We present a tensor description of Euclidean spaces that emphasizes the use of geometric vectors which leads to greater geometric insight and a higher degree of organization in analytical expressions. We demonstrate t...We present a tensor description of Euclidean spaces that emphasizes the use of geometric vectors which leads to greater geometric insight and a higher degree of organization in analytical expressions. We demonstrate the effectiveness of the approach by proving a number of integral identities with vector integrands. The presented approach may be aptly described as absolute vector calculus or as vector tensor calculus.展开更多
Utilizing stress-energy tensors which allow for a divergence-free formulation, we establish Pohozaev＇s identity for certain classes of quasilinear systems with variational structure.
I show how many connections of Γ?are presently existing from R?to β?as they are being inputted simultaneously through tensor products. I plan to address the Quantum state of this tensor connection st...I show how many connections of Γ?are presently existing from R?to β?as they are being inputted simultaneously through tensor products. I plan to address the Quantum state of this tensor connection step by step throughout the application presented. Also, I will show you how to prove that the connection is true for this tensor connection through its output method using a small bit of tensor calculus and mostly number theory.展开更多
In relativistic mechanics the time-like vector characterize the motion in spacetime with speed faster than the speed of light in vacuum c in which the line element ds2=c2dt2-dx2-dx2-dz2 is less than zero (where is inf...In relativistic mechanics the time-like vector characterize the motion in spacetime with speed faster than the speed of light in vacuum c in which the line element ds2=c2dt2-dx2-dx2-dz2 is less than zero (where is infinitesimal change in time, and are infinitesimal change in space), thus the time in relativistic mechanics can instantaneously flow [1], however in quantum mechanics although the time is treated as unobservable parameter (without any Hermitian observable operator have engine-value equivalent to time) any two physical quantity described by two non-commuting observable operatorsand fulfill , the knowledge of one immediately produce the knowledge of the other [2], thus in quantum mechanics if two particles interacted in finite temporal epoch and then separated in space the gaining of knowledge by the local measurement of physical quantity runs on one them (for example the measurement of spin direction of one particle using Stern-Gerlach experiment) immediately produce the knowledge of the complementary physical quantity of the other particle (for example the opposite spin direction of the other particle), this simply called quantum entanglement the concept that so much advanced after publication of the Jon Bell’s 1964 celebrated paper [3] in which he illustrated that we can add parameters to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, and then he conclude “there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously so that such a theory could not be Lorentz invariant”. The question now what these signals that can propagate instantaneously? The answer in this paper will be the time signals field which is defined for each constituent matter particle M and at each space point P as the measure of the total length of all occupation and leaving epochs of P by M which is representing a sequence function compactly supported only at the space point occupied by it and indexed by the number of occupation epochs of P by M, thus the flow of this time signal field from the far future to near future through the present to the near past to the far past inferable by the flow of matter particles constituting the system(such as sun, moon earth and clocks hands). Thus the present will represent in this paper a local absolute feature of time signals field defined at each space point as the set of all occupation epochs of it by matter particle, however the past and future will represent relativistic non-local features of the time signal field defined at each space point as a set of all leaving epochs between each two sequential occupation epochs, so the future after one occupation epoch is representing a past of the next one. Thus according to current representation of time, the two Mc-Taggard’s A and B series of time [4] will exist together as temporal set and then the time is real, the A-series in current theory is a set of all occupation and leaving epochs of space point by the matter particle that is consisting of the present, past and future epochs, and the B-series is the set of all leaving epochs of space points between each two sequential occupation epochs which are taking position before or after the discrete occupation epochs between them and then before or after each other.展开更多
The cosmological constant, Λ, represents dark energy. The dark energy hypothesis (DEH) replaces Λ with a variable quantity, the cosmological parameter: Λ=1a2η2In this formula, “a” is the scale factor and η the ...The cosmological constant, Λ, represents dark energy. The dark energy hypothesis (DEH) replaces Λ with a variable quantity, the cosmological parameter: Λ=1a2η2In this formula, “a” is the scale factor and η the conformal time: adη = cdt. A companion paper (DEH II) develops and explores a cosmological model with this variable parameter. This paper portrays the origin of the cosmological parameter in the uncoupling of time and space in the early universe from a prior state in which the comoving coordinates x0 = η and x1 = χ, the cosmic latitude, are coupled. In this hypothesis dark matter is a co-product of the decoupling, but its nature remains mysterious.展开更多
文摘We present a tensor description of Euclidean spaces that emphasizes the use of geometric vectors which leads to greater geometric insight and a higher degree of organization in analytical expressions. We demonstrate the effectiveness of the approach by proving a number of integral identities with vector integrands. The presented approach may be aptly described as absolute vector calculus or as vector tensor calculus.
