dmm,
@dmm@mathstodon.xyz avatar

Born in 1835, Josef Stefan was an ethnic Carinthian Slovene physicist, mathematician, and poet of the Austrian Empire [1].

During his lifetime Stefan published nearly 80 scientific articles, most appearing in the Bulletins of the Vienna Academy of Sciences.

Stefan is perhaps best known for his study of blackbody radiation [2] and for discovering what we now call Stefan's law, a physical power law which states that the total radiation from a blackbody is proportional to the fourth power of its (thermodynamic) temperature. Stefan's law was later extended to grey bodies by one of Stefan's students, Ludwig Boltzmann [3], and is now known as the Stefan–Boltzmann law [4].

I wrote a bit about blackbody radiation and the famous Stefan–Boltzmann law here: https://davidmeyer.github.io/qc/oscillators.pdf, but it looks like I got distracted (again) and never finished. The LaTeX source is here: https://www.overleaf.com/read/xjmyvksvtztb. In any event, as always questions/comments/corrections/* greatly appreciated.

References

[1] "Josef Stefan", https://en.wikipedia.org/wiki/Josef_Stefan

[2] "Josef Stefan’s – Black Bodies and Thermodynamic Temperature", http://scihi.org/josef-stefans-thermodynamics/

[3] "Ludwig Boltzmann", https://mathshistory.st-andrews.ac.uk/Biographies/Boltzmann/

[4] "Stefan–Boltzmann law", https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law

johncarlosbaez,
@johncarlosbaez@mathstodon.xyz avatar

@dmm - how did Stefan find his law? Empirically? You could find it using dimensional analysis if you knew the dimensions of the Stefan-Boltzmann constant, but I don't think there's any way to guess the 1/T⁴ factor in that constant without some input from physics.

dmm,
@dmm@mathstodon.xyz avatar

@johncarlosbaez From what I can understand Stefan came up with the law empirically.

johncarlosbaez,
@johncarlosbaez@mathstodon.xyz avatar

@dmm - okay, that's interesting! So that set up a challenge to figure out where that T⁴ came from. And ultimately it comes in part from space being 3-dimensional. E.g. if space were 2-dimensional, we'd get T³ in the Stefan-Boltzmann law.

dmm,
@dmm@mathstodon.xyz avatar

@johncarlosbaez Interesting in that it always puzzled me as to why (T^4)

johncarlosbaez,
@johncarlosbaez@mathstodon.xyz avatar

@dmm - here's a paper that derives the Stefan-Boltzmann law in any dimension:

https://arxiv.org/abs/quant-ph/0510002

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