The 1935 Einstein–Podolsky–Rosen (EPR) paper, “Can Quantum–Mechanical Description of Physical Reality Be Considered Complete?”, stands as a landmark in the foundational debates over quantum mechanics. While the paper has since become one of Einstein’s most cited works, it initially received little attention, and the feature of non-locality, which was central to the argument in the paper, was largely neglected for decades. In this paper, I offer two reasons for this early neglect of non-locality in the immediate aftermath of EPR. First, early responses to the EPR paper defended the completeness of quantum mechanics by reformulating the thought experiment the authors had presented, thereby obscuring the feature of quantum mechanics the authors had wished to highlight. Bohr’s influential reply, for instance, substituted the specific thought experiment presented by EPR with the two-slit experiment, thus suppressing the entanglement between spatially separated systems. A second reason for the marginalization of non-locality was the tendency to see Einstein’s critique of quantum mechanics as proceeding from a commitment to determinism, though this in fact played no role in the EPR paper or in his later writings and correspondence. This paper argues that the failure to recognize non-locality was partly a result of the rhetorical manoeuvring by EPR’s critics, but also to a broader philosophical climate dominated by concerns over determinism, which effectively eclipsed all other conceptual issues, Only with Bell’s theorem in the 1960s did non-locality return as a serious focus of foundational inquiry.
The determination of the tropical year constitutes a fundamental problem at the intersection of celestial mechanics, astronomy, and historical timekeeping. As a physically defined quantity arising from the combined effects of orbital motion and axial precession, the tropical year provides the natural reference for civil calendar systems. This study examines the historical development of Julian-derived calendars as successive approximations to the tropical year, interpreted within a unified physical and mathematical framework. From the Julian calendar through the Gregorian reform to the Revised Julian system of Milutin Milanković, these calendars are analyzed as rational approximations to a slowly varying astronomical quantity. Within this framework, an adjusted Julian scheme is introduced as a theoretical extension of this tradition. Rather than constituting a proposal for reform, it serves to elucidate the limiting behavior of fixed calendrical systems when applied to a time-dependent physical quantity. The analysis demonstrates that calendar design is inherently epoch-dependent and reflects a continuous interaction between physical theory, mathematical structure, and historical practice. The results contribute to the understanding of timekeeping as a physical as well as cultural problem.
The tumultuous history of measurements of the deceleration parameter q0, one of a few key cosmological parameters, yields historical, theoretical, and epistemological reasons for studying it. A wide variety of observational methods and techniques, combined with evolutionary, astrophysical, cosmological, and observational selection effects, as well as various, and often contradictory assumptions behind various models, led to widely differing values of q0 (from − 2 to + 36!) over a span of half a century. Moreover, there was an inevitable epistemic trade-off between observational sensitivity and statistical wealth of data. While there certainly was a diversity of theoretical predictions for q0 among various cosmological models, our analysis indicates that the main historical cause of such a large and confusing scatter of empirical values was the persistent failure to appreciate the scope and tempo of evolutionary change in various astronomical sources. We survey and sort out this historical context, providing some preliminary general lessons for ongoing and future endeavors of similar complexity.
The special theory of relativity as we understand it today owes much to the figure of Hermann Minkowski. His are several fundamental concepts that appear in current textbooks. However, his contributions are not always recognized. Furthermore, some historians of science judge him with a certain severity, undermining the importance of his contributions. He himself provoked this attitude to some extent by arguing in his articles that mathematicians were in a better position than physicists to understand the new theory. This article is devoted to the figure of Minkowski in two aspects. On the one hand, we analyze the status of Minkowski’s original ideas in the special theory of relativity as currently studied and taught. We show that some textbooks of reference in physics do not properly acknowledge the contributions of Minkowski. On the other hand, we will illustrate with some examples how the figure of Minkowski is perceived by historians. We see that even today he has his supporters and detractors.
Max Planck is widely recognised for founding quantum theory. In his 1900 seminal work on black-body radiation, he also provided a numerical estimation of the elementary charge. This result, however, was embedded within his broader theoretical development and was not presented as a primary result, so that his contemporaries likely approached it with caution. Planck himself acknowledged that the theoretical basis that led to this estimate was fragile and explicitly noted that further experimental work was needed to confirm it. Remarkably, despite these limitations, his estimate closely matched values later confirmed by precise experiments. In this study, we examine how Planck’s contemporaries received and cited this estimate. We first situate his work within the scientific context of black-body radiation, then we analyse primary literature from 1901 to 1921, covering journals from Europe and the USA, to trace patterns of citation and engagement with Planck’s elementary charge estimate. Finally, a statistical bibliometric analysis quantifies these trends, revealing the visibility and impact of Planck’s work across different journals, national contexts, and scientific communities.
