Several authors (including myself) have made claims, none of which has been convincingly rebutted, that the flatness problem, as formulated by Dicke and Peebles, is not really a problem but rather a misunderstanding. In particular, we all agree that no fine-tuning in the early Universe is needed in order to explain the fact that there is no strong departure from flatness, neither in the early Universe

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

Determinism is generally regarded as one of the main characteristics of classical physics, that is, the physics of the eighteenth and nineteenth century. However, an inquiry into eighteenth and nineteenth century physics shows that the aim of accounting for all phenomena on the basis of deterministic equations of motion remained far out of reach. Famous statements of universal determinism, such as

Academician A. D. Sakharov’s idea concerning the emission of atomic flux from hot plasma (1951) inspired scientists of A. F. Ioffe Physico-Technical Institute to create the first in the world instrument called Neutral Atom Analyzer in 1960 and then in 1961 to use it successfully on the Alpha device (USSR, 1958–1963). Now the analysis of fluxes of fast atoms referred to as Neutral Particle Analysis

In this paper, we describe the history of the LHCb experiment over the last three decades, and its remarkable successes and achievements. LHCb was conceived primarily as a \({b} \)-physics experiment, dedicated to \(CP\) violation studies and measurements of very rare \({{b}} \) decays; however, the tremendous potential for \({c} \)-physics was also clear. At first data taking, the versatility of the

We present some historical and philosophical reflections on the paper “On the Relation Between the Expansion and the Mean Density of the Universe”, published by Albert Einstein and Willem de Sitter in 1932. In this famous work, Einstein and de Sitter considered a relativistic model of the expanding universe with both the cosmological constant and the curvature of space set to zero. Although the Einstein-deSitter

In this admittedly personal account of the history of atomistic simulations of fluids (at the atomic or molecular level), I will focus on the competing efforts to reach the boundary between atoms and the continuum. The prevailing wisdom was that thermal fluctuations at the atomistic scale—both time (a few mean collision times) and space (a few atomic spacings)—would make the connection virtually impossible

Nikhilranjan Sen (1894–1963), popularly known as N.R. Sen, is known as the Father of Applied Mathematics and founder of the Calcutta School of Relativity Theory. He did Ph.D. in Berlin under the Nobel Laureate Max von Laue. In Berlin he came in contact with renowned physicists like Max Planck, Albert Einstein and their contemporaries. The present article, which is based on the primary sources, discusses

Editor’s note: One of the most important developments in theoretical particle physics at the end of the 20th century and beginning of the twenty-first century has been the development of effective field theories (EFTs). Pursuing an effective field theory approach is a methodology for constructing theories, where a set of core principles is agreed upon, such as Lorentz symmetry and unitarity, and all

This is a tutorial for the many-worlds theory by Everett, which includes some of my personal views. It has two main parts. The first main part shows the emergence of many worlds in a universe consisting of only a Mach–Zehnder interferometer. The second main part is an abridgment of Everett’s long thesis, where his theory was originally elaborated in detail with clarity and rigor. Some minor comments

In the late 1970s, the embryonic UK research community in molecular simulation – physicists and physical chemists – organised itself around CCP5, one of a set of Collaborative Computational Projects in different fields. CCP5 acted to develop and use the software required by an evolving and expanding scientific agenda, to exploit quickly and efficiently the revolution in computing hardware and to educate

The widespread positivist approach of physics research in Italy at the turn of the XIX and XX centuries did not provide a fertile ground for the scientific debate on the atomic structure of matter, which instead raged beyond the Alps in those same years and which gave birth, during the 1920s, to the quantum revolution. Experimental investigations in spectroscopy and radioactivity were carried out with

In 1921, the experimental physicist Rudolf Ladenburg put forward the first quantum interpretation of optical dispersion. Theoretical physicists had tried to explain dispersion from the point of view of quantum theory ever since 1913, when Niels Bohr proposed his quantum model of atom. Yet, their theories proved unsuccessful. It was Ladenburg who gave a breakthrough step toward our quantum understanding

The Japanese theoretical physicist Ryogo Kubo made remarkable contributions to statistical mechanics and condensed matter physics, amongst which his name is most widely associated with the linear response theory. Despite his importance in the history of modern physics, however, historians have paid him little attention. Using his unpublished manuscripts in a newly organized archive, this paper examines

My discussions with John Bell about reality in quantum mechanics are recollected. I would like to introduce the reader to Bell’s vision of reality which was for him a natural position for a scientist. Bell had a strong aversion against “quantum jumps” and insisted to be clear in phrasing quantum mechanics, his “words to be forbidden” proclaimed with seriousness and wit – both typical Bell characteristics

