Volume 47, Issue 5, May 1979
 Editorial
 Papers


Contemporary American physics fiction
View Description Hide DescriptionThe great post‐Newtonian revolution in physical science culminated with Einstein’s general theory of relativity in the second decade of our century, and with the establishment of the quantum theory in the third decade. The responses of literature over the past half century to these changes in world view have served as stimulating examples of cultural interchange. The novels of Thomas Pynchon, William Gaddis, Robert Coover, Joseph McElroy, Don DeLillo, and Robert Pirsig make use of the new physics as metaphor for three traditional activities of novelists: examining order and disorder, questioning cause and effect, and seeking unity in the human and physical universes.

Bode’s law and the ’’missing moons’’ of Saturn
View Description Hide DescriptionA theory concerning the orbital spacing patterns in the solar system, more intriguing than many of the traditional topics to our general studies astronomy students and useful pedagogically since it is accessible to such students in quantitative as well as qualitative terms, is presented. The orbital distributions of the planets and major satellite systems are fitted with a Bode‐type form. The Saturnian system requires vacant orbitals if the best fit is to have an accuracy comparable to that obtained for the other systems. One pattern of vacant orbitals is shown to be consistent with what would be expected if Titan produced resonant perturbations on the forming satellite system.

Spin and uncertainty in the interpretation of quantum mechanics
View Description Hide DescriptionA rigorous derivation of the Schrödinger theory from the Pauli (or Dirac) theory implies that the Schrödinger equation describes an electron in an eigenstate of spin. Furthermore, the ground‐state kinetic energy is completely determined by the electron spin density. This can be explained by interpreting the spin as an orbital angular momentum, which is necessarily accompanied by a kinetic energy. Thus, t h e s p i n i s a z e r o‐p o i n t a n g u l a r m o m e n t u m a s s o c i a t e d w i t h t h e z e r o‐p o i n t e n e r g y o f t h e e l e c t r o n. Since the dispersion in electron momentum is determined by the zero‐point energy, the Heisenberg uncertainty relations for an electron can be interpreted as a property of the electronspin motion. The kinetic interpretation of spin and the statistical interpretation of quantum mechanics can be jointly sustained by regarding the electron as a point particle. It follows that stationary electron states are sources of fluctuating electric fields. There is reason to believe that these fluctuating fields are responsible for the Van der Waals force and can be identified with electromagnetic vacuum field fluctuations. The kinetic interpretation of spin then implies that the Van der Waals forces are spin dependent. These ideas are not only consistent with the conventional mathematical formalism of quantum mechanics, they provide a more complete and coherent interpretation of many details in the formalism than does the alternative Copenhagen interpretation. They present some difficulties, however, which, if the kinetic interpretation of spin is correct, probably require some modification of quantum electrodynamics to be resolved.

A windmill’s theoretical maximum extraction of power from the wind
View Description Hide DescriptionThe fraction of the kinetic energy of the wind impinging on its area, that a wind turbine can convert to useful power, has been shown by Betz in an idealized laminar‐flow model to have an upper limit of 16/27 or 59%. The limit is here simply rederived and it is shown how deviations from the idealized model, involving rotational kinetic energy of the downwind stream and turbulent mixing from outside the boundaries of the idealized stream, can either increase or decrease the power available. The limit is thus not a strict upper limit in practice.

Intrinsic angular momentum of light
View Description Hide DescriptionA familiar theorem involving a balance between net torque and rate of change of angular momentum in the electromagnetic field is rederived. This version of the theorem includes the intrinsic torques exerted by the fields on the polarized medium. It is seen that these terms lead naturally to the expression for the intrinsic angular momentum carried by a localized pulse of electromagnetic radiation. In the present treatment the expressions for the external and intrinsic angular momenta arise naturally as separate entities, in contrast to standard treatments, in which both arise out of what is evidently only the external angular momentum.

Equivalence of Einstein’s 1925 unified field theory and his relativistic theory of the nonsymmetric field
View Description Hide DescriptionIt is shown that Einstein’s final unified field theory, the relativistic theory of the nonsymmetric field, is identical to a theory Einstein proposed in 1925.

Inexpensive time‐of‐flight velocity measurements
View Description Hide DescriptionAn inexpensive circuit useful in time‐of‐flight velocity measurements is described. Its use for bullet velocity determination in connection with the ballistic pendulum demonstration of momentum conservation is described. Mechanical construction considerations are outlined.

