The conceptual analysis (CA) method in theories of microchannels: Application to quantum theory. Part I. Fundamental concepts

A method is proposed that should facilitate the construction of theories of submicroscopic particles (denoted as theories of microchannels) in a way similar to the use of group-theoretical methods. The conceptual analysis (CA) method is based on the analysis of the basic concepts of a theory; it permits a determination of necessary conditions imposed on the mathematical apparatus (of the theory) which then appear as a mathematical representation of the structures obtained in a formal scheme of a theory. A pertinent conceptual analysis leads to a new definition (relativization) of the concept empirical implication. The approach may be characterized as realistic and operational. The application of the CA method is illustrated on the example of quantum theory. In Part I the algebraic structure of a partially ordered, up-ward directed, bounded set is deduced from the rudimentary concepts. In Parts II and III, we shall deduce the Hilbert-space structure (well established in quantum mechanics) from postulates on some essential idealizations accepted in the theory. Whereas Part II is concerned with the idealizations of existing quantum theories based on the Hilbert-space formalism, Part I may be considered as a general basis for a wider class of theories.Dedicated to Prof. G. Ludwig on the occasion of his 60th birthday.     

Raman effect of light on argon atoms

Scalar scattering of light on the 3p and 3s subshells of the argon atom (Stokes scattering) and anti-Stokes scattering on the excited 4p and 4s states of argon are examined in the Hartree-Fock approximation. The calculation is made in a velocity form and in a length form. It is shown that the value in the r form is 1.5–2 times greater than in the form.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 36–42, January, 1977.     

Some properties of topological geons

We investigate the Finkelstein-Misner geons for a non-simply-connected space-time manifold (M, g ₀). We use relations between different Lorentzian structures unequivalent tog ₀ and topological properties ofM given by the Morse theory. It implies that to some pieces of geons we have to associate Wheeler's worm-holes. Geons that correspond to time-orientable Lorentz structures are related tog ₀ by Morse functions that describe the attaching of a handle of index one. In the case of geons associated to time-nonorientable Lorentzian structures, appropriate handles are related to loops along which the notion of time reverses. If we assume electromagnetic properties of geons, then only four species, v, e, p, m, of different geons can exist and geon m has to decay according to mv+p+e.     

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.     

Tetrahedron equations and the relativisticS-matrix of straight-strings in 2+1-Dimensions

The quantumS-matrix theory of straight-strings (infinite one-dimensional objects like straight domain walls) in 2+1-dimensions is considered. TheS-matrix is supposed to be purely elastic and factorized. The tetrahedron equations (which are the factorization conditions) are investigated for the special two-colour model. The relativistic three-stringS-matrix, which apparently satisfies this tetrahedron equation, is proposed.     

On measurement and irreversible processes

The nature of physical measurements performed on microscopic systems is discussed, and it is suggested that the procedures which are conventionally referred to as measurements fall into at least three different categories. The connection between observation processes and irreversible processes is stressed. The customary quantum mechanical treatment of irreversible processes is discussed, and its deficiencies from the philosophical point of view are criticized. The standpoint that quantum mechanics should not be considered as a basic philosophical system but rather as an immensely useful tool is defended. Some attempts at developing a more basic theory are discussed, and a hypothesis is put forward concerning the role of entropy within some possible future nonlocal hidden-variable theory.     

Theoretical study of thermal diffusivity of superlattices in measurements using “mirage” technique

A complete theoretical treatment for the determination of thermal diffusivity of superlattices by the mirage technique has been performed. An effective medium approximation model of the thermal conductivity and thermal diffusivity of both sublayers is presented, which is different from the simple models with the thermal diffusivity or thermal conductivity in series or parallel. The numerical calculation of the transverse component of the probe beam deflection in the mirage effect shows that the results obtained from the complete thermal-wave theory and the medium approximation model, for the optically and thermally thick superlattices, are in good agreement with each other. However, the further study on the thermally thin superlattices shows that either the series or the parallel model of the thermal conductivity should be chosen according to whether the thermal impedance of the superlattice is larger or less than that of substrate, respectively.     

Wave chaos in quantum systems with point interaction

We study perturbations of the quantized version ₀ of integrable Hamiltonian systems by point interactions. We relate the eigenvalues of to the zeros of a certain meromorphic function . Assuming the eigenvalues of ₀ are Poisson distributed, we get detailed information on the joint distribution of the zeros of and give bounds on the probability density for the spacings of eigenvalues of . Our results confirm the wave chaos phenomenon, as different from the quantum chaos phenomenon predicted by random matrix theory.SFB 237 Essen-Bochum-Düsseldorf     

Stiff magnetic field lines. I. A geometrical foundation

It is shown that the foliation of a space-time manifold of codimension 2 provides a basis for the study of the deformation of magnetic field lines. It is found that the fluid flow vector and the curvature vector of a nongeodesic stiff magnetic field line are always orthogonal. Further, it is shown that the metric tensor of the 2-space orthogonal to the Maxwellian string is Lie-transported along the magnetic field lines when the magnetic field lines are stiff. If there exists a spacelike Killing vector field parallel to the magnetic field, then the magnetic field lines must be stiff.     

