An assessment of Evans' unified field theory II

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations. We now propose a variational principle for Evans' theory and show that it yields two field equations. The second field equation is algebraic in the torsion and we can resolve it with respect to the torsion. It turns out that for all physical cases the torsion vanishes and the first field equation, together with Evans' unified field theory, collapses to an ordinary Einstein equation.Comment: 11 pages of late

An assessment of Evans' unified field theory I

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe theta and a (metric compatible) Lorentz connection Gamma. These two potentials yield the field strengths torsion T and curvature R. Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe theta to be proportional to four extended electromagnetic potentials A; these are assumed to encompass the conventional Maxwellian potential in a suitable limit. The viable Einstein-Cartan(-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans' ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete.Comment: 39 pages of latex, modified because of referee report, mistakes and typos removed, partly reformulated, taken care of M.W.Evans' rebutta

Maxwell's field coupled nonminimally to quadratic torsion: Induced axion field and birefringence of the vacuum

We consider a possible (parity conserving) interaction between the electromagnetic field $F$ and a torsion field $T^\alpha$ of spacetime. For generic elementary torsion, gauge invariant coupling terms of lowest order fall into two classes that are both nonminimal and {\it quadratic} in torsion. These two classes are displayed explicitly. The first class of the type $\sim F T^2$ yields (undesirable) modifications of the Maxwell equations. The second class of the type $\sim F^2 T^2$ doesn't touch the Maxwell equations but rather modifies the constitutive tensor of spacetime. Such a modification can be completely described in the framework of metricfree electrodynamics. We recognize three physical effects generated by the torsion: (i) An axion field that induces an {\em optical activity} into spacetime, (ii) a modification of the light cone structure that yields {\em birefringence} of the vacuum, and (iii) a torsion dependence of the {\em velocity of light.} We study these effects in the background of a Friedmann universe with torsion. {\it File tor17.tex, 02 August 2003}Comment: 6 page

Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations

In 1922, Cartan introduced in differential geometry, besides the Riemannian curvature, the new concept of torsion. He visualized a homogeneous and isotropic distribution of torsion in three dimensions (3d) by the "helical staircase", which he constructed by starting from a 3d Euclidean space and by defining a new connection via helical motions. We describe this geometric procedure in detail and define the corresponding connection and the torsion. The interdisciplinary nature of this subject is already evident from Cartan's discussion, since he argued - but never proved - that the helical staircase should correspond to a continuum with constant pressure and constant internal torque. We discuss where in physics the helical staircase is realized: (i) In the continuum mechanics of Cosserat media, (ii) in (fairly speculative) 3d theories of gravity, namely a) in 3d Einstein-Cartan gravity - this is Cartan's case of constant pressure and constant intrinsic torque - and b) in 3d Poincare gauge theory with the Mielke-Baekler Lagrangian, and, eventually, (iii) in the gauge field theory of dislocations of Lazar et al., as we prove for the first time by arranging a suitable distribution of screw dislocations. Our main emphasis is on the discussion of dislocation field theory.Comment: 31 pages, 8 figure

Avoiding degenerate coframes in an affine gauge approach to quantum gravity

In quantum models of gravity, it is surmized that configurations with degenerate coframes could occur during topology change of the underlying spacetime structure. However, the coframe is not the true Yang--Mills type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring this ``hidden" piece within the framework of the affine gauge approach to gravity, one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. This is an important advantage for quantization.Comment: 14 pages, Preprint Cologne-thp-1993-H

Prognostic implications of coronary calcification in patients with obstructive coronary artery disease treated by percutaneous coronary intervention: A patient-level pooled analysis of 7 contemporary stent trials

Objective To investigate the long- Term prognostic implications of coronary calcification in patients undergoing percutaneous coronary intervention for obstructive coronary artery disease. Methods Patient-level data from 6296 patients enrolled in seven clinical drug-eluting stents trials were analysed to identify in angiographic images the presence of severe coronary calcification by an independent academic research organisation (Cardialysis, Rotterdam, The Netherlands). Clinical outcomes at 3-years follow-up including all-cause mortality, death-myocardial infarction (MI), and the composite end-point of all-cause death-MI- Any revascularisation were compared between patients with and without severe calcification. Results Severe calcification was detected in 20% of the studied population. Patients with severe lesion calcification were less likely to have undergone complete revascularisation (48% vs 55.6%, p<0.001) and had an increased mortality compared with those without severely calcified arteries (10.8% vs 4.4%, p<0.001). The event rate was also high in patients with severely calcified lesions for the combined end-point death-MI (22.9% vs 10.9%; p<0.001) and death-MI- Any revascularisation (31.8% vs 22.4%; p<0.001). On multivariate Cox regression analysis, including the Syntax score, the presence of severe coronary calcification was an independent predictor of poor prognosis (HR: 1.33 95% CI 1.00 to 1.77, p=0.047 for death; 1.23, 95% CI 1.02 to 1.49, p=0.031 for death-MI, and 1.18, 95% CI 1.01 to 1.39, p=0.042 for death-MI- Any revascularisation), but it was not associated with an increased risk of stent thrombosis. Conclusions Patients with severely calcified lesions have worse clinical outcomes compared to those without severe coronary calcification. Severe coronary calcification appears as an independent predictor of worse prognosis, and should be considered as a marker of advanced atherosclerosis

Economic outcomes of percutaneous coronary intervention with drug-eluting stents versus bypass surgery for patients with left main or three-vessel coronary artery disease: One-year results from the SYNTAX trial

Objectives: To evaluate the cost-effectiveness of alternative approaches to revascularization for patients with three-vessel or left main coronary artery disease (CAD). Background: Previous studies have demonstrated that, despite higher initial costs, long-term costs with bypass surgery (CABG) in multivessel CAD are similar to those for percutaneous coronary intervention (PCI). The impact of drug-eluting stents (DES) on these results is unknown. Methods: The SYNTAX trial randomized 1,800 patients with left main or three-vessel CAD to either CABG (n = 897) or PCI using paclitaxel-eluting stents (n = 903). Resource utilization data were collected prospectively for all patients, and cumulative 1-year costs were assessed from the perspective of the U.S. healthcare system. Results: Total costs for the initial hospitalization were $5,693/patient higher with CABG, whereas follow-up costs were$2,282/patient higher with PCI due mainly to more frequent revascularization procedures and higher outpatient medication costs. Total 1-year costs were thus $3,590/patient higher with CABG, while quality-adjusted life expectancy was slightly higher with PCI. Although PCI was an economically dominant strategy for the overall population, cost-effectiveness varied considerably according to angiographic complexity. For patients with high angiographic complexity (SYNTAX score > 32), total 1-year costs were similar for CABG and PCI, and the incremental cost-effectiveness ratio for CABG was$43,486 per quality-adjusted life-year gained. Conclusions: Among patients with three-vessel or left main CAD, PCI is an economically attractive strategy over the first year for patients with low and moderate angiographic complexity, while CABG is favored among patients with high angiographic complexity

The unexpected resurgence of Weyl geometry in late 20-th century physics

Weyl's original scale geometry of 1918 ("purely infinitesimal geometry") was withdrawn by its author from physical theorizing in the early 1920s. It had a comeback in the last third of the 20th century in different contexts: scalar tensor theories of gravity, foundations of gravity, foundations of quantum mechanics, elementary particle physics, and cosmology. It seems that Weyl geometry continues to offer an open research potential for the foundations of physics even after the turn to the new millennium.Comment: Completely rewritten conference paper 'Beyond Einstein', Mainz Sep 2008. Preprint ELHC (Epistemology of the LHC) 2017-02, 92 pages, 1 figur