bluuebunny/crossref_metadata_2025 huggingface dataset:
Maximum work from a finite reservoir by sequential Carnot cycles
Authors: Ondrechen Mary Jo , Andresen Bjarne , Mozurkewich Michael , Berry R. Stephen
Published: March 2005

The production of work from a heat source with finite heat capacity is discussed. We examine the conversion of heat from such a source first by a single Carnot engine and then by a sequence of Carnot engines. The optimum values of the operating temperatures of these engines are calculated. The work production and efficiency of a sequence with an arbitrary number of engines is derived, and it is shown that the maximum available work can be extracted only when the number of cycles in the sequence becomes infinite. The results illustrate the importance of recovery or bottoming processes in the optimization of work-producing systems. In addition, the present model illuminates one practical limitation of the Carnot cycle: The Carnot efficiency is only obtainable from a heat source with infinite heat capacity. However, another cycle, somewhat reminiscent of the Otto and Brayton cycles, is derived which will provide the maximum efficiency for a heat source with a finite heat capacity.
Turning quickly: A variational approach
Authors: Palffy-Muhoray P. , Unruh W. G.
Published: March 2005

The problem of changing direction with limited acceleration in the least amount of time is considered. The quickest turn is shown to be the one which minimizes the path length in velocity-space under the given constraints. The problem where initial and final conditions are symmetric is examined in some detail.
Fresnel–Arago laws for interference in polarized light: A demonstration experiment
Authors: Henry M.
Published: March 2005

The author makes a experimental investigation of the influence of polarization of light on interference patterns. (AIP)
Kepler’s third law
Authors: Tan A. , Chameides W. L.
Published: March 2005

There are slight differences in the standards of Kepler’s third law in the different textbooks. The authors work out an average r, that over the arc lengths of the orbit and show that such an average is equal to the semimajor axis.(AIP)
Relation between bound-state energies and the nature of force laws
Authors: Swenson Robert J.
Published: March 2005

Virial theorem is applied to a system of particles interacting via an an arbitrary power-law central force.(AIP)
Two electrohydrodynamic demonstrations
Authors: Hart F. X. , Massey J. S.
Published: March 2005

The author illustrates two demonstration experiments to show the practical application of electrodynamic phenomena.(AIP)
Probability, statistics, and the World Series of baseball
Authors: Krane Kenneth S.
Published: March 2005

The author offers a calculation of the probabilities and statistics of various set scores of the World Series of baseball.(AIP)
Didactic comments on wave propagation
Authors: Tomusiak E. L. , Montalbetti R.
Published: March 2005

Propagation of waves or pulses in strings is discussed.(AIP)
Gravitational lens
Authors: Higbie J.
Published: March 2005

A plastic lens is described which will bend light rays parallel to the lens axis in the same way as a static (Schwarzschild) gravitational field. This allows one to observe the optical distortions caused by a (nonrotating) black hole directly. The double-imaging property is discussed with particular application to the recently announced double quasar which is suspected to be a gravitational double image of a single quasar. A detailed cosmological model calculation is performed in order to place limits on the mass of the galaxy acting as the lens. It is seen that if the double quasar is a double image and if the lens is a massive galaxy then we will have established that the quasar redshift is cosmological rather than gravitational. The gravitational lens thus occupies a key role in resolving this question.
Anhysteretic magnetization and tape recorder bias
Authors: Rossing Thomas D.
Published: March 2005

Many misleading or incorrect explanations of tape recorder bias have appeared in trade journals and popular magazines. These explanations, which tend to ignore magnetic hysteresis, are particularly confusing to physics students. A brief discussion of bias and its effect on recorded magnetization is presented, along with several references to reliable sources for further reading on the subject.
The origin of the Julian Period: An application of congruences and the Chinese Remainder Theorem
Authors: Reese Ronald Lane , Everett Steven M. , Craun Edwin D.
Published: March 2005

In 1583, Joseph Justus Scaliger introduced the Julian Period of 7980 years, which is the basis of the Julian Day system of counting days sequentially from 1 January 4713 BC. It is not commonly known how this date was chosen as the origin of the system. This paper formulates the problem as an application of the theory of congruences and the Chinese Remainder Theorem. Scaliger’s interesting original solution to the problem is also reviewed.
The concept of temperature and its dependence on the laws of thermodynamics
Authors: Ehrlich Philip
Published: March 2005

It is argued that the temperature concept has a richer theoretical basis than is generally appreciated. The importance of an absolute comparative concept of temperature is emphasized. A set of necessary and sufficient conditions for the existence and metricization of the temperature quantity is examined. It is shown that these conditions are all consequences of the laws of thermodynamics together with a number of ancillary thermodynamic assumptions. The absolute comparative concept of temperature as well as the absolute scale are introduced without employing the concept of a thermometer. The general notion of a thermometer is introduced as an addendum to thermodynamics.
The difference between difference tones and rapid beats
Authors: Hall Donald E.
Published: March 2005

