, hy- drogen bonding plays a key role in the formation of a gelatinous aggregate. In the range of 22--38 ℃, hydrophobic bonds accompanied by hydrogen bonds are involved in the formation compact aggregates. When temperature is above 38 ℃ the hydrophobic effect formed in the HLC monomer results in the loss of its ability to self-interact.展开更多
The gravitational collapse of a massless scalar field with a self-interaction term λφ~4 in anti-de Sitter space is investigated.We numerically investigate the effect of the self-interaction term on the critical ampl...The gravitational collapse of a massless scalar field with a self-interaction term λφ~4 in anti-de Sitter space is investigated.We numerically investigate the effect of the self-interaction term on the critical amplitudes,forming time of apparent horizon,stable island,and energy transformation.The results show that a positiveλsuppresses the formation of black hole,while a negativeλenhances the process.We define two susceptibilities to characterize the effect of the self-interaction on the black hole formation,and find that near the critical amplitude,there exists a universal scaling relation with the critical exponentα≈0.74 for the time of black hole formation.展开更多
This paper investigates static axially symmetric models in self-interacting Brans-Dicke gravity. We discuss physically feasible sources of models, derive field equations as well as evolution equations from Bianchi ide...This paper investigates static axially symmetric models in self-interacting Brans-Dicke gravity. We discuss physically feasible sources of models, derive field equations as well as evolution equations from Bianchi identities and construct structure scalars. Using these scalars and evolution equations, the inhomogeneity factors of the system are evaluated. It is found that structure scalars related to double dual of Riemann tensor control the density inhomogeneity. Finally, we obtain exact solutions of homogenous isotropic and inhomogeneous anisotropic spheroid models. It turns out that homogenous solutions reduce to Schwarzschild type interior solutions for a spherical case. We conclude that homogenous models involve homogenous distribution of scalar field whereas inhomogeneous correspond to inhomogeneous sca/ar field.展开更多
Quantum gravity is an attempt to resolve incompatibilities between general relativity and quantum theory. Primordial field theory incorporates gravity and electrodynamics and has derived fermion mass gap, half integra...Quantum gravity is an attempt to resolve incompatibilities between general relativity and quantum theory. Primordial field theory incorporates gravity and electrodynamics and has derived fermion mass gap, half integral spin, and fractional charges. This paper extends PFT to hadron physics with a “solenoidal flux”-based explanation of quark confinement differing significantly from Lattice QCD “color flux”-based construction. The theory is presented qualitatively and used to predict hadronic and nuclear properties. Electrodynamic-based analogies help yield numerical results far more intuitively than corresponding QCD results. The origins of QCD and PFT are discussed. A more quantitative description of hadron dynamics is in progress.展开更多
This paper formulates two different boundary-element＋Born series schemes for wave propagation simulation in multilayered media by incorporating a Born series and boundary integral equations. The first scheme directly...This paper formulates two different boundary-element＋Born series schemes for wave propagation simulation in multilayered media by incorporating a Born series and boundary integral equations. The first scheme directly decomposes the resulting boundary integral equation matrix into the self-interaction operators associated with each boundary itself and the extrapolation operators expressing cross-interactions between different boundaries in a subregion. For the second scheme, the matrix dimension is firstly reduced to a half by the elimination of the traction field in the equations. The resulting new matrix can also be split into the self-interaction matrices associated each subregion itself and the extrapolation matrices interpreting cross-interactions between different subregions in a whole model. Both the numerical schemes avoid the inversion of the relatively much larger boundary integral equation matrix of a full-waveform BE method and hence save computing time and memory greatly. The two schemes are validated by calculating synthetic seismograms for a homogeneous layered model, compared with the full-waveform BE numerical solution. Numerical experiments indicate that both the BEM＋Born series modeling schemes are valid and effective. The tests also confirm that the second modeling scheme has a faster convergence in comparison with the first one.展开更多
In this paper the optimal precursors for wintertime Eurasian blocking onset are acquired by solving a nonlinear optimization problem whose objective function is constructed based on a blocking index with a triangular ...In this paper the optimal precursors for wintertime Eurasian blocking onset are acquired by solving a nonlinear optimization problem whose objective function is constructed based on a blocking index with a triangular T21, three-level, quasi-geostrophic global spectral model. The winter climatological state is chosen as the reference basic state. Numerical results show that the optimal precursors are characterized by a baroclinic pattern with a westward tilt with height, which are mainly located upstream of the blocking region. For an optimization time of 5 days, these perturbations are mainly localized over the Northeast Atlantic Ocean and continental Europe. With the extension