Max Abraham's and Tullio Levi-Civita's approach to Einstein Theory of Relativity

This work deals with the theory of Relativity and its diffusion in Italy in the first decades of the XX century. Not many scientists belonging to Italian universities were active in understanding Relativity, but two of them, Max Abraham and Tullio Levi-Civita left a deep mark. Max Abraham engaged a substantial debate against Einstein between 1912 and 1914 about electromagnetic and gravitation aspects of the theories. Levi-Civita played a fundamental role in giving Einstein the correct mathematical instruments for the General Relativity formulation since 1915. This work, which doesn't have the aim of a mere historical chronicle of the events, wants to highlight two particular perspectives: on one hand, the importance of Abraham-Einstein debate in order to clarify the basis of Special Relativity, to observe the rigorous logical structure resulting from a fragmentary reasoning sequence and to understand Einstein's thinking; on the other hand, the originality of Levi-Civita's approach, quite different from the Einstein's one, characterized by the introduction of a method typical of General Relativity even to Special Relativity and the attempt to hide the two Einstein Special Relativity postulates.

Sostanzialismo e relazionalismo dello spaziotempo alla luce della relatività generale

Until recently the debate on the ontology of spacetime had only a philosophical significance, since, from a physical point of view, General Relativity has been made "immune" to the consequences of the "Hole Argument" simply by reducing the subject to the assertion that solutions of Einstein equations which are mathematically different and related by an active diffeomorfism are physically equivalent. From a technical point of view, the natural reading of the consequences of the "Hole Argument” has always been to go further and say that the mathematical representation of spacetime in General Relativity inevitably contains a “superfluous structure” brought to light by the gauge freedom of the theory. This position of apparent split between the philosophical outcome and the physical one has been corrected thanks to a meticulous and complicated formal analysis of the theory in a fundamental and recent (2006) work by Luca Lusanna and Massimo Pauri entitled “Explaining Leibniz equivalence as difference of non-inertial appearances: dis-solution of the Hole Argument and physical individuation of point-events”. The main result of this article is that of having shown how, from a physical point of view, point-events of Einstein empty spacetime, in a particular class of models considered by them, are literally identifiable with the autonomous degrees of freedom of the gravitational field (the Dirac observables, DO). In the light of philosophical considerations based on realism assumptions of the theories and entities, the two authors then conclude by saying that spacetime point-events have a degree of "weak objectivity", since they, depending on a NIF (non-inertial frame), unlike the points of the homogeneous newtonian space, are plunged in a rich and complex non-local holistic structure provided by the “ontic part” of the metric field. Therefore according to the complex structure of spacetime that General Relativity highlights and within the declared limits of a methodology based on a Galilean scientific representation, we can certainly assert that spacetime has got "elements of reality", but the inevitably relational elements that are in the physical detection of point-events in the vacuum of matter (highlighted by the “ontic part” of the metric field, the DO) are closely dependent on the choice of the global spatiotemporal laboratory where the dynamics is expressed (NIF). According to the two authors, a peculiar kind of structuralism takes shape: the point structuralism, with common features both of the absolutist and substantival tradition and of the relationalist one. The intention of this thesis is that of proposing a method of approaching the problem that is, at least at the beginning, independent from the previous ones, that is to propose an approach based on the possibility of describing the gravitational field at three distinct levels. In other words, keeping the results achieved by the work of Lusanna and Pauri in mind and following their underlying philosophical assumptions, we intend to partially converge to their structuralist approach, but starting from what we believe is the "foundational peculiarity" of General Relativity, which is that characteristic inherent in the elements that constitute its formal structure: its essentially geometric nature as a theory considered regardless of the empirical necessity of the measure theory. Observing the theory of General Relativity from this perspective, we can find a "triple modality" for describing the gravitational field that is essentially based on a geometric interpretation of the spacetime structure. The gravitational field is now "visible" no longer in terms of its autonomous degrees of freedom (the DO), which, in fact, do not have a tensorial and, therefore, nor geometric nature, but it is analyzable through three levels: a first one, called the potential level (which the theory identifies with the components of the metric tensor), a second one, known as the connections level (which in the theory determine the forces acting on the mass and, as such, offer a level of description related to the one that the newtonian gravitation provides in terms of components of the gravitational field) and, finally, a third level, that of the Riemann tensor, which is peculiar to General Relativity only. Focusing from the beginning on what is called the "third level" seems to present immediately a first advantage: to lead directly to a description of spacetime properties in terms of gauge-invariant quantites, which allows to "short circuit" the long path that, in the treatises analyzed, leads to identify the "ontic part” of the metric field. It is then shown how to this last level it is possible to establish a “primitive level of objectivity” of spacetime in terms of the effects that matter exercises in extended domains of spacetime geometrical structure; these effects are described by invariants of the Riemann tensor, in particular of its irreducible part: the Weyl tensor. The convergence towards the affirmation by Lusanna and Pauri that the existence of a holistic, non-local and relational structure from which the properties quantitatively identified of point-events depend (in addition to their own intrinsic detection), even if it is obtained from different considerations, is realized, in our opinion, in the assignment of a crucial role to the degree of curvature of spacetime that is defined by the Weyl tensor even in the case of empty spacetimes (as in the analysis conducted by Lusanna and Pauri). In the end, matter, regarded as the physical counterpart of spacetime curvature, whose expression is the Weyl tensor, changes the value of this tensor even in spacetimes without matter. In this way, going back to the approach of Lusanna and Pauri, it affects the DOs evolution and, consequently, the physical identification of point-events (as our authors claim). In conclusion, we think that it is possible to see the holistic, relational, and non-local structure of spacetime also through the "behavior" of the Weyl tensor in terms of the Riemann tensor. This "behavior" that leads to geometrical effects of curvature is characterized from the beginning by the fact that it concerns extensive domains of the manifold (although it should be pointed out that the values of the Weyl tensor change from point to point) by virtue of the fact that the action of matter elsewhere indefinitely acts. Finally, we think that the characteristic relationality of spacetime structure should be identified in this "primitive level of organization" of spacetime.