In the second half of the 19th century, a special practice of research and training in physics took shape in Pisa, characterized by a particular attention to theoretical studies and to combining experimental activity with a profound mastery of mathematical tools. This peculiar approach, started by Carlo Matteucci and Ottaviano Mossotti, continued and spread by Riccardo Felici, Enrico Betti, Adolfo

Interest in Brownian motion was shared by different communities: this phenomenon was first observed by the botanist Robert Brown in 1827, then theorised by physicists in the 1900s, and eventually modelled by mathematicians from the 1920s, while still evolving as a physical theory. Consequently, Brownian motion now refers to the natural phenomenon but also to the theories accounting for it. There is

The quantum theory of dispersion was an important conceptual advancement which led out of the crisis of the old quantum theory in the early 1920s and aided in the formulation of matrix mechanics in 1925. The theory of Charles Galton Darwin, often cited only for its reliance on the statistical conservation of energy, was a wave-based attempt to explain dispersion phenomena at a time between the theories

ω symbol was erroneously capitalized in several equations and in the text of the article. The Publisher’s erratum provides the correct article. The Publisher apologizes for the inconvenience.

The idea of gravitational collapse can be traced back to the first solution of Einstein’s equations, but in these early stages, compelling evidence to support this idea was lacking. Furthermore, there were many theoretical gaps underlying the conviction that a star could not contract beyond its critical radius. The philosophical views of the early 20th century, especially those of Sir Arthur S. Eddington

This interview is focused on university studies and early career in relativity physics including thesis work under Leopold Infeld dealing with gravitational waves. Trautman’s recollections include the collaboration with Ivor Robinson and relationships with relevant personalities like Felix Pirani, Jerzy Plebanski, Roger Penrose and Peter Bergmann.

Considered one of the founding fathers of integral geometry, Luis Santaló has contributed to various areas of mathematics. His work has applications in number theory, in the theory of differential equations, in stochastic geometry, in functional analysis, and also in theoretical physics. Between the 1950’s and the 1970’s, he wrote a series of papers on general relativity and on the attempts at generalizing

For some time, even after the Feynman diagrams and rules were publicly known, the foundations of Feynman’s quantum electrodynamics remained mostly private. Its stupendous efficiency then appeared like magic to most of his competitors. The purpose of this essay is to reveal the hidden contrivances of this magic, in a journey from field-less electrodynamics to the Feynman diagrams.

Neutrino beams obtained from proton accelerators were first operated in 1962. Since then, neutrino beams have been intensively used in particle physics and evolved in many different ways. We describe the characteristics of various neutrino beams, relating them to the historical development of the physics studies and discoveries. We also discuss some of the ideas still under consideration for future

Since early models of wave propagation in both stationary and moving media during the nineteenth century, the Lorentz transformation (LT) has played a key role in describing characteristic wave phenomena, e.g., the Doppler shift effect. In these models LT connects two different events generated by wave propagations, as observed in two reference systems and the synchronism is absolute. In relativistic

This essay concerns the study of gravitation and general relativity at King’s College London (KCL). It covers developments since the nineteenth century but its main focus is on the quarter of a century beginning in 1955. At King’s research in the twenty-five years from 1955 was dominated initially by the study of gravitational waves and then by the investigation of the classical and quantum aspects

We analyze Feynman’s work on the response of an amplifier performed at Los Alamos and described in a technical report of 1946, as well as lectured on at the Cornell University in 1946–47 during his course on Mathematical Methods. The motivation for such a work was Feynman’s involvement in the Manhattan Project, for which the necessity emerged of feeding the output pulses of counters into amplifiers

The Einstein Archives contain a considerable collection of calculations in the form of working sheets and scratch paper, documenting Einstein’s scientific preoccupations during the last three decades of his life until his death in 1955. This paper provides a brief description of these documents and some indications of what can be expected from a more thorough investigation of these notes.

This paper offers background and perspective on a little-known memoir by Ludvig Lorenz on light scattering by spheres, which was published in Danish in 1890. It is a companion to an English translation of the memoir appearing separately. Apart from introducing Lorenz and some of his contributions to optics and electrodynamics, the paper focuses on the emergence, content and reception of the 1890 memoir

This paper aims at contributing to the history of early computational statistical mechanics. The topic concerns the physics near a critical point and how long it took for Monte Carlo (MC) simulations to be seriously considered by the community as a valid and important tool to analyze critical phenomena. We will focus on one of the leading scientific figures behind this effort: Kurt Binder, whose scientific

In the mid-1980s, the cost of investment in infrastructure for particle accelerators and colliders at the highest energy had risen to such level that the host laboratory (CERN) could no longer afford the cost of development of new detector technology required for the experiments. Large particle colliders were identified by the tools of the future for high-energy physics research, and a long-term view

