In quantum mechanics, the energy of a hydrogen atom is minimized when the principal quantum number n is 1. However, the author has previously pointed out that the hydrogen atom has a state where n=0. An electron in th...In quantum mechanics, the energy of a hydrogen atom is minimized when the principal quantum number n is 1. However, the author has previously pointed out that the hydrogen atom has a state where n=0. An electron in the state where n=0has zero rest mass energy. However, a hydrogen atom has an energy level even lower than the n=0state. This is hard to accept from the standpoint of common sense. Thus, the author has previously pointed out that an electron at the energy level where n=0has zero energy because the positive energy mec2and negative energy −mec2cancel each other out. This paper elucidates the strange relationship between the momentum of a photon emitted when a hydrogen atom is formed by an electron with such characteristics, and the momentum acquired by the electron.展开更多
The integrated power and attitude control for a bias momentum attitudecontrol system is investigated. A pair of counter-spinning wheels is used to provide the biasangular momentum and store/ discharge energy for power...The integrated power and attitude control for a bias momentum attitudecontrol system is investigated. A pair of counter-spinning wheels is used to provide the biasangular momentum and store/ discharge energy for power requirement of the devices on the spacecraft.The roll/yaw motion is controlled by pitch magnetic dipole moment. The torque-based control law ofthe wheels is designed, so that the desired pitch control torque is provided and the operation ofcharging/discharging energy is carried out based on the given power. System singularity in thecontrol law of wheels is fully avoided by keeping the wheels counter-spinning. A power managementscheme using kinetic energy feedback is proposed to keep energy balance, which can avoid wheelsaturation caused by superfluous energy. The minimum moment of inertia of the wheels is limited bythe maximum bias angular momentum and the minimum energy, such constrains are analyzed incombination with the geometrical method. Numerical simulation results are presented to demonstratethe effectiveness of the control scheme.展开更多
In 1935 Dirac established the physical wave equations in the de-Sitter spaces but neither energy-momentum operators nor their conservative laws were given. In this article it is proved that in the de-Sitter group ther...In 1935 Dirac established the physical wave equations in the de-Sitter spaces but neither energy-momentum operators nor their conservative laws were given. In this article it is proved that in the de-Sitter group there is a subgroup group isomorphic to the Heisenberg group and the generators of this groups are the energy-momentum operators which obey a conservative law.展开更多
Through a comparison between the expressions of master balance laws and the conservation laws derived by Noether＇s theorem, a unified master balance law and six physically possible balance equations for micropolar co...Through a comparison between the expressions of master balance laws and the conservation laws derived by Noether＇s theorem, a unified master balance law and six physically possible balance equations for micropolar continuum mechanics are naturally deduced. Among them, by extending the well-known conventional concept of energymomentum tensor, the rather general conservation laws and balance equations named after energy-momentum, energy-angular momentum and energy-energy are obtained. It is clear that the forms of the physical field quantities in the master balance law for the last three cases could not be assumed directly by perceiving through the intuition. Finally, some existing results are reduced immediately as special cases.展开更多
Einstein’s energy-momentum relationship, which holds in an isolated system in free space, contains two formulas for relativistic kinetic energy. Einstein’s relationship is not applicable in a hydrogen atom, where po...Einstein’s energy-momentum relationship, which holds in an isolated system in free space, contains two formulas for relativistic kinetic energy. Einstein’s relationship is not applicable in a hydrogen atom, where potential energy is present. However, a relationship similar to that can be derived. That derived relationship also contains two formulas, for the relativistic kinetic energy of an electron in a hydrogen atom. Furthermore, it is possible to derive a third formula for the relativistic kinetic energy of an electron from that relationship. Next, the paper looks at the fact that the electron has a wave nature. Five more formulas can be derived based on considerations relating to the phase velocity and group velocity of the electron. This paper presents eight formulas for the relativistic kinetic energy of an electron in a hydrogen atom.展开更多
