Methodological imperfection and formalizations of scientific activity

Any mathematical formalization of scientific activity allows for imperfections in the methodology that is formalized. These can be of three types, dirty, rotten, and dammed. Restricting mathematical attention to those methods that cannot be construed to be imperfect drastically reduces the class of objects that must be analyzed, and relates all other objects to these more regular ones. Examples are drawn from empirical logic.     

Intersubjectivity,relativistic covariance,and conditionals: response to C. I. J. M. Stuart

A misunderstanding persists between Stuart and me, which I do my best to clarify. Bayesian inverse subjectivities versus relativistic covariance and physical intersubjectivity are discussed. A joint number of chances formalism taking care of the propagation of the probability of causes is proposed.     

Cosmological surrealism: More than “eternal reality” is needed

Inflationary cosmology makes the universe eternal and provides for recurrent universe creation, ad infinitum — making it also plausible to assume that our Big Bang was also preceeded by others, etc.. However, GR tells us that in the parent universe's reference frame, the newborn universe's expansion will never start. Our picture of reality in spacetime has to be enlarged.Wolfson Distinguished Chair in Theoretical Physics.Also on leave from the University of Texas, Center for Particle Physics, Austin, Texas.     

On some frequent but controversial statements concerning the Einstein-Podolsky-Rosen correlations

Quite often the compatibility of the EPR correlations with the relativity theory has been questioned; it has been stated that the first in time of two correlated measurements instantaneously collapses the other subsystem; it has been suggested that a causal asymmetry is built into the Feynman propagator. However, the EPR transition amplitude, as derived from the S matrix, is Lorentz andCPT invariant; the correlation formula is symmetric in the two measurements irrespective of their time ordering, so that the link of the correlations is the Feynman zigzag, and that causality isCPT invariant at the microlevel; finally, although the Feynman propagator has theP andCT symmetries, no causal asymmetry follows from that. As for Stapp's views concerning process and becoming, and his Whiteheadean concept of an advancing front, I object that they belong to factlike macrophysics, and are refuted at the microlevel by the EPR phenomenology, which displays direct Fokker-like space-time connections. The reason for this is a radical one. The very blending of a space-time picture and of a probability calculus is a paradox. The only adequate paradigm is one denying objectivity to space-time—but this, of course, is also required by the complementary of the x and the k pictures, which only look compatible at the macrolevel. Therefore, the classical objectivity must yield in favor of intersubjectivity. Only the macroscopic preparing and measuring devices have factlike objectivity; the transition of the quantal system takes place beyond both thex and thek 4-spaces. Then, the intrinsic symmetries between retarded and advanced waves, and statistical prediction and retrodiction, entails that the future has no less (but no more) existence than the past. It is the future that is significant in creative process, the elementary forms of which should be termed precognition or psychokinesis—respectively symmetric to the factlike taboos that we can neither know into the future nor act into the past. It is gratifying that Robert Jahn, at the Engineering School of Princeton University, is conducting (after others) conclusive experiments demonstrating low level psychokinesis—a phenomenon implied by the very symmetry of the negentropy-information transition. So, what pierces the veil of maya is the (rare) occurrence of paranormal phenomena. The essential severance between act and potentia is not a spacelike advancing front, but the out of and the into factlike space-time. Finally, I do not feel that an adequate understanding of the EPR phenomenology requires going beyond the present status of relativistic quantum mechanics. Rather, I believe that the potentialities of this formalism have not yet been fully exploited.     

Evolutionary drive: The effect of microscopic diversity,error making,and noise

In order to model any macroscopic system, it is necessary to aggregate both spatially and taxonomically. If average processes are assumed, then kinetic equations of population dynamics can be derived. Much effort has gone into showing the important effects introduced by non-average effects (fluctuations) in generating symmetry-breaking transitions and creating structure and form. However, the effects of microscopic diversity have been largely neglected. We show that evolution will select for populations which retain variability, even though this is, at any given time, loss-making, predicting that we shall not observe populations with optimal behavior, but populations which can learn. This lesser short-term efficiency may be why natural diversity is so great. Evolution is seen to be driven by the noise to which it leads.     

