Response functions of free mass gravitational wave antennas

Rainer Weiss and collaborators have from first principles derived the response of a free mass interferometer (or 2-arm gravitational wave antenna) to plane polarized gravitational waves [1]. We here obtain equivalent formulas (generalized slightly to allow for arbitrary elliptical polarization) by a simple differencing of the 3-pulse Doppler response functions of two 1-arm antennas [2]. A 4-pulse response function is found, with quite complicated angular dependences for arbitrary incident polarization. The differencing method can as readily be used to write exact response functions (3n+1 pulse!) for antennas having multiple passes, or having more arms.The research described in this paper was carried out at the Jet Propulsion Laboratory, under contract with the National Aeronautics and Space Administration.     

Bohr's discussion of the fourth uncertainty relation revisited

Bohr's 1930 derivation of the uncertainty relation c ² m th bears a close relationship to Einstein's 1913 derivation of the gravitational redshift via the equivalence principle. A rewording of Bohr's argument is presented here, not taking the last step of acceleration as equivalent to a uniform gravity field, thus yielding a derivation of the formula c ² m th, avoiding Treder's 1971 objection.     

Inertia,relativity and cosmology

Starting with the idea that the inertia of bodies is a general property of all kinds of their potential energy, the author arrives at the two fundamental megaphysical equations (I, II)⁰ +c²=0,⁰ =0 where⁰ is the scalar gravitational potential due to the smoothed-out universe,⁰ is its electrostatic potential andc denotes the light velocity in vacuo.The first equation means physically that the cosmic potential⁰ determines uniquely the velocity of light and consequently the pseudo-Euclidean geometry in an inertial frame, in the absence of local gravitational fields. This fact implies the validity of the law of inertia in a non-empty universe only, in full agreement with Mach's principle.If we adopt, for the cosmic potential, that of Seeliger, differing from the Newtonian potential by the exponential factor exp (–r/r_g), we can use Eq. (I) to estimate the lower limit of the range r_g of gravitational interaction within the limits (10¹⁰–10¹²) light years. This suggests a steadystate model of the universe consisting of an unlimited number of finite regions (sub-universes) oscillating independently of each other. Such a superlarge-scale model universe is in agreement with the observed galactic red shift and yet it fulfils the perfect cosmological principle.     

Hamiltonian formulation of general relativity in terms of Dirac spinors

The Dirac spinors and matrices are used in combination with the Arnowitt-Deser-Misner formalism in order to obtain yet another formulation of Hamiltonian general relativity, together with a new form of the Gauss-Codazzi equations. The relation with Ashtekar's variables is analyzed; it is shown, for instance, that the matrices are equivalent to the electric field variable. The electric and magnetic decomposition of the gravitational field is also studie using Dirac matrices.     

КОГЕРЕНТНОЕ ИЗЛУЧЕН ИЕ СИНХРОТРОННЫХ СГУ СТКОВ ЭЛЕКТРОНОВ В ЗАМКНУТ ОМ РЕЗОНАТОРЕ

. , .

---

The coherent radiation of synchrotron electron clusters in a closed resonator

A study is made of the electromagnetic interaction of electrons in thin relativistic clusters during coherent radiation in a synchrotron. The magnitude and form of the tangential component of the force, acting on an isolated electron of a cluster of electrons, is expressed.

---

---

. . .     

Studium der photodielektrischen Erscheinung an lumineszierenden Zinkkadmiumsulfiden

Zusammenfassung Die spektrale Abhägigkeit der photodielektrischen Eigenschaften der lumineszierenden Zinkkadmiumsulfide verschiedener Zusammensetzung zeigt, da eine Beimengung von Kupfer das Eintreten von Zuständen mit groer Polarisierbarkeit hervorruft, die eine Änderung der realen Komponente der Dielektrizitätskonstanten zur Folge haben. Die Kupferkonzentration kann dabei so gering sein, da sie in der Lumineszenzemission gar nicht zur Geltung kommt. Die Infrarotmaxima der Verluste entsprechen Niveaus, die von anderen Autoren und mit anderen Methoden festgestellt wurden. Das Maximum des Exzitationsspektrums im Bereiche des Ausläufers der Absorptionskante hängt mit dem Maximum der Änderung der realen Komponente der Dielektrizitätskonstante zusammen.