Einstein’s energy-momentum relationship is a formula that typifies the special theory of relativity (STR). According to the STR, when the velocity of a moving body increases, so does the mass of the body. The STR ass...Einstein’s energy-momentum relationship is a formula that typifies the special theory of relativity (STR). According to the STR, when the velocity of a moving body increases, so does the mass of the body. The STR asserts that the mass of a body depends of the velocity at which the body moves. However, when energy is imparted to a body, this relation holds because kinetic energy increases. When the motion of an electron in an atom is discussed at the level of classical quantum theory, the kinetic energy of the electron is increased due to the emission of energy. At this time, the relativistic energy of the electron decreases, and the mass of the electron also decreases. The STR is not applicable to an electron in an atom. This paper derives an energy-momentum relationship applicable to an electron in an atom. The formula which determines the mass of an electron in an atom is also derived by using that relationship.展开更多
Bohr assumed a quantum condition when deriving the energy levels of a hydrogen atom. This famous quantum condition was not derived logically, but it beautifully explained the energy levels of the hydrogen atom. Theref...Bohr assumed a quantum condition when deriving the energy levels of a hydrogen atom. This famous quantum condition was not derived logically, but it beautifully explained the energy levels of the hydrogen atom. Therefore, Bohr’s quantum condition was accepted by physicists. However, the energy levels predicted by the eventually completed quantum mechanics do not match perfectly with the predictions of Bohr. For this reason, it cannot be said that Bohr’s quantum condition is a perfectly correct assumption. Since the mass of an electron which moves inside a hydrogen atom varies, Bohr’s quantum condition must be revised. However, the newly derived relativistic quantum condition is too complex to be assumed at the beginning. The velocity of an electron in a hydrogen atom is known as the Bohr velocity. This velocity can be derived from the formula for energy levels derived by Bohr. The velocity <em>v </em>of an electron including the principal quantum number <em>n</em> is given by <em>αc</em>/<em>n</em>. This paper elucidates the fact that this formula is built into Bohr’s quantum condition. It is also concluded in this paper that it is precisely this velocity formula that is the quantum condition that should have been assumed in the first place by Bohr. From Bohr’s quantum condition, it is impossible to derive the relativistic energy levels of a hydrogen atom, but they can be derived from the new quantum condition. This paper proposes raising the status of the previously-known Bohr velocity formula.展开更多
If an electron emits all of its rest mass energy mec2, the relativistic energy of the electron will become zero. According to the special theory of relativity, an electron whose relativistic energy is zero does not ha...If an electron emits all of its rest mass energy mec2, the relativistic energy of the electron will become zero. According to the special theory of relativity, an electron whose relativistic energy is zero does not have photon energy. In this paper, however, an electron is regarded as having photon energy mec2 and negative energy −mec2, even when its relativistic energy is zero. The state where relativistic energy is zero is achieved due to the positive energy and negative energy canceling each other out. Relativistic energy becomes zero for an electron in a hydrogen atom when the principle quantum number n is zero. The author has already pointed out the existence of an energy level with n=0. If this model is used, it is possible for an electron in the state with n=0 to emit additional photons, and transition to negative energy levels. The existence of negative energy specific to the electron has previously been nothing more than a conjecture. However, this paper aims to theoretically show the existence of negative energy based on a discussion using an ellipse. The results show that the electron has latent negative energy.展开更多
We have obtained exact static plane-symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of invariant , taking into account their own gravitational field. It is shown th...We have obtained exact static plane-symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of invariant , taking into account their own gravitational field. It is shown that the initial set of the Einstein and spinor field equations with a power-law nonlinearity have regular solutions with a localized energy density of the spinor field only if m=0 (m is the mass parameter in the spinor field equations). Equations with power and polynomial nonlinearities are studied in detail. In this case, a soliton-like configuration has negative energy. We have also obtained exact static plane-symmetric solutions to the above spinor field equations in flat space-time. It is proved that in this case soliton-like solutions are absent.展开更多
