String Theory, Loop Quantum Gravity and Eternalism

Eternalism, the view that what we regard locally as being located in the past, the present and the future equally exists, is the best ontological account of temporal existence in line with special and general relativity. However, special and general relativity are not fundamental theories and several research programs aim at finding a more fundamental theory of quantum gravity weaving together all we know from relativistic physics and quantum physics. Interestingly, some of these approaches assert that time is not fundamental. If time is not fundamental, what does it entail for eternalism and the standard debate over existence in time? First, I will argue that the non-fundamentality of time to be found in string theory entails standard eternalism. Second, I will argue that the non-fundamentality of time to be found in loop quantum gravity entails atemporal eternalism, namely a novel position in the spirit of standard eternalism

Priority Monism Beyond Spacetime

I will defend two claims. First, Schaffer's priority monism is in tension with many research programs in quantum gravity. Second, priority monism can be modified into a view more amenable to this physics. The first claim is grounded in the fact that promising approaches to quantum gravity such as loop quantum gravity or string theory deny the fundamental reality of spacetime. Since fundamental spacetime plays an important role in Schaffer's priority monism by being identified with the fundamental structure, namely the cosmos, the disappearance of spacetime in these views might undermine classical priority monism. My second claim is that priority monism can avoid this issue with two moves: first, in dropping one of its core assumptions, namely that the fundamental structure is spatio-temporal, second, by identifying the connection between the non-spatio-temporal structure and the derivative spatio-temporal structure with mereological composition

The geometry of proper quaternion random variables

Second order circularity, also called properness, for complex random variables is a well known and studied concept. In the case of quaternion random variables, some extensions have been proposed, leading to applications in quaternion signal processing (detection, filtering, estimation). Just like in the complex case, circularity for a quaternion-valued random variable is related to the symmetries of its probability density function. As a consequence, properness of quaternion random variables should be defined with respect to the most general isometries in $4D$, i.e. rotations from $SO(4)$. Based on this idea, we propose a new definition of properness, namely the $(\mu_1,\mu_2)$-properness, for quaternion random variables using invariance property under the action of the rotation group $SO(4)$. This new definition generalizes previously introduced properness concepts for quaternion random variables. A second order study is conducted and symmetry properties of the covariance matrix of $(\mu_1,\mu_2)$-proper quaternion random variables are presented. Comparisons with previous definitions are given and simulations illustrate in a geometric manner the newly introduced concept.Comment: 14 pages, 3 figure

The No Self View and the Meaning of Life

Several philosophers, both in Buddhist and Western philosophy, claim that the self does not exist. The no-self view may, at first glance, appear to be a reason to believe that life is meaningless. In the present article, I argue indirectly in favor of the no-self view by showing that it does not entail that life is meaningless. I then examine Buddhism and argue, further, that the no-self view may even be construed as partially grounding an account of the meaning of life

Spacetime Emergence in Quantum Gravity: Functionalism and the Hard Problem

Spacetime functionalism is the view that spacetime is a functional structure implemented by a more fundamental ontology. Lam and Wüthrich have recently argued that spacetime functionalism helps to solve the epistemological problem of empirical coherence in quantum gravity and suggested that it also (dis)solves the hard problem of spacetime, namely the problem of offering a picture consistent with the emergence of spacetime from a non-spatio-temporal structure. First, I will deny that spacetime functionalism solves the hard problem by showing that it comes in various species, each entailing a different attitude towards, or answer to, the hard problem. Second, I will argue that the existence of an explanatory gap, which grounds the hard problem, has not been correctly taken into account in the literature

Nonparametric estimation of the heterogeneity of a random medium using Compound Poisson Process modeling of wave multiple scattering

In this paper, we present a nonparametric method to estimate the heterogeneity of a random medium from the angular distribution of intensity transmitted through a slab of random material. Our approach is based on the modeling of forward multiple scattering using Compound Poisson Processes on compact Lie groups. The estimation technique is validated through numerical simulations based on radiative transfer theory.Comment: 23 pages, 8 figures, 21 reference

Higher Order Statistsics of Stokes Parameters in a Random Birefringent Medium

We present a new model for the propagation of polarized light in a random birefringent medium. This model is based on a decomposition of the higher order statistics of the reduced Stokes parameters along the irreducible representations of the rotation group. We show how this model allows a detailed description of the propagation, giving analytical expressions for the probability densities of the Mueller matrix and the Stokes vector throughout the propagation. It also allows an exact description of the evolution of averaged quantities, such as the degree of polarization. We will also discuss how this model allows a generalization of the concepts of reduced Stokes parameters and degree of polarization to higher order statistics. We give some notes on how it can be extended to more general random media

Pulsation Frequencies and Modes of Giant Exoplanets

We calculate the eigenfrequencies and eigenfunctions of the acoustic oscillations of giant exoplanets and explore the dependence of the characteristic frequency and the eigenfrequencies on several parameters: the planet mass, the planet radius, the core mass, and the heavy element mass fraction in the envelope. We provide the eigenvalues for degree $l$ up to 8 and radial order n up to 12. For the selected values of l and n, we find that the pulsation eigenfrequencies depend strongly on the planet mass and radius, especially at high frequency. We quantify this dependence through the calculation of the characteristic frequency which gives us an estimate of the scale of the eigenvalue spectrum at high frequency. For the mass range 0.5 < M_P < 15 M_J, and fixing the planet radius to the Jovian value, we find that the characteristic frequency is ~164.0 * (M_P/M_J)^(0.48) microHz, where M_P is the planet mass and M_J is Jupiter's mass. For the radius range from 0.9 to 2.0 R_J, and fixing the planet's mass to the Jovian value, we find that the characteristic frequency is ~164.0 * (R_P/R_J)^(-2.09) microHz, where R_P is the planet radius and R_J is Jupiter's radius. We explore the influence of the presence of a dense core on the pulsation frequencies and on the characteristic frequency of giant exoplanets. We find that the presence of heavy elements in the envelope affects the eigenvalue distribution in ways similar to the presence of a dense core. Additionally, we apply our formalism to Jupiter and Saturn and find results consistent with both the observationnal data of Gaulme et al. (2011) and previous theoretical work.Comment: Accepted for publication in the Astrophysical Journal; 15 Figures and 11 Table

Evaluating Monetary Policy Rules in Estimated Forward-Looking Models: A Comparison of US and German Monetary Policies.

In this paper, we estimate two small, forward-looking, macroeconomic models for the US and Germany and we compare the implied optimal monetary policy rules. Both models have a standard structure: an I-S curve, a Phillips curve, a short term interest-rate rule and a long term interest rate determined by the Expectations Hypothesis. They are intended to fit the data while allowing for some forward-looking behavior. They are estimated from 1968 to 1998, using the full-information maximum-likelihood procedure, so that forward-looking expectations are fully model-consistent. In order to evaluate monetary policy, we compute optimal policy frontiers and we perform some simulations of the model. German optimal monetary policy is found to require a more persistent and slightly stronger response to inflation and output than the US optimal policy.Forward-looking model ; monetary policy rules