The influence of the relativistic motion of the reference frame on the light reflection law is in... more The influence of the relativistic motion of the reference frame on the light reflection law is investigated. The method is based on applying the relativistic aberration affect for three light signals: incident, normal and reflected rays. The form of the reflection law in the moving reference frame is substantially modified and includes an additional parameter which is the velocity vector of the reference frame. It is shown that the reflected ray, as measured by a moving observer, would not in general be in the same plane as the incident and normal rays. A general method to transform the form of any rigid surface in 3-dimensional space with respect to the arbitrary directed relative motion of the reference frame is detailed. This method is based on the light signals processes and the invariance of the light velocity under Lorentz transformations. It is shown that a moving observer will measure a plane surface as a hyperboloid. That observer will also measure a spherical surface as an ellipsoid. A right line in the plane is seen by a moving observer as a hyperbola. The whole analysis is extended to the case of a uniform media.
The known possibility to consider the (vacuum) Maxwell equations in a curved space-time as Maxwel... more The known possibility to consider the (vacuum) Maxwell equations in a curved space-time as Maxwell equations in flat space-time(Mandel'stam L.I., Tamm I.E.) taken in an effective media the properties of which are determined by metrical structure of the curved model is studied. Metrical structure of the curved space-time generates effective constitutive equations for electromagnetic fields, the form of four corresponding symmetrical tensors is found explicitly for general case of an arbitrary Riemannian space - time. Four constitutive tensors are not independent and obey some additional constraints between them. Several simple examples are specified in detail:itis given geometrical modeling of the anisotropic media (magnetic crystals) and the geometrical modeling of a uniform media in moving reference frame in the Minkowsky electrodynamics -- the latter is realized trough the use of a non-diagonal metrical tensor determined by 4-vector velocity of the moving uniform media. Also t...
The influence of the relativistic motion of the reference frame on the light reflection law is in... more The influence of the relativistic motion of the reference frame on the light reflection law is investigated. The method is based on applying the relativistic aberration affect for three light signals: incident, normal and reflected rays. The form of the reflection law in the moving reference frame is substantially modified and includes an additional parameter which is the velocity vector of the reference frame. It is shown that the reflected ray, as measured by a moving observer, would not in general be in the same plane as the incident and normal rays. A general method to transform the form of any rigid surface in 3-dimensional space with respect to the arbitrary directed relative motion of the reference frame is detailed. This method is based on the light signals processes and the invariance of the light velocity under Lorentz transformations. It is shown that a moving observer will measure a plane surface as a hyperboloid. That observer will also measure a spherical surface as an...
We present a relativistic space-time diagram that displays in true magnitudes the readings (dayti... more We present a relativistic space-time diagram that displays in true magnitudes the readings (daytimes) of two inertial reference frames clocks. One reference frame is the rest frame for one clock. This diagram shows that two events simultaneous in one reference frames are not compulsory simultaneous in the other frame. This approach has a bi-dimensional character.
We compare the results obtained by interpreting some fundamental relativistic experiments from th... more We compare the results obtained by interpreting some fundamental relativistic experiments from the point of view of two alternative theories: Einstein's special relativity theory and the Lorentz-Poincare theory admitting the existence of a special reference frame relative to which we can measure absolute velocities. The experiments that we consider here are the time dilation, the radar echo, the Doppler Effect and the radar detection. The most important result is that both theories lead to the Lorentz-Einstein transformations for the space-time coordinates of the same event. This conclusion enables us to assert that the anisotropy in the light propagation fades away in the case of these particular experiments.
We present an introduction to special relativity kinematics stressing the part played by clocks s... more We present an introduction to special relativity kinematics stressing the part played by clocks synchronized following a procedure proposed by Einstein.
We present a space-time diagram that displays in true values the space-time coordinates of events... more We present a space-time diagram that displays in true values the space-time coordinates of events associated with the apparent and actual positions of a point like source moving with constant velocity. We use it in order to construct the actual shape of a moving luminous profile or to determine the relationship between apparent and actual distances. We show that the simple fact that light propagates at finite speed has important consequences like "length contraction" or "length dilation" the effects being sensitive against the "approaching" and the "receding" character of the source relative to an observer located at the origin of the inertial reference frame.