In Italy, in the decades surrounding Italian Unification—especially in the early years of the Kingdom of Italy—figures such as Pietro Blaserna and Carlo Matteucci commented critically on the state of the physical sciences, addressing institutional and pedagogical arrangements as much as research practices. At the same time, an alternative mode of knowledge production was emerging: an “epistemology of the province”—an analytical and historiographical category for forms of scientific research and experimental practice that were locally rooted yet sustained by supra-local circuits of communication and validation. This article examines such a provincial epistemic configuration through the work of Alessandro Serpieri (1823–1885), a scientist whose career at the University of Urbino spanned thirty-seven years. The analysis centres on three paradigmatic case studies: the first Italian replication of Foucault’s pendulum (30 March 1851); pioneering research into duplex telegraphy (1854–1855); and investigations of the first Bell telephones in Italy (1877–1878). These episodes collectively demonstrate how Serpieri’s locally grounded practice remained consistently engaged with the most advanced international technological debates. Across these episodes, Serpieri’s trajectory moves from mechanical and astronomical phenomena to electrotechnical questions and culminates in his study of the telephone, which foregrounds the listener as an active component in the device’s operation. He argued that much of the apparatus’s effectiveness in transmitting sound should instead be attributed to the listener’s interpretative capacity. This claim invites a retrospective comparison with later themes in cybernetics and the cognitive sciences, while remaining grounded in Serpieri’s nineteenth-century vocabulary of perception, judgement, and interpretation. Serpieri’s work thus encourages us to read provincial science not as a peripheral appendage, but as a productive epistemic environment, capable of transforming marginal constraints into methodological opportunities and of challenging centre–periphery hierarchies in the production of original knowledge.
Gupta was among the first to attempt the quantization of Einstein’s nonlinear theory of gravity. He had an independent program to quantize gravity in a manner akin to electromagnetism, which spanned at least two decades. He adopted the flat-space views of Rosen and Papapetrou and built his theory around these ideas. Although he was well known for his work in quantum electrodynamics, little is known about his work in quantum gravity. For that reason, in this paper, we try to present a historical overview of his research program.
Between 1933 and 1937, the treatment of relativistic spin-1/2 particles, initially rooted in Hole theory, evolved into the modern framework of quantum field theory. This paper reconstructs the crucial stages of that transition by examining the formal and physical progress of the numerous authors who shaped the field's modern formalism. This historical study traces the development of fermionic field theory in full, beginning with the foundational work of the 1920s, focussing on the results of the 1930s, and concluding with the influential synthesis of Wolfgang Pauli in 1941, the content of which has shaped the subsequent tradition. Within this framework, particular emphasis is given to Ettore Majorana's 1937 quantisation procedure and argument for anti-commuting fermionic quantum fields. This study demonstrates that Majorana's work was not merely a technical variant, but the definitive rejection of the concept of negative energy solutions, whose conceptual clarity and educational value remain vital today.
Two striking, physically wrong assumptions are asserted in the 1940 Frisch-Peierls' Memorandum: The Memorandum ignores the known large scattering cross section while inventing a hypothetical fission cross section that is twenty times larger than the known fission cross section in 1940. The point of this paper is to show how Frisch used Peierls' approximate solution to his nonstandard chain reaction–diffusion equation along with the two wrong cross-section assumptions to make the Memorandum's famous critical radius prediction. Frisch's two 'vastly optimistic' cross sections were essential for getting the neutron multiplication number ν ≈ 2.3 (the average number of neutrons per fission event) into the right place in Peierls' partial differential equation. If we simply translate Frisch's assumptions as stated in the 1940 Memorandum directly into equations, then the prediction that R = 0.8 L with a correspondingly too small mean free path L = 2.6 m falls out from Peierls' approximate solution of his partial differential equation. Under these assumptions, the mean free path is identical with the fission mean free path. Summarizing, following the shortest path that Frisch could have taken leads us directly to R = 0.8 L and the end of the mystery of how he could have predicted the tiny critical radius.
