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What did Kramers and Kronig do and how did they do it?

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Bohren, Craig F·2010·European Journal of Physics

DOI 10.1088/0143-0807/31/3/014

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Abstract

Over time the account of how the Kramers–Kronig (dispersion) relations between the real and imaginary parts of response functions were derived in 1926 and 1927 has been transmogrified into anecdotes about what might have been done but was not. Although Kramers obtained both members of a pair of relations, Kronig obtained only one. Both authors appealed to specific models of an atomic gas rather than to the general arguments about linearity, causality and analyticity in modern model-independent derivations. Kramers merely speculated on whether the specific results he obtained might have a more general validity. Neither author showed that a signal cannot travel faster than c in any medium for which the dispersion relations are satisfied. Indeed, they did not mention, even obliquely, signal speeds and causality. Despite their magical aura, Kramers–Kronig relations are translations into somewhat cryptic frequency language of statements clearer in time language.

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K
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Index
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Authors: Bohren, C. F.
Affiliations: Pennsylvania State University (US)
Corresponding author: Bohren, Craig F
ORCID: Bohren, Craig F
Venue: European Journal of Physics
Publisher: IOP Publishing
Published: 2010-03-30
Volume: 31
Issue: 3
Pages: 573-577
ISSN: 0143-0807 (ISSN-L)
1361-6404
DOI: 10.1088/0143-0807/31/3/014
OpenAlex: W2026692979
Cited by: 112
References: 11
Citations by year: 2026: 4 · 2025: 9 · 2024: 6 · 2023: 2 · 2022: 9 · 2021: 5 · 2020: 8 · 2019: 34 · 2018: 4 · 2017: 8 · 2016: 4 · 2015: 5 · 2014: 6 · 2013: 2 · 2012: 3
FWCI: 17.73
Type: journal article
Language: en
Open access: bronze
doi.org
Locations: European Journal of Physics (publishedVersion)
Topics: Social Sciences › Arts and Humanities › History and Philosophy of Science › History of Science and Medicine
Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
Social Sciences › Arts and Humanities › History and Philosophy of Science › Historical Studies and Socio-cultural Analysis
Keywords: Kramers-Kronig relations, dispersion relation, response functions, causality, analyticity, signal propagation speed, history of physics, Kramer

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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

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What did Kramers and Kronig do and how did they do it?

Abstract

Overview

Integrity signals

Verification

Claims the paper makes

Self-check

Citations

Cites

Cited by

Related

Metadata

Record

About these checks