Poincaré’s Relativistic Physics: Its Origins and Nature

Henri Poincaré (1854–1912) developed a relativistic physics by elevating the empirical inability to detect absolute motion, or motion relative to the ether, to the principle of relativity, and its mathematics ensured that it would be compatible with that principle. Although Poincaré’s aim and theory were similar to those of Albert Einstein (1879–1955) in creating his special theory of relativity, Poincaré’s relativistic physics should not be seen as an attempt to achieve Einstein’s theory but as an independent endeavor. Poincaré was led to advance the principle of relativity as a consequence of his reflections on late nineteenth-century electrodynamics; of his conviction that physics should be formulated as a physics of principles; of his conventionalistic arguments on the nature of time and its measurement; and of his knowledge of the experimental failure to detect absolute motion. The nonrelativistic theory of electrodynamics of Hendrik A.Lorentz (1853–1928) of 1904 provided the means for Poincaré to elaborate a relativistic physics that embraced all known physical forces, including that of gravitation. Poincaré did not assume any dynamical explanation of the Lorentz transformation, which followed from the principle of relativity, and he did not seek to dismiss classical concepts, such as that of the ether, in his new relativistic physics. Shaul Katzir teaches in the Graduate Program in History and Philosophy of Science, Bar Ilan University.     

Thermal dilatation of polymers

The glass-transition temperature, T_g, is the narrow temperature interval (usually approximated by a point) above which long-range mobility of macromolecular segments exists and below which it ceases. For such mobility to be realized two prerequisites are required: (1) a free volume sufficiently large to accomodate the moving segment must exist, or be formed, adjacently to it, and (2) the segment itself must possess sufficiently high thermal energy to overcome the energy barrier confining it to its equilibrium position. The high segmental mobility reflects a relatively low packing density, D, and is reflected in a relatively high coefficient of thermal expansion, α.     

Generalized inverse of linear transformations: a geometric approach

A generalized inverse of a linear transformation A:

→

, where

and

are arbitrary finite dimensional vector spaces, is defined using only geometrical concepts of linear transformations. The inverse is uniquely defined in terms of specified subspaces $\text{L}$ ?

, $\text{M}$ ?

and a linear transformation N satisfying some conditions. Such an inverse is called the $\text{LM}$N-inverse. A Moore-Penrose type inverse is obtained by choosing N = 0. Some optimization problems are considered by choosing

and

as inner product spaces. Our results extend without any major modification of proofs to bounded linear operators with closed range on Hilbert spaces.     

The effect of adsorbed oxygen on the surface potential of n-GaAs(110)

Potential variations on semiconductor surfaces are often mapped using a combination of constant current topographic and local surface photo-voltage (SPV) imaging. SPV imaging provides a direct measurement of surface-potential variations at large lateral distances from a charged defect or adsorbate. However, directly above the defect, variations in the SPV signal need to be interpreted in terms of surface screening, traps, and band bending. We have examined these effects using isolated oxygen atoms on a GaAS(110) surface, which is free of surface states. We interpret variations in the SPV signal in terms of a simple electrostatic model which considers the oxygen-induced Coulomb potential and corresponding image potential, both of which affect the surface density of states.     

Manipulating nonadiabatic conical intersection dynamics by optical cavities

Optical cavities hold great promise to manipulate and control the photochemistry of molecules. We demonstrate how molecular photochemical processes can be manipulated by strong light–matter coupling. For a molecule with an inherent conical intersection, optical cavities can induce significant changes in the nonadiabatic dynamics by either splitting the pristine conical intersections into two novel polaritonic conical intersections or by creating light-induced avoided crossings in the polaritonic surfaces. This is demonstrated by exact real-time quantum dynamics simulations of a three-state two-mode model of pyrazine strongly coupled to a single cavity photon mode. We further explore the effects of external environments through dissipative polaritonic dynamics computed using the hierarchical equation of motion method. We find that cavity-controlled photochemistry can be immune to external environments. We also demonstrate that the polariton-induced changes in the dynamics can be monitored by transient absorption spectroscopy.

Optical cavities hold great promise to manipulate and control the photochemistry of molecules.     

Relativistic electronic structure theory

The theoretical and technical foundations are presented for the efficient relativistic electronic structure theories to treat heavy-atomic molecular systems. This review contains two surveys of four-component and two-component quasi-relativistic approaches. First, we review our highly efficient computational scheme for four-component relativistic ab initio molecular orbital (MO) methods over generally contracted spherical harmonic Gaussian-type spinors (GTSs). Illustrative calculations, which are performed with a new four-component relativistic ab initio molecular orbital program package REL4D, clearly show the efficiency of our computational scheme by the Dirac-Hartree-Fock (DHF) and Dirac-Hartree-Fock (DKS) methods. Next, in the two-component quasi-relativistic framework, two relativistic Hamiltonians, RESC and higher order Douglas-Kroll (DK) Hamiltonians, are introduced, and several illustrative calculations are shown. Numerical results for several systems show that good accuracy can be obtained with our third-order DK (DK3) Hamiltonian.     

A deprotection procedure using SO3H silica gel to remove non-silyl protecting groups

Protecting groups are indispensable in organic synthesis and there is a great need for a variety of deprotection methods. Here, we investigated the scope of the application of a deprotection procedure using SO₃H silica gel, which we have previously reported as a desilylation procedure. Under these conditions, -OMOM, -OSEM, -OTHP, and -OAc groups and dimethyl acetal were cleaved. Pivaloyloxy, benzyloxy and methoxy carbonyl groups remained intact and selective deprotection of TBS groups in the presence of other protecting groups was accomplished. We succeeded in cleaving an acetyl group on a secondary alcohol in a highly polar nortropine derivative. Our findings here provide another deprotection option and would be helpful in the synthesis of multifunctional compounds.     

Many-body effects in molecular photoionization in intense laser fields; time-dependent Hartree-Fock simulations

The time evolution of the reduced single electron density matrix for eight electrons in a one-dimensional finite box potential driven by an intense laser field is calculated by numerically integrating the time-dependent Hartree-Fock equations. We study the effects of the Coulomb interaction, field intensity, and frequency on the time profile of the ionization process. Our computed saturation ionization intensity (Isat) is in good agreement with experimental results for decatetraene [Ivanov et al. J. Chem. Phys. 117, 1575 (2002)].