Simultaneous production of two pure tones with frequencies f1 and f2 is associated both with auditory beats (rapid fluctuations in loudness) and with audible difference tones. Since the same frequency f1−f2 is encountered in both cases, students tend to think a difference tone is nothing more than a beat phenomenon whose frequency is high enough to be in the audible range. But, in fact, these are two entirely distinct effects. This article discusses how to convincingly present this difference at three levels: (1) simple theory of added and multiplied waveforms; (2) visual demonstration with electronic Fourier analyzer; and (3) audible demonstration. These show that our ears can literally hear and distinguish two separate phenomena.
Physics of photography course for fine arts students: The view camera
Authors: Galli Anthony John , Brumage W. H. , Cawood Gary
Published: March 2005

Elementary optical considerations are used to show how depth of field, exposure correction, and Scheimpflug focusing are obtained for a view camera. Although designed primarily for photography majors taking a ’’physics of photography’’ course, the material discussed could form the basis of an optics laboratory experiment for physics majors.
Pedagogy of spin in nonrelativistic quantum mechanics
Authors: Williams Brian , Robinson Terence
Published: March 2005

The quantum-mechanical properties of electron spin are developed systematically from a nonrelativistic Hamiltonian. The correct values of the magnetic moment of the electron, the spin-orbit coupling energy of atomic electrons, the Darwin correction, and the angular momentum of the electron are obtained directly without explicitly including any relativity beyond classical electromagnetism.
Quantum bouncer in a closed court
Authors: Aguilera-Navarro V. C. , Iwamoto H. , Ley-Koo E. , Zimerman A. H.
Published: March 2005

The study of the quantum bouncer in a closed court is used to illustrate some concepts and techniques of quantum mechanics at different levels.
Polytropic, differentially rotating cylinders
Authors: Simon Sheridan A. , Czysz Michael F. , Everett Karen , Field Christopher
Published: March 2005

Infinite cylinders composed of polytropic material can possess nearly arbitrary rotation fields while retaining the fundamental simplicity of one-dimensional structures. The physical properties of these objects can be easily calculated and understood by junior–senior level physics students even without access to a large computing facility. Analytical results are presented here for polytropic index 0 and 1 as well as numerical results for polytropic index 1.5.
Driven ’’portulum’’: A rolling ball as a simple oscillating system
Authors: Marschall Laurence A.
Published: March 2005

A classroom demonstration, a variation of the simple swinging pendulum, is described. In our ’’portulum,’’ a ball, driven by short blasts of air, rolls along a curved tube. The design of this device, its construction, and its usefulness to the teaching of physics are discussed. It is also shown that the oscillations of the rolling ball have the same mathematical form as the oscillations of a ball swinging along the same path, but with a lower frequency.
Resolving time effect on counting statistics
Authors: Kyker Granvil C.
Published: March 2005

The observed variance in the counts recorded from a radioactive source is related to the response time of the detector, in a way which is readily exploited as an intermediate laboratory exercise.
Where is the energy stored in a gravitational field?
Authors: Peters P. C.
Published: March 2005

The meaning and location of energy density in gravitational fields is considered in analogy with the energy density in electrostatic fields. The fact that energy density of gravitational fields acts as a source of gravitation makes the localization, in principle, an observable possibility. A nonlinear Newtonian theory of gravity is explored, and the sensitivity of the predicted perihelion precession to the location of energy density is discussed. Problems associated with identification of gravitational energy density in general relativity are pointed out, together with the similar effects generated by gravitational stresses. Comparison with the nonlinear Newtonian theory allows one to determine the various effects which contribute to the general relativistic perihelion precession.
Applications of Mellin transforms to the statistical mechanics of ideal quantum gases
Authors: Grandy W. T. , Rosa S. Goulart
Published: March 2005

It is well known that the Boltzmann partition function for noninteracting particles factors into a product of N single-particle partition functions. We show here that, in much the same way, the logarithm of the grand partition function of quantum statistical mechanics for ideal gases is represented by a contour integral containing the single-particle partition function. The unification achieved in this way is illustrated by applications to field-free nonrelativistic particles, collections of relativistic particles, systems in the presence of a uniform mangetic field, and inhomogeneous systems in equilibrium. Both Fermi and Bose statistics are encompassed in the treatment.
Parallax distance, time, and the twin ’’paradox’’
Authors: Unruh W. G.
Published: March 2005

An extension to all space-time points of the definition of time and of distance for any observer, accelerating or not, by means of a parallax viewing of events is undertaken. The twin ’’paradox’’ is analyzed in terms of this definition, and it is shown that during the period of acceleration, the accelerated observer sees the other traveler recede and go backward in ’’time.’’ This motion completely reconciles the calculations both observers make regarding the reading of each other’s clocks when they meet again.
Speed of sound by a time-of-flight method
Authors: Albergotti J. C.
Published: March 2005

The author measured the velocity of sound by a time-of-flight method using a system consisting of a demonstrations board, two transduces, ulatrasonic circuit board, and batteries.(AIP)
Inexpensive digital thermometer
Authors: Edmunds D. L. , Cowen J. A.
Published: March 2005