According to the conventional theory it is difficult to define the energy-momentum tensor which is locally conservative. The energy-momentum tensor of the gravitational field is defined. Based on a cosmological model ...According to the conventional theory it is difficult to define the energy-momentum tensor which is locally conservative. The energy-momentum tensor of the gravitational field is defined. Based on a cosmological model without singularity, the total energy-momentum tensor is defined which is locally conservative in the general relativity. The tensor of the gravitational mass is different from the energy-momentum tensor, and it satisfies the gravitational field equation and its covariant derivative is zero.展开更多
In this work we investigate the possibility to represent physical fields as Einstein manifold. Based on the Einstein field equations in general relativity, we establish a general formulation for determining the metric...In this work we investigate the possibility to represent physical fields as Einstein manifold. Based on the Einstein field equations in general relativity, we establish a general formulation for determining the metric tensor of the Einstein manifold that represents a physical field in terms of the energy-momentum tensor that characterises the physical field. As illustrations, we first apply the general formulation to represent the perfect fluid as Einstein manifold. However, from the established relation between the metric tensor and the energy-momentum tensor, we show that if the trace of the energy-momentum tensor associated with a physical field is equal to zero then the corresponding physical field cannot be represented as an Einstein manifold. This situation applies to the electromagnetic field since the trace of the energy-momentum of the electromagnetic field vanishes. Nevertheless, we show that a system that consists of the electromagnetic field and non-interacting charged particles can be represented as an Einstein manifold since the trace of the corresponding energy-momentum of the system no longer vanishes. As a further investigation, we show that it is also possible to represent physical fields as maximally symmetric spaces of constant scalar curvature.展开更多
In classical quantum theory, the Rydberg constant is a fundamental physical constant that plays an important role. It comes into play as an indispensable physical constant in basic formulas for describing natural phen...In classical quantum theory, the Rydberg constant is a fundamental physical constant that plays an important role. It comes into play as an indispensable physical constant in basic formulas for describing natural phenomena. However, relativity is not taken into account in this Rydberg formula for wavelength. If the special theory of relativity is taken into account, R<sub>∞</sub> can no longer be regarded as a physical constant. That is, we have continued to conduct experiments to this day in an attempt to determine the value of a physical constant, the Rydberg constant, which does not exist in the natural world.展开更多
In a vacuum spacetime equipped with the Bondi’s radiating metric which is asymptotically flat at spatial infinity including gravitational radiation (Condition D),we establish the relation between the ADM total energy...In a vacuum spacetime equipped with the Bondi’s radiating metric which is asymptotically flat at spatial infinity including gravitational radiation (Condition D),we establish the relation between the ADM total energy-momentum and the Bondi energy-momentum for perturbed radiative spatial infinity.The perturbation is given by defining the"real"time as the sum of the retarded time,the Euclidean distance and certain function f.展开更多
The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-mom...The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-momentum and energy-moment of momentum tensors are presented. The concrete forms of surface conservation laws for micropolar thermomechanical continua are derived . The existing related results are naturally derived as special cases from the results proposed in this paper . The incomplete degrees of the existing surface conservation laws are clearly seen from the process of the deduction. The surface conservation laws for nonlocal micropolar thermomechanical continua may be easily obtained via localization .展开更多
In many areas of physics and chemistry, the Rydberg constant is a fundamental physical constant that plays an important role. It comes into play as an indispensable physical constant in basic equations for describing ...In many areas of physics and chemistry, the Rydberg constant is a fundamental physical constant that plays an important role. It comes into play as an indispensable physical constant in basic equations for describing natural phenomena. The Rydberg constant appears in the formula for calculating the wavelengths in the line spectrum emitted from the hydrogen atom. However, this Rydberg wavelength formula is a nonrelativistic formula derived at the level of classical quantum theory. In this paper, the Rydberg formula is rewritten as a wavelength formula taking into account the theory of relativity. When this is done, we come to an unexpected conclusion. What we try to determine by measuring spectra wavelengths is not actually the value of the Rydberg constant <em>R</em><sub>∞</sub> but the value <em>R</em><sub><em>n</em>,<em>m</em></sub> of Formula (18). <em>R</em><sub>∞</sub> came into common use in the world of nonrelativistic classical quantum theory. If the theory of relativity is taken into account, <em>R</em><sub>∞</sub> can no longer be regarded as a physical constant. That is, we have continued to conduct experiments to this day in an attempt to determine the value of a physical constant, the Rydberg constant, which does not exist in the natural world.展开更多
