Two recent publications illustrate the range of research conducted at the Vatican Observatory, from studying the work of Galileo to developing mathematical methods for understanding the Big Bang.
In April, Frs. Gabriele Gionti (S.J.) and Matteo Galaverni (Diocese of Reggio Emilia–Guastalla, Italy) of the Observatory published “On the canonical equivalence between Jordan and Einstein frames” in the European Physical Journal C. Albert Einstein’s “General Relativity” is understood as the theory of gravity that better fits the experimental as well as observational data and describes the large-scale structure of the Universe today. However, questions persist about the laws of physics at the very first moments of the Universe, and about the physics of gravity on very small scales. Researchers have proposed theories of Quantum Gravity, which combine General Relativity with Quantum Mechanics (the physics that applies at the smallest scales), but the physics community is divided regarding these different theories.
Frs. Gionti and Galaverni show in their paper that they can transform or “map” the solutions of an alternative theory of gravity into General Relativity through a mathematical trick of looking at the problem through two different mathematical “frames”, known as the “Jordan” and “Einstein” frames. The question is whether the solutions given through these two frames are equally applicable to the real world that astronomers observe. Separate calculations done in the two frames involving things that are observable and that yield the same result in both will help to answer this. Gionti and Galaverni also show that there is a similar map between alternative theories of gravity and a peculiar behavior of gravity called “anti-Newtonian” or “anti-gravity”.
The April paper builds on work the two priests published in 2022 in the journal Physical Review D, and their research continues. Now they are studying in detail the consequences of these transformations for spherically symmetric solutions. These could be useful for investigating various kinds of objects within the Universe, including Black Holes and their entropy.
Today gravity explains the structure of the Universe, and also the tides of the seas on Earth. Galileo did not think in such terms, which were beyond the physics of his time. He theorized that tides were caused by the double motion of the Earth proposed by Copernicus (yearly revolution about the sun, plus daily rotation); this motion would provide a daily “push-pull” that caused the seas to rise and fall in their basins—the tides.
A daily “push”, however, implied high tides occurring but once per day in some seas (likewise for low tides). In a 1616 essay, Galileo claimed that this occurs in Lisbon, Portugal. It does not.
Galileo was soon informed of his error. But he argued again in his 1632 Dialogue for his tides theory as evidence favoring Copernicus, now omitting mention of Lisbon. He cited no other location where single daily tides occurred. This left him vulnerable to criticism, both in his own time and by scholars today, that he pursued his tidal theory despite its obvious inadequacies. Moreover, omitting Lisbon was omitting known information that contradicted his theory—very improper conduct for a scientist.
However, Christopher M. Graney of the Vatican Observatory followed correspondence between Galileo and Giovanfrancesco Buonamici in 1629-30, and found that Buonamici correctly informed Galileo about where single tides do indeed occur, in what today is known as Indonesia. Therefore, Graney argues in “Galileo and Buonamici on the tides of the sea: was something omitted from the Dialogue?”, published in March in the Journal for Astronomical History and Heritage, that Galileo had the supporting example for his theory that he needed, but in Indonesia, not Lisbon. The omission of it from the Dialogue, Graney argues, was likely an oversight—one of great consequence.
Both papers are freely available:
- Gionti, G., Galaverni, M. On the canonical equivalence between Jordan and Einstein frames. European Physical Journal C 84, 265 (2024). https://doi.org/10.1140/epjc/s10052-024-12586-z
- Graney, C. Galileo and Buonamici on the tides of the sea: was something omitted from the Dialogue? Journal of Astronomical History and Heritage 27, 200 (2024). https://doi.org/10.3724/SP.J.1440-2807.2024.01.11