On Essential Incompleteness of Hertz’s Experiments on Propagation of Electromagnetic Interactions

The historical background of the 19th century electromagnetic theory is revisited from the standpoint of the opposition between alternative approaches in respect to the problem of interactions. The 19th century electrodynamics became the battle-field of a paramount importance to test existing conceptions of interactions. Hertzs experiments were designed to bring a solid experimental evidence in favor of one of them. The modern scientific method applied to analyze Hertzs experimental approach as well as the analysis of his laboratory notes, dairy and private letters show that Hertzs crucial experiments cannot be considered as conclusive at many points as it is generally implied. We found that alternative Helmholtzs electrodynamics did not contradict any of Hertzs experimental observations of transverse components as Maxwells theory predicted. Moreover, as we now know from recently published Hertzs dairy and private notes, his first experimental results indicated clearly on infinite rate of propagation. Nevertheless, Hertzs experiments provided no further explicit information on non-local longitudinal components which were such an essential feature of Helmholtzs theory. Necessary and sufficient conditions for a decisive choice on the adequate account of electromagnetic interactions are discussed from the position of modern scientific method.     

Robert Hooke’s Seminal Contribution to Orbital Dynamics

During the second half of the seventeenth century, the outstanding problem in astronomy was to understand the physical basis for Keplers laws describing the observed orbital motion of a planet around the Sun. In the middle 1660s,Robert Hooke (1635–1703) proposed that a planets motion is determined by compounding its tangential velocity with the change in radial velocity impressed by the gravitational attraction of the Sun, and he described his physical concept to Isaac Newton (1642–1726) in correspondence in 1679. Newton denied having heard of Hookes novel concept of orbital motion, but shortly after their correspondence he implemented it by a geometric construction from which he deduced the physical origin of Keplers area law,which later became Proposition I, Book I, of his Principia in 1687.Three years earlier, Newton had deposited a preliminary draft of it, his De Motu Corporum in Gyrum (On the Motion of Bodies), at the Royal Society of London, which Hooke apparently was able to examine a few months later, because shortly there-after he applied Newtons construction in a novel way to obtain the path of a body under the action of an attractive central force that varies linearly with the distance from its center of motion (Hookes law). I show that Hookes construction corresponds to Newtons for his proof of Keplers area law in his De Motu. Hookes understanding of planetary motion was based on his observations with mechanical analogs. I repeated two of his experiments and demonstrated the accuracy of his observations.My results thus cast new light on the significance of Hookes contributions to the development of orbital dynamics, which in the past have either been neglected or misunderstood.Michael Nauenberg is Professor Emeritus of Physics at the University of California, Santa Cruz. His primary research has been in theoretical physics, but he also has written several articles and coedited a book on the historical development of dynamics by Huygens, Newton, and Hooke.     

Gravity as Archimedes’ Thrust and a Bifurcation in that Theory

Eulers interpretation of Newtons gravity (NG) as Archimedes thrust in a fluid ether is presented in some detail. Then a semi-heuristic mechanism for gravity, close to Eulers, is recalled and compared with the latter. None of these two gravitational ethers can obey classical mechanics. This is logical since the ether defines the very reference frame, in which mechanics is defined. This concept is used to build a scalar theory of gravity: NG corresponds to an incompressible ether, a compressible ether leads to gravitational waves. In the Lorentz–Poincaré version, special relativity is compatible with the ether, but, with the heterogeneous ether of gravity, it applies only locally. A correspondence between metrical effects of uniform motion and gravitation is assumed, yet in two possible versions (one is new). Dynamics is based on a (non-trivial) extension of Newtons second law. The observational status for the theory with the older version of the correspondence is summarized.     

Current controlled negative resistance phenomenon in SbPbSe system

Thin film Al/Sb₂Pb₁Se₇/Al metal-glass-metal sandwiched structures prepared using thermal evaporation technique have been studied. The I–V measurements showed that the devices switched from high resistance OFF state to a low resistance ON state when a particular voltage appeared across it. The OFF state I–V characteristics showed non-ohmic behaviour while in the ON state the devices displayed purely linear characteristics. The switching voltage (V _th) was found to depend on film thickness and temperature of the device. A linear relation between V_th and temperature was observed.     