---

-

- , , . , . , . .

---

---

Nunmehr im Physikalischen Institut der Karlsuniversität, Prag.     

К ВОПРОСУ ТЕОРИИ КОЭР ЦИТИВНОЙ СИЛЫ ТОНКИХ ЛИСТОВ

- . , - . . - . 1956 .     

Усовершенствование рентгенометрическо го метода определения дефекто в решетки третьего ро да в поликристаллическ их и порошкообразных материалах

, . .     

Time Multidimension in Gravity

The influence of possible additional (hidden) components of time on a body's motion in the field of a gravitational wave is considered. Contrary to the one-time theory, oscillations of the body height and width sizes in a plane perpendicular to the direction of the wave propagation occur independently from one another. This peculiarity can be used for the experimental check of emission of gravitational waves with distinct time trajectories in cosmic cataclysms. An interesting analogy between electromagnetic and gravitation quantities is discussed in the context of time multidimension.     

The quantum theory of multipole radiation in a dielectric

The potentials of an electromagnetic field of multipoles in a dielectric, which is realized by a dielectric sphere having a perfectly conducting surface, are derived. The diagonal values of the energy for thez component of the angular momentum and the square of the angular momentum of the field are determined and also the ratio between thez component of the angular momentum and the energy and the ratio between the square of the angular momentum and the square of the energy. It is shown that the total angular momentum can be divided in the usual way into orbital and spin parts but that these parts cannot be interpreted as the orbital and spin angular momentum because their eigenvalues cannot be the eigenvalues of any operator of infinitesimal rotation. In the commutation rules of a multipole field the vector character of the field is to a certain extent suppressed and the spin of the photon in a state with a certain value of the energy, parityz component of the angular momentum and the square of the angular momentum is not defined.

---

, . ,z— , , z— . , , , , , - . , ,z— .

---

---

In conclusion the author thanks Dr. . Muziká for directing the work, F. Samek for valuable remarks and discussion and J. Kvasnica for help in preparing the paper for publication and for adding a number of remarks.     

Comparison of the structure of island deposits of gold on NaCl produced by thermal vaporization and by cathode sputtering

A comparison was made of island deposits of gold on NaCl, produced by thermal vaporization (thermal Au/NaClid) and cathode sputtering (cathode Au/NaClid). In thermal Au/NaClid, two orientations of the gold microcrystals with respect to the NaCl (100) shear face were observed; multiply twinned particles were formed. In cathode Au/NaClid, only one orientation is present and the formation of complex particles is not observed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 46–50, November, 1971.     

Feynman integral and complex classical trajectories

Let _t be an analytic solution of the Schrödinger equation with the initial condition . Let _t be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then _t (x) _t (x)¹ ( _t (x)), where _t (x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations.     

Change in primary extinction of X-rays in solid solution of NaCl-CdCl2

The Suzuki model of regions with a hyperstructure was verified, the dependence of their size on the cooling rate was found and it was determined that they disappear at temperatures between 250° and 300°C according to their composition. Up to 1000 Å their structure is coherent with a matrix lattice and their formation is not accompanied by a decrease in the primary extinction. Regions above 1000 Å are partially incoherent and their formation and disappearance are apparent by a change in the primary extinction.

---

NaCl-CdCl₂

, , , 250°–300°C . , 1000 Å, . , 1000 Å, .

---

---

The author would like to thank I. Kunzlová, and M. Lébl for preparing the crystals of NaCl-CdCl₂ solid solution and Dr. Trnka for determining the cadmium Concentration in them.     

Matter and light wave interferometry in gravitational fields

We consider the problem of finding the quantum mechanical phase associated with the propagation of a particle in a given external gravitational field, and conclude that it ism ds. In weak fieldsh this allows us to calculate the gravitationally induced phase on a freely traveling particle as 1/2 h P dx whereP is the ordinary momentum. This formula has the expected Newtonian limit and is then used to calculate effects in matter wave interferometry such as those due to gravity waves and the dragging of the ether frame by rotating bodies. Light wave interferometry is then considered and is shown to be also described by 1/2 h K dx , whereK is the wave vector of the light, and the integral is along the path of the ray. Matter and light wave interferometry are compared in various cases.A preliminary version of this work was presented at the Grenoble Workshop on Neutron Interferometry, June 1978.     

