The axiomatic foundations of the theory of special relativity

In this paper it is shown that (1) linear transformations more general than the Lorentz transformation—containing the Palacios and the Lorentz transformation as special cases—(2) and the principle of the constancy of the velocity of light (taken originally by Einstein together with the supposition of the linearity of transformation as fundamental hypotheses of the theory of special relativity)—can be deduced from Maxwell's equations for the electromagnetic fieldin vacuo (A ₁), the principle of relativity (A ₂) and the two following axioms (which do not contain explicitly the hypothesis of the isotropy of space!): (A ₃) to every event in the Galilean reference systemS there corresponds one and only one event in the systemS so that these two systems are connected by reversible single-valued functions, continuously differentiable as their inverse transformations, (A ₄) the constant relative velocitiesv _ss andv _ss betweenS andS are each other equal in magnitude and opposite in signv _ss =–v _ss To obtain uniquely the Lorentz transformation the following axiom has to be added: (A ₅) the distanceD of any two points at rest inS, situated in a plane orthogonal to the relative velocity betweenS andS is measuredS as independent of the sense of the velocity, i.e. if one changesv _ss into –v _ss the distanceD does not vary for an observer inS. Results of our theory are the ideas that (a) the fact that the Lorentz transformation is not the unique transformation leaving Maxwell's equations for the electromagnetic field in all Galilean systems of reference invariant but that there exists a more general transformation (containing these two transformations as special cases) leaving Maxwell's equations invariant; (b) that the Michelson-Morley as well as the Fizeau experiment does not represent an experimental proof in favour of the theory of special relativity. At the end of the paper the mutual relations between the principle of relativity (the axiomA ₁ together with the axiomA ₂), the axiomA ₅ and the possibility of the discernibility as well as the indiscernibility of right and left at the macrocosmic level is discussed.     

Beitrag zum Phasendiagramm von Zn-Sb

Zusammenfassung In der vorliegenden Arbeit werden die Ergebnisse der Röntgenstrukturstudie der Phasen im System Zn-Sb beschrieben. Es wurde das Grundprisma, die Symmetrie und die Anzahl der stöchiometrischen Einheiten in der Zelle in -Zn₄Sb₃ bestimmt. Bei Zn₃Sb₂ wurde festgestellt, da die Hochtemperaturphase bei langsamer Abkühlung auf die Raumtemperatur in -Zn₄Sb₃ und Zn zerfällt.

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Zn-Sb

Zn-Sb. , -Zn₄Sb₃. Zn₃Sb₂ , -Zn₄Sb₃ u Zn.

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Ich danke allen Mtarbeitern des instituts für technische Physik für ihre unterstützung, die mir die Durchführung dieser Arbeit ermöglichte, insbesondere den Kollegen Dr. K. Toman und Dr. A. Línek.     

Pulsations and chaos in laser-produced plasmas

A general criterion is proposed predicting the onset of chaotic behavior for parametric processes in a laser-produced plasma. The conditions when the transition to the stochastic regime occur are determined for various parametric instabilities excited when a high intensity laser interacts with a plasma. The complicated temporal structure observed in 3/2₀, 2₀, 1₀, and fast electron emission in experiments using high-intensity (I10^15–17 W/cm²), short ( _L 40–200 psec) Nd laser pulses is attributed to the reflection seeded SBS instability being driven into this regime.Lebedev Physics Institute, Leninsky Prospect 53, Moscow 117924 Russia.     

