arXiv subjects

Daniel Parrochia

Publications and source records attributed to Daniel Parrochia.

11 recordsLinked to original sources

arXiv2026

From Schwartz Space to Structural Aging (Towards a small history of Old Age mathematics)

Starting with some historical considerations, we examine the various attempts to model old age that fall within the realm of mathematical physics. For example, we study the mathematical theory of declining functions, which, since Laurent Schwartz's work on distributions, are generally defined on what is called a "Schwartz space." We explain how this essentially analytic formalization applies to the representation of the decline of vitality (or of a number of vital functions). We then show that there exist many other possible formalizations that utilize the resources of algebra, in particular the theory of "inclines" of Cao, Kim, and Roush and that of relational structures, on which an algebraic notion of "age," in Cameron's sense, can be defined. But we maintain, in conclusion, that a more positive representation of old age, consistent, moreover, with what a number of cultural sources from Antiquity to the 20th century tell us, should mobilize another type of formalization, capable of selecting, within the overall debate between the living being and its environment, persistent structures that do not decline amidst the decline of others.

math.GM↗

arXiv2025

Cosmology and Philosophy

Scientific cosmology has now reached its period of maturity with the establishment of a standard model, which is the theory of an expanding universe. The question of whether this expansion resolves itself, in the past, into a singularity identifiable with an absolute beginning, or whether the universe in which we are is only one of the multiple possible universes existing either in space or in time, is still under debate. Moreover, the assimilation of the beginning of the universe to a "creation" has often been contested by theology, which, since Thomas Aquinas, if not since the Fathers of the Church, tends to carefully distinguish the two. In the following article, after briefly summarizing some points in the recent history of scientific cosmology, we will attempt to present in broad outline the standard model that scientists have arrived at. Then, we will undertake to study some of the problems it raises as well as the alternative theories that can be opposed to it. Finally, we will discuss the problematic links that scientific cosmology continues to maintain with philosophy and theology, notably the thorny question of creation from nothing ({\it creatio ex nihilo}).

physics.hist-ph↗

arXiv2023

On complemented, uniquely complemented and uniquely complemented nondistributive lattices (a historical and epistemological note about a mathematical mystery)

Complemented lattices and uniquely complemented lattices are very important, not only in mathematics, but also in physics, biology, and even in social sciences. They have been investigated for a long time, especially by Huntington, Birkhoff, Dilworth and others. And yet, on some of these structures - namely, uniquely complemented nondistributive lattices -, despite the many existing articles concerning them, we basically know very little. In this article, we situate these lattest structures in the context of complemented and uniquely complemented lattices, offering a general overview of the links between these lattices and others, close to them, such as the orthocomplemented lattices of physics as well as various other partially ordered sets. We finally show how uniquely complemented nondistributive lattices have been constructed with the technique of free lattices.

math.HO↗

arXiv2023

Global warming in figures and the question of its treatment: some historical and epistemological views

We first recall fundamentals of elementary climate physics: solar constant, radiative balance, greenhouse effect, astronomical parameters of the climate (theory of Milankovitch). Without disputing the analyzes of climatologists and the famous Keeling curve revealing in an indisputable way the increase in CO$_{2}$ in the atmosphere since the industrial revolution, we nevertheless insist on the main contributor to the greenhouse effect which is, as we know, water vapor. Faced with the difficulties that there will be in imposing zero-carbon policies everywhere in the world (and especially in developing countries), we show that it would perhaps be in our interest to act on soil drought, which amounts, in fact, to being interested in the clouds. The decrease in cloud cover, due to a lack of water fixation in the soil, in fact increases the general temperature and therefore the greenhouse effect. Acting on CO$_{2}$ will always have, in this context, much less effect than acting on water vapor, even indirectly. Despite the difficulty of making this action sustainable, due to the balance of atmospheric water vapor and the oceans, it would be in our interest not to neglect this path and also possibly increase forest cover for this purpose, given the problems of setting up zero-carbon policy on a global scale. In desperation, one can also consider protecting the Earth with an artificial dust cloud.

physics.soc-ph↗

arXiv2023

A "network of networks" (from history to algebra)

Recall first the algebraic treatment of flows or tensions in a transportation network $N$, i.e. a connected antisymmetric 1-graph $G(X, U)$. Assume that, unusually, we take the values of flows (resp. tensions) in $\mathbb{C}$. So the algebraic lattices $\Gamma$ of flow (resp. tension) values associated to $G(X, U)$ are lattices of $\mathbb{C}$. These lattices are congruent modulo the action of the special linear group SL($2, \mathbb{C}$). Then, it is well known one can define a lattice function $G_{k}(\Gamma)$, as a modular function of weight $2k$, on the set $\mathcal{R}$ of all lattices of $\mathbb{C}$. Let now $N_{1}, N_{2}, ..., N_{p}$ be connected antisymmetric 1-graphs and $C_{n}$, the set of hermitian symmetric matrices $n \times n$. Let also $\mathcal{R'} $ be the set of all the lattices of $C_{n}$. The previous structure can be transposed to any $ n \times n $ symmetric hermitian matrices of flow (or tension) values of the $G_{i}$. In this case, the Siegel space $S_{n}= C_{n}$ replaces the Poincar\'{e} half-plane, and the symplectic group Sp$(2n, \mathbb{R})$ takes the place of the special linear group SL($2, \mathbb{C}$). We get now the new lattice function as a function of all the lattices of $S_{n}$, i.e. a model of the "network of networks" $\mathcal{R'}$. In the end, we study the tree of minimal length of $\mathcal{R'}$.

