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 this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The est...In this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The established coordinate transformations, referred to as modified Lorentz transformations because they have almost identical form to the Lorentz transformations, also comply with the requirement of invariance of the Minkowski line element. Particularly, the minimum universal speed can be associated with the phase speed of de Broglie matter wave. As application, we also discuss the possibility to formulate relativistic classical and quantum mechanics for the special relativity associated with the modified Lorentz transformations, which describes physical processes that represent an expansion or a collapsing of massive quantum particles.展开更多
In this work, we show that by restricting to the subgroup of time-independent coordinate transformations, then it is possible to derive the Ricci flow from the Bianchi identities. To achieve this, we first show that t...In this work, we show that by restricting to the subgroup of time-independent coordinate transformations, then it is possible to derive the Ricci flow from the Bianchi identities. To achieve this, we first show that the field equations of the gravitational field, the Newton’s second law of classical dynamics, and the Maxwell field equations of the electromagnetic field all share the same mathematical structure. Consequently, the Ricci flow itself may be regarded as dynamical equations used to describe physical processes associated with the gravitational field, such as the process of smoothing out irregularities of distribution of matter in space.展开更多
In this work, we examine the geometric character of the field equations of general relativity and propose to formulate relativistic field equations in terms of the Riemann curvature tensor. The resulted relativistic f...In this work, we examine the geometric character of the field equations of general relativity and propose to formulate relativistic field equations in terms of the Riemann curvature tensor. The resulted relativistic field equations are also integrated into the general framework that we have presented in our previous works that all known classical fields can be expressed in the same dynamical form. We also discuss a possibility to reformulate the field equations of general relativity so that the Ricci curvature tensor and the energy-momentum tensor can appear symmetrically in the field equations without violating the conservation law stated by the covariant derivative.展开更多
In this work, we introduce the new concept of fourth rank energy-momentum tensor. We first show that a fourth rank electromagnetic energy-momentum tensor can be constructed from the second rank electromagnetic energy-...In this work, we introduce the new concept of fourth rank energy-momentum tensor. We first show that a fourth rank electromagnetic energy-momentum tensor can be constructed from the second rank electromagnetic energy-momentum tensor. We then generalise to construct a fourth rank stress energy-momentum tensor and apply it to Dirac field of quantum particles. Furthermore, since the established fourth rank energy-momentum tensors have mathematical properties of the Riemann curvature tensor, thus it is reasonable to suggest that quantum fields should also possess geometric structures of a Riemannian manifold.展开更多
<p align="justify"> <span style="font-family:Verdana;"><span style="font-family:Verdana;font-size:12px;">In this work, we extend our work on the Heisenberg model of the ...<p align="justify"> <span style="font-family:Verdana;"><span style="font-family:Verdana;font-size:12px;">In this work, we extend our work on the Heisenberg model of the neutron formulated as a dwarf hydrogen-like atom under the influence of the More General Exponential Screened Coulomb Potential (MGESCP) to show that an atomic nucleus may possess a molecular structure made up of atoms bonding together by a potential used to describe the strong force associated with a generalised Yukawa MGESCP potential. We show that the neutrons and protons are arranged into narrow lattices therefore they may fold to form three-dimensional shells by bonding similar to hydrogen bonding. In particular, the nucleons may form stable structures such as that of fullerenes in which the vertices are occupied by the nucleons which are simply just protons. For example, a nucleus with a total number of 60 nucleons may arrange itself into the topological structure of a buckminsterfullerene. We also apply </span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;font-size:12px;">Schr</span></span><span style="font-family:;"><span style="font-family:;font-size:12px;"></span><span style="text-align:left;widows:2;text-transform:none;background-color:#ffffff;font-style:normal;text-indent:0px;display:inline !important;font-family:Verdana;white-space:normal;orphans:2;float:none;letter-spacing:normal;font-size:12px;font-weight:400;word-spacing:0px;font-variant-ligatures:normal;font-variant-caps:normal;-webkit-text-stroke-width:0px;text-decoration-style:initial;text-decoration-color:initial;">ö</span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;font-size:12px;">dinger</span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;font-size:12px;"> wave equation with central field approximation to describe the quantum dynamics of nuclei of atomic atoms that now possess the physical structure of a dwarf molecular ion.</span></span> </p>展开更多
We propose a reformulation of Newton’s second law of motion for charged particles and possible applications of the reformulation to quantum dynamics. We show that the negative energy states arising from the Dirac equ...We propose a reformulation of Newton’s second law of motion for charged particles and possible applications of the reformulation to quantum dynamics. We show that the negative energy states arising from the Dirac equation in relativistic quantum mechanics can be verified using the reformulating framework. We also discuss possible hidden dynamics underlying the concept of quantum jumps in quantum mechanics as outlined in Schr<span style="font-size:12px;white-space:nowrap;">ö</span>dinger’s article: ARE THERE QUANTUM JUMPS? In this case, we show that the hidden dynamics of quantum jumps are also determined by the Coulomb interaction between charged particles.展开更多
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 this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The established coordinate transformations, referred to as modified Lorentz transformations because they have almost identical form to the Lorentz transformations, also comply with the requirement of invariance of the Minkowski line element. Particularly, the minimum universal speed can be associated with the phase speed of de Broglie matter wave. As application, we also discuss the possibility to formulate relativistic classical and quantum mechanics for the special relativity associated with the modified Lorentz transformations, which describes physical processes that represent an expansion or a collapsing of massive quantum particles.