Élie Cartan’s “généralisation de la notion de courbure” (1922) arose from a creative evaluation of the geometrical structures underlying both, Einstein’s theory of gravity and the Cosserat brothers generalized theory of elasticity. In both theories groups operating in the infinitesimal played a crucial role. To judge from his publications in 1922–24, Cartan developed his concept of generalized spaces

The traveling-wave tube is a critical subsystem for satellite data transmission. Its role in the history of wireless communications and in the space conquest is significant, but largely ignored, even though the device remains widely used nowadays. This paper presents, albeit non-exhaustively, circumstances and contexts that led to its invention, and its part in the worldwide (in particular in Europe)

Fusion research was driven by the oil shocks in 1970’s and the concern about climate change during 20th century. This paper addressed the scientific research history of JT-60, the tokamak that achieved record fusion performances and opened the way toward the continuous operation of a tokamak fusion reactor through its scientific discoveries. The paper also highlighted technical struggles to improve

This paper elucidates the close connections between hydrodynamic models of two-dimensional fluids and reduced models of plasma dynamics in the presence of a strong magnetic field. The key element is the similarity of the Coriolis force to the Lorentz force. The reduced plasma model, the Hasegawa–Mima equation, is equivalent to the two-dimensional ion vortex equation. The paper discusses the history

This oral history interview presents Roald Z. Sagdeev’s story of plasma physics in Russia. It chronicles the Russian school’s achievements in basic, laboratory, fusion and space plasma physics. The interview begins with memories of Sagdeev’s graduate student days in Moscow and then describes his work at the Kurchatov Institute of Atomic Energy (1956–1961), the Budker Institute of Nuclear Physics in

The two main methodologies of computational Statistical Mechanics, namely the stochastic Monte Carlo and the deterministic Molecular Dynamic methods, were developed in the USA in the mid 1950’s. In the present paper we show how these “computer experiments” migrated to Europe in the 60s, and first bloomed at the Orsay Science Faculty, before spreading throughout Europe. Collaborations between the Orsay

The paper traces the early stages of Berni Alder’s scientific accomplishments, focusing on his contributions to the development of Computational Methods for the study of Statistical Mechanics. Following attempts in the early 50s to implement Monte Carlo methods to study equilibrium properties of many-body systems, Alder developed in collaboration with Tom Wainwright the Molecular Dynamics approach

I summarize, at its 41st – and what would have been Bruno Zumino’s 94th – birthday, the history of the discoveries of Supergravity, and some of its structure and later developments.

The cosmological constant was proposed 100 years ago in order to make the model of static Universe, imagined then by most scientists, possible. Today it is the main candidate for the physical essence causing the observed accelerated expansion of our Universe. But, as well as a hundred years ago, its nature is unknown. This paper is devoted to the story of invention of Λ by Albert Einstein in 1917,

We provide an account of John Wheeler’s transition from his work on elementary particle physics (in which particles provided the ultimate ontology in his worldview), to his work on gravitation and general relativity (in which spacetime geometry was the ultimate object out of which all other things were composed). We also describe his early work on quantum gravity largely as a long-standing attempt

Evidence that a model of hard spheres exhibits a first-order solid-fluid phase transition was provided in the late fifties by two new numerical techniques known as Monte Carlo and Molecular Dynamics. This result can be considered as the starting point of computational statistical mechanics: at the time, it was a confirmation of a counter-intuitive (and controversial) theoretical prediction by J. Kirkwood

The main purpose of this paper is to analyse the earliest work of Léon Rosenfeld, one of the pioneers in the search of Quantum Gravity, the supposed theory unifying quantum theory and general relativity. We describe how and why Rosenfeld tried to face this problem in 1927, analysing the role of his mentors: Oskar Klein, Louis de Broglie and Théophile De Donder. Rosenfeld asked himself how quantum mechanics

This oral history interview touches upon important topics like the dynamics of the discovery, in 1995, of 51 Pegasi b – the first extrasolar planet ever found around a normal star other than the Sun – the development of better and better equipment that made it possible, the importance it had in shaping a new community of scholars dealing with this new field of research, and, more at large, the cultural

We present a centennial review of the history of the term known as the cosmological constant. First introduced to the general theory of relativity by Einstein in 1917 in order to describe a universe that was assumed to be static, the term fell from favour in the wake of the discovery of the expanding universe, only to make a dramatic return in recent times. We consider historical and philosophical