of the optimization time to 8 days, these perturbations are distributed more upstream and extensively in the zonal direction. Wave spectrum analysis reveals that the optimal precursors are composed of not only synoptic-scale （wave numbers 5-18） waves, but planetary-scale （wave numbers 0-4） waves as well. The synoptic-scale optimal precursors are mainly located in the mid-latitude area, while the planetary-scale optimal precursors focus primarily on the high- latitude region. The formation of a strong planetary-scale positive blocking anomaly is accompanied by the reinforcement of synoptic-scale perturbations and further fragmentation into two branches, in which the northern branch is generally stronger than the southern one. The eddy forcing arising from the selfinteraction of synoptic-scale disturbances is shown to be crucial in triggering the dipole blocking anomaly, and the planetary-scale optimal precursor provides the initial favorable background conditions for blocking onset.展开更多
What is the quantum system? Consider the wave-function of the electron—what we call “single particle wave-function”—and assume that it contains N wave-packets. If we pass all the wave-packets through an electric f...What is the quantum system? Consider the wave-function of the electron—what we call “single particle wave-function”—and assume that it contains N wave-packets. If we pass all the wave-packets through an electric field, all are deflected, as if each one of them contains an electron. However, if we bring any two wave-packets to travel close to one another, they don’t repel one another, as if at least one of them contains no charge. In trying to solve the measurement problem of the quantum mechanics (QM), different interpretations were proposed, each one coming with a particular ontology. However, only one interpretation paid explicit attention to the contradiction mentioned above. This interpretation was proposed by S. Gao who named it “random discontinuous motion” (RDM), because it assumes the existence of a particle that jumps from place to place at random. The particle carries all the physical properties of the respective type of particle, mass, charge, magnetic momentum, etc. It jumps under the control of an “instantaneous condition” about which Gao did not give details so far. Along with presenting problems of the QM that this interpretation solves, this text reveals difficulties vis-à-vis entanglements and the special relativity.展开更多
In this paper, the reaction mechanism of HOCO with its radical has been investigated deeply by density functional theory（DFT）, while the geometries and harmonic vibration frequencies of the reactants, intermediates,...In this paper, the reaction mechanism of HOCO with its radical has been investigated deeply by density functional theory（DFT）, while the geometries and harmonic vibration frequencies of the reactants, intermediates, transition states and products have been calculated at the B3LYP/6-311＋＋G＊＊ level. The CCSD（T）/cc-p VQZ method was used to further calculate the single-point energy of each stationary point along the reaction channel. The result shows that channels（b） and（d） via carbon-carbon intermediates are competing with the ones（e）,（f）,（i） and（l） through carbon-oxygen intermediates, and the six channels are dominant for the title reaction to produce HCOOH and CO2. The result also indicates that the hydrogen abstraction from the HOCO radical can be performed quickly by the self-interaction of HOCO in the absence of other radicals or atoms, which indirectly proves for the first time that the ground-state cis-HOCO radical is not decomposed by the tunneling effect. In addition, the charges of natural population analysis（NPA） and the variation of chemical bonds have been analyzed by the Natural Bond Orbital（NBO） method along with the important reaction path.展开更多
The effect of trace elements with zero self-interaction coefficient on crystallization temperature of iron carbon alloys was studied and the mathematic equation was developed based on thermodynamics in the present res...The effect of trace elements with zero self-interaction coefficient on crystallization temperature of iron carbon alloys was studied and the mathematic equation was developed based on thermodynamics in the present researeh. With the equation developed in this paper, the effects of nitrogen on crystallization temperature of Fe-3.45C-2.15Si0. 16Mn and Fe-3.45C-2. 15Si-0. 80Mn alloys were discussed.展开更多
A transition or rare-earth metal is modeled as the atom immersed in a jellium at intermediate electron gas densities specified by? rs=4.0. The ground states of the spherical jellium atom are constructed based on the H...A transition or rare-earth metal is modeled as the atom immersed in a jellium at intermediate electron gas densities specified by? rs=4.0. The ground states of the spherical jellium atom are constructed based on the Hohenberg-Kohn-Sham density-functional formalism with the inclusion of electron-electron self-interaction corrections of Perdew and Zunger. Static and dynamic polarizabilities of the jellium atom are deduced using time-dependent linear response theory in a local density approximation as formulated by Stott and Zaremba. The calculation is extended to include the intervening elements In, Xe, Cs, and Ba. The calculation demonstrates how the Lindhard dielectric function can be modified to apply to non-simple metals treated in the jellium model.展开更多