文摘Utilizing stress-energy tensors which allow for a divergence-free formulation, we establish Pohozaev＇s identity for certain classes of quasilinear systems with variational structure.
文摘I show how many connections of Γ?are presently existing from R?to β?as they are being inputted simultaneously through tensor products. I plan to address the Quantum state of this tensor connection step by step throughout the application presented. Also, I will show you how to prove that the connection is true for this tensor connection through its output method using a small bit of tensor calculus and mostly number theory.
文摘In relativistic mechanics the time-like vector characterize the motion in spacetime with speed faster than the speed of light in vacuum c in which the line element ds2=c2dt2-dx2-dx2-dz2 is less than zero (where is infinitesimal change in time, and are infinitesimal change in space), thus the time in relativistic mechanics can instantaneously flow [1], however in quantum mechanics although the time is treated as unobservable parameter (without any Hermitian observable operator have engine-value equivalent to time) any two physical quantity described by two non-commuting observable operatorsand fulfill , the knowledge of one immediately produce the knowledge of the other [2], thus in quantum mechanics if two particles interacted in finite temporal epoch and then separated in space the gaining of knowledge by the local measurement of physical quantity runs on one them (for example the measurement of spin direction of one particle using Stern-Gerlach experiment) immediately produce the knowledge of the complementary physical quantity of the other particle (for example the opposite spin direction of the other particle), this simply called quantum entanglement the concept that so much advanced after publication of the Jon Bell’s 1964 celebrated paper [3] in which he illustrated that we can add parameters to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, and then he conclude “there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously so that such a theory could not be Lorentz invariant”. The question now what these signals that can propagate instantaneously? The answer in this paper will be the time signals field which is defined for each constituent matter particle M and at each space point P as the measure of the total length of all occupation and leaving epochs of P by M which is representing a sequence function compactly supported only at the space point occupied by it and indexed by the number of occupation epochs of P by M, thus the flow of this time signal field from the far future to near future through the present to the near past to the far past inferable by the flow of matter particles constituting the system(such as sun, moon earth and clocks hands). Thus the present will represent in this paper a local absolute feature of time signals field defined at each space point as the set of all occupation epochs of it by matter particle, however the past and future will represent relativistic non-local features of the time signal field defined at each space point as a set of all leaving epochs between each two sequential occupation epochs, so the future after one occupation epoch is representing a past of the next one. Thus according to current representation of time, the two Mc-Taggard’s A and B series of time [4] will exist together as temporal set and then the time is real, the A-series in current theory is a set of all occupation and leaving epochs of space point by the matter particle that is consisting of the present, past and future epochs, and the B-series is the set of all leaving epochs of space points between each two sequential occupation epochs which are taking position before or after the discrete occupation epochs between them and then before or after each other.
文摘The cosmological constant, Λ, represents dark energy. The dark energy hypothesis (DEH) replaces Λ with a variable quantity, the cosmological parameter: Λ=1a2η2In this formula, “a” is the scale factor and η the conformal time: adη = cdt. A companion paper (DEH II) develops and explores a cosmological model with this variable parameter. This paper portrays the origin of the cosmological parameter in the uncoupling of time and space in the early universe from a prior state in which the comoving coordinates x0 = η and x1 = χ, the cosmic latitude, are coupled. In this hypothesis dark matter is a co-product of the decoupling, but its nature remains mysterious.