We consider the sticky collision between two sphere of equal rest mass, moving with equal but opp... more We consider the sticky collision between two sphere of equal rest mass, moving with equal but opposite speeds in a horizontal plane. The collision takes place on the pan of a high sensitivity balance. The conditions of mechanical and thermal equilibrium are studied showing that heat developed in the rest frame of the system has a corresponding inertial mass.
Starting with a thought experiment proposed by Kard 10 , which derives the formula that accounts ... more Starting with a thought experiment proposed by Kard 10 , which derives the formula that accounts for the relativistic effect of length contraction, we present a "two line" transparent derivation of the Lorentz-Einstein transformations for the space-time coordinates of the same event. Our derivation make uses of Einstein's clock synchronization procedure.
Considering a system of non-interacting particles characterized by the number N of its constituen... more Considering a system of non-interacting particles characterized by the number N of its constituents and by its Kelvin temperature T, we reduce the transformation of the Kelvin temperature to the transformation mass.
Considering that the rays in the Michelson-Morley interferometer perform the radar detection of i... more Considering that the rays in the Michelson-Morley interferometer perform the radar detection of its mirrors, we use a relativistic diagram that displays, at a convenient scale, their location and the path of the rays. This approach convinces us that the rays that come from the two arms interfere with zero phase difference without using the usual ingredient, length contraction.
The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in ... more The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in presence of electrical sources and arbitrary media is investigated within the matrix formalism. The symmetry of the matrix Maxwell equation under transformations of the complex rotation group SO(3.C) is demonstrated explicitly. In vacuum case, the matrix form includes four real $4 \times 4$ matrices $\alpha^{b}$. In
After having shown that the corresponding components of a four vector transform via the same tran... more After having shown that the corresponding components of a four vector transform via the same transformation factors as the space-time coordinates of the same event do, we design a relativistic diagram that displays in true values theirs components. One diagram works for events generated by tardyons whereas a second diagram works for events generated by light signals or photons. We consider both approaching and receding tardyons respectively photons in each case. We also show how the relativistic diagram for radar and photographic detections of moving profiles.
Journal of Electromagnetic Waves and Applications, 2006
We propose a simple relativistic derivation of the electric and the magnetic fields generated by ... more We propose a simple relativistic derivation of the electric and the magnetic fields generated by an electric point charge moving with constant velocity. Our approach is based on the radar detection of the point space coordinates where the fields are measured. The same equations were previously derived in a relatively complicated way 2 based exclusively on general electromagnetic field equations and without making use of retarded potentials or relativistic equations.
The Riemann-Silberstein-Majorana-Oppenheimer approach to the Maxwell electrodynamics in presence ... more The Riemann-Silberstein-Majorana-Oppenheimer approach to the Maxwell electrodynamics in presence of electrical sources and arbitrary media is investigated within the matrix formalism. The symmetry of the matrix Maxwell equation under transformations of the complex rotation SO(3,C) group is demonstrated explicitly. For vacuum, the matrix form includes four real 4 × 4 matrices α b. In the presence of a medium the matrix form requires two sets of 4 × 4 matrices, α b and β b , simple and symmetrical realization of which is given. Minkowski constitutive relations in the case of arbitrary linear media are given in a short algebraic form based on the use of complex 3-vector fields. The matrix formulation in the Esposito's form based on the use of two electromagnetic 4-vector is studied and discussed.
On the different forms of the Maxwell's electromagnetic equations in a uniform media Two know... more On the different forms of the Maxwell's electromagnetic equations in a uniform media Two known, alternative to each other, forms of the Maxwell's electromagnetic equations in a moving uniform media are investigated and discussed. Approach commonly used after Minkowski is based on the two tensors: H ab = (D, H/c) and F ab = (E, cB) which transform independently of each other at Lorentz transitions; relationships between fields D = ǫ 0 ǫE, B = µ 0 µH change their form at Lorentz transformations and have the form of the Minkowski equations depending on the 4-velocity u a of the moving media under an inertial reference frame. In this approach, the wave equation for electromagnetic potential involve explicitly the u a-velocity of the moving media. So, the electrodynamics by Minkowski implies the absolute nature of the mechanical motion. An alternative formalism (Rosen and others) may be developed in the new variables: c = 1/ In these variables, the Maxwell's equations can be ...
