Search Results (41 total)

The field equations of a noncovariant theory of gravitation, based on the existence of a preferred frame of reference in the universe, are applied to the homogeneous isotropic cosmological model. One is naturally led to a particular value of the previously undetermined constant present in the equations. The second-order equation determining the radius of the universe can be integrated to give a first-order equation similar to that of general relativity, but with an additional term that can lead to oscillations without any singular state. One obtains a conservation law for the total energy, which is found to be positive definite.

Since there seems to exist a preferred frame of reference in the universe, determined by the large-scale distribution of matter, a theory of gravitation is considered which resembles the general theory of relativity in being based on the equivalence principle, but is without the covariance principle. This theory leads to the same results as general relativity in the three crucial tests. The formalism can be modified to take into account the solar oblateness observed by Dicke and Goldenberg.

It is shown that if the wave function of a massive body is ψ=Σc_nψ_n, where the ψ_n are macroscopically distinguishable states, then the observation of interferences between the various ψ_n requires inconceivable laboratory conditions (e.g., the experiment may last longer than the lifetime of the universe). It is therefore proposed to interpret Σc_nψ_n as a mixture of states, and not as a superposition. This new interpretation of wave functions is consistent with experience and is free from the paradoxical features of the "orthodox" measurement theory.

By means of the analogy that exists between the gravitational field, in the weak, quasi-static case, and the electromagnetic field, uncertainty relations are obtained for the average values of some of the Christoffel symbols measured in two domains, similar to those for the components of the quantized electromagnetic field. Furthermore, it is shown that there exists a limitation on the accuracy to which the average value of a single one of these Christoffel symbols can be measured. The existence of uncertainty relations provides an argument in support of the standpoint that the gravitational field must be quantized.

It is shown that the cumulative effects of the nonlinear terms in Einstein's equations rule out the possibility of stable small oscillations of a gravitational field about an equilibrium state, if the latter is supposed to be Minkowskian at infinity. The perturbation, if unlimited in time, rather tends to take infinite values at large distances from its source. This can be interpreted as an instability of gravitational radiation fields, and raises doubts concerning the validity of the linearized theory at large distances from the source.

For a single electron interacting with the quantized transverse electromagnetic field it is found that, in the one-dimensional case, the Schrödinger equation can be put into a form like that of a system of coupled harmonic oscillators. From the classical frequencies of the normal modes of oscillation of such a system the quantal energy can be determined. While the perturbation method gives a logarithmic divergence in the interaction energy, one finds by the present method that the energy diverges like the square root of a logarithm.

It is shown for a general class of scalar nonlinear classical field theories, in which singularities are excluded and particles are represented by small regions in which the field is intense, that the interaction between two particles is described by the Yukawa potential at large distances.

It is proposed to treat the spin of a particle phenomenologically by considering the particle as a small rotating sphere, the rotation of which is described by euler parameters. If the rotation is quantized in the space of the euler parameters, one obtains both integral and half-integral values for the spin. In this way one arrives at a formalism in which the spin components can be represented as differential operators in the Schroedinger representation.

Calculations are carried out along the lines of the work of Fermi and Yang in which the π-meson is considered as a composite particle formed from a proton and an anti-neutron. On the assumption of a vector interaction it is found that the ¹S₀ state must be excluded because its energy goes to zero as the interaction goes to zero, while the ³P₀ state appears to give an acceptable solution. On the assumption of a tensor interaction it is found that ¹S₀ and ³P₀ solutions both exist, but for opposite signs of the interaction. The tensor interaction must therefore be excluded since it would lead to the formation of a composite particle by a proton and a neutron. Using the vector interaction one finds that the ground state is a ³P₁, but that there are other states with j=0,1 and 2 lying near it, the proximity depending on the interaction range assumed.

It is shown that, for a particle to be at rest in a static, axially symmetric gravitational field, the force on the particle must vanish. This result is then generalized to the case of an arbitrary static gravitational field.

To take account of the fact that the existence of a fundamental length a, the classical electron radius, sets a limit to the accuracy with which the position of a point can be measured, it is proposed to introduce two spaces, an "abstract" space consisting of points, and an "observable" space in which one deals with elementary volumes correlated to the points of the former by means of a statistical distribution function in the form of a three-dimensional Gaussian error function. Such a function is not Lorentz invariant, but one can obtain Lorentz covariance in the observable space by carrying out the usual Lorentz transformation in the abstract space. If one assumes that the usual equations for wave fields, in which the fundamental particles are regarded as points, are valid in the abstract space, then one can obtain corresponding equations in the observable space, with the particles behaving as if they had finite volumes. The difficulties associated with infinite self-energies and singularities in the interactions between particles, as calculated by the usual perturbation method, disappear, but the difficulty associated with the divergence of the series of successive orders of perturbations remains.

Covariant conditions for rigid-body motion are set up. They are equivalent to those proposed by Born and lead to the linear speed-distance law for the case of rotation about an axis. This result and also a discussion of the transformation equations in going over to a rotating frame of reference are used as arguments for the desirability of retaining the concept of rigid rotation with the linear speed-distance law, contrary to the opinion expressed by Hill. The rotation question is also considered from the standpoint of angular velocity, and one is lead rather naturally to two fluid velocity distributions, one of which was found by Hill. The expression for the spatial distance between two points on a rotating disk obtained by Berenda is derived without the use of the assumption introduced by the latter.

The equations of the classical field theory of elementary particles proposed by one of the authors were integrated numerically for the static, spherically-symmetric case. A solution was obtained corresponding essentially to minimum energy, and hence describing a classical electron according to the theory. It was found that the frequency associated with the solution was zero, to within the accuracy of the calculations, for the case of minimum energy. Hence the theory, in its present form, is not capable of accounting for the Sommerfeld fine-structure constant, as had seemed possible.

The Zeeman effect of praseodvmium has been studied at fields up to 95,000 oersteds over the range 2400 to 7100A. g and J values have been determined for 74 Pr II levels from resolved Zeeman patterns of 141 lines. With these data, together with new wave-length data from the M.I.T.-W.P.A. Wavelength Project which have been applied to the spectroscopic interval sorter and interval recorder, a quadratic term array has been set up which accounts for 312 lines. This array is consistent with King's temperature classification of the lines and with all previous hyperfine structure observations. It is self-consistent in g values to an average deviation of 0.005 unit, and in wave numbers to an average deviation of 0.08 cm^-1. Previously published hyperfine structure measurements were found insufficiently precise to aid the classification, but were of value in its verification. The lowest term of Pr II is found to be f³(⁴I^o)·s-⁵I^o₄. Most of the strong lines showing hyperfine structure arise from the f³s configuration.

It is shown that it is possible to account for the principal results obtained by Miller in his "ether-drift" experiments, on the basis of a flat-space theory of gravitation, as due to the motion of the earth in the gravitational field of all the matter and energy in the universe.

The possibility is considered of interpreting the formalism of the general theory of relativity in terms of flat space, the fundamental tensor g_μν being regarded as describing the gravitational field but having no direct connection with geometry. The resulting theory in general leads to the same predictions as the Einstein theory, but there are cases where the predictions differ. The present theory may explain the principal results obtained by D. C. Miller in his "ether-drift" experiments. The implications of the theory for cosmology are briefly touched upon.