Inexpensive digital thermometer was designed and constructed. The device consists of a temperature sensor, an analog-to-digital converter, which drives 6-digit LED display , and associated power supplies. (AIP)
Density of states for wave packets
Authors: Tanttila W. H.
Published: March 2005

The author indicates a derivation that gives the same result g(ν)/V but for a quite different reason than that due to the application of periodic boundary conditions used in Born’s development for a wave of an infinite sinusoidal phase.(AIP)
Discovering induction
Authors: Harrison David
Published: March 2005

A technique used to introduce the concept of induction is discussed.(AIP)
Motion of the Earth as viewed from the moon and the Y-suspended pendulum
Authors: Crowell A. D.
Published: March 2005

In the early nineteeth century, James Dean, the first Professor of Mathematics and Natural Philosophy at the University of Vermont, published a paper describing the effects of the librations of the moon on the apparent motion of the Earth in the sky of the moon. He noted that this motion could be simulated by the motion of a Y-suspended pendulum. Within a short time, Nathaniel Bowditch, the self-taught mathematician, navigator, and actuary, published a complete analysis of the two-dimensional oscillator, including derivations and drawings of the mathematical curves usually known as Lissajous figures, some forty years before their description by J. A. Lissajous. This paper gives an account of the contributions of Dean and Bowditch to this problem.
Stable solutions using the Euler approximation
Authors: Cromer Alan
Published: March 2005

A minor modification of the standard Euler approximation for the solution of oscillatory problems in mechanics yields solutions that are stable for arbitrarily large number of iterations, regardless of the size of the iteration interval. The period of a nonlinear oscillator converges rapidly to its exact value as the size of the iteration interval is decreased. In two dimensions, closed orbits are given for the two-body Kepler problem and the restricted three-body problem can be iterated indefinitely to produce space-filling orbits. In this new approximation, the difference ΔE between the initial energy and the energy after n iterations is bounded, oscillatory, and zero when averaged over half a cycle of the motion.
Compensated R
C integrators
Authors: Cross Rodney C. , Collins George A.
Published: March 2005

This paper describes an integrator, consisting only of passive components, which represents an order of magnitude improvement over the simple RC integrator.
Classical limit for the ground-state energy
Authors: El-Batanouny F. M.
Published: March 2005

The ground-state energy of a particle moving in one dimension in a limited region is studied in the classical limit. It is found that as h/→0, the limit of the ground-state energy E0 coincides with the minimum classical energy.
Dulong–Petit law in a van der Waals theory of the crystalline state
Authors: de Llano M. , Ramírez S. , Vucetich H.
Published: March 2005

It is shown that the correct Dulong and Petit law of specific heat can be obtained within a previous generalization of the van der Waals theory which admits the presence of the crystalline state for a simple monatonic substance, if the proper modification of the crystalline mean field is made.
Cartan’s rule in particle optics
Authors: Salandin Gian Antonio , Vascon Mario
Published: March 2005

A familiar beam dynamic condition is rederived making use of matrix methods.
Origin of the force on a current-carrying wire in a magnetic field
Authors: McKinnon W. R. , McAlister S. P. , Hurd C. M.
Published: March 2005

The microscopic origin of the force F = L(i×B) which acts on a wire of length L carrying a current i in a magnetic induction B, is considered.(AIP)
Coriolis acceleration without vectors
Authors: Boyd J. N. , Raychowdhury P. N.
Published: March 2005

The authors consider the physical meaning of Coriolis acceleration in the general motion of a particle with respect to an acelerated coordinate system. (AIP)
Invariant speed in special relativity
Authors: Srivastava Ajit Mohan
Published: March 2005

A simple proof is given that the electromagnetic phenomena are not intrinsic to special relativity as the second postulate tends to suggest. (AIP)
Resource letter SP-2: Symmetry and group theory in physics
Authors: Rosen Joe
Published: March 2005

The author has selected material relevant to symmetry and group theory in physics. Entries are marked E (elementary), I (intermediate), and A (advanced) to designate their level. Articles selected for incorporation in a reprint volume (to be published seperately by the American Association of Physics Teachers) are marked with an asterisk().
Stability and oscillations of a soap film: An analytic treatment
Authors: Durand Loyal
Published: March 2005

In this paper we consider the stability and oscillations (or small motions) of a soap film suspended between parallel coaxial rings. The problem of determining the equilibrium shape of such a film is a standard problem in the calculus of variations, and is often used to introduce variational methods in mechanics texts. However, the stability of the resulting surfaces is usually not discussed, and the small-motion problem is not analyzed in any standard reference. We show that both the stability and small-motion problem can be treated quite easily using eigenfunction methods familiar in elementary quantum mechanics. We use these methods to determine the range of parameters for which the solutions to the variational problem (the extremal surfaces) are stable, and analyze the small motions of the film (with examples) near both extremal and nonextremal surfaces.
Little group for photons and gauge transformations
Authors: Han D. , Kim Y. S.
Published: March 2005

Based on Weinberg’s work on Lorentz-transformation properties of massless particles, we discuss the little group for photons and gauge transformations from a pedagogical standpoint. It is pointed out that the ’’translational’’ degrees of freedom associated with the photon little group can generate a transformation which guarantees the transversality of the four-vector representation for photons. This little-group transformation, which leaves the photon momemtum invariant, can be regarded as a gauge transformation.
The Doppler demon
Authors: Denur Jack
Published: March 2005