Two known, alternative to each other, forms of the Maxwell's electromagnetic equations in a m... more Two known, alternative to each other, forms of the Maxwell's electromagnetic equations in a moving uniform media are investigated and discussed. Approach commonly used after Minkowski is based on the two tensors: H^{ab} = (D, H /c) and F^{ab} = (E, cB) which transform independently of each other at Lorentz transitions; relationships between fields change their form at Lorentz transformations
IEEE Transactions on Industry and General Applications, 1967
Several experimental vehicles have been built by the General Motors Corporation to investigate th... more Several experimental vehicles have been built by the General Motors Corporation to investigate the technical feasibility of a battery-powered electric car using a variable speed induction motor. This paper describes the control scheme for the first experimental car-Electrovair I. It is a standard 1964 Corvair in which the engine was removed and replaced by an electric drive. The battery voltage is transformed by a voltage modulator to a smoothly varying direct voltage applied to an inverter. The inverter converts the input direct voltage to a 3-phase, variable frequency, alternating voltage driving a squirrel cage induction motor. Electrovair I was followed by Electrovair II, where the separate functions of the modulator and inverter were combined in a modulating inverter. The first part of the paper is a general description of the control scheme of Electrovair I and a discussion of the critical control parameters governed by the motor and overall system requirement. The rest describes the various control features; for example, reversing the motor, controlling the power for maximum acceleration, and safety provisions. CONTROL SCHEME DESCRIPTION THE basic components of the control scheme for Electrovair I are a voltage modulator, a filter, an inverter, and a 13000 r/min, 3-phase squirrel cage induction motor, shown in Fig. 1. The voltage modulator (chopper) converts the constant battery voltage applied to the input into a pulsating voltage at the output where the average value is changed smoothly from a minimum to the maximum value. Due to high conversion efficiency and the law of conservation of energy, the modulator behaves essentially like a current transformer, and the relationship between the average input and output voltages and currents may be approximated by the equation E1/E2 = I2/Il. The filter smooths the pulsating modulator output into a direct voltage applied to the inverter. The inverter changes this voltage to a 3-phase, 120-degree rectangular voltage of amplitude equal to the input voltage, but of variable frequency. The frequency of the inverter is controlled automatically so that the squirrel cage induction motor operates at a Manuscript
The influence of the relativistic motion of the reference frame on the light reflection law is in... more The influence of the relativistic motion of the reference frame on the light reflection law is investigated. The method is based on applying the relativistic aberration affect for three light signals: incident, normal and reflected rays. The form of the reflection law in the moving reference frame is substantially modified and includes an additional parameter which is the velocity vector of the reference frame. It is shown that the reflected ray, as measured by a moving observer, would not in general be in the same plane as the incident and normal rays. A general method to transform the form of any rigid surface in 3-dimensional space with respect to the arbitrary directed relative motion of the reference frame is detailed. This method is based on the light signals processes and the invariance of the light velocity under Lorentz transformations. It is shown that a moving observer will measure a plane surface as a hyperboloid. That observer will also measure a spherical surface as an ellipsoid. A right line in the plane is seen by a moving observer as a hyperbola. The whole analysis is extended to the case of a uniform media.
The known possibility to consider the (vacuum) Maxwell equations in a curved space-time as Maxwel... more The known possibility to consider the (vacuum) Maxwell equations in a curved space-time as Maxwell equations in flat space-time(Mandel'stam L.I., Tamm I.E.) taken in an effective media the properties of which are determined by metrical structure of the curved model is studied. Metrical structure of the curved space-time generates effective constitutive equations for electromagnetic fields, the form of four corresponding symmetrical tensors is found explicitly for general case of an arbitrary Riemannian space - time. Four constitutive tensors are not independent and obey some additional constraints between them. Several simple examples are specified in detail:itis given geometrical modeling of the anisotropic media (magnetic crystals) and the geometrical modeling of a uniform media in moving reference frame in the Minkowsky electrodynamics -- the latter is realized trough the use of a non-diagonal metrical tensor determined by 4-vector velocity of the moving uniform media. Also t...
