Biomedical subjects

I E Segal

Publications and source records attributed to I E Segal.

At least 19 recordsLinked to original sources

PubMed1999

Is redshift-dependent evolution of galaxies a theoretical artifact?

The physical validity of the hypothesis of (redshift-dependent) luminosity evolution in galaxies is tested by statistical analysis of an intensively studied complete high-redshift sample of normal galaxies. The necessity of the evolution hypothesis in the frame of big-bang cosmology is confirmed at a high level of statistical significance; however, this evolution is quantitatively just as predicted by chronometric cosmology, in which there is no such evolution. Since there is no direct observational means to establish the evolution postulated in big-bang studies of higher-redshift galaxies, and the chronometric predictions involve no adjustable parameters (in contrast to the two in big-bang cosmology), the hypothesized evolution appears from the standpoint of conservative scientific methodology as a possible theoretical artifact.

Astronomical Phenomena↗

PubMed1998

Cosmological implications of a large complete quasar sample.

Objective and reproducible determinations of the probabilistic significance levels of the deviations between theoretical cosmological prediction and direct model-independent observation are made for the Large Bright Quasar Sample [Foltz, C., Chaffee, F. H., Hewett, P. C., MacAlpine, G. M., Turnshek, D. A., et al. (1987) Astron. J. 94, 1423-1460]. The Expanding Universe model as represented by the Friedman-Lemaitre cosmology with parameters qo = 0, Lambda = 0 denoted as C1 and chronometric cosmology (no relevant adjustable parameters) denoted as C2 are the cosmologies considered. The mean and the dispersion of the apparent magnitudes and the slope of the apparent magnitude-redshift relation are the directly observed statistics predicted. The C1 predictions of these cosmology-independent quantities are deviant by as much as 11sigma from direct observation; none of the C2 predictions deviate by >2sigma. The C1 deviations may be reconciled with theory by the hypothesis of quasar "evolution," which, however, appears incapable of being substantiated through direct observation. The excellent quantitative agreement of the C1 deviations with those predicted by C2 without adjustable parameters for the results of analysis predicated on C1 indicates that the evolution hypothesis may well be a theoretical artifact.

Journal Article↗

PubMed1998

The Black-Scholes pricing formula in the quantum context.

A natural explanation for extreme irregularities in the evolution of prices in financial markets is provided by quantum effects. The lack of simultaneous observability of relevant variables and the interference of attempted observation with the values of these variables represent such effects. These characteristics have been noted by traders and economists and appear intrinsic to market dynamics. This explanation is explored here in terms of a corresponding generalization of the Wiener process and its role in the Black-Scholes-Merton theory. The differentiability of the Wiener process as a sesquilinear form on a dense domain in the Hilbert space of square-integrable functions over Wiener space is shown and is extended to the quantum context. This provides a basis for a corresponding generalization of the Ito theory of stochastic integration. An extension of the Black-Scholes option pricing formula to the quantum context is deduced.

Journal Article↗

PubMed1994

Convergence of quantum electrodynamics in a curved modification of Minkowski space.

The interaction and total hamiltonians for quantum electrodynamics, in the interaction representation, are entirely regular self-adjoint operators in Hilbert space, in the universal covering manifold M of the conformal compactification of Minkowski space Mo. (M is conformally equivalent to the Einstein universe E, in which Mo may be canonically imbedded.) In a fixed Lorentz frame this may be expressed as convergence in a spherical space with suitable periodic boundary conditions in time. The traditional relativistic theory is the formal limit of the present variant as the space curvature vanishes.

Journal Article↗

PubMed1993

Geometric derivation of the chronometric redshift.

The chronometric redshift-distance relation z = tan 2(1/2rho), where rho is the distance in radians in the Einstein metric, is derived by an elementary geometric analysis comparable to that in traditional analysis of the expanding universe model. The differential dTt of Einstein time evolution Tt through time t, as applied to the local Minkowski coordinates x, takes the form sec2(1/2t). At the point of observation t = rho, implying that for a sufficiently localized source, observed wave lengths are a factor of sec2(1/2rho) greater than the corresponding emitted wave lengths.

Journal Article↗

PubMed1993

The redshift-distance relation.