The large-scale structure of DM cannot be directly seen, but it is believed it can be inferred from the distribution of visible galaxies formed from ordinary matter. Bright visible galaxies that emit the Lyman <i&...The large-scale structure of DM cannot be directly seen, but it is believed it can be inferred from the distribution of visible galaxies formed from ordinary matter. Bright visible galaxies that emit the Lyman <i>α</i> (Ly<i>α</i>) emission line of the hydrogen atom (Ly<i>α</i> galaxies) are used to observe the large-scale structure of distant space. However, recently Momose <i>et al</i>. have reported cases where the large-scale structures of DM indicated by Ly<i>α</i> galaxies and other galaxies fail to match. This raises the possibility that Ly<i>α</i> galaxies may not correctly indicate the large-scale structure of DM. In the currently accepted cold DM model, DM and neutral hydrogen gas are thought to interact only through the mutual effects of gravity. However, according to Suto, DM and ordinary matter are like two sides of the same coin. By giving and receiving approximately 2<i>m</i><sub>e</sub><i>c</i><sup>2</sup> (1.022 MeV), it is possible to mutually convert between the two. If, in future observations of the density distribution of interstellar gas using Ly<i>α</i> emission lines, unexpected data is obtained that cannot be explained based only on absorption by neutral hydrogen gas, then the author believes the problem can be solved with Suto’s DM model.展开更多
It is a challenge to investigate the interrelationship between the geometric structure and performance of sensor networks due to the increasingly complex and diverse architecture of them.This paper presents two new fo...It is a challenge to investigate the interrelationship between the geometric structure and performance of sensor networks due to the increasingly complex and diverse architecture of them.This paper presents two new formulations for the information space of sensor networks,including Lagrangian and energy–momentum tensor,which are expected to integrate sensor networks target tracking and performance evaluation from a unified perspective.The proposed method presents two geometric objects to represent the dynamic state and manifold structure of the information space of sensor networks.Based on that,the authors conduct the property analysis and target tracking of sensor networks.To the best of our knowledge,it is the first time to investigate and analyze the information energy-momentum tensor of sensor networks and evaluate the performance of sensor networks in the context of target tracking.Simulations and examples confirm the competitive performance of the proposed method.展开更多
The energy levels of a hydrogen atom, derived by Bohr, are known to be approximations. This is because the classical quantum theory of Bohr does not take the theory of relativity into account. In this paper, the kinet...The energy levels of a hydrogen atom, derived by Bohr, are known to be approximations. This is because the classical quantum theory of Bohr does not take the theory of relativity into account. In this paper, the kinetic energy and momentum of an electron in a hydrogen atom are treated relativistically. A clearer argument is developed while also referring to papers published in the past. The energy levels of a hydrogen atom predicted by this paper almost match the theoretical values of Bohr. It is difficult to experimentally distinguish the two. However, this paper predicts the existence of an n = 0 energy level that cannot be predicted even with Dirac’s relativistic quantum mechanics. The only quantum number treated in this paper is n. This point falls far short of a finished quantum mechanics. However, even in discussion at the level of this paper, it can be concluded that quantum mechanics is an incomplete theory.展开更多
文摘In quantum mechanics, the energy of a hydrogen atom is minimized when the principal quantum number n is 1. However, the author has previously pointed out that the hydrogen atom has a state where n=0. An electron in the state where n=0has zero rest mass energy. However, a hydrogen atom has an energy level even lower than the n=0state. This is hard to accept from the standpoint of common sense. Thus, the author has previously pointed out that an electron at the energy level where n=0has zero energy because the positive energy mec2and negative energy −mec2cancel each other out. This paper elucidates the strange relationship between the momentum of a photon emitted when a hydrogen atom is formed by an electron with such characteristics, and the momentum acquired by the electron.
