The rastall model and Stapp's proof of nonlocality

Recently two distinct arguments have been given (by Stapp, and Bedford and Stapp) to prove that a model proposed by Rastall for the statistics of EPR-correlated spin-1/2 particles, which happens to violate the Bell inequality, conflicts with locality. Neither argument makes use of the fact that the Rastall model violates the Bell inequality; therefore both seem to provide independent support for a more general proof of Stapp's, which allegedly establishes that any model violating this inequality, including quantum mechanics, must imply the existence of nonlocal influences. However, it is shown here that both of these arguments are invalid under an indeterministic interpretation of quantum mechanics, a conclusion which agrees with the same criticism made by other authors but directed against Stapp's more general proof of nonlocality.2. For a clarification and defence of Kraus' claim, see the discussion of the broken square problem in [7], Sec. 2.1.3. These strict [anti-] correlations do not rigorously exclude the possibility that the L and R meterscould register +1, –1 [+1, +1] or –1, +1 [–1, –1] for any pair in the measured sample; by the law of large numbers, they only render these possibilities highly improbable. However, I shall follow Rastall, Bedford and Stapp in regarding such possibilities as strictly impossible (cf. also Note 9).4. Eberhard, himself, uses his discovery that matching is sufficient for BI to attempt a proof, in the style of Stapp [1], that BILOC.5. A world or state of affairs is properly specified only after a list of the truth values forall of the propositions describingall of the events which occur in that world is provided. Since there exist various possible permutations of these truth values, we must hypothetically consider, for instance in the first part of this example, the two (in general, uncountably infinite)classes of worlds: those with the meters set to measurea andc and those with the meters set toa andd. Each class can be further divided into subclasses according to the values that the various responses take on in each world. The idea that a counterfactual supposition leads to a class of worldssufficiently similar (by some standard of similarity) to the actual world is exploited in Lewis' [13] semantics for counterfactuals; but I shall not need to adopt any particular semantics of counterfactuals here beyond using some standard valid inferences involving them.6. To be fully rigorous, this demand should be broken down into: (a) supposing that RM is true at the actual world; and (b) demanding that the truth of physical laws as depicted by RM be independent of whether or not measurements are undertaken. For a more thorough discussion, see the justification of the principle CUW in [7].7. Kraus [14] objects to Stapp's argument on the grounds that it invokes concepts without direct observational meaning. But presumably then he would rejectany use of counterfactuals (including their use in Stapp's more general proof) on the same grounds. Also, it is worth adding (to Stapp's [5] own reply to Kraus) that Kraus' additional charge that Stapp's argument is suspect because it uses the language of things waiting to be measured if and when the appropriate instrument is applied misinterprets Stapp's [6] use of the word thing. For this word is used in a sense equivalent to what I have called response; and, by definition, responses are (in general, counterfactually)measured values having nothing to do with entities apart from measurement.8. Although these authors choose Lewis' semantics for analyzing counterfactuals (cf. Note 5) in their critiques, their arguments do not turn upon this choice but are motivated on physical grounds. For the same critique without the Lewis framework see [18] and my (slightly different) argument in the text.9. Strictly speaking, since improbability does not imply impossibility (cf. Note 3), the conditionals in the RM premisses of Parts 1 and 2 must also be weakened to conditionals, which weakens C1 and C2 in the same way, and hencealso undermines Stapp's argument.10. Towards the end of their paper, BS restate UR in a way that lends it easily to confusion with the stronger statement for every measurementM, there exists a particular measurement resultx, such that anM measurementwould yieldx (cf. [7] for a discussion of further instances where this confusion has occurred). Sincex = +1 or –1, this statement implies that every measurement eitherwould yield +1or would yield –1, which (as we have seen) implies determinism. (The difference between this statement and the weaker (uncontroversial) UR I adopt in the text is that the former can be obtained from the latter by distributing the would over the disjunction or.) If UR were interpreted in this stronger sense, so as to make it imply determinism (rather than just determinateness of responses in each world), then the Stapp and BS proofs could go through; although, obviously, UR would then have to be rejected by the indeterminist.     

Well-Posedness of an Integrable Generalization of the Nonlinear Schr?dinger Equation on the Circle

It is shown that the periodic initial value problem (i.v.p.) for a novel integrable generalization of the nonlinear Schrödinger equation (igNLS) is well-posed in Sobolev spaces with exponent greater than 3/2. The proof is based on a Galerkin-type approximation method. When 1/?? is not an integer, then a mollified version of the i.v.p. is solved first by applying the fundamental ODE theorem in Banach spaces. Then, deriving appropriate energy estimates, it is shown that the family of the approximate solutions thus obtained has a convergent subsequence, which at the limit gives a solution to the igNLS equation. Finally, again using energy estimates, it is shown that this solution is unique and that the data-to-solution map is continuous. When 1/?? is an integer then well-posedness is proved for the nonlocal version of this equation in the corresponding homogeneous Sobolev spaces.     