Equilibrium blackbody radiation, like all radiation, is, in general, Doppler shifted if it is emitted and/or reflected from a moving body. The relevance of this fact to the analysis of Maxwell’s demon, which has been previously neglected, is revealed in this paper. In particular, we find that, by appropriately taking advantage of this fact, Maxwell’s demon is, at least in principle, capable of operating, albeit very weakly, in violation of the Second Law of Thermodynamics.
Physics of basketball
Authors: Brancazio Peter J.
Published: March 2005

Does a knowledge of physics help to improve one’s basketball skills? Several applications of physical principles to the game of basketball are examined. The kinematics of a basketball shot is studied, and criteria are established for determining the best shooting angle at any given distance from the basket. It is found that there is an optimum shooting angle which requires the smallest launching force and provides the greatest margin for error. Some simple classroom illustrations of Newtonian mechanics based on basketball are also suggested.
Diffusion in dilute gas mixtures and the Einstein relation
Authors: McMahon D. R. A.
Published: March 2005

An Einstein relation between the mutual diffusion coefficient D12 and the effective mutual friction coefficient β12 can be derived for a dilute gas mixture from Maxwell’s transport equation. β12 may be calculated by elementary means to give Chapman’s and Enskog’s first approximation for D12. This paper emphasizes the importance of the Galilean transformation properties of β12 and D12 and shows how they provide a simple demonstration of why D12 is independent of the gas composition.
Greek atomic theory
Authors: Roller Duane H. D.
Published: March 2005

Physics began about 600 B.C. with the Ionian Greeks and reached full development within three centuries. The creation of the concept of the atom is understandable within the context of Greek physical theory; so is the rejection of the atomic theory by the Greek physicists.
Kinetic atom
Authors: Wilson David B.
Published: March 2005

In the middle of the 19th century, physicists abandoned the idea of heat as a special kind of matter in favor of the idea that heat was a ’’mode of motion’’ of ordinary matter. From this ’’dynamical’’ view of heat, they proceeded to a more precise ’’kinetic’’ theory and, along with it, the idea of the kinetic atom. This paper will survey the research of men like Joule, Kelvin, Maxwell, Clausius, and Boltzmann, as it comments on the basic conceptual issues involved in this area of the history of physics.
Rutherford–Bohr atom
Authors: Heilbron J. L.
Published: March 2005

Bohr used to introduce his attempts to explain clearly the principles of the quantum theory of the atom with an historical sketch, beginning invariably with the nuclear model proposed by Rutherford. That was sound pedagogy but bad history. The Rutherford–Bohr atom stands in the middle of a line of work initiated by J.J. Thomson and concluded by the invention of quantum mechanics. Thompson’s program derived its inspiration from the peculiar emphasis on models characteristic of British physics of the 19th century. Rutherford’s atom was a late product of the goals and conceptions of Victorian science. Bohr’s modifications, although ultimately fatal to Thomson’s program, initially gave further impetus to it. In the early 1920s the most promising approach to an adequate theory of the atom appeared to be the literal and detailed elaboration of the classical mechanics of multiply periodic orbits. The approach succeeded, demonstrating in an unexpected way the force of an argument often advanced by Thomson: because a mechanical model is richer in implications than the considerations for which it was advanced, it can suggest new directions of research that may lead to important discoveries.
Correcting a widespread error concerning the angular velocity of a rotating rigid body
Authors: Leubner C.
Published: March 2005

In obtaining the instantaneous angular velocity of a rotating rigid body, a large number of standard textbooks uses an incorrect argument by only considering the rate of change of the Euler angles but disregarding the simultaneous rate of change of the corresponding time-dependent rotation axes. Therefore, a correct and concise derivation of this quantity for a rather general case is given, which also reveals that the usual simple formula does not at all arise as the erroneous textbook reasoning suggests, but as a consequence of certain generalized commutation relations satisfied by Euler rotations.
Educational aspects of the structure of physics
Authors: Karplus Robert
Published: March 2005

The structure of physics, which consists of physical concepts and their relationships, can be treated as an instructional variable by teachers who make the following choices: defined versus derived concepts, operational versus paraphrase (formal) definitions, theoretical versus empirical relationships. Different forms of the structure of physics will emerge from treatments that differ in these respects. For beginning students, reliance on operational definitions and empirical relationships is recommended. For advanced students, paraphrase definitions and theoretical relationships lead to more efficiency and elegance.
Investigation of student understanding of the concept of acceleration in one dimension
Authors: Trowbridge David E. , McDermott Lillian C.
Published: March 2005

