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Papers by Gary Feldman
This is a straightforward derivation that adjusts the Lorentz factor of Special Relativity to inc... more This is a straightforward derivation that adjusts the Lorentz factor of Special Relativity to include uniform acceleration of an object that moves along its geodesic trajectory. The transformed factor is the same as one of the two factors generated by the Augmented Conjugate Frame Method Of Relativity. Please see the article titled The Relativity Equations Of Uniformly Accelerating Frames Of Reference for more information.
International Journal of Physics, 2018
Researchers typically use four dimensional vectors in Minkowski space-time to derive Albert Einst... more Researchers typically use four dimensional vectors in Minkowski space-time to derive Albert Einstein's Special Theory of Relativity equations. In this work, I have created an original method that uses only scalar quantities in the derivation of relativity equations. The Conjugate Frame Method reproduces the time, mass, and length equations of Special Relativity. Equations for the relativistic electric charge and relativistic temperature are also derived using this method. Unlike the equations of Special Relativity, the Conjugate Frame Method Relativity equations are applicable to both inertial and non-inertial reference frames. The creation of the Conjugate Frame Method was motivated by work done in real quaternion relativity [1,2].
International Journal of Physics
The work presented here is an extension of the work done in the article titled "The Conjugate Fra... more The work presented here is an extension of the work done in the article titled "The Conjugate Frame Method Relativity" [1]. In that work, we considered a moving reference frame that traveled at a constant speed v in a flat or curved space-time manifold. The moving reference frame traveled along a geodesic trajectory in a direction that was either directly towards or directly away from the stationary reference frame. The scalar acceleration a of the moving reference frame was equal to zero. In this work, we consider a moving reference frame that travels with a uniformly changing speed v in a flat or curved space-time manifold. The moving reference frame travels along a geodesic trajectory in a direction that is either directly towards or directly away from the stationary reference frame. The scalar acceleration a of the moving reference frame is a constant that is greater than or equal to zero. The Augmented Conjugate Frame Method is utilized in this work to derive the relativity equations of uniformly accelerating reference frames. These equations can apply to objects that are uniformly accelerated by gravitational, electric, or magnetic fields; as well as by other means, such as rocket propulsion. The relativity equations derived in this work reduce to the equations of Special Relativity when the moving reference frame has a zero scalar acceleration. The Augmented Conjugate Frame Method uses only scalar quantities in the derivation of the relativity equations of uniformly accelerating frames of reference.
In this research work, the neutron Boltzmann equation was separated into two coupled integro-diff... more In this research work, the neutron Boltzmann equation was separated into two coupled integro-differential equations describing forward and backward neutron fluence in selected materials. Linear B-splines were used to change the integro-differential equations into a coupled system of ordinary differential equations (O.D.E.'s). Difference approximations were then used to recast the O.D.E.'s into a coupled system of linear equations that were solved for forward and backward neutron fluences. Adding forward and backward fluences gave the total fluence at selected energies and depths in the material. Neutron fluences were computed in single material shields and in a shield followed by a target configuration. Comparison was made to Monte Carlo modeling of the Boltzmann equation for the same material configuration. Slabs of aluminum, copper, and Martian regolith served as single material shields. The Forward-backward model fluences are accurate for energies above 4 MeV at all depths in these media. There is less accuracy for energies below 4 MeV, but the forward-backward model results are more accurate than past calculations and provide approximately an order of magnitude improvement. An aluminum shield followed by a water target configuration was also investigated using the forward-backward model. The resulting fluence is accurate in the aluminum shield, but less accurate in the water target. It is suspected that this is largely due to inaccuracies in the material cross sections that were used in the modeling.
