George Goedecke | New Mexico State University (original) (raw)
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Papers by George Goedecke
Tectonophysics, 1991
ABSTRACT
Found Phys, 1984
In this fourth paper in a series on stochastic electrodynamics (SED), the harmonic oscillator-zer... more In this fourth paper in a series on stochastic electrodynamics (SED), the harmonic oscillator-zero-point field system in the presence of an arbitrary applied classical radiation field is studied further. The exact closed-form expressions are found for the time-dependent probability that the oscillator is in the nth eigenstate of the unperturbed SED Hamiltonian H 0 , the same H 0 as that of ordinary quantum mechanics. It is shown that an eigenvalue of H 0 is the average energy that the oscillator would have if its wave function could be just the corresponding eigenstate. The level shift for each unperturbed eigenvalue is found and shown to be unobservable for a different reason than in the corresponding QED treatment. Perturbation theory is applied to the SED Schrödinger equation to derive first-order transition rates for spontaneous emission and resonance absorption. The results agree with those of quantum electrodynamics, but the mathematics is strikingly different. It is shown that SED demands discarding the ideas of quantized energies, photons, and completeness of the Schrödinger equation, Finally, an intuitive physical SED model is suggested for the photoeffect and for Clauser's (2) coincidence experiment.
Foundations of Physics, Oct 31, 1983
This is the first in a series of papers that present a new classical statistical treatment of the... more This is the first in a series of papers that present a new classical statistical treatment of the system of a charged harmonic oscillator (HO) immersed in an omnipresent stochastic zero-point (ZP) electromagnetic radiation field. This paper establishes the Gaussian statistical properties of this ZP field using Bourret's postulate that all statistical moments of the stochastic field plane waves at a given space-time point should agree with their corresponding quantized field vacuum expectations. This postulate is more than adequate to derive the Planck spectrum classically via Boyer's and Theimer's methods, but it requires that the stochastic amplitude of each linearly polarized plane wave in the field contain two independent Gaussian random variables, not just a random phase as has sometimes been assumed. In the succeeding papers in the series, the total motion of a charged HO is described by a fully renormalized dipole-approximation Abraham-Lorentz equation. This leads without further approximation to the following major results concerning this stochastic electrodynamics (SED) of the HO: i) The ensemble-average Liouville equation for the oscillator-ZP field system in the presence of an arbitrary applied classical radiation field is exactly equivalent to the usual time-dependent Schrödinger equation supplemented by an explicit radiation reaction vector potential similar to that of the Crisp-Jaynes-Stroud theory; ii) this SED Schrödinger equation for the HO is incomplete, insmuch as there exists a companion equation that restricts initial conditions such that the corresponding Wigner phase-space distribution is always positive; iii) the wave function of the SED Schrödinger equation has the a priori significance of position probability amplitude; iv) first-order transition rates predicted for the HO by this theory agree with those predicted by quantum electrodynamics for resonance absorption and spontaneous emission, which occurs with no triggering necessary; and v) if SED is taken seriously, then the concepts of quantized energies and photons must be abandoned.
Lettere al Nuovo Cimento, 1984
ricevuto il 9 Agosto 1983; manoscritto revisionato ricevuto il 15 Maggio 1984) PACS. 03.50. -Clas... more ricevuto il 9 Agosto 1983; manoscritto revisionato ricevuto il 15 Maggio 1984) PACS. 03.50. -Classical field theory.
Journal of the Optical Society of America, 1977
A new difference equation of radiative transfer is derived, including the angular dependence of t... more A new difference equation of radiative transfer is derived, including the angular dependence of the radiation and the particle scattering properties. The scattering by the particles in close-packed media is treated in terms of suitably defined near-field differential cross ...
American Journal of Physics
US ARMY LABORATORY COMMAND ATMOSPHERIC SCIENCES LABORATORY White Sands Missile Range, NM 88002-55... more US ARMY LABORATORY COMMAND ATMOSPHERIC SCIENCES LABORATORY White Sands Missile Range, NM 88002-5501 Form Approved REPORT DOCUMENTATION PAGE 0MB No. 0704-0188
In this initial paper in a series, we first discuss why classical motions of small particles shou... more In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields the multi-coordinate Schr\"odinger equation, with its usual boundary conditions, as an essential statistical equation for the system. We derive the general "canonical quantization" rule, that the Hamiltonian operator must be the classical Hamiltonian in the NNN-dimensional metric configuration space defined by the classical kinetic energy of the system, with the classical conjugate momentum NNN-vector replaced by −ihbar-i\hbar−ihbar times the vector gradient operator in that space. We obtain these results by using conservation of probability, general tensor calculus, the Madelung transform, the Ehrenfest theorem and/or the Hamilton-Jacobi equation, and comparison with results for the charged harmonic oscillator in stochastic electrodynamics. ...