Alpha-particle superfluid bands in nuclei

The systematics of α-particle separation energy is studied from the point of view of pairing-rotational structure. Two mass regions are identified where collective pairing bands can exist. The moment of these bands is compared with linear sums of (n-n) and (p-p) bands and an increase in collectivity of factor 10 is deduced.     

On the spectra of resonant coherent Raman scattering

The spectra of resonant coherent anti-Stokes and Stokes Raman scattering of excited molecules are calculated and discussed. The interaction of light and molecules is treated semi-classically. The energy level diagram of four energy levels describing the process is used in four modifications possible for excited molecules. It is shown that non-vibrational resonances give extra maxima in some of the spectra. Comparison of the spectral structure in the Stokes and anti-Stokes components gives information on which of the four schemes the interaction is realized by. The influence of the pumping detuning on the Stokes component shape is pointed out.     

Statistical dynamics of the Lorenz model

The dynamics of the Lorenz model in the turbulent regime (r>r _T is investigated by applying methods for treating many-body systems. Symmetry properties are used to derive relations between correlation functions. The basic ones are evaluated numerically and discussed for several values of the parameterr. A theory for the spectra of the two independent relaxation functions is presented using a dispersion relation representation in terms of relaxation kernels and characteristic frequencies. Their role in the dynamics of the system is discussed and it is shown that their numerical values increase in proportion to r. The approximation of the relaxation kernels that represent nonlinear coupling between the variables by a relaxation time expression and a simple mode coupling approximation, respectively, is shown to explain the two different fluctuation spectra. The coupling strength for the modes is determined by a Kubo relation imposing selfconsistency. Comparison with the experimental spectra is made for three values ofr.     

Variation of doping-dependent propertiesin photorefractive Sr x Ba 1−x Nb 2 O 6 : Ce,Cr, Ce+Cr

In congruent Sr x Ba 1 m x Nb 2 O 6 (SBN, x =0.61) the photorefractive properties are significantly enhanced by doping with Ce or Cr. The visible and FIR absorption increases linearly with the dopand concentration up to about 10,000 v ppm (p.f.u.) of Ce or Cr or in double doped crystals (Ce+Cr). Simultaneously a decrease of the phase transition temperature T c from about 253 v K in pure SBN to about room temperature for doping concentrations (of Ce, Cr or both) of about 20,000 v ppm (p.f.u.) is found.     

Interaction in scalar theories of gravitation

It is shown that O. Bergmann's (1956) scalar field theory is similar to G. Nordström's (1912). The interaction term in the former's theory is equivalent to non-linearising the Nordström theory by including twice the energy density of the field as a source term in the Poisson-like equation. It is further shown that, if the interaction term (1+v) in Bergmann's theory is replaced by (1+v)², then the subsequent field equation appears more reasonable in that the energy density (not twice) appears as a source term.     

Does the Boltzmann Principle Need a Dynamical Correction?

In an attempt to derive thermodynamics from classical mechanics, an approximate expression for the equilibrium temperature of a finite system has been derived (M. Bianucci, R. Mannella, B. J. West and P. Grigolini, Phys. Rev. E 51: 3002 (1995)) which differs from the one that follows from the Boltzmann principle S = kln(E) via the thermodynamic relation 1/T=S / E by additional terms of dynamical character, which are argued to correct and generalize the Boltzmann principle for small systems (here (E) is the area of the constant-energy surface). In the present work, the underlying definition of temperature in the Fokker–Planck formalism of Bianucci et al., is investigated and shown to coincide with an approximate form of the equipartition temperature. Its exact form, however, is strictly related to the volume entropy S = k ln (E) via the thermodynamic relation above for systems of any number of degrees of freedom ((E) is the phase space volume enclosed by the constant-energy surface). This observation explains and clarifies the numerical results of Bianucci et al., and shows that a dynamical correction for either the temperature or the entropy is unnecessary, at least within the class of systems considered by those authors. Explicit analytical and numerical results for a particle coupled to a small chain (N~10) of quartic oscillators are also provided to further illustrate these facts.     