Key predictions of the Hubble law are inconsistent with direct observations on equitable complete samples of extragalactic sources in the optical, infrared, and x-ray wave bands-e.g., the predicted dispersion in apparent magnitude is persistently greatly in excess of its observed value, precluding an explanation via hypothetical perturbations or irregularities. In contrast, the predictions of the Lundmark (homogeneous quadratic) law are consistent with the observations. The Lundmark law moreover predicts the deviations between Hubble law predictions and observation with statistical consistency, while the Hubble law provides no explanation for the close fit of the Lundmark law. The flux-redshift law F [symbol, see text] (1 + z)/z appears consistent with observations on equitable complete samples in the entire observed redshift range, when due account is taken of flux limits by an optimal statistical method. Under the theoretical assumption that space is a fixed sphere, as in the Einstein universe, this law implies the redshift-distance relation z = tan2(r/2R), where R is the radius of the spherical space. This relation coincides with the prediction of chronometric cosmology, which estimates R as 160 +/- 40 Mpc (1 parsec = 3.09 x 10(16) m) from the proper motion to redshift relation of superluminal sources. Tangential aspects, including statistical methodology, fundamental physical theory, bright cluster galaxy samples, and proposed luminosity evolution, are briefly considered.

Journal Article↗

PubMed1992

Apparent nonlinearity of the redshift-distance relation in infrared astronomical satellite galaxy samples.

The Hubble (linear) redshift-distance law predicts values for directly observed quantities that are quite deviant from their actual values in infrared astronomical satellite (IRAS) galaxy samples. These samples are objectively defined, have modern measurements, are presently the largest such samples to which the Hubble law is theoretically applicable, and are otherwise generally considered to be statistically appropriate. The Hubble law predicts in particular that the dispersion in log flux will be much greater than it is observed to be. This type of deviation is fundamentally incapable of explanation via the assumption of any physically known type of perturbation. The Lundmark (quadratic) redshift-distance law predicts values for these directly observed quantities that are consistent with, and in fact quite close to, their actual values in the same samples. The predictions of a cubic law are typically deviant from observation but somewhat less so than those of the Hubble law. The Lundmark law accurately predicts the deviations from observation of statistical estimates predicated on either the Hubble or the cubic law. Parallel predictions for the latter laws for the results of statistical estimation predicated on the alternative laws are typically quite inaccurate. The Hubble and Lundmark laws are predicted at the low redshifts of the IRAS galaxy samples by generic big bang cosmology (BBC) and chronometric cosmology (CC), respectively. The present results confirm earlier studies of a variety of objectively defined samples of discrete sources in other wave bands that were contraindicative of BBC and indicative of CC.

Journal Article↗

PubMed1991

Is the cygnet the quintessential baryon?

The apparently new hadron-like particle ("cygnet") indicated by cosmic ray observations on certain neutron stars is predicted to be a spin 1/2 fermion of magnetic moment and charge 0 and lifetime infinity. This derives from the natural identification of the cygnet with the one hitherto unobserved fundamental fermion of chronometric particle theory, the x or "exon", which plays the role of a quintessential baryon. The "partons" are represented by the other fundamental fermions, consisting of e, nue, and numu; e.g., n = x + e+ + e-, p = x + e+ + nue. With further empirical assignments, chronometric theory has a potential for explaining diverse phenomena, such as mixing in the neutral kaon complex and the nature of the higher electrons. Its fundamental fermion and boson fields transform indecomposably under its symmetry group, the conformal group G. Theoretical elementary particles transforming irreducibly under G derive as successive quotients in a maximal chain of invariant subspaces. Mass fixing by Mach's principle breaks the symmetry down to microscopically observed covariance with respect to the Poincare group P0. The resulting representation is normally irreducible, but splits in the case of the K0 into two P0-irreducible components that are mixed by the excess of the chronometric over the relativistic energy ("gravity"), which provides a "superweak" force that may be explanatory of CP violation.

Journal Article↗

PubMed1987

The local redshift-distance relation and spatial uniformity.

Regrettably, the review of the redshift-distance relation in the review by Salpeter and Hoffman [Salpeter, E. E. & Hoffman, G. L., Jr. (1986) Proc. Natl. Acad. Sci. USA 83, 3056-3063], appears flawed. In particular, the logically inconclusive and uncertain hypothesis of local extragalactic spatial uniformity is used in an essential way. Moreover, even in conjunction with this hypothesis, the Lundmark law fits more closely than the Hubble law, on the basis of the data and criteria of Salpeter and Hoffman, when a rough approximation involved in the estimation of the galaxy luminosity function is eliminated. Specifically, the assumption that all galaxies in the redshift range 500-1700 km.s(-1) are effectively at the redshift 1100 km.s(-1) is made; when this assumption is replaced by a statistically optimal procedure that uses the precise redshifts, the relative fit of the two laws is reversed.