The European Physical Journal Plus, 2011
Following the work reported in an earlier paper (G.H. Goedecke, J. Math. Phys. 15, 789 (1974)), t... more Following the work reported in an earlier paper (G.H. Goedecke, J. Math. Phys. 15, 789 (1974)), the coordinate basis vector approach to tensor calculus is exploited fully to obtain additional and stronger results, including: i) any curved Riemannian space must be a subspace of a larger flat host space; ii) a free test particle moves uniformly on a geodesic in the host space, but experiences gravity and other pseudoforces as viewed in four-dimensional (4D) spacetime; iii) the 4D Riemann-Christoffel curvature tensor is identically equal to a geometrical tensor associated with the complementary subspace of the host space; iv) Einstein's field equations are automatically geometrized, with the stress-energy tensor expressed in terms of the contracted complementary tensor; v) there cannot be a conventional cosmological term in these field equations, except as an approximation; vi) other geometrical field equations involving the complementary subspace metric fields exist and should be physical equations; vii) the long-range two-body time-independent central forces due to all metric fields that have localized sources are inverse square or generalized Yukawa forces. Some of the relationships between this theory and Kaluza-Klein (KK) and string theories are noted; for example, some of the results derived herein must be postulated in KK theories.
Journal of the Optical Society of America, 1975
ABSTRACT
Journal of the Optical Society of America, 1975
Lettere al Nuovo Cimento, 1984
ricevuto il 9 Agosto 1983; manoscritto revisionato ricevuto il 15 Maggio 1984) PACS. 03.50. -Clas... more ricevuto il 9 Agosto 1983; manoscritto revisionato ricevuto il 15 Maggio 1984) PACS. 03.50. -Classical field theory.
Physical Review, 1964
A simple general criterion is developed, using the retarded potentials of classical electromagnet... more A simple general criterion is developed, using the retarded potentials of classical electromagnetic theory, for absence of radiation from arbitrary time-periodic charge-current distributions. The criterion is applied to rigid finitely extended distributions of charge which may undergo ...
Il Nuovo Cimento B, 1975
A new general classical motion equation for particles which interact only electromagnetically is ... more A new general classical motion equation for particles which interact only electromagnetically is shown to lead to nonrelativistic motion equations of differential-difference type, which have only causal, nonrunaway solutions, for several charge distributions.
Il Nuovo Cimento B, 1975
ABSTRACT
Tectonophysics, 1991
ABSTRACT
Found Phys, 1984
In this fourth paper in a series on stochastic electrodynamics (SED), the harmonic oscillator-zer... more In this fourth paper in a series on stochastic electrodynamics (SED), the harmonic oscillator-zero-point field system in the presence of an arbitrary applied classical radiation field is studied further. The exact closed-form expressions are found for the time-dependent probability that the oscillator is in the nth eigenstate of the unperturbed SED Hamiltonian H 0 , the same H 0 as that of ordinary quantum mechanics. It is shown that an eigenvalue of H 0 is the average energy that the oscillator would have if its wave function could be just the corresponding eigenstate. The level shift for each unperturbed eigenvalue is found and shown to be unobservable for a different reason than in the corresponding QED treatment. Perturbation theory is applied to the SED Schrödinger equation to derive first-order transition rates for spontaneous emission and resonance absorption. The results agree with those of quantum electrodynamics, but the mathematics is strikingly different. It is shown that SED demands discarding the ideas of quantized energies, photons, and completeness of the Schrödinger equation, Finally, an intuitive physical SED model is suggested for the photoeffect and for Clauser's (2) coincidence experiment.
Foundations of Physics, Oct 31, 1983
This is the first in a series of papers that present a new classical statistical treatment of the... more This is the first in a series of papers that present a new classical statistical treatment of the system of a charged harmonic oscillator (HO) immersed in an omnipresent stochastic zero-point (ZP) electromagnetic radiation field. This paper establishes the Gaussian statistical properties of this ZP field using Bourret's postulate that all statistical moments of the stochastic field plane waves at a given space-time point should agree with their corresponding quantized field vacuum expectations. This postulate is more than adequate to derive the Planck spectrum classically via Boyer's and Theimer's methods, but it requires that the stochastic amplitude of each linearly polarized plane wave in the field contain two independent Gaussian random variables, not just a random phase as has sometimes been assumed. In the succeeding papers in the series, the total motion of a charged HO is described by a fully renormalized dipole-approximation Abraham-Lorentz equation. This leads without further approximation to the following major results concerning this stochastic electrodynamics (SED) of the HO: i) The ensemble-average Liouville equation for the oscillator-ZP field system in the presence of an arbitrary applied classical radiation field is exactly equivalent to the usual time-dependent Schrödinger equation supplemented by an explicit radiation reaction vector potential similar to that of the Crisp-Jaynes-Stroud theory; ii) this SED Schrödinger equation for the HO is incomplete, insmuch as there exists a companion equation that restricts initial conditions such that the corresponding Wigner phase-space distribution is always positive; iii) the wave function of the SED Schrödinger equation has the a priori significance of position probability amplitude; iv) first-order transition rates predicted for the HO by this theory agree with those predicted by quantum electrodynamics for resonance absorption and spontaneous emission, which occurs with no triggering necessary; and v) if SED is taken seriously, then the concepts of quantized energies and photons must be abandoned.