International Journal Of Physics, 2018
The work presented here is an extension of the work done in the article titled "The Conj... more The work presented here is an extension of the work done in the article titled "The Conjugate Frame Method Relativity" [1]. In that work, we considered a moving reference frame that traveled at a constant speed v in a flat or curved space-time manifold. The moving reference frame traveled along a geodesic trajectory in a direction that was either directly towards or directly away from the stationary reference frame. The scalar acceleration a of the moving reference frame was equal to zero. In this work, we consider a moving reference frame that travels with a uniformly changing speed v in a flat or curved space-time manifold. The moving reference frame travels along a geodesic trajectory in a direction that is either directly towards or directly away from the stationary reference frame. The scalar acceleration a of the moving reference frame is a constant that is greater than or equal to zero. The Augmented Conjugate Frame Method is utilized in this work to derive the relativity equations of uniformly accelerating reference frames. These equations can apply to objects that are uniformly accelerated by gravitational, electric, or magnetic fields; as well as by other means, such as rocket propulsion. The relativity equations derived in this work reduce to the equations of Special Relativity when the moving reference frame has a zero scalar acceleration. The Augmented Conjugate Frame Method uses only scalar quantities in the derivation of the relativity equations of uniformly accelerating frames of reference.
International Journal of Physics, 2018
Researchers typically use four dimensional vectors in Minkowski space-time to derive Albert Einst... more Researchers typically use four dimensional vectors in Minkowski space-time to derive Albert Einstein's Special Theory of Relativity equations. In this work, I have created an original method that uses only scalar quantities in the derivation of relativity equations. The Conjugate Frame Method reproduces the time, mass, and length equations of Special Relativity. Equations for the relativistic electric charge and relativistic temperature are also derived using this method. Unlike the equations of Special Relativity, the Conjugate Frame Method Relativity equations are applicable to both inertial and non-inertial reference frames. The creation of the Conjugate Frame Method was motivated by work done in real quaternion relativity [1,2].
Teaching Documents by Gary Feldman
This is a straight forward derivation to transform the Lorentz Factor into one of the factors of... more This is a straight forward derivation to transform the Lorentz Factor into one of the factors of the Augmented Conjugate Frame Method of Relativity. Here SRT is an acronym for Special Relativity Theory, and ACFMR is an acronym for Augmented Conjugate Frame Method of Relativity. In the derivation, the uniform scalar acceleration is tangential to the moving object's motion at any given time. Please see the manuscript titled "The Relativity Equations Of Uniformly Accelerating Frames Of Reference" for more information.
This is a straightforward derivation that adjusts the Lorentz factor of Special Relativity to inc... more This is a straightforward derivation that adjusts the Lorentz factor of Special Relativity to include uniform acceleration of an object that moves along its geodesic trajectory. The transformed factor is the same as one of the two factors generated by the Augmented Conjugate Frame Method Of Relativity. Please see the article titled The Relativity Equations Of Uniformly Accelerating Frames Of Reference for more information.
International Journal of Physics, 2018
Researchers typically use four dimensional vectors in Minkowski space-time to derive Albert Einst... more Researchers typically use four dimensional vectors in Minkowski space-time to derive Albert Einstein's Special Theory of Relativity equations. In this work, I have created an original method that uses only scalar quantities in the derivation of relativity equations. The Conjugate Frame Method reproduces the time, mass, and length equations of Special Relativity. Equations for the relativistic electric charge and relativistic temperature are also derived using this method. Unlike the equations of Special Relativity, the Conjugate Frame Method Relativity equations are applicable to both inertial and non-inertial reference frames. The creation of the Conjugate Frame Method was motivated by work done in real quaternion relativity [1,2].
International Journal of Physics
The work presented here is an extension of the work done in the article titled "The Conjugate Fra... more The work presented here is an extension of the work done in the article titled "The Conjugate Frame Method Relativity" [1]. In that work, we considered a moving reference frame that traveled at a constant speed v in a flat or curved space-time manifold. The moving reference frame traveled along a geodesic trajectory in a direction that was either directly towards or directly away from the stationary reference frame. The scalar acceleration a of the moving reference frame was equal to zero. In this work, we consider a moving reference frame that travels with a uniformly changing speed v in a flat or curved space-time manifold. The moving reference frame travels along a geodesic trajectory in a direction that is either directly towards or directly away from the stationary reference frame. The scalar acceleration a of the moving reference frame is a constant that is greater than or equal to zero. The Augmented Conjugate Frame Method is utilized in this work to derive the relativity equations of uniformly accelerating reference frames. These equations can apply to objects that are uniformly accelerated by gravitational, electric, or magnetic fields; as well as by other means, such as rocket propulsion. The relativity equations derived in this work reduce to the equations of Special Relativity when the moving reference frame has a zero scalar acceleration. The Augmented Conjugate Frame Method uses only scalar quantities in the derivation of the relativity equations of uniformly accelerating frames of reference.