The influence of the relativistic motion of the reference frame on the light reflection law is in... more The influence of the relativistic motion of the reference frame on the light reflection law is investigated. The method is based on applying the relativistic aberration affect for three light signals: incident, normal and reflected rays. The form of the reflection law in the moving reference frame is substantially modified and includes an additional parameter which is the velocity vector of the reference frame. It is shown that the reflected ray, as measured by a moving observer, would not in general be in the same plane as the incident and normal rays. A general method to transform the form of any rigid surface in 3-dimensional space with respect to the arbitrary directed relative motion of the reference frame is detailed. This method is based on the light signals processes and the invariance of the light velocity under Lorentz transformations. It is shown that a moving observer will measure a plane surface as a hyperboloid. That observer will also measure a spherical surface as an...
We present a relativistic space-time diagram that displays in true magnitudes the readings (dayti... more We present a relativistic space-time diagram that displays in true magnitudes the readings (daytimes) of two inertial reference frames clocks. One reference frame is the rest frame for one clock. This diagram shows that two events simultaneous in one reference frames are not compulsory simultaneous in the other frame. This approach has a bi-dimensional character.
We compare the results obtained by interpreting some fundamental relativistic experiments from th... more We compare the results obtained by interpreting some fundamental relativistic experiments from the point of view of two alternative theories: Einstein's special relativity theory and the Lorentz-Poincare theory admitting the existence of a special reference frame relative to which we can measure absolute velocities. The experiments that we consider here are the time dilation, the radar echo, the Doppler Effect and the radar detection. The most important result is that both theories lead to the Lorentz-Einstein transformations for the space-time coordinates of the same event. This conclusion enables us to assert that the anisotropy in the light propagation fades away in the case of these particular experiments.
We present an introduction to special relativity kinematics stressing the part played by clocks s... more We present an introduction to special relativity kinematics stressing the part played by clocks synchronized following a procedure proposed by Einstein.
We present a space-time diagram that displays in true values the space-time coordinates of events... more We present a space-time diagram that displays in true values the space-time coordinates of events associated with the apparent and actual positions of a point like source moving with constant velocity. We use it in order to construct the actual shape of a moving luminous profile or to determine the relationship between apparent and actual distances. We show that the simple fact that light propagates at finite speed has important consequences like "length contraction" or "length dilation" the effects being sensitive against the "approaching" and the "receding" character of the source relative to an observer located at the origin of the inertial reference frame.
We consider the sticky collision between two sphere of equal rest mass, moving with equal but opp... more We consider the sticky collision between two sphere of equal rest mass, moving with equal but opposite speeds in a horizontal plane. The collision takes place on the pan of a high sensitivity balance. The conditions of mechanical and thermal equilibrium are studied showing that heat developed in the rest frame of the system has a corresponding inertial mass.
Starting with a thought experiment proposed by Kard 10 , which derives the formula that accounts ... more Starting with a thought experiment proposed by Kard 10 , which derives the formula that accounts for the relativistic effect of length contraction, we present a "two line" transparent derivation of the Lorentz-Einstein transformations for the space-time coordinates of the same event. Our derivation make uses of Einstein's clock synchronization procedure.
Considering a system of non-interacting particles characterized by the number N of its constituen... more Considering a system of non-interacting particles characterized by the number N of its constituents and by its Kelvin temperature T, we reduce the transformation of the Kelvin temperature to the transformation mass.
Considering that the rays in the Michelson-Morley interferometer perform the radar detection of i... more Considering that the rays in the Michelson-Morley interferometer perform the radar detection of its mirrors, we use a relativistic diagram that displays, at a convenient scale, their location and the path of the rays. This approach convinces us that the rays that come from the two arms interfere with zero phase difference without using the usual ingredient, length contraction.
The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in ... more The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in presence of electrical sources and arbitrary media is investigated within the matrix formalism. The symmetry of the matrix Maxwell equation under transformations of the complex rotation group SO(3.C) is demonstrated explicitly. In vacuum case, the matrix form includes four real $4 \times 4$ matrices $\alpha^{b}$. In
After having shown that the corresponding components of a four vector transform via the same tran... more After having shown that the corresponding components of a four vector transform via the same transformation factors as the space-time coordinates of the same event do, we design a relativistic diagram that displays in true values theirs components. One diagram works for events generated by tardyons whereas a second diagram works for events generated by light signals or photons. We consider both approaching and receding tardyons respectively photons in each case. We also show how the relativistic diagram for radar and photographic detections of moving profiles.
