Tales from the prehistory of Quantum Gravity. L\'eon Rosenfeld's earliest contribution

The main purpose of this paper is to analyse the earliest work of L\'eon Rosenfeld, one of the pioneers in the search of Quantum Gravity, the supposed theory unifying quantum theory and general relativity. We describe how and why Rosenfeld tried to face this problem in 1927, analysing the role of his mentors: Oskar Klein, Louis de Broglie and Th\'eophile De Donder. Rosenfeld asked himself how quantum mechanics should \textit{concretely} modify general relativity. In the context of a five-dimensional theory, Rosenfeld tried to construct a unifying framework for the gravitational and electromagnetic interaction and wave mechanics. Using a sort of "general relativistic quantum mechanics" Rosenfeld introduced a wave equation on a curved background. He investigated the metric created by what he called `quantum phenomena', represented by wave functions. Rosenfeld integrated Einstein equations in the weak field limit, with wave functions as source of the gravitational field. The author performed a sort of semi-classical approximation obtaining at the first order the Reissner-Nordstr\"om metric. We analyse how Rosenfeld's work is part of the history of Quantum Mechanics, because in his investigation Rosenfeld was guided by Bohr's correspondence principle. Finally we briefly discuss how his contribution is connected with the task of finding out which metric can be generated by a quantum field, a problem that quantum field theory on curved backgrounds will start to address 35 years later.Comment: 83 pages. Accepted for publication in the European Physical Journal (H

A data driven equivariant approach to constrained Gaussian mixture modeling

Maximum likelihood estimation of Gaussian mixture models with different class-specific covariance matrices is known to be problematic. This is due to the unboundedness of the likelihood, together with the presence of spurious maximizers. Existing methods to bypass this obstacle are based on the fact that unboundedness is avoided if the eigenvalues of the covariance matrices are bounded away from zero. This can be done imposing some constraints on the covariance matrices, i.e. by incorporating a priori information on the covariance structure of the mixture components. The present work introduces a constrained equivariant approach, where the class conditional covariance matrices are shrunk towards a pre-specified matrix Psi. Data-driven choices of the matrix Psi, when a priori information is not available, and the optimal amount of shrinkage are investigated. The effectiveness of the proposal is evaluated on the basis of a simulation study and an empirical example

Modality and its Conversational Backgrounds in the Reconstruction of Argumentation

The paper considers the role of modality in the rational reconstruction of standpoints and arguments. The paper examines in what conditions modal markers can act as argumentative indicators and what kind of cues they provide for the reconstruction of argument. The paper critically re-examines Toulmin's hypothesis that the meaning of the modals can be analyzed in terms of a field-invariant argumentative force and field-dependent criteria in the light of the Theory of Relative Modality developed within linguistic semantics, showing how this theory can provide a more adequate model for exploiting the modals as indicators. The resulting picture confirms Toulmin's intuition only in part: on the one hand the modals are always relational in nature and dependent on a contextual conversational background of propositions; on the other hand only epistemic-doxastic modals directly express a speech-act level inferential relation between a set of premises and a standpoint. Other modalities express relations (e.g. causal or final relations) better seen as part of the content of the argument whose argumentative relevance depends on the argumentation scheme employed. Thus non-epistemic modals function as argumentative indicators only indirectl

The fabrication and surface tolerance measurements of the JPL clear aperture microwave antenna

Present ground station microwave antennas of the Deep Space Network are of the symmetric dual reflector (cassegrainian) type. An investigation is being made of alternative high-performance offset antenna designs which have a clear aperture (no reflector or structural blockage) with shaped reflector surfaces. A 1.5-m, 32-GHz clear aperture model was built for experimental studies. The unique processes of fabrication, surface measurement, and alignment are described

Soil nitrogen cycling in agroecosystems as modified by biochar amendment and plant processes

2019 Summer.Includes bibliographical references.Ecosystem productivity is dependent upon cycling of nutrients, such as nitrogen (N). In agricultural systems, humans have greatly altered N cycling through the application of synthetic fertilizers such that soil N in agroecosystems is lost at higher rates than N in unmanaged systems. A variety of strategies have been assessed to reduce losses of soil N through nitrous oxide (N2O) emissions and leaching, which can negatively impact climate and water quality, respectively. The application of biochar, a carbon-rich soil amendment, has shown promise for increasing N retention in agricultural systems, but field and greenhouse studies often present less dramatic and often conflicting effects, suggesting the need for greater study in these environments. Further, the effects of biochar do not occur in isolation, but rather depend on plant processes that may affect soil N dynamics. This thesis explores these ideas through: (1) a greenhouse study considering the effects of different biochar types on N cycling with and without plants and (2) a field study looking at seasonal patterns of N cycling and fixation in alfalfa as altered by strategically-placed, low rates of biochar application. Study 1 sought to determine differential effects of biochar and plants, and raw and engineered biochar, on both fertilizer and innate soil N cycling using isotopically labelled fertilizer. While biochar effects on soil-derived N were minimal, we found that engineered biochar led to significantly higher leaching losses of fertilizer N. Plants, in contrast, were found to reduce N loss and increase overall recovery of fertilizer N. Study 2 focused on the effects of low and economically feasible application rates of two different biochars on N fixation, N loss, and mineral N availability over a growing season. We found no biochar effects on any N cycling parameter and, rather, found significant temporal effects in all N pools. Seasonal dynamics suggest connections between SIN availability and N fixation and loss. Indications of increased N loss with engineered biochar in Study 1 urge the need for greater study of biochars in combination with a variety of fertilizer types in order to provide the best recommendations to farmers. Lack of effects with biochar in Study 2 indicate that low application rates of biochar may not be useful for increasing N retention, suggesting the need to find a balance between economic and effective biochar application rates. Since both studies suggest that plant processes have more substantial impacts on N cycling than biochar amendment, via reduced N loss (Study 1) or increased symbiotic N input (Study 2), it is important that plants are included in more biochar studies such that the strength of biochar effects can be more realistically evaluated

On the Gravitational Effects of Light

[Translation of and Commentary on L\'eon Rosenfeld's "Ueber die Gravitationwirkungen des Lichtes", Zeitschrift fur Physik 65: 589-599 (1930). Originally published in German. Submitted for publication on September 26, 1930. See [1] in the Comments with References section before reading this English translation.] The gravitational field generated by an electromagnetic field is calculated using of laws of quantum mechanics and it is shown that the resulting gravitational energy turns out to be infinitely large, raising a new difficulty for the Heisenberg-Pauli quantum theory of wave fields. In addition, the transition processes in first-order approximation involving light and gravitational quanta are briefly discussed.Comment: 21 pages; no figures. Accepted for publication in EPJ