This paper describes a systematic investigation of the understanding of the concept of acceleration among students enrolled in a variety of introductory physics courses at the University of Washington. The criterion for assessing understanding of a kinematical concept is the ability to apply it successfully in interpreting simple motions of real objects. The main thrust of this study has been on the qualitative understanding of acceleration as the ratio Δv/Δt. The primary data source has been the individual demonstration interview in which students are asked specific questions about simple motions they observe. Results are reported for the success of different student populations in comparing accelerations for two simultaneous motions. Failure to make a proper comparison was due to various conceptual difficulties which are identified and described. Some implications for instruction are briefly discussed.
Physics of sprinting
Authors: Alexandrov Igor , Lucht Philip
Published: March 2005

Sprinting is described by a simple physical model. The model is used to predict the differences between the recorded times for races on a straight track and on a curve. It is shown that the choice of the running lane makes a non-negligible difference.
Extended Mach principle
Authors: Rosen Joe
Published: March 2005

A self-consistent universe picture is developed, leading to the extended Mach principle that the origin of all the laws of physics lies with the universe as a whole. The meaning of symmetry of the laws of physics and symmetry of the universe and the connection between symmetries and asymmetries of the laws of physics and those of the universe is discussed in general and for specific cases. An explanation of Hamilton’s principle is offered. Predictions of the model are presented. It is suggested that the material is very suitable for informal discussions with students.
Energy levels in helium and neon atoms by an electron-impact method
Authors: Taylor N. , Bartle K. D. , Mills D. , Beard D. S.
Published: March 2005

Electronic energy levels in noble gas atoms may be determined with a simple teaching apparatus incorporating a resonance potentials tube in which the electron beam intensity is held constant. The resulting spectra are little inferior to those obtained by more elaborate electron-impact methods and complement optical emission spectra. Singlet–triplet energy differences may be resolved, and the spectra of helium and neon may be used to illustrate the applicability of Russell–Saunders and other, ’’intermediate,’’ coupling schemes.
Justification of a ’’crucial’’ experiment: parity nonconservation
Authors: Franklin Allan , Smokler Howard
Published: March 2005

In a recent paper it was argued that the 1957 experiments on parity nonconservation were ’’crucial’’ experiments in the sense that they decided unambiguously and within a short period of time for the appropriate scientific community, between two or more competing theories or classes of theories, which were of some importance. In this paper we examine whether such a decision might be justified from a philosophical point of view. A brief history is given, the nature of the evidence evaluated, and various philosophical questions are addressed. Our conclusion is that these experiments are indeed crucial and that the decision can be justified.
The falling raindrop: Variations on a theme of Newton
Authors: Krane K. S.
Published: March 2005

The general problem of mass accretion by a drop falling through a cloud of droplets is considered as an exercise in introductory or intermediate mechanics. The kinematic behavior of the falling drop is deduced for a variety of mechanisms of mass accretion, and some special limiting conditions are discussed.
Jack and the skyhook: The beanstalk revisited
Authors: Gersten Joel , Soodak Harry , Tiersten Martin
Published: March 2005

The ’’skyhook’’ principle is discussed and applied to a uniform rope (Jack’s beanstalk) hanging from a point in the sky. The time for a transverse disturbances to travel from one end of the rope to the other (and back) is calculated.
Quantum statistics of an ideal molecular gas
Authors: Hynne F.
Published: March 2005

For an ideal gas of molecules with internal degrees of freedom, we express the canonical and grand canonical partition functions in terms of the molecular partition function. The derivation is simple and the result is exact. The many-body ground state is included naturally and Bose–Einstein condensation appears without the need of special measures. The canonical partition funtion has a form which generalizes its classical approximation, and we use if for a discussion of multiply occupied molecular states.
Statistics of the detection process in radioactive decay
Authors: Ruby Lawrence
Published: March 2005

The equation for the probability p(n,c,t) of having n radioactive atoms and c accumulated counts at time t is solved under the assumption that the emission process is independent of the detection process. The solution is the product of two binomial distributions. The detailed properties of the joint distribution are shown to be important when only a few radioactive atoms are present. The solution is extended to the case of a radioactive source which decays by multiple emissions, and the result is shown to be related to the problem of measuring the probability distribution of the number of neutrons emitted in spontaneous fission.
One- and two-dimensional hydrogen atoms
Authors: Hassoun G. Q.
Published: March 2005

Certain one- and two-dimensional reductions of the three-dimensional Schrödinger equation of the hydrogen atom are considered. These reductions are carried out from the point of view of the two common sets of space coordinates: Cartesian and spherical. The resulting systems have features that relate more readily to the old quantum theory models of Bohr and Sommerfeld than the general three-dimensional hydrogen atom. Furthermore, the considerations yield interesting insights into the quantum mechanics of the hydrogen atom and may serve as helpful intermediary preparation, in an introductory presentation of the subject, for the unreduced three-dimensional case.
Linear collisions revisited
Authors: Drugowich de Felicio J. R. , Redondo D. M.
Published: March 2005

We present a complete and elegant mathematical description of the sequence of linear collisions between two particles followed by reflection on a wall. The velocities of the particles can be obtained, at any stage of the sequence, in a direct manner. This feature of our solution allows us a priori to find, as a function of the mass ratio, the total number of collisions of each sequence. We also calculate the special ratios which make the final situation a simple reflection of the initial one.
Geometric interpretation of the Pauli spinor
Authors: Frescura F. A. M. , Hiley B. J.
Published: March 2005

