The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
What did Kramers and Kronig do and how did they do it?
Open accessAbstract
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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Citations
Cites
On the Theory of Dispersion of X-Rays
Kronig, R. D. L. (1926) · Journal of the Optical Society of America · doi:10.1364/josa.12.000547 · Cited by 2,023
Causality and the Dispersion Relation: Logical Foundations
Toll, J. S. (1956) · Physical Review · doi:10.1103/physrev.104.1760 · Cited by 1,110
Causality and Dispersion Relations
(2011) · WORLD SCIENTIFIC eBooks · doi:10.1142/9789814340755_0016 · Cited by 581
Causality and dispersion relations
Humblet, J. (1973) · Nuclear Physics A · doi:10.1016/0375-9474(73)90828-2 · Cited by 474
The speed of information in a ‘fast-light’ optical medium
Stenner, M. D., Gauthier, D. J., & Neifeld, M. A. (2003) · Nature · doi:10.1038/nature02016 · Cited by 354
Superconvergence and Sum Rules for the Optical Constants
Altarelli, M., Dexter, D. L., Nussenzveig, H. M., & Smith, D. Y. (1972) · Physical review. B, Solid state · doi:10.1103/physrevb.6.4502 · Cited by 260
Hu, B. Y.-K. (1989) · American Journal of Physics · doi:10.1119/1.15901 · Cited by 108
On the theory of absorption and dispersion in paramagnetic and dielectric media
Gorter, C. J., & Kronig, R. D. L. (1936) · Physica · doi:10.1016/s0031-8914(36)80327-9 · Cited by 84
Dispersion Theory, Sum Rules, and Their Application to the Analysis of Optical Data
Smith, D. Y. (1997) · Elsevier eBooks · doi:10.1016/b978-012544415-6.50006-6 · Cited by 68
Alternative approach to the derivation of dispersion relations for optical constants
King, F. W. (2006) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/39/33/012 · Cited by 41
Research works printed but not linked: 3
- Smith D Y, 1998, Handbook of Optical Constants of Solids I, 35
- Kramers H A, 1927, Atti del Congresso Internazionale dei Fisici, Como-Pavia-Roma, 2, 545
- de L Kronig R, 1942, Ned. Tijdschr. Natuurkd., 9, 402
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The Bouguer-Beer-Lambert Law: Shining Light on the Obscure
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A Method for Improving the Robustness of linear Kramers-Kronig Validity Tests
Schönleber, M., Klotz, D., & Ivers‐Tiffée, E. (2014) · Electrochimica Acta · doi:10.1016/j.electacta.2014.01.034 · Cited by 604
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Metadata
- 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
- 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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