Symmetries and asymmetries in classical and relativistic electrodynamics

By a comparison between Maxwell's electrodynamics classically interpreted (MT) and relativistic electrodynamics (RED), this paper discusses whether the asymmetries in MT mentioned by A. Einstein in his 1905 relativity paper are only of a conceptual nature or rather involve specific empirical claims. It is shown that in fact MT predicts strongly asymmetric behaviour for very simple interactions, and an analysis is made of the extent of the symmetry achieved by means of relativistic postulates. A low velocity experiment is suggested which could provide another test of the accuracy of RED with respect to MT.     

Boson-fermion duality in four dimensions: Comments on the paper of luther and schotte

The Fock space for the fermion field can be identified with the Fock space for the boson field, provided the overall numbers of internal degrees of freedom are the same. As a consequence, the respective free field Hamiltonian systems are equivalent (dual): the four-component neutrino model is thus equivalent to the doublet of independent (electric and magnetic, respectively) Maxwell fields, which are quantized in the Coulomb gauge. This statement arises on the field theory level, and seems to make doubtful the claim that realistic photons can be constructed from (bound) neutrino pairs: each (anti)neutrino degree should be represented by the photon-type (electric and magnetic, respectively) degree of freedom.     

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.     

Non-smoothness of event horizons of Robinson-Trautman black holes

It is shown that generic small data Robinson-Trautman space-times cannot beC ¹²³ extended beyond the r=2m Schwarzschild-like event horizon. This implies that an observer living in such a space-time can determine by local measurements whether or not he has crossed the event-horizon of the black-hole.     

An experiment to test an explanation of a possible violation of quantum theory

An experiment to test a possible explanation of the Schmidt backwards causation results is suggested. The experiment might distinguish between many- and one- world interpretations of quantum theory.     

On a “structure intermediate between quasiperiodic and random”

This paper proves rigorously that the structure factor of the structure intermediate between quasiperiodic and random introduced by Aubry. Godréche, and Luck is purely singluar continuous apart from a delta function at zero for most choices of the parameters. The result is based on a proof that a flow under a steep function over an irrational circle rotation is weakly mixing for most parameters, and on the wonderland Theorem.     

The preparation of “perfect” dendritic germanium crystals

Perfect germanium crystals with the required resistivity and small dislocation density are reproducibly prepared in the Popov Research Institute of Radiocommunications. Perfect dendrites are suitable for use, for example, in the preparation of alloy diffused transistors. The shape, pulling apparatus and actual preparation of perfect germanium dendrites are described. Some of the parameters influencing the growth of a perfect dendrite are analyzed and the optimum conditions for its growth are determined.     

Particle velocities faster than the speed of light

In connection with another article by the author, we show how it might be possible to travel faster than the speed of light. We show that for clocks and rods moving faster than the speed of light, we get instead of time dilation and Lorentz contraction, respectively, time contraction and Lorentz expansion, respectively. It is shown that this paper is in confirmation with earlier articles dealing with this subject.     

The meaning of the terms “phase” and “phase transition”

Various meanings of the terms phase and phase transition encountered in scientific literature are discussed. These terms supplement each other and cover only together all the macroscopic situations which are now denoted by this term.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 67–71, August, 1988.     

First-order transitions in spherical models: Finite-size scaling

Finite-size behavior near the first-order phase boundary of ferromagnetic spherical models is investigated for block- and cylinder-shaped systems ind dimensions. The bulk thermodynamic singularities are rounded and, asymptotically for large size, obey appropriate scaling laws. Both short-range interactions and long-range couplings, decaying like 1/r^d+ with >0, are analyzed: the short-range results agree precisely with a recently developed scaling theory forO(n) symmetric systems in the limitn. More generally, the scaling functions are universal, depending only on . Explicit aspects of the shape and interactions enter only in the spin wave or Goldstone mode contributions which appear, technically, as corrections to scaling. An appendix analyzes the truncation error in the approximation, by many-fold sums, of multivariate integrals with integrands diverging like [_ja_{j j} ² ]^- as 0.     

Hypernuclear physics

The contributed papers submitted to the session C Hypernuclear and kaon physics and not presented orally at the Conference are briefly reviewed here.Rapporteur talk at the symposium Mesons and Light Nuclei IV, Bechyn, Czechoslovakia September 5–10, 1988.