This highly personal account of evolution of cosmology spans a period of approximately six decades 1959–2017. It begins when in 1959 the author, as an undergraduate at Cambridge, was attracted to the subject by the thought provoking lectures by Fred Hoyle as well as by his popular books The Nature of Universe and The Frontiers of Astronomy. The result was that after a successful performance at the

A revolution in elementary particle physics occurred during the period from the ICHEP1968 to the ICHEP1982 with the advent of the parton model from discoveries in Deeply Inelastic electron-proton Scattering at SLAC, neutrino experiments, hard-scattering observed in p+p collisions at the CERN ISR, the development of QCD, the discovery of the J/Ψ at BNL and SLAC and the clear observation of high transverse

The present paper is a companion to the paper by Villone and Rampf (2017), titled “Hermann Hankel’s On the general theory of motion of fluids, an essay including an English translation of the complete Preisschrift from 1861” together with connected documents [Eur. Phys. J. H 42, 557–609 (2017)]. Here we give a critical assessment of Hankel’s work, which covers many important aspects of fluid dynamics

The present is a companion paper to “A contemporary look at Hermann Hankel’s 1861 pioneering work on Lagrangian fluid dynamics” by Frisch, Grimberg and Villone [Eur. Phys. J. H 42, 537–556 (2017)]. Here we present the English translation of the 1861 prize manuscript from Göttingen University “Zur allgemeinen Theorie der Bewegung der Flüssigkeiten” (On the general theory of the motion of the fluids)

The objective of this interview is to study the history of the Large Hadron Collider in the LEP tunnel at CERN, from first ideas to the discovery of the Brout–Englert–Higgs boson, seen from the point of view of a member of CERN scientific committees, of the CERN Council and a former Director General of CERN in the years of machine construction.

Here, we present an analysis of the paper “Universelle Bedeutung des Wirkungsquantums” (The universal meaning of the quantum of action), published by Jun Ishiwara in German in the “Proceedings of Tokyo Mathematico-Physical Society 8 (1915) 106–116”. In his work, Ishiwara, established in the Sendai University, Japan, proposed – simultaneously with Arnold Sommerfeld, William Wilson and Niels Bohr in

Personal recollections on theoretical particle physics in the years when the Standard Theory was formed. In the background, the remarkable development of Italian theoretical physics in the second part of the last century, with great personalities like Bruno Touschek, Raoul Gatto, Nicola Cabibbo and their schools.

We present a historical review of Einstein’s 1917 paper ‘Cosmological Considerations in the General Theory of Relativity’ to mark the centenary of a key work that set the foundations of modern cosmology. We find that the paper followed as a natural next step after Einstein’s development of the general theory of relativity and that the work offers many insights into his thoughts on relativity, astronomy

The growth of research on general relativity in Germany from its origin in 1915 to the beginning of the 1990s is described. A gradual evolution from research done by single physicists and mathematicians to the eventual institutionalizion in the form of a research institute and subdivision of physical society is brought into focus.

During the period June–July 1957 six physicists met at the Institute for Theoretical Physics of the University of Copenhagen in Denmark to work together on problems connected with the quantization of the gravitational field. A large part of the discussion was devoted to exposition of the individual work of the various participants, but a number of new results were also obtained. The topics investigated

Since the mid-1920s, different strands of research used stars as “physics laboratories” for investigating the nature of matter under extreme densities and pressures, impossible to realize on Earth. To trace this process this paper is following the evolution of the concept of a dense core in stars, which was important both for an understanding of stellar evolution and as a testing ground for the fast-evolving

This is the first part of an oral history interview on the lifelong involvement of Joel Lebowitz in the development of statistical mechanics. Here the covered topics include the formative years, which overlapped the tragic period of Nazi power and World War II in Europe, the emigration to the United States in 1946 and the schooling there. It also includes the beginnings and early scientific works with

This paper addresses the history of JET, the Tokamak that reached the highest performances and the experiment that so far came closest to the eventual goal of a fusion reactor. The reader must be warned, however, that this document is not a comprehensive study of controlled thermonuclear fusion or even of JET. The next step on this road, the ITER project, is an experimental reactor. Actually, several

Joseph Weber started thinking about possibilities for detecting gravitational waves or radiation in about 1955. He designed, built, and operated the first detectors, from 1965 until his death in 2000. This paper includes discussions of his life, earlier work on chemical kinetics and what is now called quantum electronics, his published papers, pioneering work on gravitational waves, and its aftermath

This paper aims at a historical and pedagogical presentation of some important contributions of the research on thermonuclear fusion by magnetic confinement to the study of Hamiltonian chaos. This chaos is defined with the help of Poincaré maps on a simple two-wave Hamiltonian system. A simple criterion for computing the transition to large scale chaos is introduced. A renormalization group approach