In this work I reopen the measurement problem taking into account Steven French’s recent book on the possibility of a phenomenological approach to quantum mechanics, taking into account the interpretation of London and Bauer, whom French considers the precursors of this approach. We will see to what extent French can be right in this statement, through a historical review in which the problem of measurement is contextualized. In this reopening we will have the opportunity to revisit some of the most notable contributions to this problem, such as Bohr, Born or von Neumann, among others. Current perspectives will also be added, which will help us to understand the state of the art.
In this article, I trace the early historical developments that ultimately led to the creation of the atomic bomb. Even after the weapon’s completion, a number of scientists continued to argue that nuclear armaments were indispensable for maintaining the global balance of political power [1]. This study focuses on several scientists who confronted profound moral dilemmas concerning the bomb’s use against Japan. Some openly opposed its deployment, others sought to warn a Japanese scientist in the hope of averting further devastation, and still, others expressed deep remorse in its aftermath. In addition, the experience of an individual directly affected by the bombing is discussed. By examining these episodes, this article aims to contribute to the ongoing discourse on how scientific research should be guided by ethical principles in the future.
The aim of this paper is to retrace the path that led the young Enrico Fermi to write his paper on the statistics of an ideal monatomic gas. This discovery originated in his interest, which he had shown since his formative years, in the absolute entropy constant and in the problems he highlighted in Sommerfeld’s quantization in the case of identical particle systems. The fundamental step taken by Fermi in writing his work on statistics was to apply the Exclusion Principle, formulated for electrons in an atom and which could therefore have been a pure effect due to dynamics, to a system of non-interacting particles.
Hilbert-space techniques are widely used not only for quantum theory, but also for classical physics. Two important examples are the Koopman-von Neumann (KvN) formulation and the method of “classical” wave functions. As this paper explains, these two approaches are conceptually distinct. In particular, the method of classical wave functions was not due to Bernard Koopman and John von Neumann, but was developed independently by a number of later researchers, perhaps first by Mario Schönberg, with key contributions from Angelo Loinger, Giacomo Della Riccia, Norbert Wiener, and E. C. George Sudarshan. The primary goals of this paper are to explain these two approaches, describe the relevant history in detail, and give credit where credit is due.
This paper offers a historical overview of the origins and enduring significance of gravitational particle creation, a groundbreaking discovery first formulated in Leonard Parker's 1966 doctoral thesis at Harvard University. By tracing the context in which Parker developed this idea and examining its subsequent influence, the paper highlights how the concept of gravitational particle creation advanced the study of quantum field theory in curved spacetime and profoundly shaped modern cosmology, as well as the quantum theory of black holes.
This work analyzes the extent to which the “blurred orbits” of the current model for the atom, drafted by Heisenberg in 1926, fits with the image of a bunch of wandering electrons around a nucleus. We will deal with early appearances of the concept of indistinguishable particles within the frame of quantum mechanics. Few studies have examined the use of this concept in Heisenberg’s 1926 papers on helium, in contrast to the large number of studies on its use in Bose–Einstein’s 1924 papers. We will discuss to what extent Heisenberg’s approach leads to a purely statistical interpretation of this concept. We will also study the viewpoint of Dirac, who dealt with the same topic a few months later. Although the indistinguishability of the electrons and indeterminacy are common explanations for the blurring of electron orbits, we argue that such an image is an oversimplification which masks interesting aspects of the dynamics of bound electrons, exchange processes, and the role of superposed exchanged configurations.
Seismology, which had previously relied on descriptive and observational methods, began incorporating appropriate instrumentation and effective techniques for the parametric and theoretical analysis of seismic data starting in the mid-nineteenth century. Alessandro Serpieri, rector of the Raffaello College in Urbino from 1857 to 1884, was a pioneering figure who first proposed the creation of a seismic network in Italy. A significant contribution also came from Luigi Guidi (1824–1883), director from 1861 to 1883 of the Valerio Observatory in Pesaro. Today, comprehensive coverage of study areas is essential for the high-resolution analysis of low-magnitude seismic events. To this end, a temporary seismic network was established in the Montefeltro region in December 2018 as part of a collaborative project between the University of Urbino and the National Institute of Geophysics and Volcanology. The aim was to acquire new seismic data to supplement those recorded by the National Seismic Network. The Montefeltro area, with Urbino as its provincial capital, has recently experienced seismic activity with magnitudes below 4. Data analysis indicates that the region is characterized by a seismically active basin with microseismicity, while the surrounding areas show more concentrated seismic activity in three zones: Rimini, Forlì, and along the Apennine belt. In this contribution, we review the evolution of seismological studies in the broad Montefeltro region since the seminal work of Serpieri up to present times.