Is the wave-function a physical reality traveling through our apparatus? Is it a real wave, or it is only a mathematical tool for calculating probabilities of results of measurements? Different interpretations of the ...Is the wave-function a physical reality traveling through our apparatus? Is it a real wave, or it is only a mathematical tool for calculating probabilities of results of measurements? Different interpretations of the quantum mechanics (QM) assume different answers to this question. It is shown in this article that the assumption that the wave-function is a real wave entails a contradiction with the predictions of the QM, when the special relativity is invoked. Therefore, this text concentrates on interpretations that conjecture that the reality that moves in our apparatuses is particles, and they move under the constraints of the wave-function. The de Broglie-Bohm interpretation, which matches this picture, assumes that the particle travels along a continuous trajectory. However, the idea of continuous trajectories was proved to lead to a contradiction with the quantum predictions. Therefore this interpretation is not considered here. S. Gao conjectured that the particle is in a permanent random and discontinuous motion (RDM). As it jumps all the time from place to place, the total set of occupied positions at a certain time is given by the absolute square of the wave-function. As motivation for his idea, Gao argued that if a charged particle were simultaneously in two or more locations at the same time, the copies of the particle would repel one another, destroying the wave-function. It is proved here that the quantum formalism renders this motivation wrong. Although refuting this motivation, the RDM interpretation is examined here. A couple of problems of this interpretation are examined and it is proved that they don’t lead to any observable contradictions with the QM predictions, except one problem which seems to have no solution. In all, it appears that none of the wide-spread interpretations of the QM is free of contradictions.展开更多
As pointed out in the paper preceding this one, in the case of functionals whose independent variable must obey conditions of integral normalization, conventional functional differentiation, defined in terms of an arb...As pointed out in the paper preceding this one, in the case of functionals whose independent variable must obey conditions of integral normalization, conventional functional differentiation, defined in terms of an arbitrary test function, is generally inapplicable and functional derivatives with respect to the density must be evaluated through the alternative and widely used limiting procedure based on the Dirac delta function. This leads to the determination of the rate of change of the dependent variable with respect to its independent variable at each isolated pair, , that may not be part of a functional (a set of ordered pairs). This extends the concept of functional derivative to expectation values of operators with respect to wave functions leading to a density even if the wave functions (and expectation values) do not form functionals. This new formulation of functional differentiation forms the basis for the study of the mathematical integrity of a number of concepts in density functional theory (DFT) such as the existence of a universal functional of the density, of orbital-free density functional theory, the derivative discontinuity of the exchange and correlation functional and the extension of DFT to open systems characterized by densities with fractional normalization. It is shown that no universal functional exists but, rather, a universal process based only on the density and independent of the possible existence of a potential, leads to unique functionals of the density determined through the minimization procedure of the constrained search. The mathematical integrity of two methodologies proposed for the treatment of the Coulomb interaction, the self-interaction free method and the optimized effective potential method is examined and the methodologies are compared in terms of numerical calculations. As emerges from this analysis, the optimized effective potential method is found to be numerically approximate but formally invalid, contrary to the rigorously exact results of the self-interaction-free method.展开更多
The latter half of the twentieth century yielded two tools of unprecedented power, both of which took decades to mature to their current states. The purpose of this research is to apply these to a theory of gravity an...The latter half of the twentieth century yielded two tools of unprecedented power, both of which took decades to mature to their current states. The purpose of this research is to apply these to a theory of gravity and develop the consequences of the model based on these tools. This paper presents such results without mathematical details, which are presented elsewhere. The tools are: Geometric Calculus, developed by David Hestenes, circa 1965 and Mathematica, released in 1988 by Steven Wolfram. Both tools have steep learning curves, requiring several years to acquire expertise in their use. This paper explains in what sense they are optimal.展开更多
文摘The Standard Model of Particle Physics treats four fields—the gravitational, electromagnetic, weak and strong fields. These fields are assumed to converge to a single field at the big bang, but the theory has failed to produce this convergence. Our theory proposes<em> one </em>primordial field and analyzes the evolution of this field. The key assumption is that <em>only</em> the primordial field exists—if any change is to occur, it must be based upon self-interaction, as there is nothing other than the field itself to interact with. This can be formalized as the <em>Principle</em> <em>of </em><em>Self-interaction</em> and the consequences explored. I show that this leads to the linearized Einstein field equations and discuss the key ontological implications of the theory.