Cosmological perturbations in generalized theories of gravity

The first part of the thesis concerns the study of inflation in the context of a theory of gravity called "Induced Gravity" in which the gravitational coupling varies in time according to the dynamics of the very same scalar field (the "inflaton") driving inflation, while taking on the value measured today since the end of inflation. Through the analytical and numerical analysis of scalar and tensor cosmological perturbations we show that the model leads to consistent predictions for a broad variety of symmetry-breaking inflaton's potentials, once that a dimensionless parameter entering into the action is properly constrained. We also discuss the average expansion of the Universe after inflation (when the inflaton undergoes coherent oscillations about the minimum of its potential) and determine the effective equation of state. Finally, we analyze the resonant and perturbative decay of the inflaton during (p)reheating. The second part is devoted to the study of a proposal for a quantum theory of gravity dubbed "Horava-Lifshitz (HL) Gravity" which relies on power-counting renormalizability while explicitly breaking Lorentz invariance. We test a pair of variants of the theory ("projectable" and "non-projectable") on a cosmological background and with the inclusion of scalar field matter. By inspecting the quadratic action for the linear scalar cosmological perturbations we determine the actual number of propagating degrees of freedom and realize that the theory, being endowed with less symmetries than General Relativity, does admit an extra gravitational degree of freedom which is potentially unstable. More specifically, we conclude that in the case of projectable HL Gravity the extra mode is either a ghost or a tachyon, whereas in the case of non-projectable HL Gravity the extra mode can be made well-behaved for suitable choices of a pair of free dimensionless parameters and, moreover, turns out to decouple from the low-energy Physics.

Recognizing cultural concepts: Joyce, Woolf, Mann and Musil

The purpose of this thesis is to establish a direct relationship between literature and fields of knowledge such as science and technology, by focusing on some concepts that were fundamental for both science and the humanities at the beginning of the 20th century. The concepts are those of simultaneity, multiple points of view, map, relativity and acausality. In the spirit of several recent ideas, for example Katherine Hayles’ isomorphism notion, the dissertation shows how writers such as James Joyce, Virginia Woolf, Thomas Mann and Robert Musil developed the mentioned concepts within their narratives. The working hypothesis is that those concepts were at a crossroad of human activities, and that those authors used them extensively within their narratives. It is further argued that those same concepts – as developed by Joyce in Ulysses, Woolf’s shorts stories and novels from the end of the 1910’s until the end of the1920’s, Mann’s Der Zauberberg (The Magic Mountain), and Musil’s Der Mann ohne Eigenschaften (The Man Without Qualities) — are still fundamental for our conception of time and space today. The thesis is divided into two parts. The first two chapters will analyse the concepts of simultaneity and multiple points of view and their relationship to cartography as developed within English literature and culture. The next two chapters will address the concepts of relativity and acausality, as developed within German literature and culture.