We re-examine an intuitively geometric view of the nonrelativistic Pauli spinor and extend it to show how the abstract undotted and dotted spinors of SU(2) can be interpreted in terms of the homogeneous complex coordinates of various points in a stereographic projection plane. A simplified discussion of the connection between the rotation group and special transformations (elliptic homographies) in the plane of projection is presented. Finally, we relate this view of the spinor to those based on the existence of an isotropic or null vector.
Design and fabrication of a simple schlierenscope
Authors: Mitra S. C. , Chaskar M. R. , Phadke S. A.
Published: March 2005

Since 1858 the schlieren method, originally suggested by the French astronomer Léon Foucault, has developed into a versatile tool for the investigation of phenomena involving small optical inhomogeneities in transparent media. The widescale use of this method started immediately after its discovery. This new optical method is easy to apply, noninterfering, nondestructive, free from inertia, and can produce instantaneous records of transient phenomena, and is comparatively inexpensive. This method is based on the deflection of light by the variation of refractive index of the medium. In this paper we have given the details of the construction of a simple compact schlieren experimental setup as an instructional aid.
Angular momentum eigenstates for equivalent electrons
Authors: Tuttle E. R. , Calvert J. B.
Published: March 2005

Simple and efficient methods for adding angular momenta and for finding angular momentum eigenstates for systems of equivalent electrons are developed. Seniority quantum numbers and coefficients of fractional parentage are presented in a simple manner which does not require 6- and 9-j symbols or knowledge of group theory. Several different common representations are used in specific examples. The transformation matrices between jj- and LS-coupled states are explicitly introduced as an example of change of representation and are used to find matrix elements of the spin-orbit interaction and to examine the Zeeman effect in the two representations. The material is suitable for a graduate course in quantum mechanics.
Dipole radiation: A film
Authors: Good R. H.
Published: March 2005

The author reports the production of a new animated film in super−8 cassette form,dealing with electromagnetic radiation.(AIP)
Vindications of Dirac’s electron, 1932–1934
Authors: Moyer Donald Franklin
Published: March 2005

This is the last of a three-part series. The first essay in the series described Dirac’s generalizations of quantum mechanics leading to his theory of the electron. The second essay surveyed evaluations of Dirac’s theory by other physicists, especially by Bohr who used Dirac’s speculations about negative energy electrons as evidence for the failure of quantum mechanics at nuclear dimensions. This essay shows how the material reality of positrons vindicated quantum mechanics and opened new paths for physics.
Aerodynamic effects on discus flight
Authors: Frohlich Cliff
Published: March 2005

Skilled discus throwers claim that a properly thrown discus will travel several meters farther if it is thrown against the wind, than if it is thrown along the direction of the wind. Numerical calculations confirm these claims for winds of up to about 20 m/sec and show that the extra distance is caused by the higher lift and drag forces acting on a discus that is thrown against the wind. Aerodynamic considerations influence numerous aspects of discus throwing, but these have not been dicussed in the scientific literature. In addition to reviewing the available literature, the present article calculates the effect on distance thrown caused by changes in wind velocity, altitude, air temperature, gravity, and release velocity. Some sample results are that a discus can travel: (i) 8.2 m farther against a 10-m/sec wind than with such a wind; (ii) 0.13 m farther at 0 °C than at +40 °C; (iii) 0.19 m farther with no wind at the elevation of Rome, Italy than at the elevation of Mexico City, Mexico; and (v) 0.34 m farther at the equator than at the poles.
Electromagnetic mass, relativity, and the Kaufmann experiments
Authors: Cushing James T.
Published: March 2005

This paper presents the theoretical background for and the detailed analysis of Kaufmann’s 1901–1905 experiments to determine the e/m ratio for fast electrons. Far from providing the first experimental confirmation of Einstein’s special theory of relativity, as is often claimed in physics textbooks today, these data were initially interpreted as confirming Abraham’s classical model of a rigid spherical electron and as providing evidence against special relativity. Only in 1906–1907, upon Planck’s subsequent reanalysis of Kaufmann’s 1905 data, did these experiments become evidence marginally in favor of relativity over classical models of the electron. This particular issue, of the superiority of special realtivity over classical theory in providing a fit to e/m determinations, was not definitely settled until 1914 with new extensive and accurate data obtained by Neumann. The entire episode provides another example that science does not proceed by a strict falsificationist methodology. It shows rather that a great scientist such as Einstein at times gives more weight to a theory that has a certain beauty and produces equations simple in form than he does to experimental results that apparently conflict with such a theory.
Dirac’s form of relativistic quantum mechanics
Authors: Han D. , Kim Y. S.
Published: March 2005

It is shown that Dirac’s ’’instant form’’ dynamics provides a theoretical framework in which models of relativistic quantum mechanics can be constructed. The convariant harmonic oscillator formalism discussed in previous papers is shown to be such a model. Dirac’s ’’point’’ and ’’front’’ forms are shown to generate a space-time geometry convenient for describing Lorentz deformation properties of relativistic extended hadrons.
Student experiments in spontaneous fission
Authors: Becchetti F. D. , Ying J. S.
Published: March 2005