文摘Effects of temperature on self-interaction of human-like collagen （HLC） were investigated by hydrophobic in- teraction chromatography, calorimetric measurement, and sodium dodecyl sulphate-polyacrylamide gel electropho- resis （SDS-PAGE） analysis. Results show that three types of interaction roles may exist between ttLC molecules at 3--50 ℃, which were divided into three narrower temperature ranges. In temperature range from 3--22 ℃, hy- drogen bonding plays a key role in the formation of a gelatinous aggregate. In the range of 22--38 ℃, hydrophobic bonds accompanied by hydrogen bonds are involved in the formation compact aggregates. When temperature is above 38 ℃ the hydrophobic effect formed in the HLC monomer results in the loss of its ability to self-interact.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11375247 and 11435006
文摘The gravitational collapse of a massless scalar field with a self-interaction term λφ~4 in anti-de Sitter space is investigated.We numerically investigate the effect of the self-interaction term on the critical amplitudes,forming time of apparent horizon,stable island,and energy transformation.The results show that a positiveλsuppresses the formation of black hole,while a negativeλenhances the process.We define two susceptibilities to characterize the effect of the self-interaction on the black hole formation,and find that near the critical amplitude,there exists a universal scaling relation with the critical exponentα≈0.74 for the time of black hole formation.
文摘This paper investigates static axially symmetric models in self-interacting Brans-Dicke gravity. We discuss physically feasible sources of models, derive field equations as well as evolution equations from Bianchi identities and construct structure scalars. Using these scalars and evolution equations, the inhomogeneity factors of the system are evaluated. It is found that structure scalars related to double dual of Riemann tensor control the density inhomogeneity. Finally, we obtain exact solutions of homogenous isotropic and inhomogeneous anisotropic spheroid models. It turns out that homogenous solutions reduce to Schwarzschild type interior solutions for a spherical case. We conclude that homogenous models involve homogenous distribution of scalar field whereas inhomogeneous correspond to inhomogeneous sca/ar field.
文摘Quantum gravity is an attempt to resolve incompatibilities between general relativity and quantum theory. Primordial field theory incorporates gravity and electrodynamics and has derived fermion mass gap, half integral spin, and fractional charges. This paper extends PFT to hadron physics with a “solenoidal flux”-based explanation of quark confinement differing significantly from Lattice QCD “color flux”-based construction. The theory is presented qualitatively and used to predict hadronic and nuclear properties. Electrodynamic-based analogies help yield numerical results far more intuitively than corresponding QCD results. The origins of QCD and PFT are discussed. A more quantitative description of hadron dynamics is in progress.
基金supported by National Natural Science Foundation of China (No.40830423)National Basic Research Program of China(973 Program,2009CB219403)
文摘This paper formulates two different boundary-element＋Born series schemes for wave propagation simulation in multilayered media by incorporating a Born series and boundary integral equations. The first scheme directly decomposes the resulting boundary integral equation matrix into the self-interaction operators associated with each boundary itself and the extrapolation operators expressing cross-interactions between different boundaries in a subregion. For the second scheme, the matrix dimension is firstly reduced to a half by the elimination of the traction field in the equations. The resulting new matrix can also be split into the self-interaction matrices associated each subregion itself and the extrapolation matrices interpreting cross-interactions between different subregions in a whole model. Both the numerical schemes avoid the inversion of the relatively much larger boundary integral equation matrix of a full-waveform BE method and hence save computing time and memory greatly. The two schemes are validated by calculating synthetic seismograms for a homogeneous layered model, compared with the full-waveform BE numerical solution. Numerical experiments indicate that both the BEM＋Born series modeling schemes are valid and effective. The tests also confirm that the second modeling scheme has a faster convergence in comparison with the first one.