In this research work, the neutron Boltzmann equation was separated into two coupled integro-diff... more In this research work, the neutron Boltzmann equation was separated into two coupled integro-differential equations describing forward and backward neutron fluence in selected materials. Linear B-splines were used to change the integro-differential equations into a coupled system of ordinary differential equations (O.D.E.'s). Difference approximations were then used to recast the O.D.E.'s into a coupled system of linear equations that were solved for forward and backward neutron fluences. Adding forward and backward fluences gave the total fluence at selected energies and depths in the material. Neutron fluences were computed in single material shields and in a shield followed by a target configuration. Comparison was made to Monte Carlo modeling of the Boltzmann equation for the same material configuration. Slabs of aluminum, copper, and Martian regolith served as single material shields. The Forward-backward model fluences are accurate for energies above 4 MeV at all depths in these media. There is less accuracy for energies below 4 MeV, but the forward-backward model results are more accurate than past calculations and provide approximately an order of magnitude improvement. An aluminum shield followed by a water target configuration was also investigated using the forward-backward model. The resulting fluence is accurate in the aluminum shield, but less accurate in the water target. It is suspected that this is largely due to inaccuracies in the material cross sections that were used in the modeling.
International Journal Of Physics, 2018
The work presented here is an extension of the work done in the article titled "The Conj... more The work presented here is an extension of the work done in the article titled "The Conjugate Frame Method Relativity" [1]. In that work, we considered a moving reference frame that traveled at a constant speed v in a flat or curved space-time manifold. The moving reference frame traveled along a geodesic trajectory in a direction that was either directly towards or directly away from the stationary reference frame. The scalar acceleration a of the moving reference frame was equal to zero. In this work, we consider a moving reference frame that travels with a uniformly changing speed v in a flat or curved space-time manifold. The moving reference frame travels along a geodesic trajectory in a direction that is either directly towards or directly away from the stationary reference frame. The scalar acceleration a of the moving reference frame is a constant that is greater than or equal to zero. The Augmented Conjugate Frame Method is utilized in this work to derive the relativity equations of uniformly accelerating reference frames. These equations can apply to objects that are uniformly accelerated by gravitational, electric, or magnetic fields; as well as by other means, such as rocket propulsion. The relativity equations derived in this work reduce to the equations of Special Relativity when the moving reference frame has a zero scalar acceleration. The Augmented Conjugate Frame Method uses only scalar quantities in the derivation of the relativity equations of uniformly accelerating frames of reference.
International Journal of Physics, 2018
Researchers typically use four dimensional vectors in Minkowski space-time to derive Albert Einst... more Researchers typically use four dimensional vectors in Minkowski space-time to derive Albert Einstein's Special Theory of Relativity equations. In this work, I have created an original method that uses only scalar quantities in the derivation of relativity equations. The Conjugate Frame Method reproduces the time, mass, and length equations of Special Relativity. Equations for the relativistic electric charge and relativistic temperature are also derived using this method. Unlike the equations of Special Relativity, the Conjugate Frame Method Relativity equations are applicable to both inertial and non-inertial reference frames. The creation of the Conjugate Frame Method was motivated by work done in real quaternion relativity [1,2].
This is a straight forward derivation to transform the Lorentz Factor into one of the factors of... more This is a straight forward derivation to transform the Lorentz Factor into one of the factors of the Augmented Conjugate Frame Method of Relativity. Here SRT is an acronym for Special Relativity Theory, and ACFMR is an acronym for Augmented Conjugate Frame Method of Relativity. In the derivation, the uniform scalar acceleration is tangential to the moving object's motion at any given time. Please see the manuscript titled "The Relativity Equations Of Uniformly Accelerating Frames Of Reference" for more information.