Advanced undergraduate experiments utilizing a commerically available, thin 252Cf spontaneous fission (SF) source are described. These include studies of the energy and mass distribution of the fission fragments and their energy and angular correlation. The energy loss of heavy ions traversing solid and gas absorbers is measured and their effective charges deduced. The SF rate relative to the alpha decay rate is used to infer the SF half-life. These experiments provide a useful introduction to fission, nuclear mass equations, heavy-ion physics, and related topics.
Asymptotic freedom as a spin effect
Authors: Nielsen N. K.
Published: March 2005

It is shown how both the qualitative and the quantitative features of the asymptotic freedom of quantum chromodynamics can be understood in a rather intuitive way. The starting point is the spin of the gluon, which because of the gluon self-coupling makes the vacuum behave like a paramagnetic substance. Combining this result with Lorentz invariance, we conclude that the vacuum exhibits dielectric antiscreening and hence asymptotic freedom. The calculational techniques are with some minor modifications those of the Landau theory on the diamagnetic properties of a free-electron gas.
Measurement of the atmospheric electrostatic potential gradient near sea level
Authors: Cummings Mary R. , Nicholson Howard W. , Porto Deborah R.
Published: March 2005

A simple apparatus has been constructed to measure the atmospheric electrostatic-potential gradient at the surface of the Earth. On 10 September 1979 in an open field in South Hadley, Massachusetts (elevation 250 ft) a potential gradient of 197 V/m was obtained, in reasonable agreement with previous measurements in comparable locations and under similar weather conditions.
Note on the Langrangian description of dissipative systems
Authors: Lemos Nivaldo A.
Published: March 2005

Constraints are placed on the form of the Lagrangian for dissipative systems consistent with dH/dt = dE/dt = −f(ẋ). If the dissipative force is such that f̋(ẋ)≠0, then no Lagrangian can satisfy both ∂L/∂f = f(ẋ) and the equation of motion in the form mẍ+f(ẋ)/ẋ+dV/dt = 0.(AIP)
Illustrated laboratory instructions
Authors: Vernon Robert C.
Published: March 2005

Detailed illustrated laboratory instructions are utilized to create an open laboratory withouth any instructors being present. Color prints and sound narration with color slides are used to produce laboratory instructions.(AIP)
Analysis of laser mode phases by interferometry
Authors: Ruddock I. S.
Published: March 2005

Laser mode phases are analyzed by splitting the beam into two waves that are displaced upon recombination using an interferometer. (AIP)
Ultimate Cartesian diver set
Authors: Wild R. L.
Published: March 2005

A simple Cartesian diver set is described as well as a vertical image projection system using an overhead projector. (AIP)
Rubik’s cube and a model of quark confinement
Authors: Golomb Solomon W.
Published: March 2005

Designating a +1200 rotation (’’twist’’) of a corner cell of Rubik’s cube TM (a popular geometric puzzle) as a (mathematical) quark, and a −1200 rotation of a corner cell as a (mathematical) antiquark, the same restrictions that confine physical quarks are observed to hold, viz. isolated quarks cannot arise, and in general, combinations of quarks and antiquarks can only occur if the excess of one type over the other is a multiple of three.
Simple electronic analog of a Josephson junction
Authors: Henry R. W. , Prober D. E. , Davidson A.
Published: March 2005

We describe an electronic analog of a resistively shunted Josephson junction in which the quantum phase difference of a real junction is represented by the phase difference between two oscillators, each running at approximately 100 kHz. Only three integrated circuits and an external reference oscillator are required. The circuit operates on a time scale approximately 109 times slower than a typical real junction and allows easy visualization of the time-dependent quantum phenomena of the ac Josephson effect. Characteristic current–voltage curves and waveforms obtained with the analog are shown for the cases of dc and dc plus ac current bias, and for the sudden reduction of the critical current in a current-fed, resistively loaded junction, which models a magnetically switched Josephson computer element. Other applications of the analog are discussed.
Class of Lorentz-invariant theories of gravitation
Authors: Harris Edward G.
Published: March 2005

A class of rank-n tensor theories of gravitation is considered. There is more than one theory for each n≳0. All theories are Lorentz invariant and reduce to Newton’s theory for small velocities and weak gravitational fields. Among these theories is the second-rank tensor theory of Whitehead and the spin-two theory of Fierz and Pauli. The precession of the perihelion of a planet’s orbit is calculated for those theories with n = 0, 1, 2 and compared with the prediction of general relativity.
Albert Einstein in Japan: 1922
Authors: Okamoto Ippei , Koizumi Kenkichiro
Published: March 2005

Albert Einstein’s trip to Japan in 1922 is chronicled. (AIP)
Effect of matter on the phase velocity of an electromagnetic wave
Authors: Wangsness Roald K.
Published: March 2005