Mach's principle and the reciprocal symmetry of nature

This article develops the postulate that spacetime-charge inversion invariance reflects a fundamental reciprocal symmetry in nature between the two long range forces, from which the derivation of Mach's principle (i.e., the principle that the fundamental parameters of the electromagnetically elementary charged particle are related to those describing the electromagnetically observable universe) follows quite easily. Interpreting this result, it is argued that relativity and quantum mechanics can be made conceptually compatible and mathematically consistent by this reciprocal symmetry if one realizes that relativity isboth a macroscopic, semiclassical theory (i.e., the global half of relativity, described by Eq. (1.1), including special and general relativity) and a microscopic theory (i.e., the local half of relativity, described by Eq. (2.1), including relativistic quantum mechanics and field theory). The reciprocal symmetry of nature, then, promises unique (differential and/or integral) relationships between the coordinate variables of the observers of these tworeciprocally related theories, which implies unique, consistent numerical values for the scalar curvatureR, the massM, and the critical density for closure, _c, of the observable universe [derived from the elementary particle parameters (i.e., the electron mass and Coulomb radius)]. With this symmetry we also postulate a plausible mechanism for spontaneous generation of matter from the ubiquitous (zero-mass ether) nothingness of the Dirac sea of filled negative energy states, and can consistently interpret both the positive and negative-energy state solutions of Dirac's equation for massive, spin-1/2 (i.e., fermion) particles and both the advanced and retarded potential solutions of electromagnetic field equations. It is pointed out that, with this interpretation of the advanced potential solutions from electromagnetic field theory, one can actuallyderive causality from electromagnetic theory.     

Определение средней величины кристаллик ов кварца И графита на основани и первичной экстинкц ии

— —10 ^–4 —10 ^–2 . , . , , , , , .     

Ultrasound in spin glasses

The change of the sound velocity v(,T) and the damping of sound waves (,T) in spin glasses are calculated in the frame-work of an Ising model with a random distribution of exchange interactions. The calculation is based on linearized equations of motion for the spins and on an improved mean field approximation which includes the Onsager reaction field. Near to the freezing temperatureT _f and at high temperatures v(,T) and (,T) turn out to be approximately proportional to the real and the imaginary parts of the dynamical susceptibility. For the special case of infinite range interactions atT=T _f one has v(, T_f) ( )^1/2 and (, T_f) (/)^1/2 where is the relaxation time of independent spins. However, already slightly aboveT _f the frequency dependence of both quantities becomes rather small for RKKY spin glasses. At high temperatures both, v(,T) and (,T) vary asT ^–1.SFB 125 Aachen-Jülich-Köln     

A new solution of Schmutzer's projective relativistic cosmology

Schmutzer's cosmological model on the basis of his projective unified field theory leads to a system of differential equations equivalent to a set of highly complicated Abel differential equations [1, 2]. This paper is concerned with the properties of this coupled system of differential equations. The main results of this paper are as follows, (i) We have found the explicit general solution of the cosmological equations for the case=±5/2,= ±1. (ii) The procedure of solving the general case arbitrary=0 is easily within this formalism, (iii) After having found the solution with arbitrary,=±1, one gets the corresponding solution= -, =±1. (iv) In general the coupled system of differential equations describing Schmutzer's cosmological model is equivalent to a single generalized Emden differential equation and it is identical to Emden's differential equation for special values of the parameter.     

Space-Charge Field Induced in a Photorefractive Crystal with an Applied Square-Wave Electric Field for Large Contrast of an Interference Pattern

In the quasi-static approximation, the nonlinear equation for the space-charge field E _sc formed in a photorefractive crystal with an applied square-wave voltage under the action of light with an inhomogeneous transverse intensity distribution is derived. The spatial spectrum of the field E _sc induced in a Bi₁₂TiO₂₀ crystal with typical values of the acceptor density N _A and of the product of the electron mobility by the recombination time _R is analyzed. An approximate analytical solution of the nonlinear equation is derived in the case in which the amplitudes of spatial harmonics of the spectrum E _sc form a nonmonotonic sequence. The spatial distribution of the induced electric field is calculated numerically for crystals with different parameters N _A and _R .     

A matrix method for estimating the Liapunov exponent of one-dimensional systems

Let : [0, 1][0, 1] be a piecewise monotonie expanding map. Then admits an absolutely continuous invariant measure. A result of Kosyakin and Sandler shows that can be approximated by a sequence of absolutely continuous measures _n invariant under piecewise linear Markov maps _itn. Each _itn is constructed on the inverse images of the turning points of . The easily computable measures _n are used to estimate the Liapunov exponent of . The idea of using Markov maps for estimating the Liapunov exponent is applied to both expanding and nonexpanding maps.     

