Periodic Reporting for period 1 - COGY (The Centre of Gravity Project)
Período documentado: 2023-06-01 hasta 2025-11-30
The foundations of the general theory of relativity (GR) were laid by Albert Einstein in 1915. But much of what has been built on those foundations was developed in the Renaissance Period of GR between 1955 and 1975. Indeed, without the concepts and tools formed during this Renaissance, the recent observation of gravitational waves, rewarded with the Nobel Prize in physics in 2017, and the convincing prediction of and mounting evidence for the existence of black holes, rewarded with the Nobel Prize in physics in 2020, would not have been possible. At the centre of the Renaissance of GR is Sir Roger Penrose, who developed much of the toolbox that made the successes of the Renaissance possible. Penrose built upon the work of the newly emerging international community of relativists, in particular Hermann Bondi at Cambridge, John Wheeler at Princeton, Jürgen Ehlers at Hamburg, and Stephen Hawking at Cambridge. The Centre of Gravity Project (COGY) combines pioneering research on the literary estates of the core figures of the Renaissance period with the analysis of detailed oral history. To facilitate this analysis, we at COGY have created a novel kind of database that cross-correlates the different sources. The aim is to get to the bottom of the most advanced mathematical techniques and conceptual innovations of GR, concepts like black holes and event horizons, spacetime singularities and gravitational energy. In understanding the genesis and subsequent interpretation of these concepts, the COGY project also lays the groundwork for understanding the most exciting elements of today's physics: the physics of gravitational waves as they arise from black hole and neutron star mergers, as well as of the supermassive black hole around which our entire galaxy rotates.
In addition to doing the archival work, oral history interviews and creating the database that cross-correlates the documents of the main thinkers of the Renaissance of GR, we published a series of papers outlining our first results.
Our first major achievement analyses and contextualises one of Roger Penrose’s first major results on GR. Recorded in our paper “On Penrose’s Analogy between Curved Spacetime Regions and Optical Lenses,” it combines research in mathematical physics, history of physics, and philosophy of physics in a novel way, uncovering the genesis of the analogy between curved spacetime regions and optical lenses, the mathematical details of how the analogy works, and how the analogy was interpreted and used by Sir Roger.
Speaking of achievements, one of the most important achievements of Penrose himself is the first singularity theorem of 1965 that eventually got him the Nobel Prize. One of the objectives of the COGY project is to uncover the genesis, context, and early interpretation of Penrose’s first singularity theorem, and the project has made major progress on this front. In the forthcoming paper “The Prediction and Interpretation of Singularities and Black Holes: From Einstein and Schwarzschild to Penrose and Wheeler”, the interpretation of the mathematical concept of a spacetime singularity is traced, how it changed from Einstein to Penrose, and its role in the proof of the first singularity theorem is clarified. The paper distinguishes between 8 possible interpretations of the concept, and identifies the interpretation that Penrose himself favoured in his 1965 paper and thereafter.
Two further papers are available as preprints, one of them uncovering the mathematical details of Penrose diagrams as applied to black holes, the other uncovering the more algebraic early work of Pascual Jordan on the basis of which much of the Renaissance work on exact solutions to the Einstein field equations was based.
Our first major achievement analyses and contextualises one of Roger Penrose’s first major results on GR. Recorded in our paper “On Penrose’s Analogy between Curved Spacetime Regions and Optical Lenses,” it combines research in mathematical physics, history of physics, and philosophy of physics in a novel way, uncovering the genesis of the analogy between curved spacetime regions and optical lenses, the mathematical details of how the analogy works, and how the analogy was interpreted and used by Sir Roger.
Speaking of achievements, one of the most important achievements of Penrose himself is the first singularity theorem of 1965 that eventually got him the Nobel Prize. One of the objectives of the COGY project is to uncover the genesis, context, and early interpretation of Penrose’s first singularity theorem, and the project has made major progress on this front. In the forthcoming paper “The Prediction and Interpretation of Singularities and Black Holes: From Einstein and Schwarzschild to Penrose and Wheeler”, the interpretation of the mathematical concept of a spacetime singularity is traced, how it changed from Einstein to Penrose, and its role in the proof of the first singularity theorem is clarified. The paper distinguishes between 8 possible interpretations of the concept, and identifies the interpretation that Penrose himself favoured in his 1965 paper and thereafter.
Two further papers are available as preprints, one of them uncovering the mathematical details of Penrose diagrams as applied to black holes, the other uncovering the more algebraic early work of Pascual Jordan on the basis of which much of the Renaissance work on exact solutions to the Einstein field equations was based.
As stated above, neither historians nor philosophers of physics had previously dared to undertake a detailed investigation of the mathematical and conceptual innovations brought about during the Renaissance of GR between 1955 and 1975. Thus, our pioneering results on Penrose’s concept of spacetime singularities, the details of his singularity theorem, the mathematical finery of Penrose diagrams, as well as the innovations brought about by members of the Hamburg group like Pascual Jordan and Rainer Sachs, is a significant push beyond the state of the art of the historical and philosophical analysis of the general theory of GR. These are pioneering forays into a new land yet to be fully discovered and understood. Although we are only half way up a hill, the fascinating sites we have encountered in this journey have already given us glimpses of the world we will see, upon reaching the top, spread out in front of us. We are confident that from this new found vantage point, we will find that the contours of questions and answers concerning the historical, philosophical, and mathematical understanding of General Relativity will not be found in discrete islands, but woven together in an intricate tapestry. When our understanding of the Renaissance of GR gains greater clarity, we can but be excited by what we will discover at the then advanced frontier, and find the historical and philosophical understanding of GR advanced more than it has been in decades.