On the Direction of Time: From Reichenbach to Prigogine and Penrose

The question why natural processes tend to flow along a preferred direction has always been considered from within the perspective of the Second Law of Thermodynamics, especially its statistical formulation due to Maxwell and Boltzmann. In this article, we re-examine the subject from the perspective of a new historico-philosophical formulation based on the careful use of selected theoretical elements taken from three key modern thinkers: Hans Reichenbach, Ilya Prigogine, and Roger Penrose, who are seldom considered together in the literature. We emphasize in our analysis how the entropy concept was introduced in response to the desire to extend the applicability of the Second Law to the cosmos at large (Reichenbach and Penrose), and to examine whether intrinsic irreversibility is a fundamental universal characteristics of nature (Prigogine). While the three thinkers operate with vastly different technical proposals and belong to quite distinct intellectual backgrounds, some similarities are detected in their thinking. We philosophically examine these similarities but also bring into focus the uniqueness of each approach. Our purpose is not providing an exhaustive derivations of logical concepts identified in one thinker in terms of ideas found in the others. Instead, the main objective of this work is to stimulate historico-philosophical investigations and inquiries into the problem of the direction of time in nature by way of crossdisciplinary examinations of previous theories commonly treated in literature as disparate domains.

Buracos negros estelares

A investigação dos buracos negros – objetos astronômicos cuja densidade tende ao infinito e que são capazes de produzir marcante deformação no espaço-tempo – tem experimentado grande impulso nos últimos anos. De fato, em 2015, a equipe do LIGO (Laser Interferometer Gravitational-Wave Observatory) obteve a primeira detecção das ondas gravitacionais, produzidas a partir de um sistema binário de buracos negros, o que levou à concessão do prêmio Nobel de Física aos pesquisadores Rainer Weiss, Barry C. Barish e Kip S. Thorne. Em abril de 2019 foi publicada a primeira imagem direta de um buraco negro e, no ano de 2020, três cientistas – Roger Penrose, Andrea Ghez e Reinhard Genzel – também receberam o prêmio Nobel de Física por suas significativas contribuições para esse campo de pesquisa. Os sucessos obtidos, desde a proposição de tais estruturas até a lendária “foto”, têm dependido de decisivas contribuições da matemática à física e à astronomia, permitindo, em última análise, que tais ciências empíricas saibam o que (e onde) procurar. Desde esta perspectiva, a apreciação de aspectos da abordagem matemática dos buracos negros – a partir da apresentação da métrica de Schwarzschild – é o objetivo do presente artigo.

The Moore–Penrose inverse: a hundred years on a frontline of physics research

The Moore–Penrose inverse celebrated its 100th birthday in 2020, as the notion standing behind the term was first defined by Eliakim Hastings Moore in 1920 (Bull Am Math Soc 26:394–395, 1920). Its rediscovery by Sir Roger Penrose in 1955 (Proc Camb Philos Soc 51:406–413, 1955) can be considered as a caesura, after which the inverse attracted the attention it deserves and has henceforth been exploited in various research branches of applied origin. The paper contemplates the role, which the Moore–Penrose inverse plays in research within physics and related areas at present. An overview of the up-to-date literature leads to the conclusion that the inverse “grows” along with the development of physics and permanently (maybe even more demonstrably now than ever before) serves as a powerful and versatile tool to cope with the current research problems.

Pioneros de los agujeros negros despejaron dudas de Einstein

En el presente artículo se describe, cómo están relacionados el trabajo de un teórico Roger Penrose, y dos “observadores”, Reinhard Genzel y Andrea Ghez, para escudriñar en el centro de la Vía Láctea un “objeto supermasivo”, conocido ahora como un “agujero negro”.

Le prix Nobel de physique 2020, ou la consécration des trous noirs

Trois lauréats partagent le prix Nobel de physique 2020 pour leurs découvertes sur l’un des phénomènes les plus exotiques de l’Univers, les trous noirs : le théoricien britannique Roger Penrose, l’astronome allemand Gerhard Genzel et l’astronome américaine Andrea Ghez.