Kinetic equation in the kinetic region of the dilute and nonuniform electron plasma

Mori's scaling method is used to derive the kinetic equation for a dilute, nonuniform electron plasma in the kinetic region where the space-time cutoff (b, t _c) satisfies _Dbl _f , _D t _{c f} , with _D the Debye length, _D ^–1= _p the plasma frequency, andl _f and _f the mean free path and time, respectively. The kinetic equation takes account of the nonuniformity of the order ofl _f and _D for the single-and the two-particle distribution function, respectively. Thus the Vlasov term associated with the two-particle distribution function is retained. This kinetic equation is deduced from the kinetic equation in the coherent region obtained by Morita, Mori, and Tokuyama, where the space-time cutoff of the coherent region satisfies _Dbr ₀, _Dt _{c 0}, withr ₀ the Landau length and ₀ the corresponding time scale.     

High-frequency sum rules for the quasi-one-dimensional quantum plasma dielectric tensor. II. Spin effect

We derive a high-frequency expansion for all elements of the quasi-one-dimensional quantum plasma dielectric tensor atT=0 K for quantum particles with spins. In addition to the known results for spinless case, we find that _S.5 ^Emphasis>/12 (k) and _S.5 ²³ (k) are the only frequency moments of the dielectric tensor with spin terms. Further, we find that there is no spin effect on quantum plasma dispersion for both ordinary and transverse modes propagating either along or across the external field.     

Steady-State Spectroscopic and Fluorescence Lifetime Measurements of New Two-Photon Absorbing Fluorene Derivatives

Steady-state excitation anisotropy, lifetimes, and time-resolved emission spectra of new 2-photon absorbing fluorene derivatives were measured in aprotic solvents at room temperature. Excitation anisotropy spectra in viscous silicon oil allowed the determination of the spectral position of three electronic transitions S₀ S₁, S₀ S₂, S₀ S₃ (S_i, i = 1, 2, 3 are the singlet electronic states) and the angles ( 30°) between absorption S₀ S₁ and emission S₁ S₀ dipole moments for the first electronic transition. Solvate relaxation processes in the first excited state of the investigated fluorene molecules affect the lifetimes of these states, ₁, so that experimental values of ₁ do not correspond to those calculated by Strickler and Berg theory. The influence of the molecular concentration on the fluorescence quantum yields and ₁ have been investigated.     

The magnetic structures of NdCu2 determined by single crystal neutron diffraction

We investigated the magnetic structure of NdCu₂ by means of neutron diffraction as a function of temperature between 1.5 K and 8 K in zero external field. The diffraction data were obtained on two single crystals with different orientations using the triple-axis-spectrometer TAS6 at the DR-3 reactor at Risø. Two magnetic phases were observed between 1.5K andT _N =6.5K. From 1.5 K to 4.1 K the magnetic reflections can be described by the commensurate wave vector =(3/5 0 0) and its higher harmonics 3 and 5. Below 2.5K the structure is completely squared-up. For 4.1 KT6.5 K the magnetic structure is incommensurate with the chemical lattice and can be described by the wave vector=(3/5 0 0) and its higher harmonies 3 and 5M. Below 2.5 K the structure is completely squared-up. For 4.1 K T 6.5 K the magnetic structure is incommensurate with the chemical lattice and can be described by the wave vector ^*=(0.62 0.044 0). In both phases the Nd-moments are oriented along the easyb-direction.     

n-Dimensional representations of the unified field tensor* g λν

For the first time Hlavatý represented the tensor^*g^v, defined by (15a), in terms of the unified field tensorg in the space-timeX ₄. Recently, the representations of^* g ^v in terms ofg in two- and three-dimensional generalized Riemannian space were obtained by Chung. The purpose of the present paper is to obtain the generalized representations of^* g ^v in terms ofg in a generalizedn-dimensional Riemannian spaceX _n.     

Tree graph inequalities and critical behavior in percolation models

Various inequalities are derived and used for the study of the critical behavior in independent percolation models. In particular, we consider the critical exponent associated with the expected cluster sizex and the structure of then-site connection probabilities =_n(x₁,..., x_n). It is shown that quite generally 1. The upper critical dimension, above which attains the Bethe lattice value 1, is characterized both in terms of the geometry of incipient clusters and a diagramatic convergence condition. For homogeneousd-dimensional lattices with (x, y)=O(¦x -y¦^–(d–2+), atp=p _c, our criterion shows that =1 if > (6-d)/3. The connectivity functions _n are generally bounded by tree diagrams which involve the two-point function. We conjecture that above the critical dimension the asymptotic behavior of _n, in the critical regime, is actually given by such tree diagrams modified by a nonsingular vertex factor. Other results deal with the exponential decay of the cluster-size distribution and the function ₂ (x, y). A. P. Sloan Foundation Research Fellow. Research supported in part by the National Science Foundation Grant No. PHY-8301493.Research supported in part by the National Science Foundation Grant No. MCS80-19384.     