文摘The integrated power and attitude control for a bias momentum attitudecontrol system is investigated. A pair of counter-spinning wheels is used to provide the biasangular momentum and store/ discharge energy for power requirement of the devices on the spacecraft.The roll/yaw motion is controlled by pitch magnetic dipole moment. The torque-based control law ofthe wheels is designed, so that the desired pitch control torque is provided and the operation ofcharging/discharging energy is carried out based on the given power. System singularity in thecontrol law of wheels is fully avoided by keeping the wheels counter-spinning. A power managementscheme using kinetic energy feedback is proposed to keep energy balance, which can avoid wheelsaturation caused by superfluous energy. The minimum moment of inertia of the wheels is limited bythe maximum bias angular momentum and the minimum energy, such constrains are analyzed incombination with the geometrical method. Numerical simulation results are presented to demonstratethe effectiveness of the control scheme.
基金The project partially supported by National Natural Science Foundation of China under Grant No. 10231050/A010109
文摘In 1935 Dirac established the physical wave equations in the de-Sitter spaces but neither energy-momentum operators nor their conservative laws were given. In this article it is proved that in the de-Sitter group there is a subgroup group isomorphic to the Heisenberg group and the generators of this groups are the energy-momentum operators which obey a conservative law.
基金Project supported by the National Natural Science Foundation of China (Nos.10072024 and 10472041)
文摘Through a comparison between the expressions of master balance laws and the conservation laws derived by Noether＇s theorem, a unified master balance law and six physically possible balance equations for micropolar continuum mechanics are naturally deduced. Among them, by extending the well-known conventional concept of energymomentum tensor, the rather general conservation laws and balance equations named after energy-momentum, energy-angular momentum and energy-energy are obtained. It is clear that the forms of the physical field quantities in the master balance law for the last three cases could not be assumed directly by perceiving through the intuition. Finally, some existing results are reduced immediately as special cases.
文摘Einstein’s energy-momentum relationship, which holds in an isolated system in free space, contains two formulas for relativistic kinetic energy. Einstein’s relationship is not applicable in a hydrogen atom, where potential energy is present. However, a relationship similar to that can be derived. That derived relationship also contains two formulas, for the relativistic kinetic energy of an electron in a hydrogen atom. Furthermore, it is possible to derive a third formula for the relativistic kinetic energy of an electron from that relationship. Next, the paper looks at the fact that the electron has a wave nature. Five more formulas can be derived based on considerations relating to the phase velocity and group velocity of the electron. This paper presents eight formulas for the relativistic kinetic energy of an electron in a hydrogen atom.
文摘Einstein’s energy-momentum relationship is a formula that typifies the special theory of relativity (STR). According to the STR, when the velocity of a moving body increases, so does the mass of the body. The STR asserts that the mass of a body depends of the velocity at which the body moves. However, when energy is imparted to a body, this relation holds because kinetic energy increases. When the motion of an electron in an atom is discussed at the level of classical quantum theory, the kinetic energy of the electron is increased due to the emission of energy. At this time, the relativistic energy of the electron decreases, and the mass of the electron also decreases. The STR is not applicable to an electron in an atom. This paper derives an energy-momentum relationship applicable to an electron in an atom. The formula which determines the mass of an electron in an atom is also derived by using that relationship.
文摘Bohr assumed a quantum condition when deriving the energy levels of a hydrogen atom. This famous quantum condition was not derived logically, but it beautifully explained the energy levels of the hydrogen atom. Therefore, Bohr’s quantum condition was accepted by physicists. However, the energy levels predicted by the eventually completed quantum mechanics do not match perfectly with the predictions of Bohr. For this reason, it cannot be said that Bohr’s quantum condition is a perfectly correct assumption. Since the mass of an electron which moves inside a hydrogen atom varies, Bohr’s quantum condition must be revised. However, the newly derived relativistic quantum condition is too complex to be assumed at the beginning. The velocity of an electron in a hydrogen atom is known as the Bohr velocity. This velocity can be derived from the formula for energy levels derived by Bohr. The velocity <em>v </em>of an electron including the principal quantum number <em>n</em> is given by <em>αc</em>/<em>n</em>. This paper elucidates the fact that this formula is built into Bohr’s quantum condition. It is also concluded in this paper that it is precisely this velocity formula that is the quantum condition that should have been assumed in the first place by Bohr. From Bohr’s quantum condition, it is impossible to derive the relativistic energy levels of a hydrogen atom, but they can be derived from the new quantum condition. This paper proposes raising the status of the previously-known Bohr velocity formula.