基金supported by the National Natural Science Foundation of China(Grant No.40905023)the National Key Basic Research and Development(973) Project(Grant No. 2012CB417200)
文摘In this paper the optimal precursors for wintertime Eurasian blocking onset are acquired by solving a nonlinear optimization problem whose objective function is constructed based on a blocking index with a triangular T21, three-level, quasi-geostrophic global spectral model. The winter climatological state is chosen as the reference basic state. Numerical results show that the optimal precursors are characterized by a baroclinic pattern with a westward tilt with height, which are mainly located upstream of the blocking region. For an optimization time of 5 days, these perturbations are mainly localized over the Northeast Atlantic Ocean and continental Europe. With the extension of the optimization time to 8 days, these perturbations are distributed more upstream and extensively in the zonal direction. Wave spectrum analysis reveals that the optimal precursors are composed of not only synoptic-scale （wave numbers 5-18） waves, but planetary-scale （wave numbers 0-4） waves as well. The synoptic-scale optimal precursors are mainly located in the mid-latitude area, while the planetary-scale optimal precursors focus primarily on the high- latitude region. The formation of a strong planetary-scale positive blocking anomaly is accompanied by the reinforcement of synoptic-scale perturbations and further fragmentation into two branches, in which the northern branch is generally stronger than the southern one. The eddy forcing arising from the selfinteraction of synoptic-scale disturbances is shown to be crucial in triggering the dipole blocking anomaly, and the planetary-scale optimal precursor provides the initial favorable background conditions for blocking onset.
文摘What is the quantum system? Consider the wave-function of the electron—what we call “single particle wave-function”—and assume that it contains N wave-packets. If we pass all the wave-packets through an electric field, all are deflected, as if each one of them contains an electron. However, if we bring any two wave-packets to travel close to one another, they don’t repel one another, as if at least one of them contains no charge. In trying to solve the measurement problem of the quantum mechanics (QM), different interpretations were proposed, each one coming with a particular ontology. However, only one interpretation paid explicit attention to the contradiction mentioned above. This interpretation was proposed by S. Gao who named it “random discontinuous motion” (RDM), because it assumes the existence of a particle that jumps from place to place at random. The particle carries all the physical properties of the respective type of particle, mass, charge, magnetic momentum, etc. It jumps under the control of an “instantaneous condition” about which Gao did not give details so far. Along with presenting problems of the QM that this interpretation solves, this text reveals difficulties vis-à-vis entanglements and the special relativity.
基金supported by the National Natural Science Foundation of China(50673085,20677053)the Basic Research Programs of Qingdao Science and Technology Plan(No.13-1-4-233-jch)
文摘In this paper, the reaction mechanism of HOCO with its radical has been investigated deeply by density functional theory（DFT）, while the geometries and harmonic vibration frequencies of the reactants, intermediates, transition states and products have been calculated at the B3LYP/6-311＋＋G＊＊ level. The CCSD（T）/cc-p VQZ method was used to further calculate the single-point energy of each stationary point along the reaction channel. The result shows that channels（b） and（d） via carbon-carbon intermediates are competing with the ones（e）,（f）,（i） and（l） through carbon-oxygen intermediates, and the six channels are dominant for the title reaction to produce HCOOH and CO2. The result also indicates that the hydrogen abstraction from the HOCO radical can be performed quickly by the self-interaction of HOCO in the absence of other radicals or atoms, which indirectly proves for the first time that the ground-state cis-HOCO radical is not decomposed by the tunneling effect. In addition, the charges of natural population analysis（NPA） and the variation of chemical bonds have been analyzed by the Natural Bond Orbital（NBO） method along with the important reaction path.