Journal Article↗

PubMed1987

Explanation of parity nonconservation.

Space inversion and other discrete symmetries are treated within the frame of a theory of fundamental forces based only on general considerations of causality, symmetry, and stability, without ad hoc differential equations. The basic space-time M is the Einstein universe R(1) x S(3) as a causal (or conformal) rather than a pseudo-Riemannian manifold. Its connected symmetry group is then a 15-parameter group G locally equivalent to SO(2, 4), while the isometry group K of the Einstein universe is a 7-parameter subgroup. Correlation with conventional relativistic theory is based on a canonical imbedding of Minkowski space M(0) into M, together with the unique extendability of all transformations of the scaling-extended Poincaré group P from M(0) to global transformations on M. The fundamental fermion field F and boson field B are here restricted to be real and are fully invariant under G(e), where the superscript e denotes the inclusion of space and time inversions. The role of C on F is taken over by a real matrix having the eigenvalues +/-i, that commutes with G but anticommutes with space inversion. The spin space for B consists of the real linear transformations on that for F. There is a corresponding natural total Lagrangian that is both G(e) and O(2)-gauge invariant, the latter leading to lepton and baryon number conservation, and which is nonparametric except for scale. The Weyl and Maxwell equations are deduced, and compelling identifications made for neutrinos and the photon. The e and mu neutrino pairs occur in strikingly inequivalent positions in F, appearing symmetric only in the conventional relativistic limit R --> infinity, where R is the ( G-invariant) fundamental length interpretable as the radius of the space S(3). The photon occurs as the lowest member of a coherent subfamily of B that includes natural candidates for bare versions of the W and Z particles. In the relativistic limit the interaction Lagrangian becomes a sum over all elementary processes, one of which appears as quantum electrodynamics with Majorana-type electrons.

Journal Article↗

PubMed1986

Directly observed relations in complete galaxy samples and the predictions of redshift-distance power laws.

Directly observed relations in complete galaxy samples (apparent magnitude or diameter vs. redshift) are compared with the predictions of redshift-distance power laws. The predictions are obtained by an objective, nonparametric, statistically uniform, and fully reproducible procedure. In all cases the linear law fits even more poorly than a cubic law, and the optimal law is approximately quadratic. Even a 1.2 power law is conspicuously better-fitting than a linear law. The results of the present study in terms of directly measured quantities are consistent with and confirm earlier studies in terms of theoretical quantities such as absolute magnitudes and diameters. They show that there is no positive evidence for the Hubble law in manifestly fair galaxy samples and that the law can be reconciled with the data in complete samples only, if at all, by the adjunction of a tissue of ancillary hypotheses, none of which is capable of direct observational substantiation.

Journal Article↗

PubMed1984

Reduction of scattering to an invariant finite displacement in an ambient space-time.

The scattering transformation S for a wave equation in Minkowski space M(0) is reducible (rigorously in the classical case, necessarily partially heuristically in the nonlinear quantum case) to the action of a distinguished finite transformation zeta in the ambient universal cosmos M. M(0) is invariantly imbedded in M, relative to any given point of observation, and the space-like surfaces x(0) = s in M(0) converge as s --> +/-infinity to finite light cones C(+/-) in M. The generator zeta of the infinite cyclic center of the connected group of all casuality-preserving transformations in M (isomorphic to SU(2,2)/Z(2)) carries C(-) into C(+) and acts on solutions of relativistic wave equations as S, in an invariant bundle formulation. The establishment of S is simplified, the symmetry and regularity properties of S are enhanced, the scope of the scattering concept is extended to important equations such as those of Yang-Mills (lacking an invariant separation into free and interaction components), and the treatment of bound and scattering states is more unified.

Journal Article↗

PubMed1983

Self-adjointness of the Fourier expansion of quantized interaction field Lagrangians.

Regularity properties significantly stronger than were previously known are developed for four-dimensional non-linear conformally invariant quantized fields. The Fourier coefficients of the interaction Lagrangian in the interaction representation-i.e., evaluated after substitution of the associated quantized free field-is a densely defined operator on the associated free field Hilbert space K. These Fourier coefficients are with respect to a natural basis in the universal cosmos M, to which such fields canonically and maximally extend from Minkowski space-time M(0), which is covariantly a submanifold of M. However, conformally invariant free fields over M(0) and M are canonically identifiable. The kth Fourier coefficient of the interaction Lagrangian has domain inclusive of all vectors in K to which arbitrary powers of the free hamiltonian in M are applicable. Its adjoint in the rigorous Hilbert space sense is a(-k) in the case of a hermitian Lagrangian. In particular (k = 0) the leading term in the perturbative expansion of the S-matrix for a conformally invariant quantized field in M(0) is a self-adjoint operator. Thus, e.g., if varphi(x) denotes the free massless neutral scalar field in M(0), then integralM(0):varphi(x)(4):d(4)x is a self-adjoint operator. No coupling constant renormalization is involved here.

