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There were at least seven attempts to calculate critical radii for reactors or bombs 1939–1945. Those made by Flügge and Peierls in 1939 are compared with the calculations made by Perrin (1939), Heisenberg (1939 and 1945) and Serber (1943). Fermi’s 1942 reactor calculations are not covered here because that would call for a separate paper. Heisenberg calculated the critical radius formula and some critical radii in 1939 for a reactor. He focused on reactors 1939–45 and apparently did not make a bomb calculation before his August 1945 Farm Hall Lecture where he independently reproduced the 1943 Los Alamos Primer calculation for a bomb to within the limits that he knew the fast fission cross section. Flügge attempted a ponderous alternative to a critical radius calculation. Perrin’s calculation predates the Heisenberg and Serber calculations. His theoretical choice of tamper boundary condition was not optimal but his calculation method was correct. Peierls aimed to improve on Perrin's method but did worse. Finally, we calculate the 2.1 cm critical radius stated in the Frisch–Peierls Memorandum from Peierls’ model and graph, and we also show how Frisch and Peierls likely calculated it, including why Frisch assumed a fission cross section of 10 barn in his calculation.

How was Lattice Gauge Theory born? What was it like in the “early days” of the 1970s and 80s before lattice field theory became a substantial subfield of high energy theory? How did high energy physics and condensed matter theory get together? What were the big physics problems and technical challenges of the day? This short talk looks at these topics from one person’s personal recollections, experiences and perspective.

AbstractRaoul Gatto and Bruno Touschek’s collaboration in the establishment of electron–positron colliders as a fundamental discovery tool in particle physics will be illustrated. In particular, we will tell the little-known story of how Gatto and Touschek’s pioneering visions combined to provide the theoretical foundation for AdA, the first matter–antimatter collider, and how their friendship with Wolfgang Pauli and Gerhard Lüders was crucial to their understanding of the CPT theorem, the basis for AdA’s success. We will see how these two exceptional scientists shaped physics between Rome and Frascati, from the proposal to build AdA and soon after the larger machine ADONE in 1961, to the discovery of the $$J/\Psi $$ J / Ψ particle in 1974. We will also highlight Gatto and Touschek’s contribution in mentoring an extraordinary cohort of students and collaborators whose work contributed to the renaissance of Italian theoretical physics after the Second World War and to the establishment of the Standard Model of particle physics.

AbstractThe concepts of radiative and adiabatic equilibria, introduced by Karl Schwarzschild in his seminal paper Ueber das Gleichgewicht der Sonnenatmosphäre published in January 1906, are the founding blocks of the theory of radiative transfer, stellar structure, and solar physics. Careful reading of the paper and its later English translation reveals small formal inaccuracies and ambiguities but with no consequences whatsoever for the final outcomes and conclusions. This paper offers their adjustments with respective derivations using contemporary formalism and sets Schwarzschild’s paper in context with a historical and modern perspective. Particular attention is paid to Schwarzschild’s largely forgotten limb-darkening formula for adiabatic equilibrium. The paper also reproduces Schwarzschild’s radiative equilibrium protomodel of the Sun’s atmosphere in graphical form and compares it with modern models presented in some of the most cited papers in stellar and solar physics.

Boltzmann’s work, “Ueber die sogenannte H-Curve,” discusses his demonstration of the essential characteristics of the H-curve in a clear, concise, and precise style, showcasing his efforts to persuade his peers. To make these findings more widely accessible, the author aims to provide a translated version of the original article, while also correcting some typographical errors in the mathematical expressions with explanatory footnotes. The final section offers concluding remarks with graphs and relevant references for interested readers.

AbstractThe Bohr and von Neumann views on the measurement process in quantum mechanics have been interpreted for a long time in somewhat controversial terms, often leading to misconceptions. On the basis of some textual analysis, I would like to show that—contrary to a widespread opinion—their views should be taken less inconsistent, and much closer to each other, than usually thought. As a consequence, I claim that Bohr and von Neumann are conceptually on the same side on the issue of the universality of quantum mechanics: hopefully, this might contribute to a more accurate history of the measurement problem in quantum mechanics.