Slowing down of retrieval in the hopfield model

The variation of the convergence time, as a function of the storage capacity is studied numerically for systems ranging in size fromN=1000 toN=16,000 neurons. is found to increase likeexp[–A(_c–)] as one nears the critical storage capacity _c =0.142=0.002.     

A Boltzmann map for quantum oscillators

We define a map on the space of quasifree states of the CCR or CAR of more than one harmonic oscillator which increases entropy except at fixed points ofx. The map is the composition of a doubly stochastic map T^* and the quasifree reductionQ. Under mixing conditions onT, iterates of take any initial state to the Gibbs state, provided that the oscillator frequencies are mutually rational. We give an example of a system with three degrees of freedom with energies ₁, ₂, and ₃ mutually irrational, but obeying a relation n₁₁+n₂₂=n₃₃,n _i . The iterated Boltzmann map converges from an initial statep to independent Gibbs states of the three oscillators at betas (inverse temperatures) ₁,₂, ₃ obeying the equation n₁₁₁+n₂₂₂=n₃₃₃. The equilibrium state can be rewritten as a grand canonical state. We show that for two, three, or four fermions we can get the usual rate equations as a special case.     

Form Factors and Action of on ∞-Cycles

Let be a sequence of skew-symmetric polynomials in X₁,,X_l satisfying deg_XjP_n,ln–1, whose coefficients are symmetric Laurent polynomials in z₁,,z_n. We call p an -cycle if holds for all n,l. These objects arise in integral representations for form factors of massive integrable field theory, i.e., the SU(2)-invariant Thirring model and the sine-Gordon model. The variables _a=–logX_a are the integration variables and _j=logz_j are the rapidity variables. To each -cycle there corresponds a form factor of the above models. Conjecturally all form-factors are obtained from the -cycles. In this paper, we define an action of on the space of -cycles. There are two sectors of -cycles depending on whether n is even or odd. Using this action, we show that the character of the space of even (resp. odd) -cycles which are polynomials in z₁,,z_n is equal to the level (–1) irreducible character of with lowest weight –₀ (resp. –₁). We also suggest a possible tensor product structure of the full space of -cycles.     

Nonlinear relaxation at first-order phase transitions: A Ginzburg-Landau theory including fluctuations

Kinetics of phase transitions are investigated in systems with nonconserved one-component order parameter (i.e., generalized time-dependent Ginzburg-Landau models ind dimensions). The correct static critical behavior as well as fluctuation effects on the kinetics are incorporated by a suitable adaptation of the theory on spinodal decomposition by Langer, Baron and Miller. Both the case of quenches from temperaturesT above to below the critical pointT _c and the case of magnetic field changesH from positive to negative values are treated, and both time-dependent order parameter m() and structure factorS(q, ) are obtained numerically ford=2, 3. In the case of quenches atH=0, we find that m()0 andS(q, ) —S(q, ) exp(– ^1/2/7.2) , withS(q, )q ^–2. In the case of field changes we find that forH not exceeding some critical valueH ^* the system is trapped in a metastable state with infinite lifetime. In contrast to the meanfield-spinodal, the susceptibility does not seem to diverge atH ^*. These results are compared with other treatments, in particular the Monte Carlo simulations of kinetic Ising models by Binder and Müller-Krumbhaar. While our theory describes some properties of the metastable states reasonably,H ^* distinctly exceeds the observed limit of metastability. We argue that the present theory does not take into account nucleation fluctuations, and also fails to describe correctly the domain growth in the late stages of the relaxation. Contrary to Langer et al. we suggest that universality holds for nonlinear relaxation and spinodal decomposition nearT _c .Supported in part by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 130