physics.hist-ph↗

arXiv2021

On von Weizs\"{a}cker's philosophy of Quantum Mechanics

We are interested here in the program of reconstruction of quantum mechanics of the German physicist and philosopher Carl Friedrich von Weizs\"{a}cker, which still has some supporters today. In the major part of this article, we limit ourselves to examining purely epistemological and philosophical questions. The theory of the German physicist is often interpreted with reference to Kant, but the most of the time in a rather vague way (categories of understanding, theory of experience). We can afford to be more precise. First we situate the theory of fundamental alternatives (or Ur-alternatives) of von Weizs\"{a}cker in the lineage of the Kantian theory of the transcendental Ideal. We then show that the physicist only substitutes for the classical logic, on which Kant relied, a quantum logic allowing to generate, from the alternatives, via the local isomorphism between certain spinor groups and groups linked to space-time, the whole of physical reality to which we have access. After examining some problems, we finally show how this perspective leads to a quantum theory of information.

physics.hist-ph↗

arXiv2020

Pacotte tree networks, graph theory and projective geometry

The notion of tree network has sparked renewed interest in recent years, particularly in computer science and biology (neural network). However, this notion is usually interpreted in an extremely restrictive way: essentially linked to data processing, today tree networks are hybrid network topologies in which star networks are generally interconnected via bus networks. These networks are, most often, hierarchical and regular, and each of their nodes can have an arbitrary number of child nodes. At the outset, however, the notion of tree network, introduced in 1936 by Belgian physicist Julien Pacotte, was quite different: more general and, at the same time, more constrained, it should also serve an ambitious objective: the reconstruction of mathematics from concrete empirical structures. Usually poorly commented on and poorly understood (especially by philosophers), it had no real posterity. In this article, we first try to clarify this notion of "tree network" in the sense of Julien Pacotte, which makes it possible to eliminate the bad interpretations to which this notion has given rise. To this end, we use the language and concepts of graph theory and formalize the main properties of these networks which, contrary to popular belief, are not, in general, trees. In a second part, we then try to follow and explain, step by step, how Pacotte intended, using concepts borrowed from projective geometry, to reconstruct all of mathematics from such a network.

physics.hist-ph↗

arXiv2020

Are there really many worlds in the "Many-worlds interpretation" of Quantum Mechanics?

Since the 1970s, the Everett-Wheeler many-worlds interpretation (MWI) of Quantum Mechanics (1955) has been much in the news. One wonders about the worlds in question, their branches, their splittings, their number. It is most often ignored that this language is not that of Everett, whom Wheeler very quickly stopped supporting. Moreover, for some interpreters, the real meaning of Everett ideas is not the coexistence of many worlds, but the existence of a single quantum one. In this context, what should we think of attempts to verify Everett thesis? What about the connexion between MWI and the cosmological multiverse? How to understand the links between the quantum world and the classical one? This article tries to answer some of these questions.

physics.hist-ph↗

arXiv2019

Some remarks on history and pre-history of Feynman path integral

One usually refers the concept of Feynman path integral to the work of Norbert Wiener on Brownian motion in the early 1920s. This view is not false and we show in this article that Wiener used the first path integral of the history of physics to describe the Brownian motion. That said, Wiener, as he pointed out, was inspired by the work of some French mathematicians, particularly Gateaux and Levy. Moreover, although Richard Feynman has independently found this notion, we show that in the course of the 1930s, while searching a kind of geometrization of quantum mechanics, another French mathematician, Adolphe Buhl, noticed by the philosopher Gaston Bachelard, had himself been close to forge such a notion. This reminder does not detract from the remarkable discovery of Feynman, which must undeniably be attributed to him. We also show, however, that the difficulties of this notion had to wait many years before being resolved, and it was only recently that the path integral could be rigorously established from a mathematical point of view.

physics.hist-ph↗

arXiv2019

Majorana equation and its consequences in physics and philosophy

We focus here on the work of the italian physicist Ettore Majorana, and more particularly on his 1937 article on the symmetrical theory of the electron and the positron, probably one of the most important theory for contemporary thought. We recall the context of this article (Dirac relativistic electron wave equation) and analyze how Majorana deduces his own equation from a very general variational principle. After having rewritten Majorana equation in a more contemporary language, we study its implications in condensed matter physics and their possible applications in quantum computing. Finally, we describe some of the consequences of Majorana approach to philosophy.

physics.hist-ph↗

arXiv2019

on some (so-called) paradoxes of quantum physics

This article is devoted to the study of which appears as the most famous paradoxes of quantum theory (Schrodinger cat, EPR argument and Aspect experiments, delayed choice experiments and retrocausality problems). Through these experiments, physics raises so fundamental questions that it borders, at the limit, with metaphysics. The present article supports the idea that the difficulties encountered, so puzzling they are, manifest only a transitional state of the evolution of physics, that can be expected to be outdated one day. In the meantime, caution is necessary to avoid the excesses that could lead to metaphysical considerations a little too premature.

quant-ph↗