文摘If an electron emits all of its rest mass energy mec2, the relativistic energy of the electron will become zero. According to the special theory of relativity, an electron whose relativistic energy is zero does not have photon energy. In this paper, however, an electron is regarded as having photon energy mec2 and negative energy −mec2, even when its relativistic energy is zero. The state where relativistic energy is zero is achieved due to the positive energy and negative energy canceling each other out. Relativistic energy becomes zero for an electron in a hydrogen atom when the principle quantum number n is zero. The author has already pointed out the existence of an energy level with n=0. If this model is used, it is possible for an electron in the state with n=0 to emit additional photons, and transition to negative energy levels. The existence of negative energy specific to the electron has previously been nothing more than a conjecture. However, this paper aims to theoretically show the existence of negative energy based on a discussion using an ellipse. The results show that the electron has latent negative energy.
文摘We have obtained exact static plane-symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of invariant , taking into account their own gravitational field. It is shown that the initial set of the Einstein and spinor field equations with a power-law nonlinearity have regular solutions with a localized energy density of the spinor field only if m=0 (m is the mass parameter in the spinor field equations). Equations with power and polynomial nonlinearities are studied in detail. In this case, a soliton-like configuration has negative energy. We have also obtained exact static plane-symmetric solutions to the above spinor field equations in flat space-time. It is proved that in this case soliton-like solutions are absent.
文摘According to the conventional theory it is difficult to define the energy-momentum tensor which is locally conservative. The energy-momentum tensor of the gravitational field is defined. Based on a cosmological model without singularity, the total energy-momentum tensor is defined which is locally conservative in the general relativity. The tensor of the gravitational mass is different from the energy-momentum tensor, and it satisfies the gravitational field equation and its covariant derivative is zero.
文摘In this work we investigate the possibility to represent physical fields as Einstein manifold. Based on the Einstein field equations in general relativity, we establish a general formulation for determining the metric tensor of the Einstein manifold that represents a physical field in terms of the energy-momentum tensor that characterises the physical field. As illustrations, we first apply the general formulation to represent the perfect fluid as Einstein manifold. However, from the established relation between the metric tensor and the energy-momentum tensor, we show that if the trace of the energy-momentum tensor associated with a physical field is equal to zero then the corresponding physical field cannot be represented as an Einstein manifold. This situation applies to the electromagnetic field since the trace of the energy-momentum of the electromagnetic field vanishes. Nevertheless, we show that a system that consists of the electromagnetic field and non-interacting charged particles can be represented as an Einstein manifold since the trace of the corresponding energy-momentum of the system no longer vanishes. As a further investigation, we show that it is also possible to represent physical fields as maximally symmetric spaces of constant scalar curvature.
文摘In classical quantum theory, the Rydberg constant is a fundamental physical constant that plays an important role. It comes into play as an indispensable physical constant in basic formulas for describing natural phenomena. However, relativity is not taken into account in this Rydberg formula for wavelength. If the special theory of relativity is taken into account, R<sub>∞</sub> can no longer be regarded as a physical constant. That is, we have continued to conduct experiments to this day in an attempt to determine the value of a physical constant, the Rydberg constant, which does not exist in the natural world.
基金partially supported by the National Natural Science Foundation of China(Grant Nos.10231050,10421001)the National Key Basic Research Project of China(Grant No.2006CB805905)the Innovation Project of Chinese Academy of Sciences
文摘In a vacuum spacetime equipped with the Bondi’s radiating metric which is asymptotically flat at spatial infinity including gravitational radiation (Condition D),we establish the relation between the ADM total energy-momentum and the Bondi energy-momentum for perturbed radiative spatial infinity.The perturbation is given by defining the"real"time as the sum of the retarded time,the Euclidean distance and certain function f.