Journal Article↗

PubMed1982

Spatial homogeneity and redshift-distance laws.

Spatial homogeneity in the radial direction of low-redshift galaxies is subjected to Kafka-Schmidt V/V(m) tests using well-documented samples. Homogeneity is consistent with the assumption of the Lundmark (quadratic redshift-distance) law, but large deviations from homogeneity are implied by the assumption of the Hubble (linear redshift-distance) law. These deviations are similar to what would be expected on the basis of the Lundmark law. Luminosity functions are obtained for each law by a nonparametric statistically optimal method that removes the observational cutoff bias in complete samples. Although the Hubble law correlation of absolute magnitude with redshift is reduced considerably by elimination of the bias, computer simulations show that its bias-free value is nevertheless at a satistically quite significant level, indicating the self-inconsistency of the law. The corresponding Lundmark law correlations are quite satisfactory satistically. The regression of redshift on magnitude also involves radial spatial homogeneity and, according to R. Soneira, has slope determining the redshift-magnitude exponent independently of the luminosity function. We have, however, rigorously proved the material dependence of the regression on this function and here exemplify our treatment by using the bias-free functions indicated, with results consistent with the foregoing argument.

Journal Article↗

PubMed1982

Chronometric cosmology and fundamental fermions.

It is proposed that the fundamental fermions of nature are modeled by fields on the chronometric cosmos that are not precisely spinors but become such only in the nonchronometric limit. The imbedding of the scale-extended Poincaré group in the linearizer of the Minkowskian conformal group defines such fields, by induction.

Journal Article↗

PubMed1981

Covariant chronogeometry and extreme distances: Elementary particles.

We study a variant of elementary particle theory in which Minkowski space, M(0), is replaced by a natural alternative, the unique four-dimensional manifold M with comparable properties of causality and symmetry. Free particles are considered to be associated (i) with positive-energy representations in bundles of prescribed spin over M of the group of causality-preserving transformations on M (or its mass-conserving subgroup) and (ii) with corresponding wave equations. In this study these bundles, representations, and equations are detailed, and some of their basic features are developed in the cases of spins 0 and (1/2). Preliminaries to a general study are included; issues of covariance, unitarity, and positivity of the energy are treated; appropriate quantum numbers are indicated; and possible physical applications are discussed.

Journal Article↗

PubMed1980

Some recent tests of the chronometric cosmology.

Two papers comparing particular samples of galaxies and quasars with certain predictions of the chronometric cosmology, and reporting significant deviations, are shown not to be altogether correct in their theoretical procedures. It is shown in addition that although the data employed in these papers are in part privately held, published data on similar samples fit the chronometric predictions satisfactorily, and fail to fit nonevolutionary Friedmann models with conventional values for q(0). As a check on and a refinement of our statistical analysis, the magnitude bias was removed from several well-documented samples by maximum-likelihood estimation of the individual probabilities in the differential luminosity function, without constraint on its form. The same conclusions as earlier follow, both in the classic regime of bright low-redshift galaxies and that of quasars.

Journal Article↗

PubMed1980

Statistical invalidation of the Hubble law.

An optimal nonparametric technique for elimination of the observation cutoff bias, on the assumption of a given theoretical cosmology, is applied to the redshift-magnitude and redshift-angular diameter relationships in objectively specified large galaxy samples. The estimates obtained on the assumptions of linear and square redshift-distance laws are uniformly and strongly favorable to the square law. The question of whether the relative inferiority of the linear law can scientifically be ascribed to ancillary extragalactic phenomena is addressed by nonparametric crosstesting of the alternative hypotheses. Each law is used to predict the results of a statistical analysis based on the alternative law by using the given data and computer simulations. The result is that the square law predicts with statistical exactitude the results of the analyses of the linear law; but the linear law predicts with near certainty that the fit of the square law will be much worse than is observed. In the absence of independent validation of a variety of ancillary hypotheses that have been adduced in connection with the linear law, it seems necessary to conclude that the Hubble law lacks an objective statistical foundation.

Journal Article↗