Hilbert's 'World Equations' and His Vision of a Unified Science

In summer 1923, a year after his lectures on the `New Foundation of Mathematics' and half a year before the republication of his two notes on the `Foundations of Physics,' Hilbert delivered a trilogy of lectures in Hamburg. In these lectures, Hilbert expounds in an unusually explicit manner his epistemological perspective on science as a subdiscipline of an all embracing science of mathematics. The starting point of Hilbert's considerations is the claim that the class of gravitational and electromagnetic field equations implied by his original variational formulation of 1915 provides valid candidate `world equations,' even in view of attempts at unified field theories \'a la Weyl and Eddington based on the concept of the affine connection. We give a discussion of Hilbert's lectures and, in particular, examine his claim that Einstein in his 1923 papers on affine unified field theory only arrived at Hilbert's original 1915 theory. We also briefly comment on Hilbert's philosophical viewpoints expressed in these lectures.Comment: 23 pages; to appear in Einstein Studie

Charge symmetry of the nuclear force as off-shell constraint

Off-shell changes are generated in the 1S0 nucleon-nucleon interaction using the Reid soft-core potential and unitary transformations of short range. Charge symmetry is assumed for the nuclear force. The same off-shell variations of the Reid potential are employed as the hadronic part of the proton-proton interaction and as neutron-neutron interaction. The Reid potential fits the experimental proton-proton data. It also accounts for the neutron-neutron scattering length with satisfying accuracy. The off-shell behavior of the Reid potential is varied in two different ways. First, off-shell changes are performed which preserve the fit to the proton-proton data. Most transformed potentials of the type attempted here are unable to yield the correct experimental value of the neutron-neutron scattering length and have to be rejected. A simple practical rule is given according to which the off-shell changes consistent with the neutron-neutron scattering length can be selected. Second, off-shell changes are performed which leave the neutron-neutron scattering length unaltered. Transformed potentials of this type have usually been employed in nuclear-structure calculations. The potentials which exhibit large off-shell effects in nuclear structure are unable to account for the experimental proton-proton data. Their off-shell effects are therefore of no physical significance, and the potentials have to be rejected. A simple practical rule is given according to which the off-shell changes consistent with the experimental proton-proton data can be selected

Role of the neutron charge form factor in electron scattering from the three-nucleon system

We investigate the effects which the experimental uncertainty of the neutron charge form factor can have on the charge form factors of 3H and 3He. NUCLEAR REACTIONS Elastic electron scattering, charge form factors, three-nucleon systems

Three-body force from kinematical effects in the three-nucleon system

A Galilean-noninvariant correction to ordinary one-boson-exchange potentials is derived. It gives rise to a three-body force in the three-nucleon system. Its importance for the properties of the three-nucleon bound state is tested and found to be small. This result justifies the common practice which neglects the dependence of the one-boson-exchange potentials on the total momentum of the interacting pair in many-nucleon systems

Off-energy-shell continuation of the nucleon-nucleon and meson-nucleon transition matrices in the presence of inelasticities

A technique for constructing the nucleon-nucleon transition matrices T in the presence of inelastic channels is given. The present technique avoids the usual potential fit and continues T off the energy shell directly consistent with the two-body scattering data and consistent with the properties of possible two-body bound states. The respective T matrices are determined by a real symmetric matrix function ⟨E1α1|σ|E2α2⟩ of the continuous energy variable E and the discrete eigenchannel label α. The on-shell part of σ is given by the eigenphases; the arbitrariness of T is the off-shell continuation of the phase-shift matrix ⟨Eα1|σ|Eα2⟩ into two dimensions. The present technique of constructing T makes the experimental nucleon-nucleon and meson-nucleon scattering data readily available as input for nuclear theory extended to include baryon resonances

Polarization effects in pion electroproduction from 3He

Inelastic electron scattering from 3He is studied in the kinematic region of pion production. Inclusive processes with polarization of the electron probe and of the 3He target are described in the plane wave impulse approximation. The question to what extent polarized 3He can serve in this kinematic regime as a substitute for unavailable neutron spin targets is discussed

Polarized deep-inelastic lepton scattering from the polarized two- and three-nucleon bound states

A relativistic description of polarized deep-inelastic lepton scattering from polarized nuclei is presented. It is based on front form dynamics. Convolution formulas for the nuclear spin structure functions gA1 and gA2 are derived. They require the front form spin distributions of nuclei and the nucleonic spin structure functions. The description is applied to the deuteron and the trinucleon bound states. The numerical calculations show that relativistic effects arising from the consistent quantum mechanical treatment of spin are small. Simple approximations to the convolution formulas for gA1 and gA2 are justified. The approximative convolution formulas allow the subtraction of nuclear effects from measured spin structure functions and therefore the experimental determination of the neutron spin structure functions. Polarized 3He turns out to be a rather reliable effective neutron spin target for deep-inelastic scattering of polarized leptons. The differences between descriptions based on front form and on instant form dynamics are also discussed

Suppressing the aromatic cycle of the dimethyl ether to hydrocarbons reaction on zeolites

The influence of the zeolite framework type on the conversion of dimethyl ether (DME) to hydrocarbons (DTH) was investigated for *MRE, MFI and TON zeolite catalysts. Remarkable differences in the catalytic performance of the materials were observed. In particular, the *MRE zeolite showed an exceptionally high yield of olefins (90%) with a substantial ratio of products in the chain length range C$_5$-C$_{11}$. Additionally, the longevity of the *MRE zeolite clearly exceeded previously reported data. The comparison of mechanistic parameters (Hydrogen-Transfer-Index HTI$_{Ci}$ and C$_3$/C$_2$ ratio) demonstrated for this zeolite, that the formation of aromatics in the reaction network can be almost completely suppressed under suitable reaction conditions. By varying the reaction parameters temperature, DME partial pressure and weight hourly space velocity (WHSV), it was possible to identify the optimal combination of selectivity and deactivation resistance for each material. The olefin-rich DTH product of the *MRE zeolite offers manifold possibilities for further conversion to valuable renewably produced low-emission fuels like gasoline or jet fuel

Expression of Intermediate Filaments and Germ Cell Markers in the Developing Bovine Ovary: An Immunohistochemical and Laser-Assisted Microdissection Study

In the present investigation, bovine ovary prenatal development was studied using immunohistochemistry and laser-assisted microdissection (LAM). A major aim of this study was to evaluate the protein expression pattern of intermediate filaments (IF) and distinguish S100 protein (S100 alpha and S100 beta protein) isoforms during prenatal follicle differentiation, subsequently correlating them with germ cell marker expression. A development-specific expression pattern of different keratins as well as vimentin was detected in the prenatal bovine ovary; K18-specific expression was found during all developmental stages (i.e. in surface epithelium, germ cell cord somatic cells, and follicle cells), and keratins 5, 7, 8, 14, and 19 and vimentin had a stage-specific expression pattern in the different cell populations of the prenatal ovaries. Additionally, our results represent new data on the expression pattern of germ cell markers during bovine ovary prenatal development. S100 alpha and beta protein was localized to oocyte cytoplasm of different follicle stages, and S100 alpha staining could be observed in granulosa cells. Furthermore, through isolation of characteristic ovary cell populations using LAM, specific confirmation of some genes of interest (KRT8, KRT18, S100 alpha, S100 beta, and OCT4, DDX4) could be obtained by RT-PCR in single cell groups of the developing bovine ovary.© 2015 S. Karger AG, Base