Anderson localization and wave absorption

Experimental signatures of classical wave localization in the absence and in the presence of attenuation are analyzed. The different regimes of the attenuation, reflection, and transmission coefficients for the diffusive and localized regimes are discussed. Apparent contradictory results presented previously by John and Anderson on the renormalization of absorption by localization are reconciled and shown to apply to different situations.     

Analytic continuation of group representations. III

The connection between the ideas of contraction and analytic continuation of Lie algebras and their representations is discussed, with particular emphasis on the contraction of the Poincaré to the Galilean group.This research was supported in part by the Office of Air Force Scientific Research AF 49 (638)-1440.     

Infrared lattice bands of some pearls

From analysis of anisotropical lattice bands properties of 50 reflection spectra both of the CO stretching and bending bands measured from some pearl (Ca⁺⁺CO ₃ ^–– or Ca⁺⁺HCO ₃ ^–– layer) we discussed following subjects.i) Quantized properties present both in reflectivity and in energy. ii) classifications of the Optical Activity. iii) Polar distributions of the CO₃ oscillators in Ca⁺⁺CO ₃ ^–– surface mono-layer. iv) Force constants of these oscillators. v) Step variation of the dipolemoment and their influences to the degree of Optical Activity. vi) Two types of hysteresis loops of the values of Y_N (M_2Jbend ()/M_1Jstret. ()) derived from the oscillators which are at innert-state, at weak active-state and at active-state.     

The use of time-dependent projection operators in the derivation of master equations

In this paper we generalize our previous work on the use of time-dependent projection operators for the derivation of master equations for general systems. Previously we had generalized the usual time-independent projection operator approach to include time-dependent projection operators, in which the relevant part of the full density operator is considered to be the uncorrelated part of the full density operator. The irrelevant part of the density operator was then the part describing the correlations between the coupled systems. In the present work we present new time-dependent projections operators which have the property that some correlations between the interacting subsystems are placed in the relevant part of the distribution function and the remaining correlations are placed in the irrelevant part of the distribution function.     

Atomic versus ionized states in many-particle systems and the spectra of reduced density matrices: A model study

We study the spectrum of appropriate reduced density matrices for a model consisting of one quantum particle (electron) in a classical fluid (of protons) at thermal equilibrium. The quantum and classical particles interact by a shortrange, attractive potential such that the quantum particle can form atomic bound states with a single classical particle. We consider two models for the classical component: an ideal gas and the cell model of a fluid. We find that when the system is at low density the spectrum of the electron-proton pair density matrix has, in addition to a continuous part, a discrete part that is associated with atomic bound states. In the high-density limit the discrete eigenvalues disappear in the case of the cell model, indicating the existence of pressure ionization or a Mott effect according to a general criterion for characterizing bound and ionized electron-proton pairs in a plasma proposed recently by M. Girardeau. For the ideal gas model, on the other hand, eigenvalues remain even at high density.     

Economic demography in fuzzy spatial dilemmas and power laws

Adaptive agents, playing the iterated Prisoners Dilemma (IPD) in a two-dimensional spatial setting and governed by Pavlovian strategies (higher success-higher chance to stay), are used to approach the problem of cooperation between self-interested individuals from a novel angle: We investigate the effect of different possible measures of success (MS) used by players to asses their performance in the game. These MS involve quantities such as: the players utilities U, his cumulative score (or capital) W, his neighborhood welfare, etc. To handle an imprecise concept like success the agents use fuzzy logic. The degree of cooperation, the economic demography and the efficiency attained by the system depend dramatically on the MS. Specifically, patterns of segregation or exploitation are observed for some MS. On the other hand, power laws, that may be interpreted as signatures of critical self-organization (SOC), constitute a common feature for all the MS.     

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.     

Hyperfine interactions in muonium-impurity complexes in silicon

The properties of paramagnetic complexes formed by muonium located near acceptor and donor impurities in silicon are calculated using the quantum chemical methods. The calculated data are compared to the experimentally observed characteristics of normal and anomalous muonium centers.     

Dark body and black hole horizons

The formula for the horizon of a Newtonian dark body is given and compared to that of a relativistic black hole: a Newtonian dark body has at least one hair.     