Journal of Electromagnetic Waves and Applications, 2006
We propose a simple relativistic derivation of the electric and the magnetic fields generated by ... more We propose a simple relativistic derivation of the electric and the magnetic fields generated by an electric point charge moving with constant velocity. Our approach is based on the radar detection of the point space coordinates where the fields are measured. The same equations were previously derived in a relatively complicated way 2 based exclusively on general electromagnetic field equations and without making use of retarded potentials or relativistic equations.
The Riemann-Silberstein-Majorana-Oppenheimer approach to the Maxwell electrodynamics in presence ... more The Riemann-Silberstein-Majorana-Oppenheimer approach to the Maxwell electrodynamics in presence of electrical sources and arbitrary media is investigated within the matrix formalism. The symmetry of the matrix Maxwell equation under transformations of the complex rotation SO(3,C) group is demonstrated explicitly. For vacuum, the matrix form includes four real 4 × 4 matrices α b. In the presence of a medium the matrix form requires two sets of 4 × 4 matrices, α b and β b , simple and symmetrical realization of which is given. Minkowski constitutive relations in the case of arbitrary linear media are given in a short algebraic form based on the use of complex 3-vector fields. The matrix formulation in the Esposito's form based on the use of two electromagnetic 4-vector is studied and discussed.
On the different forms of the Maxwell's electromagnetic equations in a uniform media Two know... more On the different forms of the Maxwell's electromagnetic equations in a uniform media Two known, alternative to each other, forms of the Maxwell's electromagnetic equations in a moving uniform media are investigated and discussed. Approach commonly used after Minkowski is based on the two tensors: H ab = (D, H/c) and F ab = (E, cB) which transform independently of each other at Lorentz transitions; relationships between fields D = ǫ 0 ǫE, B = µ 0 µH change their form at Lorentz transformations and have the form of the Minkowski equations depending on the 4-velocity u a of the moving media under an inertial reference frame. In this approach, the wave equation for electromagnetic potential involve explicitly the u a-velocity of the moving media. So, the electrodynamics by Minkowski implies the absolute nature of the mechanical motion. An alternative formalism (Rosen and others) may be developed in the new variables: c = 1/ In these variables, the Maxwell's equations can be ...
Two known, alternative to each other, forms of the Maxwell's electromagnetic equations in a m... more Two known, alternative to each other, forms of the Maxwell's electromagnetic equations in a moving uniform media are investigated and discussed. Approach commonly used after Minkowski is based on the two tensors: H^{ab} = (D, H /c) and F^{ab} = (E, cB) which transform independently of each other at Lorentz transitions; relationships between fields change their form at Lorentz transformations
IEEE Transactions on Industry and General Applications, 1967
Several experimental vehicles have been built by the General Motors Corporation to investigate th... more Several experimental vehicles have been built by the General Motors Corporation to investigate the technical feasibility of a battery-powered electric car using a variable speed induction motor. This paper describes the control scheme for the first experimental car-Electrovair I. It is a standard 1964 Corvair in which the engine was removed and replaced by an electric drive. The battery voltage is transformed by a voltage modulator to a smoothly varying direct voltage applied to an inverter. The inverter converts the input direct voltage to a 3-phase, variable frequency, alternating voltage driving a squirrel cage induction motor. Electrovair I was followed by Electrovair II, where the separate functions of the modulator and inverter were combined in a modulating inverter. The first part of the paper is a general description of the control scheme of Electrovair I and a discussion of the critical control parameters governed by the motor and overall system requirement. The rest describes the various control features; for example, reversing the motor, controlling the power for maximum acceleration, and safety provisions. CONTROL SCHEME DESCRIPTION THE basic components of the control scheme for Electrovair I are a voltage modulator, a filter, an inverter, and a 13000 r/min, 3-phase squirrel cage induction motor, shown in Fig. 1. The voltage modulator (chopper) converts the constant battery voltage applied to the input into a pulsating voltage at the output where the average value is changed smoothly from a minimum to the maximum value. Due to high conversion efficiency and the law of conservation of energy, the modulator behaves essentially like a current transformer, and the relationship between the average input and output voltages and currents may be approximated by the equation E1/E2 = I2/Il. The filter smooths the pulsating modulator output into a direct voltage applied to the inverter. The inverter changes this voltage to a 3-phase, 120-degree rectangular voltage of amplitude equal to the input voltage, but of variable frequency. The frequency of the inverter is controlled automatically so that the squirrel cage induction motor operates at a Manuscript
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Papers by George Spix