Einstein's expression ‘Drama of Ideas’ to describe the history of fundamental physics is especially suitable for the problem of quantum gravity (QG). The problem was identified by Einstein in 1916 based on an empirico-cosmological argument that was cosmologically flawed and empirically immeasurable. In 1929, the problem was strikingly underestimated by prominent figures in quantum theory, W. Heisenberg and W. Pauli. In 1929, Bohr, basing on the puzzling results of recent nuclear experiments and theoretical quantum limitations, hypothesized that the law of conservation of energy does not hold in nuclear physics. The young Russian physicist Landau enthusiastically supported Bohr's ‘beautiful idea’ and in 1931 proposed its theoretical justification, which, however, was rejected by Bohr. In late 1932, Landau realized that Bohr's hypothesis was incompatible with Einstein's theory of gravity. This meeting of two fundamental theories prompted Matvei Bronstein to investigate the quantization of gravity in-depth. In 1935, he proposed the first physical theory of QG for the weak gravity and revealed how deep the QG problem was for strong gravity. He showed that the gravitational field at a point in space–time is in principle unobservable and concluded that a complete theory of QG would require the ‘rejection of a Riemannian geometry… and perhaps also the rejection of our ordinary concepts of space and time, replacing them by some much deeper and non-evident concepts’. Until now, despite thousands of publications on QG, the problem remains a great challenge in theoretical physics.

AbstractIn spring 1949 about 70 physicists from eight countries met in Florence to discuss recent trends in statistical mechanics. This scientific gathering, co-organized by the Commission on Thermodynamics and Statistical Mechanics of the International Union of Pure and Applied Physics (IUPAP) and the Italian Physical Society (SIF), initiated a tradition of IUPAP-sponsored international conferences on statistical mechanics that lasts to this day. In 1977, when this conference series took the name of StatPhys, the foundational role of the Florence conference was recognized by retrospectively naming it StatPhys1. This paper examines the dual scientific and social significance of the conference, situating it in the broader contexts of the post-World War II reconstruction in Italian physics and of the revitalization of the international science organization. Through an analysis of IUPAP archives and Italian records, we illustrate how the event’s success hinged on the aligned objectives of its organizers. Internationally, it was instrumental in defining the scientific and organizational foundations for the activities of IUPAP commissions during a critical phase of IUPAP’s history, when the Union was resurging on the international scene after the inactivity of the interwar period. Nationally, the conference served as a cornerstone in SIF’s strategy to re-establish Italian physics’ international stature and to aid the domestic revitalization of physics through the internationalization of its activities, notably of its flagship journal, Il Nuovo Cimento. This analysis not only sheds light on the conference’s impact but also informs recent discussions in the history of science about the multiple roles of international scientific conferences.

The onset and the development of the concept of exchange force in quantum physics are historically reconstructed, starting from Heisenberg’s seminal contributions in 1926 and going through the great developments in nuclear physics, which allowed the emergence of the idea of force mediating virtual quanta. Although most of such work was performed in Europe, the last and decisive effort in this long path was carried out by Japanese scientists in the 1930s. This is the main focus of the present work, which retraces the achievements of Yukawa and Tomonaga, whose results and mutual interactions are carefully analyzed and related to those of European physicists.

AbstractPascual Jordan was the first to propose the law of interference of probability amplitudes as a principle of quantum mechanics. We analyze the role of probabilistic ideas played in this proposal from a historical perspective. In particular, we point out the relation between the usual theory of probability that Jordan called elementary and quantum mechanics. Jordan was the first to stress the analogy between the law of total probability and the law of interference. In this regard, we speculate about the intellectual path Jordan might have followed in order to arrive at the interference law. We do not oppose the usual probability to quantum probability. Instead, we are convinced, as Jordan was, that the rules of quantum mechanics are the rules of a probability theory that has ceased to be elementary.

AbstractWe reconstruct the intriguing case of the formation of the Naples group of Statistical Mechanics, which took more than two decades, from the first steps at the end of 1960 aimed at acquiring skills and knowledge abroad, until the formal establishment of the group at the beginning of the 1990 s. A number of important results were obtained seamlessly during this period by Antonio Coniglio and his large number of collaborators, but although favorable opportunities for the formation of the group emerged, starting from the beginning of the 1980 s, several factors (including a certain disinterest in supporting research in Italy) effectively delayed the formation of a group by about a decade. We here provide a fairly comprehensive picture of the relevance of the group of Neapolitan statistical physicists even before its formation, also reviewing the main contributions achieved by these people both during the process of formation of the group and in the first decade of its life.