Coupling characteristics of photo-induced Bragg gratings in depressed- and matched-cladding fibre

Experimental transmission spectra of ultraviolet (u.v.)-written Bragg gratings in depressed- and matched-cladding fibre are characterized and compared. In particular, we discuss how the location and strength of the spectral features vary with the degree of blazing, or angular tilt of the grating. The fine-structure detail on the short-wavelength side of the fundamental Bragg line is attributed to power coupling between the forwardpropagating fundamental (LP₀₁) mode and discrete, backward-propagating cladding modes. Resonances corresponding to backward-propagating LP_0n and LP_1n modes are identified, and their relative strengths are compared with theoretical overlap calculations. Physical arguments are presented that explain the pronounced ghost-grating notch that appears in the transmission spectra of blazed, fibre Bragg gratings in depressed-cladding fibre.     

Investigation of multibaryonic resonances with strangeness equal to and different from zero

Results on a search for Λp, ΛΛ, Λpp, K^op, pp, 3p and 4p resonances are presented. The Λp effective-mass spectrum reveals three significant peaks (more than 4 s.d.) at 2058, 2127 and 2252 MeV. The first two peaks are shown to be due to effects of the negative Λp and Σp scattering lengths respectively, whereas the third peak is interpreted as a Λp resonance of (2251.4 ± 3.9) MeV mass and Λ = (21.1 ± 5.4) MeV full width. The two enhancements observed in the ΛΛ effective-mass spectrum may be due to the effect of the negative ΛΛ scattering length and to a ΛΛ resonance of ～2370 MeV mass. No enhancements in other effective-mass spectra are observed. The results of this work suggest a condition for the possibility of resonance formation depending on the total hypercharge of the system considered.     

Determination of the spectral reflection coefficients of friable materials in the 0.7–15μ wavelength region

A new attachment to the IKS-12 infrared spectrometer is described. It measures the spectral reflection coefficient of loose materials and is based on the hemispherical mirror method. It is shown that the losses of reflected radiation may be allowed for by the introduction of special coefficients. Reflection spectra are reported for sand and soil in the wavelength region 0.7 –15 .     

Spectral Gaps of Quantum Hall Systems with Interactions

A two-dimensional quantum Hall system without disorder for a wide class of interactions including any two-body interaction with finite range is studied by using the Lieb–Schultz–Mattis method [Ann. Phys. (N.Y.) 16:407 (1961)]. The model is defined on an infinitely long strip with a fixed, large width, and the Hilbert space is restricted to the lowest (n _max+1) Landau levels with a large integer n _max. We prove that, for a noninteger filling of the Landau levels, either (i) there is a symmetry breaking at zero temperature or (ii) there is only one infinite-volume ground state with a gapless excitation. We also prove the following two theorems: (a) If a pure infinite-volume ground state has a nonzero excitation gap for a noninteger filling , then a translational symmetry breaking occurs at zero temperature. (b) Suppose that there is no non-translationally invariant infinite-volume ground state. Then, if a pure infinite-volume ground state has a nonzero excitation gap, the filling factor must be equal to a rational number. Here the ground state is allowed to have a periodic structure which is a consequence of the translational symmetry breaking. We also discuss the relation between our results and the quantized Hall conductance, and phenomenologically explain why odd denominators of filling fractions giving the quantized Hall conductance are favored exclusively.     

The molecular spectroscopy studies of ligands coordination in Pd(0,1,1V) complexes

In Pd(0) complexes with different arilphosphines ( PdL₂'L), thriphenylphosphine has been shown to oxidate into thriphenyl-phosphinoxide yielding, PdL₂'0L. EPR spectra this compounds ( in polycrystall form) are typical powder spectra whith rhombic symmetry ( g₁=2.089; g₂=2.040; g₃=2.011 ±0.005) for Pd(1) complexes with d⁹ electron configuration ( in organic solvents dimerization into diamagnetic form (PdL₂')₂).Comparison of ³¹P NMR spectra of palladium complexes in differend oxidation states has shown continuous diminution of electron density on P-atom from Pd(0) to Pd(1V) complexes (from 10.2 to 24.9 p.p.m.)     

Symmetry properties of a charged fluid in the general theory of relativity

The problem of specifying the symmetry properties of a charged fluid in space-time V₄, which has a definite group of motions, is considered. It is shown that if nonempty spacetime V₄ with an energy-momentum tensor for the charged fluid has symmetry (i.e., admits a group of motions), then the mass density, the pressure, and the four-velocity of the fluid inherits this symmetry, and for an electromagnetic field the relationL f _ij =7.*f _ij is satisfied. The necessary and sufficient conditions are found so that =0 in the case of a one-parameter group. Then additional relationships between and the structure constants are obtained in the case of an r-parameter group. It is shown that under certain conditions the symmetry properties obtained for charged matter are necessary and sufficient conditions for the symmetry of space-time V₄.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 113–117, November, 1978.     