On the origin of Kaluza’s idea of unification and its relation to earlier work by Thirring

We argue that the starting point of Kaluzas idea of unifying electrodynamics and gravity was the analogy between gravitation and electromagnetism which was pointed out by Einstein and Thirring. It seems that Kaluzas attention was turned to this point by the three papers on the Lense–Thirring effect and the analogy between gravitation and electromagnetism which were published a short time before Kaluzas paper was submitted. We provide here also an English translation of the third of these papers (Phys. Zeits. 19: 204, 1918).     

The ground state of the Bose gas

The mathematical formalism describing the Bose gas at zero temperature is analysed with the aid of methods that have recently been successful in relativistic quantum field theory. First the spectrum conditions for an infinitely extended system are given and the algebra of observables and the algebra of field operators are defined. General properties of states over these algebras are discussed and theorems are given which connect the linked cluster property, translation invariance and the purity of the states. It is proved that pure states over the algebra of observables have the property of factorisable off-diagonal long range order. The class of quasi free states is defined and of these states those which are translation invariant and possess the linked cluster property are analysed. It is shown that this class of states contains a subclass of pure states of the Bogoliubov type and a subclass of states which are mixtures of non-translationally invariant pure states. The applications of these quasi free states to the interacting Bose gas are summarized.     

A possible test of quantum electrodynamics by means of polarization effects in electron-nucleon scattering

The differential cross-section is given for the electromagnetic scattering of polarized relativistic electrons on polarized nucleons. The finite size of each particle is taken into account by means of two form-factors. The effect of the possible non-punctiform structure of the electron on the polarization effects in scattering is discussed. It is shown that the internal structure of the anomalous magnetic moment of the electron would show itself in the cross-section by terms depending on the transversal polarization of the incident electrons.

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Summary of results of a diploma-thesis for the degree of graduate physicist.

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In conclusion the author wishes to express his sincere gratitude to prof. V. Votruba and J. Kvasnica for suggesting this problem, for helpful discussions and valuable advice.     

Analysis of signal-to-noise ratio of the laser Doppler velocimeter

The signal-to-shot-noise ratio of the photocurrent of a laser Doppler anemometer is calculated as a function of the parameters which describe the system. It is found that the S/N is generally a growing function of receiver area, that few large particles are better than many small ones, and that generally the fringe or differential mode configuration is equal to, or better than, the reference beam mode.     

ИЗЛУЧЕНИЕ ЭЛЕКТРИЧЕ СКОГО ДИПОЛЯ НАД ГРАН ИЦЕЙ ДВУХ СРЕД

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Far-field techniques for the characterization of single-mode fibres

The characterization of single-mode fibres is important not only for determining the system parameters for a particular fibre, but also for the specification of fibres for manufacturing purposes. We present a detailed analysis of two new methods of characterizing single-mode fibres. The strip integrated far-field method involves measuring the light power passed by a thin slit scanned across the far-field pattern and the area integrated far-field method involves measuring the light power passed by a knife edge scanned across the far-field pattern. It is shown that, for either method, the measured data is related to the transverse offset transmission coefficient by the Fourier-cosine transform and hence that the far-field r.m.s. spot-size can be directly calculated. Noise analysis shows that the area integrated far-field method is superior to the strip integrated far-field method and similar to the far-field mask method when a broadband light source is used to measure the far-field r.m.s. spot-size. It is also shown that the area integrated far-field method has smaller systematic errors than the far-field mask method.     

The many faces of a character

We prove an identity between three infinite families of polynomials which are defined in terms of bosonic, fermionic, and one-dimensional configuration sums. In the limit where the polynomials become infinite series, they give different-looking expressions for the characters of the two integrable representations of the affine su(2) algebra at level one. We conjecture yet another fermionic sum representation for the polynomials which is constructed directly from the Bethe-ansatz solution of the Heisenberg spin chain.     

