Soldner, Einstein, gravitational light deflection and factors of two

The Stern-Gerlach experiment revisited

The Stern-Gerlach-Experiment (SGE) of 1922 is a seminal benchmark experiment of quantum physics providing evidence for several fundamental properties of quantum systems. Based on today's knowledge we illustrate the different benchmark results of the SGE for the development of modern quantum physics and chemistry. The SGE provided the first direct experimental evidence for angular momentum quantization in the quantum world and thus also for the existence of directional quantization of all angular momenta in the process of measurement. It measured for the first time a ground state property of an atom, it produced for the first time a `spin-polarized' atomic beam, it almost revealed the electr…

Einstein's Washington Manuscript on Unified Field Theory

In this note, we point attention to and briefly discuss a curious manuscript of Einstein, composed in 1938 and entitled "Unified Field Theory," the only such writing, published or unpublished, carrying this title without any further specification. Apparently never intended for publication, the manuscript sheds light both on Einstein's modus operandi as well as on the public role of Einstein's later work on a unified field theory of gravitation and electromagnetism.

Multiple Perspectives on the Stern-Gerlach Experiment

Different or conflicting accounts of the same episode in the history of science may arise from viewing that episode from different perspectives. The metaphor suggests that conflicting accounts can be seen as complementary, constructing a multi-dimensional understanding, if the different perspectives can be coordinated. As an example, I discuss different perspectives on the Stern-Gerlach experiment. In a static interpretation, the SGE has been viewed as an experiment that allows the determination of the magnetic moment of silver atoms. Based on the concept of magnetic momentum arising from orbital angular momentum, the original experiment was designed in 1922 as an experimentum crucis to dec…

Multicanonical multigrid Monte Carlo method.

To further improve the performance of Monte Carlo simulations of first-order phase transitions we propose to combine the multicanonical approach with multigrid techniques. We report tests of this proposition for the d-dimensional ${\mathrm{\ensuremath{\Phi}}}^{4}$ field theory in two different situations. First, we study quantum tunneling for d=1 in the continuum limit, and second, we investigate first-order phase transitions for d=2 in the infinite volume limit. Compared with standard multicanonical simulations we obtain improvement factors of several, and of about one order of magnitude, respectively.

Exploring Gravitational Lensing

In this article, we discuss the idea of gravitational lensing, from a systematic, historical and didactic point of view. We show how the basic lensing equation together with the concepts of geometrical optics opens a space of implications that can be explored along different dimensions. We argue that Einstein explored the idea along different pathways in this space of implication, and that these explorations are documented by different calculational manuscripts. The conceptualization of the idea of gravitational lensing as a space of exploration also shows the feasibility of discussing the idea in the classroom using some of Einstein's manuscripts.

Václav Hlavatý on intuition in Riemannian space

Abstract We present a historical commentary together with an English translation of a mathematical-philosophical paper by the Czech differential geometer and later proponent of a geometrized unified field theory Vaclav Hlavatý (1894–1969). The paper was published in 1924 at the height of interpretational debates about recent advancements in differential geometry triggered by the advent of Einstein's general theory of relativity. In the paper he argued against a naive generalization of analogical reasoning valid for curves and surfaces in three-dimensional Euclidean space to the case of higher-dimensional curved Riemannian spaces. Instead, he claimed, the only secure ground to arrive at resu…

Einstein's Working Sheets and His Search For a Unified Field Theory

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.

Physics meets Bohemia Einstein in Bohemia Michael D. Gordin Princeton University Press, 2020. 360 pp.

In Einstein in Bohemia, Michael Gordin seeks to illuminate the elusive sig­nificance of Einstein9s brief tenure in Prague, both for the biography of the famous physi­cist and for the cultural history of Bohemia. An expert in the his­tory of modern physical sciences and of Russian, European, and American history, Gordin pulls together a wealth of infor­mation about the wider context of Einstein9s stay in Prague and of the cultural, scientific, and political history of Bohemia.