An optimal estimator for the correlation of CMB anisotropies with Large Scale Structures and its application to WMAP-7year and NVSS

In the thesis we present the implementation of the quadratic maximum likelihood (QML) method, ideal to estimate the angular power spectrum of the cross-correlation between cosmic microwave background (CMB) and large scale structure (LSS) maps as well as their individual auto-spectra. Such a tool is an optimal method (unbiased and with minimum variance) in pixel space and goes beyond all the previous harmonic analysis present in the literature. We describe the implementation of the QML method in the {\it BolISW} code and demonstrate its accuracy on simulated maps throughout a Monte Carlo. We apply this optimal estimator to WMAP 7-year and NRAO VLA Sky Survey (NVSS) data and explore the robustness of the angular power spectrum estimates obtained by the QML method. Taking into account the shot noise and one of the systematics (declination correction) in NVSS, we can safely use most of the information contained in this survey. On the contrary we neglect the noise in temperature since WMAP is already cosmic variance dominated on the large scales. Because of a discrepancy in the galaxy auto spectrum between the estimates and the theoretical model, we use two different galaxy distributions: the first one with a constant bias $b$ and the second one with a redshift dependent bias $b(z)$. Finally, we make use of the angular power spectrum estimates obtained by the QML method to derive constraints on the dark energy critical density in a flat $\Lambda$CDM model by different likelihood prescriptions. When using just the cross-correlation between WMAP7 and NVSS maps with 1.8° resolution, we show that $\Omega_\Lambda$ is about the 70\% of the total energy density, disfavouring an Einstein-de Sitter Universe at more than 2 $\sigma$ CL (confidence level).

Implicazioni teoriche e sperimentali della sincronizzazione assoluta nella teoria della relatività speciale

Sono indagate le implicazioni teoriche e sperimentali derivanti dall'assunzione, nella teoria della relatività speciale, di un criterio di sincronizzazione (detta assoluta) diverso da quello standard. La scelta della sincronizzazione assoluta è giustificata da alcune considerazioni di carattere epistemologico sullo status di fenomeni quali la contrazione delle lunghezze e la dilatazione del tempo. Oltre che a fornire una diversa interpretazione, la sincronizzazione assoluta rappresenta una estensione del campo di applicazione della relatività speciale in quanto può essere attuata anche in sistemi di riferimento accelerati. Questa estensione consente di trattare in maniera unitaria i fenomeni sia in sistemi di riferimento inerziali che accelerati. L'introduzione della sincronizzazione assoluta implica una modifica delle trasformazioni di Lorentz. Una caratteristica di queste nuove trasformazioni (dette inerziali) è che la trasformazione del tempo è indipendente dalle coordinate spaziali. Le trasformazioni inerziali sono ottenute nel caso generale tra due sistemi di riferimento aventi velocità (assolute) u1 e u2 comunque orientate. Viene mostrato che le trasformazioni inerziali possono formare un gruppo pur di prendere in considerazione anche riferimenti non fisicamente realizzabili perché superluminali. È analizzato il moto rigido secondo Born di un corpo esteso considerando la sincronizzazione assoluta. Sulla base delle trasformazioni inerziali si derivano le trasformazioni per i campi elettromagnetici e le equazioni di questi campi (che sostituiscono le equazioni di Maxwell). Si mostra che queste equazioni contengono soluzioni in assenza di cariche che si propagano nello spazio come onde generalmente anisotrope in accordo con quanto previsto dalle trasformazioni inerziali. L'applicazione di questa teoria elettromagnetica a sistemi accelerati mostra l'esistenza di fenomeni mai osservati che, pur non essendo in contraddizione con la relatività standard, ne forzano l'interpretazione. Viene proposto e descritto un esperimento in cui uno di questi fenomeni è misurabile.