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Four-space hyperfluid flow as a model of electromagnetism
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from certain special types of spectra (for instance from much steeper spectra). This possibility is only briefly discussed here: it will be more fully discussed in a companion paper. The nuclear reactions possibly responsible for the alteration of the ratios after their formation are discussed next. Finally, the observations of these elements in natural settings are summarized, compared and discussed in terms of the formation and destruction rates, and some conclusions are drawn. One of t.he main results of this paper is that, within the uncertainty of the evaluation, the meteoritic llB to 1°B ratio is equal to its formation ratio on CNONe. This result therefore leads, for the formation of the light elements in the solar system, to a model basically different from the F.G.H. one. The ?Li to 6Li formation ratio has a value smaller than the meteoritic one, but the alteration can be ascribed to (p, CZ) reactions at temperatures between 2 and 4 million degrees at the bottom of the surface convective zone of the young sun, and this process would not alter the llB/lOB ratio. A tentative picture of the history of the solar system would go as follows: from energetic considerations, we are led to think that the Li Be B have been formed even before the Hayashi (fully convective) phase of the sun. The 7Li/6Li ratio would then have been altered during the Hayashi phase. This material would still later have been separated from the sun. An alternative picture is also sketched, based on the assumption of a special type of proton spectrum, of the kind mentioned above. of Lattice Vibrations. TASUSHI TABASHI, Dublin Institute for Advanced Studies, Dublin, Ireland. A new method of quantization of lattice vibrations is proposed, which provides a simple relation between the Green’s functions and the wavefunctions. Our method makes crucial use of the generalized Ward identity to obtain conserved quantities directly from the equation of motion without recourse to the usual Lagrangian or Hamiltonian formalism. By using this identity and a new identity associated with the equation of motion of the lattice vibration, we est,ablish the close relation between the vacuum expectation value of bilinear forms of phonon fields and the Green’s function. The frequency spectrum is expressed in terms of the Green’s function. The reduction formula technique is discussed briefly. Quantizatl’on
Four-Space Hype&id Flow as a Model of Electromagnetism. ROGER L. GAMBLIN, IBM System Development Division, Endicott, New York 13764. A formal model of the electromagnetic field, which is based upon the equations of ordinary three-space incompressible, inviscid, rotational fluid flow, is introduced. This model is a four-space theory which, however, reduces to the three-space picture of fluid-flow in any three-dimensional subspace of four-space. It is for this reason that the entity considered by the model is called a four-space hyperfluid. Vector operations and fluid concepts are defined in four-space according to their reduction to customary concepts in three-space. It is found that if the electromagnetic-field four-potential is considered to be t,he velocity potential for the four-fluid, the electromagnetic field arises as the rotational flow of this fluid. Two of Maxwell’s equations arise from the four-space identity div curl A = 0, and the other two arise from curl curl A, provided charge and current are considered to be regions of four-space flow vorticity. The energy-momentum relations of the electromagnetic field arise from considering the forces associated with vortex flow of the fluid in any threesubspace. The model is not an aether theory since electromagnetic radiation arises from the space metric and not from any assumed compressional or inertial properties of the fluid. The model is not related to the flow of a relativistic fluid because the velocity is a secondrank tensor and not a vector field.
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from certain special types of spectra (for instance from much steeper spectra). This possibility is only briefly discussed here: it will be more fully discussed in a companion paper. The nuclear reactions possibly responsible for the alteration of the ratios after their formation are discussed next. Finally, the observations of these elements in natural settings are summarized, compared and discussed in terms of the formation and destruction rates, and some conclusions are drawn. One of t.he main results of this paper is that, within the uncertainty of the evaluation, the meteoritic llB to 1°B ratio is equal to its formation ratio on CNONe. This result therefore leads, for the formation of the light elements in the solar system, to a model basically different from the F.G.H. one. The ?Li to 6Li formation ratio has a value smaller than the meteoritic one, but the alteration can be ascribed to (p, CZ) reactions at temperatures between 2 and 4 million degrees at the bottom of the surface convective zone of the young sun, and this process would not alter the llB/lOB ratio. A tentative picture of the history of the solar system would go as follows: from energetic considerations, we are led to think that the Li Be B have been formed even before the Hayashi (fully convective) phase of the sun. The 7Li/6Li ratio would then have been altered during the Hayashi phase. This material would still later have been separated from the sun. An alternative picture is also sketched, based on the assumption of a special type of proton spectrum, of the kind mentioned above. of Lattice Vibrations. TASUSHI TABASHI, Dublin Institute for Advanced Studies, Dublin, Ireland. A new method of quantization of lattice vibrations is proposed, which provides a simple relation between the Green’s functions and the wavefunctions. Our method makes crucial use of the generalized Ward identity to obtain conserved quantities directly from the equation of motion without recourse to the usual Lagrangian or Hamiltonian formalism. By using this identity and a new identity associated with the equation of motion of the lattice vibration, we est,ablish the close relation between the vacuum expectation value of bilinear forms of phonon fields and the Green’s function. The frequency spectrum is expressed in terms of the Green’s function. The reduction formula technique is discussed briefly. Quantizatl’on
Four-Space Hype&id Flow as a Model of Electromagnetism. ROGER L. GAMBLIN, IBM System Development Division, Endicott, New York 13764. A formal model of the electromagnetic field, which is based upon the equations of ordinary three-space incompressible, inviscid, rotational fluid flow, is introduced. This model is a four-space theory which, however, reduces to the three-space picture of fluid-flow in any three-dimensional subspace of four-space. It is for this reason that the entity considered by the model is called a four-space hyperfluid. Vector operations and fluid concepts are defined in four-space according to their reduction to customary concepts in three-space. It is found that if the electromagnetic-field four-potential is considered to be t,he velocity potential for the four-fluid, the electromagnetic field arises as the rotational flow of this fluid. Two of Maxwell’s equations arise from the four-space identity div curl A = 0, and the other two arise from curl curl A, provided charge and current are considered to be regions of four-space flow vorticity. The energy-momentum relations of the electromagnetic field arise from considering the forces associated with vortex flow of the fluid in any threesubspace. The model is not an aether theory since electromagnetic radiation arises from the space metric and not from any assumed compressional or inertial properties of the fluid. The model is not related to the flow of a relativistic fluid because the velocity is a secondrank tensor and not a vector field.