Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1401.8048

A Note On Einstein, Bergmann, and the Fifth Dimension

Edward Witten
View original source ↗Read source document ↗Export metadata ↓

Abstract

This note is devoted to a detail concerning the work of Albert Einstein and Peter Bergmann on unified theories of electromagnetism and gravitation in five dimensions. In their paper of 1938, Einstein and Bergmann were among the first to introduce the modern viewpoint in which a four-dimensional theory that coincides with Einstein-Maxwell theory at long distances is derived from a five-dimensional theory with complete symmetry among all five dimensions. But then they drew back, modifying the theory in a way that spoiled the five-dimensional symmetry and looks contrived to modern readers. Why? According to correspondence of Peter Bergmann with the author, the reason was that the more symmetric version of the theory predicts the existence of a new long range field (a massless scalar field). In 1938, Einstein and Bergmann did not wish to make this prediction. (Based on a lecture at the Einstein Centennial Celebration at the Library of Alexandria, June, 2005.

Explore related subjects

physics.hist-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Edward Witten. 2014-01-31. A Note On Einstein, Bergmann, and the Fifth Dimension. https://arxiv.org/abs/1401.8048

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Price of Removing the Scaffolding: Maxwell wrote something about Amp`ere that years later would be done to him

In the history of physics, the name scaffolding has been given to whatever served to raise a theory and is afterwards removed because, it is said, it is no longer needed. This article documents, from the originals, what it cost Maxwell's theory when that method was applied to it: what was removed from it, who did it, with what argument, and how over the years it had to be recovered because it was understood that it was needed after all. It also records what Maxwell himself missed in Amp`ere, what he calls the traces of the scaffolding: the template with which Amp`ere himself had given shape to his work.

physics.hist-ph↗
arXiv2026

Astrobiology and the Transformation of Scientific Epistemology

Astrobiology occupies an unusual position within the philosophy of science. Confronted with the n = 1 problem - having only a single example of life to study - it attempts to investigate life beyond Earth while relying entirely on Earth's biosphere as its reference point, a constraint that creates unique epistemic challenges. Unlike traditional sciences with clear predictive frameworks, astrobiology operates as what we might call a transient science: a discipline functioning without foundational certainties, relying predominantly on abductive reasoning, and confronting hypotheses that may remain untestable for decades. It is, in essence, a science of absence - of evidence, certainty, and analogy - where progress lies in refining conceptual and experimental tools to recognize unfamiliar forms of life. This positions astrobiology alongside emerging fields like artificial intelligence and cognitive science within a broader transformation of how scientific knowledge is constructed when dealing with phenomena that transcend direct empirical access.

physics.hist-ph↗
arXiv2026

The wavelength of light as Thomas Young invented it

This paper documents Thomas Young's invention of a concept which he alternately refers to as the ''magnitude'', ''breadth'', ''interval'' or ''length of an undulation'' of light. First, the paper highlights that Young was first to link some concept of a wavelength to a theory of optics and to assign a precise value to this length for each component of the colour spectrum. Then, it sets out an explanation of how Young made up these values. Finally, it examines the reasons why Young introduced an optical wavelength into his theory of light, insofar as these reasons might in turn shed light on why he was first to do so.

physics.hist-ph↗