1 Berggren, J.L.; Goldstein, Bernard R. (eds.) From ancient omens to statistical mechanics: Essays on the exact sciences presented to Asger Aaboe. (Acta historica scientiarum naturalium et medicinalium, 39.) xix + 298 pp., illus., notes, index. Copenhagen: University Library, 1987. Contains a biography of Aaboe and a list of his publications. Papers in this volume are indexed separately in the present bibliography.

Current Bibliography of the History of Science and Its Cultural Influences, 1989

The composition of two pure Lorentz transformations (boosts) parametrized by non-parallel velocities is equivalent to a boost combined with a pure spatial rotation - the Thomas rotation. Thirty years elapsed from Thomas's 1926 calculation for the precessional application until an explicit result for the Thomas rotation angle appropriate to two finite boost velocities appeared in the literature. Over the years there have been a number of papers that have produced results by various methods for the Thomas rotation angle but none by direct Lorentz matrix methods. This paper repairs that deficiency by presentation of an explicit Lorentz matrix proof of sufficient conciseness to show that the much-vaunted complexity of the direct approach has been considerably overstated. The demonstration fills a gap at a fundamental level in the development of the basics of special relativity.

Thomas rotation: a Lorentz matrix approach

In this chapter, dedicated to the 60th Anniversary of Themistocles M. Rassias, Mobius transformation and Einstein velocity addition meet in the hyperbolic geometry of Bolyai and Lobachevsky. It turns out that Mobius addition that is extracted from Mobius transformation of the complex disc and Einstein addition from his special theory of relativity enable the introduction of Cartesian coordinates and vector algebra as novel tools in the study of hyperbolic geometry.

Möbius Transformation and Einstein Velocity Addition in the Hyperbolic Geometry of Bolyai and Lobachevsky

In 1909, Arnold Sommerfeld used geometric calculations to show that the relativistic addition of two noncollinear velocities on an imaginary-radius sphere is a noncommutative operation Sommerfeld was the first to use the geometric phase method to calculate the angle between the resulting velocities depending on the order in which they are added For this, he related the value of this angle to the excess of the spherical triangle formed by the two original velocities and their sum In 1931, Sommerfeld applied his method to analyze the Thomas precession

http://iopscience.iop.org/article/10.3367/UFNe.0180.201009d.0965/pdf

Noncommutative nature of the addition of noncollinear velocities in special relativity and the geometric phase method (commemorating the publication centennial of A Sommerfeld's work)

We present a heuristic argument to deduce the non-intuitive Thomas factor for an atomic electron revolving in its orbit about the nucleus. The argument, which is simple, pedagogical and accessible to physics beginners, uses elementary notions of classical electromagnetism rather than the advanced relativity concepts which are needed in any standard textbook derivation.

The non-intuitive \case{1}{2} Thomas factor: a heuristic argument with classical electromagnetism

Sommerfeld's 1931 presentation of his derivation of the Thomas precession is set in its historical context. Some aspects of his particular geometrical approach are also discussed.

Sommerfeld's way to the Thomas precession

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

L Belloni

Author Tools

Chat about Author

Papers

Sommerfeld's way to the Thomas precession