Lettere al Nuovo Cimento, 1984
ricevuto il 9 Agosto 1983; manoscritto revisionato ricevuto il 15 Maggio 1984) PACS. 03.50. -Clas... more ricevuto il 9 Agosto 1983; manoscritto revisionato ricevuto il 15 Maggio 1984) PACS. 03.50. -Classical field theory.
Journal of the Optical Society of America, 1977
A new difference equation of radiative transfer is derived, including the angular dependence of t... more A new difference equation of radiative transfer is derived, including the angular dependence of the radiation and the particle scattering properties. The scattering by the particles in close-packed media is treated in terms of suitably defined near-field differential cross ...
American Journal of Physics
US ARMY LABORATORY COMMAND ATMOSPHERIC SCIENCES LABORATORY White Sands Missile Range, NM 88002-55... more US ARMY LABORATORY COMMAND ATMOSPHERIC SCIENCES LABORATORY White Sands Missile Range, NM 88002-5501 Form Approved REPORT DOCUMENTATION PAGE 0MB No. 0704-0188
In this initial paper in a series, we first discuss why classical motions of small particles shou... more In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields the multi-coordinate Schr\"odinger equation, with its usual boundary conditions, as an essential statistical equation for the system. We derive the general "canonical quantization" rule, that the Hamiltonian operator must be the classical Hamiltonian in the NNN-dimensional metric configuration space defined by the classical kinetic energy of the system, with the classical conjugate momentum NNN-vector replaced by −ihbar-i\hbar−ihbar times the vector gradient operator in that space. We obtain these results by using conservation of probability, general tensor calculus, the Madelung transform, the Ehrenfest theorem and/or the Hamilton-Jacobi equation, and comparison with results for the charged harmonic oscillator in stochastic electrodynamics. ...
The European Physical Journal Plus, 2011
Following the work reported in an earlier paper (G.H. Goedecke, J. Math. Phys. 15, 789 (1974)), t... more Following the work reported in an earlier paper (G.H. Goedecke, J. Math. Phys. 15, 789 (1974)), the coordinate basis vector approach to tensor calculus is exploited fully to obtain additional and stronger results, including: i) any curved Riemannian space must be a subspace of a larger flat host space; ii) a free test particle moves uniformly on a geodesic in the host space, but experiences gravity and other pseudoforces as viewed in four-dimensional (4D) spacetime; iii) the 4D Riemann-Christoffel curvature tensor is identically equal to a geometrical tensor associated with the complementary subspace of the host space; iv) Einstein's field equations are automatically geometrized, with the stress-energy tensor expressed in terms of the contracted complementary tensor; v) there cannot be a conventional cosmological term in these field equations, except as an approximation; vi) other geometrical field equations involving the complementary subspace metric fields exist and should be physical equations; vii) the long-range two-body time-independent central forces due to all metric fields that have localized sources are inverse square or generalized Yukawa forces. Some of the relationships between this theory and Kaluza-Klein (KK) and string theories are noted; for example, some of the results derived herein must be postulated in KK theories.
Journal of the Optical Society of America, 1975
ABSTRACT
Journal of the Optical Society of America, 1975
Lettere al Nuovo Cimento, 1984
ricevuto il 9 Agosto 1983; manoscritto revisionato ricevuto il 15 Maggio 1984) PACS. 03.50. -Clas... more ricevuto il 9 Agosto 1983; manoscritto revisionato ricevuto il 15 Maggio 1984) PACS. 03.50. -Classical field theory.
Physical Review, 1964
A simple general criterion is developed, using the retarded potentials of classical electromagnet... more A simple general criterion is developed, using the retarded potentials of classical electromagnetic theory, for absence of radiation from arbitrary time-periodic charge-current distributions. The criterion is applied to rigid finitely extended distributions of charge which may undergo ...
Il Nuovo Cimento B, 1975
A new general classical motion equation for particles which interact only electromagnetically is ... more A new general classical motion equation for particles which interact only electromagnetically is shown to lead to nonrelativistic motion equations of differential-difference type, which have only causal, nonrunaway solutions, for several charge distributions.
Il Nuovo Cimento B, 1975
ABSTRACT