Anti-photon

It should be apparent from the title of this article that the author does not like the use of the word photon, which dates from 1926. In his view, there is no such thing as a photon. Only a comedy of errors and historical accidents led to its popularity among physicists and optical scientists. I admit that the word is short and convenient. Its use is also habit forming. Similarly, one might find it convenient to speak of the aether or vacuum to stand for empty space, even if no such thing existed. There are very good substitute words for photon, (e.g., radiation or light), and for photonics (e.g., optics or quantum optics). Similar objections are possible to use of the word phonon, which dates from 1932. Objects like electrons, neutrinos of finite rest mass, or helium atoms can, under suitable conditions, be considered to be particles, since their theories then have viable non-relativistic and non-quantum limits. This paper outlines the main features of the quantum theory of radiation and indicates how they can be used to treat problems in quantum optics.It is a pleasure to join in the 60th birthday celebration of the Director, Herbert Walther, of the Max-Planck-Institute for Quantum Optics at Garching, and wish him much happiness and many more years of his very great scientific creativity.     

The problem of the imperfection of a world,itself created by a perfect god

The two main arguments concern(1) the presence of an enlightened complementarity between philosophic (including scientific) and religious (not including mystic) thought, and(2) the necessity to postulate a threefold relationship whenever one is to gain knowledge of any kind. They are both inspired by physics (from Bohr's strict complementarity, resp. from Newton's fundamental postulate).God's perfection resides at least in Symmetry in a generalized (not restrictively spatial) sense. Yet, as the argument goes, Space does not exist as a thing. Consequently, the Great Geometer (God) cannot dwell within a World He creates, and it is wrong to speak about His (God's) existence; for, existence is bound to the temporal, and Time is, together with the World, part of God's creation. Thus the only possible creation consists in God separating World and Time from Himself: This is the paradigm of Symmetry-breaking.Polytheistic mythologies all assume such and such imperfection of their deities; hence perfection is meaningful for monotheism only. A relationship of a threefold (trinitary) nature must then obtain between God, World, and Time; this is analogous to Newton's postulate relating force, momentum and time. Just as the latter and its specific generalizations must be found true by verification, the said threefold relationship must also be found true: within philosophic thoughtmore geometrico (in a generalized sense), within religious thoughtmore hymnometrico. Yet the complementarity (called enlightened) arising between the two kinds of thought is of a higher nature than Bohr's strict complementarity. While it can be understood from the role assumed by language itself, it can however only be disposed of within mystic contemplation.Dedicated to Sir KARL POPPER on the occasion of his 90th birthday.     

Stationary solutions of the bogoliubov hierarchy equations in classical statistical mechanics. 3

We continue the analysis of the conjugate equation for the generating function of a Gibbs random point field corresponding to a stationary solution of the classical BBGKY hierarchy. This equation was established and partially investigated in the preceding papers under the same title. In the present paper we reduce a general theorem about the form of solutions of the conjugate equation to a statement which relates to a special case where the interacting particles constitute a quasi—one dimensional configuration.     

Traffic Jams in a Lattice-Gas Model

We propose a simple lattice-gas model characterized by two states of atoms, the thermalized state, which is the same as in the standard lattice-gas model, and the running state, where the atoms jump in one direction only. The model exhibits the existence of traffice jams (bunching of thermalized atoms in compact groups), the nonlinear dependence of mobility on the jump probability, and the hysteresis.     

The first and second nearest neighbour Cr3+ pairs in ruby

The irreducible representations of the states of the first and second nearest neighbour Cr³⁺ pairs in ruby were deduced from the known states of the single ions by the group theoretical method of induction. The summetry selection rules and polarizations for electric dipole radiation are discussed.Supported by the Deutsche Forschungsgemeinschaft within the Sonderforschungsbereich 65 Frankfurt-Darmstadt.     

Standpoint cosmology

An unorthodox cosmology is based on a notion of standpoint, distinguishing past from future, realized through Hilbert-space representation of the complex conformai group for 3+1spacetime and associated coherent states. Physical (approximate) symmetry attaches to eight-parameter complex Poincaré displacements, interpretable as growth of standpoint age (one parameter), boost of matter energy-momentum in standpoint rest frame (three parameters) and displacement of matter location in a compact U(1)O(4)/O(3) spacetime attached to standpoint (four parameters). An initial condition (at big bang) is characterized by a huge dimensionless parameter that breaks dilation invariance. Four major length scales are recognized, called Planck, particle, lab, and Hubble, with separations controlled by ; all physical concepts, including spacetime, depend on wideness of scale separation.