We derive the addition of velocities in special relativity from the Minkowski’s space-time diagram. We only need to draw some world lines on the diagram, measure the lengths and divide the two lengths for obtaining t...We derive the addition of velocities in special relativity from the Minkowski’s space-time diagram. We only need to draw some world lines on the diagram, measure the lengths and divide the two lengths for obtaining the velocity. We also give the theoretical background for this method. This method is so simple that it is worth for undergraduate students to acquire the addition of velocities in special relativity.展开更多
Is it possible to demonstrate the velocity addition without using a variable time (as it is done in theory of relativity)? The topic of this paper is to propose and demonstrate an alternative expres-sion based on the ...Is it possible to demonstrate the velocity addition without using a variable time (as it is done in theory of relativity)? The topic of this paper is to propose and demonstrate an alternative expres-sion based on the conservation of linear momenta. The method proposed here is to start from a physical object (and not from a mathematical point), i.e. from an object with a mass. And the hy-pothesis is inertial mass to be different from gravitational mass. Then, when impulses are added, we get an expression of the velocity addition itself. When numerical predictions are compared with experimental results, the differences are lower than the measures uncertainty. And these numerical results are much close to those predicts by the theory of relativity, nevertheless with a little difference at high velocities. If this demonstration and this expression were validated, it would allow giving an alternative explanation to some experiments and nature observations as Doppler Effect on light celerity. But first, it would be necessary to get from laboratories more precise experimental results, in order to validate or not this hypothesis of the sum of linear momenta with a Variable Inertial Mass.展开更多
In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyp...In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyperbolic space, which are the analogues of the geometric construction of inversions with respect to a circle on the complex plane. These results are then applied to Lorentz transformation and Einstein velocity addition to obtain geometric illustrations. We gain new insights into the relationship between special relativity and hyperbolic geometry.展开更多
In this study, the effects of pre-carburization of catalyst, hydrogen addition to methane feed and the space velocity of methane on the catalytic performance in methane to benzene （MTB） reaction were discussed in de...In this study, the effects of pre-carburization of catalyst, hydrogen addition to methane feed and the space velocity of methane on the catalytic performance in methane to benzene （MTB） reaction were discussed in detail over Mo/HZSM-5 catalyst at 1023 K and 0.3 MPa. Compared with the non-precarburized catalyst, the Mo catalyst pre-carburized under the flow of CHa＋4H2 at 973 K was found to have the higher activity and better stability. Further 6% H2 addition to the methane feed suppressed the aromatic type of coke formation effectively, and improved the stability of catalyst markedly, moreover gave a much longer reaction life of catalyst （53 h at 1023 K and 5400 ml/（g-h）） and much more formation amounts of benzene and hydrogen. With increase of methane space velocity, both the naphthalene formation selectivity and the coke formation selectivity were decreased by the shortened contact time; the benzene formation selectivity and total formation amount before the complete deactivation of catalyst were increased markedly, while the total naphthalene and coke formation amounts did not change much. At high methane space velocity （≥5400 ml/（g·h））, a new middle temperature coke derived from the high temperature aromatic coke was formed on the catalyst; all the coke formed could be burnt off at lower temperature in oxygen, compared with those obtained at low space velocity. Considering the benzene formation amount and catalyst stability together, 5400 ml/（g·h） was proved to be the most efficient methane space velocity for benzene production.展开更多
This article is devoted to the key concept of modern electrodynamics—the invariance of the speed of light. The general principle of relativity is considered in detail. Some critical remarks to the relativistic invari...This article is devoted to the key concept of modern electrodynamics—the invariance of the speed of light. The general principle of relativity is considered in detail. Some critical remarks to the relativistic invariance and to the Lorentz transformations are presented. The general invariance of Maxwell equations is discussed. Different theoretical expectations for possible results of Michelson-Morley experiment and some physical consequences are considered. Some critical remarks to the notion of the light speed and its constancy are given. The relativistic law for velocity addition, including strangeness of a noncollinear addition and a superluminal motion, is discussed. Critical analysis of two works which proof the need for existence of an invariant velocity is consequentially made.展开更多
文摘We derive the addition of velocities in special relativity from the Minkowski’s space-time diagram. We only need to draw some world lines on the diagram, measure the lengths and divide the two lengths for obtaining the velocity. We also give the theoretical background for this method. This method is so simple that it is worth for undergraduate students to acquire the addition of velocities in special relativity.
文摘Is it possible to demonstrate the velocity addition without using a variable time (as it is done in theory of relativity)? The topic of this paper is to propose and demonstrate an alternative expres-sion based on the conservation of linear momenta. The method proposed here is to start from a physical object (and not from a mathematical point), i.e. from an object with a mass. And the hy-pothesis is inertial mass to be different from gravitational mass. Then, when impulses are added, we get an expression of the velocity addition itself. When numerical predictions are compared with experimental results, the differences are lower than the measures uncertainty. And these numerical results are much close to those predicts by the theory of relativity, nevertheless with a little difference at high velocities. If this demonstration and this expression were validated, it would allow giving an alternative explanation to some experiments and nature observations as Doppler Effect on light celerity. But first, it would be necessary to get from laboratories more precise experimental results, in order to validate or not this hypothesis of the sum of linear momenta with a Variable Inertial Mass.
文摘In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyperbolic space, which are the analogues of the geometric construction of inversions with respect to a circle on the complex plane. These results are then applied to Lorentz transformation and Einstein velocity addition to obtain geometric illustrations. We gain new insights into the relationship between special relativity and hyperbolic geometry.
文摘In this study, the effects of pre-carburization of catalyst, hydrogen addition to methane feed and the space velocity of methane on the catalytic performance in methane to benzene （MTB） reaction were discussed in detail over Mo/HZSM-5 catalyst at 1023 K and 0.3 MPa. Compared with the non-precarburized catalyst, the Mo catalyst pre-carburized under the flow of CHa＋4H2 at 973 K was found to have the higher activity and better stability. Further 6% H2 addition to the methane feed suppressed the aromatic type of coke formation effectively, and improved the stability of catalyst markedly, moreover gave a much longer reaction life of catalyst （53 h at 1023 K and 5400 ml/（g-h）） and much more formation amounts of benzene and hydrogen. With increase of methane space velocity, both the naphthalene formation selectivity and the coke formation selectivity were decreased by the shortened contact time; the benzene formation selectivity and total formation amount before the complete deactivation of catalyst were increased markedly, while the total naphthalene and coke formation amounts did not change much. At high methane space velocity （≥5400 ml/（g·h））, a new middle temperature coke derived from the high temperature aromatic coke was formed on the catalyst; all the coke formed could be burnt off at lower temperature in oxygen, compared with those obtained at low space velocity. Considering the benzene formation amount and catalyst stability together, 5400 ml/（g·h） was proved to be the most efficient methane space velocity for benzene production.
文摘This article is devoted to the key concept of modern electrodynamics—the invariance of the speed of light. The general principle of relativity is considered in detail. Some critical remarks to the relativistic invariance and to the Lorentz transformations are presented. The general invariance of Maxwell equations is discussed. Different theoretical expectations for possible results of Michelson-Morley experiment and some physical consequences are considered. Some critical remarks to the notion of the light speed and its constancy are given. The relativistic law for velocity addition, including strangeness of a noncollinear addition and a superluminal motion, is discussed. Critical analysis of two works which proof the need for existence of an invariant velocity is consequentially made.