A contribution to the theory of the triple crystal diffractometer

The first part of the paper gives a general equation for triple-crystal arrangement with perfect crystals on the assumption that the third crystal is rotated. It is shown that in the case of perfect crystals the shape of the reflection curve is practically independent of the vertical divergence. The case of mosaic crystals is also solved and the possibility of rotation by other than the third crystal is considered. A method is proposed for investigating the imperfection of a crystal which is different from methods used up to now. The paper is supplemented by some experimental results.

---

, . , . , , . , . .

     

Collisionless kinetic equations for massive particles with spins 1/2 and 0 in gravitational and electromagnetic fields

We define a covariant and gauge-invariant generalization of the Wigner functions of particles with spins 1/2 and 0. The collisionless kinetic equations are obtained for these particles in external gravitational and electromagnetic fields in the quasiclassical approximation; also obtained are the momentum representations of the energy-momentum tensor, current, and spin tensor, taking into account the effects of the spin's interaction with the gravitational field an electromagnetic field. The following notation is used: e and m are the charge and mass of the particles; is Planck's constant; (x) are the covariant-fixed Dirac matrices; ^,=(1/4)[, ]: a(^b)=(1/2) (a b +ab ); [A, B]=A·B – B·A; A,B=A·B+B·A; g(x)=det(g (x));R = –...; the speed of light c=1.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 47–53, September, 1990.The author wishes the thank Yu. G. Ignat'ev and members of the seminar in General Relativistic Statistics and Cosmology of the Kazan' Pedagogical Institute for useful discussions.     

Electronic processes andZ centres in NaCl and KC1 crystals

The paper gives the experimental results of the team-work study of coloured pure and Ca doped NaCl and KC1 crystals. The mechanism of the formation ofR centres by coagulation ofF centres and of the formation ofZ centres fromF centres, cation vacancies and Ca ions is discussed. An alternative model forZ ₃ centres is proposed. The possible connections between physical and chemical behaviour are indicated.

---

Z- NaCl 1

NaCl KCl . R- F- Z- F-, Ca. Z ₃-. .

---

---

This work was presented by the courtesy of Prof. R. Maurer at the Symposium on Color Centers, Corvallis, Oregon (1959).

---

The authors wish to express their gratitude to K. Suk, K. Listoová and M. Javrková for carefully carrying out the measurements and I. Kunzlová and L. Nováková for preparing the crystals.     

Summation formulae in the theory of thin films

On the basis of general summation formulae for light reflected and transmitted by a thin film the author derives formulae for a thin dielectric film, for a thin metallic film and for a system of thin dielectric films. This solution is based on Stokes's principle of reversibility, which is the idea unifying the cases into one theory. In conclusion he gives the solution of a general case, dealing with light reflected and transmitted by a system of thin dielectric and metallic films.

---

, . , , . , .

     

ЗАТУХАНИЕ КОЛЕБАНИЙ ЧАСТИЦ В ОБЩЕМ ПОЛЕ С ПЕРИОДИЧЕСКОЙ СТРУКТУРОЙ I

, , . , . .

---

The damping of particle oscillations in a general field with periodic structure I

A liner theory is derived, discussing the dynamics of particles in the region of an equilibrium orbit in a general electromagnetic field, which forms a periodic system. The total particle damping is determined from the Hamiltonian found and from dissipative forces brought out by a classical reaction radiation. Relations for the damping of the synchrotron oscillations are derived from the study of the appropriate phase space.

     

A study of the influence of dislocations on some of the magnetic properties of permalloy alloys

The influence of dislocations produced during plastic pulling on some magnetic properties is studied experimentally with special attention to the coercive force of Fe-Ni alloys with a cubic face-centred lattice. Vicena's theory of the influence of dislocations on the coercive force is rendered more accurate and the dependences of the coercive force on the plastic lengthening of the samples are derived for the above-mentioned alloys; the results are compared with the measured dependences. The observed anomalies are explained.

---

-

, , - n . . .

---

---

In conclusion the author would like to thank J. Kaczér for many suggestions and advice, F. Kroupa for advice and cooperation in the theoretical part of the paper and particularly J. Grolmus for carefully carrying out the many measurements and for all-round help in the experimental work. He also thanks V. Kamberský for carrying out some of the measurements and finally V. Janovec for some remarks and for carefully reading the paper.