Interference among reradiated fields from atomic and molecular dipoles is usually used to account for the effect of matter on the phase velocity of an electromagnetic wave. A simple derivation of this effect is given based on the use of Hertz vectors. This treatment can be generalized to the case of a moving medium and the calculation of the Fresnel drag coefficient.
Motion of a sphere on a tilted turntable
Authors: Romer Robert H.
Published: March 2005

Motion of a solid sphere on a tilted turntable is considered. (AIP)
Mildly retarded oscillator
Authors: Blanchard C. H.
Published: March 2005

Mildly retarded one-dimensional oscillator is considered. (AIP)
Lamb shift in nonrelativistic quantum electrodynamics
Authors: Grotch Howard
Published: March 2005

The bound electron self-energy or Lamb shift is calculated in nonrelativistic quantum electrodynamics. Retardation is retained and also the σ⋅Brad interaction previously dropped in other nonrelativistic approaches is kept. The results are finite without the introduction of a cutoff, and they lead to a Lamb shift in hydrogen of 1030.9 MHz, which is about 2.5% less than the standard relativistic calculation.
Ball rolling on a turntable: Analog for charged particle dynamics
Authors: Burns Joseph A.
Published: March 2005

For a ball to roll without slip across the surface of a rotating platform, a frictional force of the form Aωd×v is required, where A is a known constant, ωd is the platform’s angular velocity, and v is the particle’s velocity relative to inertial space. Since this force is of the same form as that experienced by a charged particle moving through a magnetic field, the ball executes only closed circular orbits. Other similarities to the charged particle problem are easily demonstrated: for example, drift velocities are produced normal to any external force lying in the plane of the disk, and an adiabatic invariant can be defined for the case when the disk changes its spin rate.
Fact and illusion in the speed-of-light determinations of the Römer type
Authors: Karlov L.
Published: March 2005

Speed-of-light determinations by the principle first used by Römer gain their meaning either from an assumed constancy of this speed for all directions or else from an assumed constancy for all closed paths. The observed result, in either case, evaluates the corresponding constant. It is therefore incorrect to hold that Römer’s method objectively gives a one-way speed. These circumstances are illustrated by analysis of a laboratory experiment proposed by G. B. Brown.
Lorentz-invariant potentials and the nonrelativistic limit
Authors: Bloch Ingram , Crater Horace
Published: March 2005

We discuss a relativistic particle affected simultaneously by two static potentials, a Lorentz scalar and the time component of a four-vector. We show that the scalar potential has effects on the motion of a particle that are distinctively different from those of a four-vector potential. With the aid of an example we show that, in both classical and quantum mechanics, there are two inequivalent but compatible criteria of nonrelativistic behavior: (mean) kinetic energy much smaller than rest energy and nonrelativistic potential energy independent of total energy. The second of these is the correct condition for use of nonrelativistic methods, but it is the first that is usually invoked to justify their use. The two criteria are equivalent only when the scalar potential has a (mean) value much less in magnitude than the particle’s rest energy. If this condition is not satisfied, nonrelativistic formalisms such as ordinary Newtonian mechanics and the Schrödinger equation may be inadequate even if v/c is small. On the other hand, it is possible that a large S may permit relativistic energy relations to be written in a nonrelativistic form even if v/c is not small. Such an influence of the size of the scalar potential on what is considered nonrelativistic behavior is unfamiliar and is rarely mentioned in textbooks and other publications. In our opinion, it should be better known.
Teaching classical statistical mechanics: A simulation approach
Authors: Sauer G.
Published: March 2005

A one-dimensional model of an ideal gas is proposed in order to study the development of disordered motion in Newtonian mechanics. A Monte Carlo procedure for the simulation of the statistical ensemble of an ideal gas with fixed total energy is developed. The comparison of both approaches is utilized for a pseudoexperimental foundation of statistical mechanics. The theoretical prediction of the Maxwell–Boltzmann distribution is derived from the Monte Carlo procedure.
Simplified models of completely degenerate, differentially rotating stars
Authors: Simon Sheridan A. , Hurley Donna
Published: March 2005

The properties of differentially rotating, completely degenerate sections of infinite cylinders are examined. Their construction is simple, with variables depending only on the radial cylindrical coordinate. They are found to possess important characteristics which qualitatively resemble much more complicated two-dimensional models of differentially rotating degenerate stars: (1) an analog of the Chandrasekhar limit; (2) a limit to uniform rotation imposed by centrifugal breakup; (3) massive, differentially rotating structures of moderate radius can be constructed; and (4) models obey the Solberg–Ho/iland criterion for stability of the rotation field and appear to be stable against inverse beta decay and general relativistic collapse. These characteristics combined with the simplicity of construction make these models useful in the study of the structure and evolution of differentially rotating stars.
Power demand in walking and pace optimization
Authors: Bellemans A.
Published: March 2005

The power expenditure in walking is presented as the sum of the work required for accelerating and decelerating the legs, plus the gravitational work associated to the lift of the trunk at each step. These two contributions are, respectively, inversely and directly proportional to pace length. As a consequence this model predicts an optimal pace, for a given speed, which corresponds to minimal power demand. This is in agreement with experiments on subjects walking on a treadmill. The model is primarily of pedagogical interest and its quantitative predictions not very accurate.