Demonstration of dispersive effects
View Description Hide DescriptionA method to simulate the dispersive properties of various media is described. We have used it to demonstrate to an Electromagnetic Theory class, the dispersion of a pulsed electromagnetic wave propagating in an unbounded dielectric medium. In addition, the characteristics of the electromagnetic precursors (Sommerfeld and Brillouin) have also been demonstrated.

Rigidly connected accelerated clocks
View Description Hide DescriptionStandard clocks at rest in (i) a rigidly hyperbolically accelerated reference frame, (ii) on a rotating disk, and (iii) on the surface of the earth are considered. Special relativity is sufficient to predict the behavior of the clocks in cases (i) and (ii). In case (iii), however, gravitational effects are important, which is taken account of by use of the principle of equivalence. It is concluded that in cases (i) and (ii) clocks connected along a line in the direction of the acceleration do not maintain Einstein synchronization. As to the rate of standard clocks on the surface of the earth, the drifts caused by the rotating motion of the earth and the deviation of the earth’s surface from a sphere cancel each other. On the geoid this cancellation is exact. This means that the synchronization of clocks at every position at the mean sea level, no matter how far apart on the earth they are located, is not destroyed by these effects. Owing to tidal effectsclocks on the earth at different positions in the solar gravitational field do not maintain their synchronization. This effect is several orders of magnitude less than the above ones.

Elementary treatment of some difficulties in the construction of irreducible representations of the rotation group in terms of products of the spin‐1/2 representation
View Description Hide DescriptionIn order to understand in detail how the representations of the rotation group are constructed from products of the spin‐1/2 representation, a clear distinction must be maintained between three related but conceptually different quantities: a vector in an abstract vector space, its components in some chosen basis, and its representatives. The rotation group provides an example that these are indeed different concepts, and that paradoxes result if they are confused.

Electrostatic problems? Relax!
View Description Hide DescriptionWe describe the numerical methods of relaxation and over‐relaxation for solving Laplace’s equation for a system of conductors. These methods are quite tractable nowadays using only modest sized computers. Several simple (analytically solvable) though moderately complicated (arising from experimental situations) examples of their use are given.

Multichannel analyzer built from a microcomputer
View Description Hide DescriptionA 1024 channel multichannel analyzer has been built using eight‐bit S‐100 bus microcomputer hardware. The analyzer has pulse height analysis and multiscaling data acquisition modes. A Mössbauer control signal is provided. The output modes are an oscilloscope display, print data, and send data to another computer. The system’s hardware and software are described. Costs and advantages relative to commercial multichannels are discussed.

Demonstration of reduced gas pressure in a centrifugal field
View Description Hide DescriptionA simple effective demonstration of the reduced pressure in a gas trapped in a centrifugal field is shown by the force necessary to separate two plates (radius R, angular velocity ω) rotating in loose mutual contact. Agreement with the calculated value, F=πρR ^{4}ω^{2}/4, is good, where it is assumed that the air trapped between the plates approximates an ideal gas of density, ρ, which obeys Boltzmann’s distribution law in the centrifugal field.

Analytical and numerical solution of the Schrödinger equation for a surface potential barrier including spin‐orbit interaction
View Description Hide DescriptionWe consider the problem of an electron interacting with a surface potential barrier which includes the spin‐orbit interaction. An exact solution of the Schrödinger equation is given for the case of a step potential. For smooth barrier profiles, the time‐ dependent Schrödinger equation is numerically solved, and the time evolution of the spin‐up and spin‐down components of a wave packet is displayed in a series of pictures.

Magnetic multipole expansions using the scalar potential
View Description Hide DescriptionUsing the magnetic scalar potential, the multipole expansion is derived for the magnetostatic field outside a localized current distribution.

Two‐capacitor problem: A more realistic view
View Description Hide DescriptionA popular circuit problem encountered in introductory physics and electromagnetics texts is discussed here in a more realistic manner by considering the self‐inductance of the circuit. For practical values of the circuit parameters, the model usually put forth to solve this problem, a series R C circuit, appears inappropriate.
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 Notes and Discussions


Combinatorial rules for batteries
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Jacobians and curvilinear metrics
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Determination of ultrasonic velocity in liquids using optical diffraction by short acoustic pulses
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