文摘The effect of trace elements with zero self-interaction coefficient on crystallization temperature of iron carbon alloys was studied and the mathematic equation was developed based on thermodynamics in the present researeh. With the equation developed in this paper, the effects of nitrogen on crystallization temperature of Fe-3.45C-2.15Si0. 16Mn and Fe-3.45C-2. 15Si-0. 80Mn alloys were discussed.
文摘A transition or rare-earth metal is modeled as the atom immersed in a jellium at intermediate electron gas densities specified by? rs=4.0. The ground states of the spherical jellium atom are constructed based on the Hohenberg-Kohn-Sham density-functional formalism with the inclusion of electron-electron self-interaction corrections of Perdew and Zunger. Static and dynamic polarizabilities of the jellium atom are deduced using time-dependent linear response theory in a local density approximation as formulated by Stott and Zaremba. The calculation is extended to include the intervening elements In, Xe, Cs, and Ba. The calculation demonstrates how the Lindhard dielectric function can be modified to apply to non-simple metals treated in the jellium model.
文摘Is the wave-function a physical reality traveling through our apparatus? Is it a real wave, or it is only a mathematical tool for calculating probabilities of results of measurements? Different interpretations of the quantum mechanics (QM) assume different answers to this question. It is shown in this article that the assumption that the wave-function is a real wave entails a contradiction with the predictions of the QM, when the special relativity is invoked. Therefore, this text concentrates on interpretations that conjecture that the reality that moves in our apparatuses is particles, and they move under the constraints of the wave-function. The de Broglie-Bohm interpretation, which matches this picture, assumes that the particle travels along a continuous trajectory. However, the idea of continuous trajectories was proved to lead to a contradiction with the quantum predictions. Therefore this interpretation is not considered here. S. Gao conjectured that the particle is in a permanent random and discontinuous motion (RDM). As it jumps all the time from place to place, the total set of occupied positions at a certain time is given by the absolute square of the wave-function. As motivation for his idea, Gao argued that if a charged particle were simultaneously in two or more locations at the same time, the copies of the particle would repel one another, destroying the wave-function. It is proved here that the quantum formalism renders this motivation wrong. Although refuting this motivation, the RDM interpretation is examined here. A couple of problems of this interpretation are examined and it is proved that they don’t lead to any observable contradictions with the QM predictions, except one problem which seems to have no solution. In all, it appears that none of the wide-spread interpretations of the QM is free of contradictions.
文摘As pointed out in the paper preceding this one, in the case of functionals whose independent variable must obey conditions of integral normalization, conventional functional differentiation, defined in terms of an arbitrary test function, is generally inapplicable and functional derivatives with respect to the density must be evaluated through the alternative and widely used limiting procedure based on the Dirac delta function. This leads to the determination of the rate of change of the dependent variable with respect to its independent variable at each isolated pair, , that may not be part of a functional (a set of ordered pairs). This extends the concept of functional derivative to expectation values of operators with respect to wave functions leading to a density even if the wave functions (and expectation values) do not form functionals. This new formulation of functional differentiation forms the basis for the study of the mathematical integrity of a number of concepts in density functional theory (DFT) such as the existence of a universal functional of the density, of orbital-free density functional theory, the derivative discontinuity of the exchange and correlation functional and the extension of DFT to open systems characterized by densities with fractional normalization. It is shown that no universal functional exists but, rather, a universal process based only on the density and independent of the possible existence of a potential, leads to unique functionals of the density determined through the minimization procedure of the constrained search. The mathematical integrity of two methodologies proposed for the treatment of the Coulomb interaction, the self-interaction free method and the optimized effective potential method is examined and the methodologies are compared in terms of numerical calculations. As emerges from this analysis, the optimized effective potential method is found to be numerically approximate but formally invalid, contrary to the rigorously exact results of the self-interaction-free method.
文摘The latter half of the twentieth century yielded two tools of unprecedented power, both of which took decades to mature to their current states. The purpose of this research is to apply these to a theory of gravity and develop the consequences of the model based on these tools. This paper presents such results without mathematical details, which are presented elsewhere. The tools are: Geometric Calculus, developed by David Hestenes, circa 1965 and Mathematica, released in 1988 by Steven Wolfram. Both tools have steep learning curves, requiring several years to acquire expertise in their use. This paper explains in what sense they are optimal.
