In 1937 the Jahn-Teller (JT) effect addressed the instability (potential or actual) of non-linear symmetric molecules with degenerate orbital electronic states. In view of the large variety of JT activity that has taken place since then, we might broaden our perspective to look at works whose subjects fall under the more general heading of "Strong interactions between two dissimilar systems" (where one system is usually bosonic and the other fermionic). In these intervening years we find several highly important works in Physics and Chemistry that come under this heading and were either connected with, or arose from, JT systems, problems and approaches. Apart from high temperature superconductors, we mention Yang-Mills gauge-forces, symmetry breaking (in elementary particles), conical intersections in molecular potential surfaces, surface crossings between them in chemical reactions, entanglements in the quantum theory of measurements and Berry phases. We elaborate on the last two topics. We show first that the slow evolution of a T coupling from the weak to strong regime can model the quantum mechanical three-state measurement situation, when the positions of the nuclei acts as the measuring device. We then employ recently derived integral relations between component moduli and phases in a time dependent wave-function to demonstrate the equivalence between the state-reduction and the phase decoherence interpretations of the measurement process.

Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of barotropic magnetohydrodynamics can be derived. The variational principle is given in terms of six independent functions for non-stationary barotropic flows and three independent functions for stationary barotropic flows. This is less then the seven variables which appear in the standard equations of barotropic magnetohydrodynamics which are the magnetic field B the velocity field v and the density ρ.The equations obtained for non-stationary barotropic magnetohydrodynamics resemble the equations of Frenkel, Levich & Stilman [1]. The connection between the Hamiltonian formalism introduced in [1] and the present Lagrangian formalism (with Eulerian variables) will be discussed.Finally the relations between barotropic magnetohydrodynamics topological constants and the functions of the present formalism will be elucidated.

The general theory of relativity (GR) is symmetric under smooth coordinate transformations, also known as diffeomorphisms. The general coordinate transformation group has a linear subgroup denoted as the Lorentz group of symmetry, which is also maintained in the weak field approximation to GR. The dominant operator in the weak field equation of GR is thus the d’Alembert (wave) operator, which has a retarded potential solution. Galaxies are huge physical systems with dimensions of many tens of thousands of light years. Thus, any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects are neglected in the present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper, we will show that, by taking general relativity seriously without neglecting retardation effects, one can explain the radial velocities of galactic matter in the M33 galaxy without postulating dark matter. It should be stressed that the current approach does not require that velocities v are high; in fact, the vast majority of galactic bodies (stars, gas) are substantially subluminal—in other words, the ratio of vc≪1. Typical velocities in galaxies are 100 km/s, which makes this ratio 0.001 or smaller. However, one should consider the fact that every gravitational system, even if it is made of subluminal bodies, has a retardation distance, beyond which the retardation effect cannot be neglected. Every natural system, such as stars and galaxies and even galactic clusters, exchanges mass with its environment, for example, the sun loses mass through solar wind and galaxies accrete gas from the intergalactic medium. This means that all natural gravitational systems have a finite retardation distance. The question is thus quantitative: how large is the retardation distance? For the M33 galaxy, the velocity curve indicates that the retardation effects cannot be neglected beyond a certain distance, which was calculated to be roughly 14,000 light years; similar analysis for other galaxies of different types has shown similar results. We demonstrate, using a detailed model, that this does not require a high velocity of gas or stars in or out of the galaxy and is perfectly consistent with the current observational knowledge of galactic and extra galactic material content and dynamics.