常温0～1GPa压力下重晶石的拉曼光谱研究

利用碳化硅压腔装置研究了高压下重晶石的S-O对称伸缩振动v987和对称弯曲振动v452及v462的拉曼光谱变化特征.实验结果表明:在常温和0～1GPa压力范围内重晶石稳定,其拉曼谱峰随压力升高向高波数方向移动,二者的关系表达式分别为:v987=0.004 4p+987.42,v452=0.002 3p+452.6,v462=0.001 8p+462.42,而且伸缩振动受压力的影响比弯曲振动大.重晶石的987 cm-1拉曼谱峰强度约为石英464 cm-1拉曼谱峰的六倍,可作为压腔中良好的压力标定物.实验得到压力与重晶石987 cm-1峰偏移量的关系为:p(MPa)=223.16×(△vp)987-90.35(987 cm-1相似文献   

26 ℃和常压至1.5 GPa压力下2-甲基戊烷拉曼光谱研究

利用碳化硅压腔在常压至1.5 GPa和26 ℃条件下对液态2-甲基戊烷进行了拉曼光谱测量,讨论了C—H拉曼峰频率、强度、面积、以及谱峰宽度随压力升高的变化规律。实验结果表明,2-甲基戊烷的拉曼位移在2 800～30 00 cm-1范围内的CH₃和CH₂的伸缩振动谱峰随着压力的增大均连续向高波数位移,其拉曼位移与压力的关系可以表示为ν_as(CH₃)=0.013 1p+2 960.1,ν_s(CH₃)=0.008 8p+2 871.0,ν_as(CH₂)=0.008 9p+2 930.2,ν_as(CH₂)’=0.007 0p+2 903.1和ν_s(CH₂)=0.007 9p+2 844.7。另外处理实验结果时发现,在0～1.5 GPa条件下,2-甲基戊烷的ν_as(CH₃)拉曼位移可以进行压力标定,其方程为：P(MPa)=76.2(Δν_p)_{2 960}+21.65(r2=0.995 8)。该压力体标定剂,适合于不希望有Si和Al等元素出现的体系。     

Third-order nonlinear susceptibility of Mg II and Ca II ions

The nonlinear coefficient ⁽³⁾ (3) of the singly ionized atoms Mg II and Ca II has been calculated for a wide range of incident wavelengths from v.u.v. to i.r. In some parts of the spectrum the magnitude of the nonlinear susceptibility is comparable to that of the alkali metal vapours.     

Raman spectra of aragonite at the pressure of 0.1-2 GPa and ambient temperature

Raman spectra of aragonite were studied at ambient temperature and pressure of 0.1 - 2 GPa in a moissanite anvil cell using Raman spectrum technique. The relations between the Raman shifts of aragonite and the system pressure are given as follows: v153 (cm(-1)) = 0.003 5p (MPa) +154.0, v206 = 0.006 0p + 206.3, v704 = 0.002 1p + 704.2, v1085 = 0.003 5p + 1 085.3. No phase transition occurred in aragonite within the range of experimental pressure. Similar to other carbonate minerals (magnesite, dolomite), the measured relative pressure-shift of the Raman line of the symmetric stretching vibration of aragonite is greater at 0.1-2 GPa than at ultrahigh pressure, which indicates that the C-O bond compressibility of the CO3 groups is related to the pressure, and it is more compressible at 0.1 - 2 GPa than at higher pressure.     

Asymptotic Structure in the Classically Forbidden Region of the Hooke’s Atoms

The two-electron Hooke's atom - a quantum mechanical system with two electrons bound in a harmonic potential - is well known for its exact analytical properties at certain oscillator strengths. The Hooke's atoms with more than two electrons offer more scope for valuable practical applications. In this work, we study the asymptotic structure of these Hooke's atoms in the classically forbidden region. The leading-order term of the long-range expression for the KS exchange-correlation potential v xc (r) is shown to be-1/r. The second and third higher order terms are also exactly obtained. Various components of v xc (r) are also studied. It is shown that the leading term of O(1/r) in vxc (r) is due to the pure Pauli correlation, while the leading contribution of the Coulomb correlation is of O(1/r3 ). Neither of them makes contribution to the term of O(1/r2 ), which is shown to be solely due to the kinetic correlation effect. Results for the two-electron Hooke's atom were obtained before in the literature. Our results reduce to those of the two-electron Hooke's atom as a special case.