I study Heisenberg's 1939 chain reaction equation as an eigenvalue problem for nonspherical shapes and apply it to calculate the criticality condition of the cylindrical 1945 Haigerloch reactor experiment B8. I also discuss Heisenberg's B8 criticality analysis where he relied on his 1939 spherical result that the neutron current ratio is infinite at criticality. I show that that result holds for a sphere but not for a cylinder. His wrong expectation for a cylinder has recently been assumed in simulations of B8. Heisenberg and Wirtz applied an inconsistent mix of spherical and axial extrapolations to B8 that led Heisenberg to predict that they needed a radial increase of 20 cm to reach criticality. The B8 reactor was designed with the height twice the radius, H = 2R, so that a sphere of radius R fits perfectly inside the cylinder, apparently with the application of his 1939 spherical calculation in mind. I solve Heisenberg's reactor equation for axial symmetry and the full tamper boundary condition. Diffusion theory with the tamper then predicts that the reactor should have been slightly subcritical, while Heisenberg's albedo boundary condition predicts slight supercriticality. Diffusion theory therefore predicts that the reactor was very near to criticality. I also consider how the reactor's designers may have arrived at a nearly correct size of B8 without doing a correct cylindrical calculation.
The paper examines the historical development and context of several seismographs preserved in the Physics Laboratory and Museum of Science and Technology at the University of Urbino Carlo Bo. In the second half of the nineteenth century, these instruments were used by Alessandro Serpieri (1823–1885), a Scolopian priest and a pioneer of Italian seismology. Following a brief biographical overview of the scientist, the study examines three principal instruments currently on display in the museum: the “protoseismograph” by Michele Stefano De Rossi (1878) and two seismographs designed by the Urbino-based instrument-maker Achille Scateni (c. 1882). In addition to these surviving instruments, the study also discusses a seismograph invented by Serpieri in 1873, known only through contemporary descriptions and illustrations. This study re-examines their history and mechanical functioning using archival documents, publications from the period, and direct analysis of the instruments, focusing on Luigi Palmieri’s influence on Serpieri’s seismograph design. It highlights the scientific heritage of Urbino’s Physics Laboratory and the pivotal collaboration between Serpieri and Scateni, locating their advancements in Italian instrumental seismology within the context of the birth of quantitative seismometry which complemented continuing observational methods in the late nineteenth century. In particular, it suggests how the interplay between local instrumental innovation and national scientific networks fostered the development of modern seismometry in Italy.
Building on Schrödinger's original formulation of quantum mechanics from 1926, which initially involved a fourth-order differential equation, this article explores the mechanical analogy between this first Schrödinger equation without potential V and the dynamic behavior of vibrating elastic structures in the specific case of a particle in a potential well. Revisiting this fourth-order approach, we find a mathematical equivalence with the modern second-order Schrödinger equation which is strictly equivalent to the initial fourth-order Schrödinger equation in this specific case, while also revealing the possibility of solutions positive and negative masses. These results resonate with recent experimental observations on Bose–Einstein condensates and spin–orbit coupled exciton–polaritons. Following this research, it seems that negative mass effects should appear in the particular case of particles in a potential well situation close to this specific case like a Bose–Einstein condensate at a temperature close to 0 or another quantum entity in a cavity well.
The Manila Observatory, established in 1865, was a leading centre for geophysical research in the Far East for 80 years (1865–1945). It conducted pioneering studies in meteorology, geomagnetism, seismology, volcanology, and astronomy. Instrumental seismology began at the Observatory shortly after its founding, and its early development exhibited distinctive characteristics: It developed more rapidly than in Spain (the dominating power at that time) and it became a unique example of the Italian seismological tradition, particularly endogenous meteorology, taking root in Asia. Early Italian instruments such as seismographs, tromometers, and seismic telephones were installed and used extensively in Manila. By 1890, the Observatory became the central station of the Philippine seismological network. However, seismological research in the Philippines was not confined to the Observatory; other significant developments, especially in engineering seismology, also emerged during this period. This study offers an introductory analysis and evaluation of the early stages of instrumental seismology in the Philippines, highlighting its roots in the Italian seismological tradition—particularly the theories of endogenous meteorology—and its related scientific research.