A finite size analysis of the structure factor in the antiferromagnetic Heisenberg (AFH) model

From a finite size analysis we extract the structure factorS(p, N=) of the one dimensional AFH-model in the groundstate: The gross structure is well described byL (p) = –ln(1– ^p ). The fine structure which only contributes a few percent reveals a pronounced non-linear behavior inL(p) with a maximum atp=0.20 and a minimum atp=0.82.     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

Stochastic Ornstein–Uhlenbeck Capacitors

We introduce and study a class of random capacitor systems which are both charged and discharged stochastically. A capacitor is fed by a random inflow with stationary and independent increments. Discharging occurs according to a Markovian rate which is linear in the capacitors level. The resulting capacitor dynamics are Markovian, stochastically cyclic, and regenerative. We coin these systems Lévy-charged Ornstein–Uhlenbeck capacitors. Various random quantities associated with these systems are analyzed, including: the time-to- discharge; the duration of the charging cycle; the trajectory and the peak height of the capacitor level during a charging cycle; and, the capacitors stationary equilibrium level. Furthermore, we show that there are sharp distinctions between these capacitor systems and corresponding standard Lévy-driven Ornstein–Uhlenbeck systems.     

Nonequilibrium response of a disordered Ising chain

The relaxation behaviour of a model disordered system is studied. The model considered is a nearest neighbour Ising chain in which the bond strengths are distributed at random between the discrete values +J and -J with equal probability. The system is prepared in a given state and is allowed to relax to a new state of equilibrium. This approach to equilibrium is probed by means of an applied, weak, time-dependent magnetic field. The relevant physical quantity is a nonequilibrium susceptibility which is calculated exactly. A comparison between this, and the corresponding quantity for the pure chain, reveals certain distinctive features of the time-dependent properties of disordered systems.Deceased     

Rate equations and transient phenomena in semiconductor lasers

This contribution attempts to review certain resonance effects which occur in the dynamic behaviour of semiconductor lasers. To study these effects theoretically, a rate equation approach is used for single-mode operation in the region of lasing threshold.The two basic rate equations are given and their transient solutions discussed. The existence of two time constants in these equations, viz. the electron lifetime _e and the photon lifetime _e; gives rise to a characteristic resonance frequency in the GHz region. This resonance manifests itself in transient spiking effects, in quantum noise phenomena, and in high-frequency modulation experiments. In a modified form the resonance frequency may also be studied in lasers with external cavities and in double-diode configurations (or, equivalently, conventional devices with non-uniform excitation along the cavity length).In the latter two examples mentioned above, the resonance is excited by optical feedback of the laser radiation into the active medium via a lossy or insufficiently inverted region. In the spiking oscillations commonly observed at the commencement of laser operation, the initial population overshoot is the cause of the resonance. For the case of quantum noise it is the requirement that the photon and electron populations have integer values which supplies the driving force-a true quantum effect. High-frequency modulation experiments directly reveal the same resonance frequency where a strong maximum in modulation intensity occurs.A part of this work was reported at the Conference on Semiconductor Injection Lasers and their Applications, Cardiff, March 1972.     

КРУЧЕНИЕ ПРИЗМАТИЧЕ СКИХ СТЕРЖНЕЙ ШВЕЛЛЕ РНОГО ПОПЕРЕЧНОГО СЕЧЕНИЯ

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State automorphisms in axiomatic quantum mechanics

A new metric which we call the intrinsic metric is introduced on the states of the generalized logic of quantum mechanics. It is shown that every automorphism on is an isometry. A norm can be defined on the linear spanE of which reduces to the intrinsic metric on. IfX is the completion ofE then every automorphism, on has a unique extension to a linear isometry onX. A comparison is made between these results and those of Kroniff.     

Underdetermination,Realism, and Theory Appraisal: An Epistemological Reflection on Quantum Mechanics

This paper examines the epistemological significance of the present situation of underdetermination in quantum mechanics. After analyzing this underdetermination at three levels---formal, ontological, and methodological---the paper considers implications for a number of variants of the thesis of scientific realism in fundamental physics and reassesses Lakatos characterization of progress in physical theory in light of the present situation. Next, this paper considers the implications of underdetermination for Weinbergs dream of a final theory. Finally, the paper concludes by suggesting how one might still think of realism and progress in fundamental physics despite the possibility of persistent underdetermination in quantum mechanics.This paper draws from my Ph.D. dissertation, Ontological Commitments and Theory Appraisal in the Interpretation of Quantum Mechanics (University of Notre Dame, 1998). It was presented at the James T. Cushing Memorial Conference on Philosophical Issues in Physics, University of Notre Dame, November 2002. My thanks to the participants on that occasion for their comments and questions.     

Rational forms for twistings of enveloping algebras of simple Lie algebras

We give rational forms for twistings of classical enveloping algebras. We also remark a link with the generalized formalism of Gurevich, Manin, and Cartier.