文摘In this work, we show that by restricting to the subgroup of time-independent coordinate transformations, then it is possible to derive the Ricci flow from the Bianchi identities. To achieve this, we first show that the field equations of the gravitational field, the Newton’s second law of classical dynamics, and the Maxwell field equations of the electromagnetic field all share the same mathematical structure. Consequently, the Ricci flow itself may be regarded as dynamical equations used to describe physical processes associated with the gravitational field, such as the process of smoothing out irregularities of distribution of matter in space.
文摘In this work, we examine the geometric character of the field equations of general relativity and propose to formulate relativistic field equations in terms of the Riemann curvature tensor. The resulted relativistic field equations are also integrated into the general framework that we have presented in our previous works that all known classical fields can be expressed in the same dynamical form. We also discuss a possibility to reformulate the field equations of general relativity so that the Ricci curvature tensor and the energy-momentum tensor can appear symmetrically in the field equations without violating the conservation law stated by the covariant derivative.
文摘In this work, we introduce the new concept of fourth rank energy-momentum tensor. We first show that a fourth rank electromagnetic energy-momentum tensor can be constructed from the second rank electromagnetic energy-momentum tensor. We then generalise to construct a fourth rank stress energy-momentum tensor and apply it to Dirac field of quantum particles. Furthermore, since the established fourth rank energy-momentum tensors have mathematical properties of the Riemann curvature tensor, thus it is reasonable to suggest that quantum fields should also possess geometric structures of a Riemannian manifold.
文摘<p align="justify"> <span style="font-family:Verdana;"><span style="font-family:Verdana;font-size:12px;">In this work, we extend our work on the Heisenberg model of the neutron formulated as a dwarf hydrogen-like atom under the influence of the More General Exponential Screened Coulomb Potential (MGESCP) to show that an atomic nucleus may possess a molecular structure made up of atoms bonding together by a potential used to describe the strong force associated with a generalised Yukawa MGESCP potential. We show that the neutrons and protons are arranged into narrow lattices therefore they may fold to form three-dimensional shells by bonding similar to hydrogen bonding. In particular, the nucleons may form stable structures such as that of fullerenes in which the vertices are occupied by the nucleons which are simply just protons. For example, a nucleus with a total number of 60 nucleons may arrange itself into the topological structure of a buckminsterfullerene. We also apply </span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;font-size:12px;">Schr</span></span><span style="font-family:;"><span style="font-family:;font-size:12px;"></span><span style="text-align:left;widows:2;text-transform:none;background-color:#ffffff;font-style:normal;text-indent:0px;display:inline !important;font-family:Verdana;white-space:normal;orphans:2;float:none;letter-spacing:normal;font-size:12px;font-weight:400;word-spacing:0px;font-variant-ligatures:normal;font-variant-caps:normal;-webkit-text-stroke-width:0px;text-decoration-style:initial;text-decoration-color:initial;">ö</span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;font-size:12px;">dinger</span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;font-size:12px;"> wave equation with central field approximation to describe the quantum dynamics of nuclei of atomic atoms that now possess the physical structure of a dwarf molecular ion.</span></span> </p>
文摘We propose a reformulation of Newton’s second law of motion for charged particles and possible applications of the reformulation to quantum dynamics. We show that the negative energy states arising from the Dirac equation in relativistic quantum mechanics can be verified using the reformulating framework. We also discuss possible hidden dynamics underlying the concept of quantum jumps in quantum mechanics as outlined in Schr<span style="font-size:12px;white-space:nowrap;">ö</span>dinger’s article: ARE THERE QUANTUM JUMPS? In this case, we show that the hidden dynamics of quantum jumps are also determined by the Coulomb interaction between charged particles.