基金the National Natural Science Foundation of China (10072024) the Research Foundation of Liaoning Education Committee (990111001)
文摘The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-momentum and energy-moment of momentum tensors are presented. The concrete forms of surface conservation laws for micropolar thermomechanical continua are derived . The existing related results are naturally derived as special cases from the results proposed in this paper . The incomplete degrees of the existing surface conservation laws are clearly seen from the process of the deduction. The surface conservation laws for nonlocal micropolar thermomechanical continua may be easily obtained via localization .
文摘In many areas of physics and chemistry, the Rydberg constant is a fundamental physical constant that plays an important role. It comes into play as an indispensable physical constant in basic equations for describing natural phenomena. The Rydberg constant appears in the formula for calculating the wavelengths in the line spectrum emitted from the hydrogen atom. However, this Rydberg wavelength formula is a nonrelativistic formula derived at the level of classical quantum theory. In this paper, the Rydberg formula is rewritten as a wavelength formula taking into account the theory of relativity. When this is done, we come to an unexpected conclusion. What we try to determine by measuring spectra wavelengths is not actually the value of the Rydberg constant <em>R</em><sub>∞</sub> but the value <em>R</em><sub><em>n</em>,<em>m</em></sub> of Formula (18). <em>R</em><sub>∞</sub> came into common use in the world of nonrelativistic classical quantum theory. If the theory of relativity is taken into account, <em>R</em><sub>∞</sub> can no longer be regarded as a physical constant. That is, we have continued to conduct experiments to this day in an attempt to determine the value of a physical constant, the Rydberg constant, which does not exist in the natural world.
文摘The large-scale structure of DM cannot be directly seen, but it is believed it can be inferred from the distribution of visible galaxies formed from ordinary matter. Bright visible galaxies that emit the Lyman <i>α</i> (Ly<i>α</i>) emission line of the hydrogen atom (Ly<i>α</i> galaxies) are used to observe the large-scale structure of distant space. However, recently Momose <i>et al</i>. have reported cases where the large-scale structures of DM indicated by Ly<i>α</i> galaxies and other galaxies fail to match. This raises the possibility that Ly<i>α</i> galaxies may not correctly indicate the large-scale structure of DM. In the currently accepted cold DM model, DM and neutral hydrogen gas are thought to interact only through the mutual effects of gravity. However, according to Suto, DM and ordinary matter are like two sides of the same coin. By giving and receiving approximately 2<i>m</i><sub>e</sub><i>c</i><sup>2</sup> (1.022 MeV), it is possible to mutually convert between the two. If, in future observations of the density distribution of interstellar gas using Ly<i>α</i> emission lines, unexpected data is obtained that cannot be explained based only on absorption by neutral hydrogen gas, then the author believes the problem can be solved with Suto’s DM model.
基金supported by the National Natural Science Foundation of China(No.51875014)。
文摘It is a challenge to investigate the interrelationship between the geometric structure and performance of sensor networks due to the increasingly complex and diverse architecture of them.This paper presents two new formulations for the information space of sensor networks,including Lagrangian and energy–momentum tensor,which are expected to integrate sensor networks target tracking and performance evaluation from a unified perspective.The proposed method presents two geometric objects to represent the dynamic state and manifold structure of the information space of sensor networks.Based on that,the authors conduct the property analysis and target tracking of sensor networks.To the best of our knowledge,it is the first time to investigate and analyze the information energy-momentum tensor of sensor networks and evaluate the performance of sensor networks in the context of target tracking.Simulations and examples confirm the competitive performance of the proposed method.
文摘The energy levels of a hydrogen atom, derived by Bohr, are known to be approximations. This is because the classical quantum theory of Bohr does not take the theory of relativity into account. In this paper, the kinetic energy and momentum of an electron in a hydrogen atom are treated relativistically. A clearer argument is developed while also referring to papers published in the past. The energy levels of a hydrogen atom predicted by this paper almost match the theoretical values of Bohr. It is difficult to experimentally distinguish the two. However, this paper predicts the existence of an n = 0 energy level that cannot be predicted even with Dirac’s relativistic quantum mechanics. The only quantum number treated in this paper is n. This point falls far short of a finished quantum mechanics. However, even in discussion at the level of this paper, it can be concluded that quantum mechanics is an incomplete theory.
