Talk:Planck's law

Symbol for spectral radiance
The symbol for spectral irradiance used in the Wikipedia article of the same name is L not B. L is also the ISO 80000 recommended symbol for this quantity. This article should use L instead of B for consistency.

"Old quantum theory" categorization
I confess I do not understand this revert. The Planck law belongs to the historical period known as the old quantum theory; indeed, it inaugurated that period. That the result is empirically correct doesn't change the historical fact that it was first deduced as what we would now call a semiclassical approximation. XOR&#39;easter (talk) 16:17, 14 March 2023 (UTC)


 * "Old" in "Old quantum theory" refers not to a time range but to the fact that the said theory is no longer considered valid. Contrary to that, the Planck law remains perfectly sound. It doesn't matter how the equation was originally deduced/derived. Evgeny (talk) 16:41, 14 March 2023 (UTC)
 * I agree with here. Planck's law remains valid even after the development of Bose-Einstein statistics, while BKS theory has no application, also Bohr's model and Bohr-Sommerfeld quantization remain as very crude rules of thumb. The category should not be confused with Category:Foundational quantum physics--ReyHahn (talk) 16:44, 14 March 2023 (UTC)
 * Category:Foundational quantum physics is an ill-defined and WP:SYNTH-y term that contradicts with the accepted term quantum foundations, whereas the literature classifies the Planck law as part of the old quantum theory, along with BKS and the like . XOR&#39;easter (talk) 17:56, 14 March 2023 (UTC)
 * I cannot see in any of the links you provided that Planck's law (not his thoughts etc. at that time) is considered part of the old quantum theory; it's just your interpretation. Of course, one cannot give a historical description of the quantum mechanics development without mentioning Planck. But again, we are talking here not about his (early) *interpretation* of the postulated functional dependence between the temperature of black body and its radiation intensity, but the dependence (the law) itself. Which remains absolutely correct today. For a category like "*History* of quantum mechanics", perhaps this article might be OK to list. But not for the outdated theory that the old QM is. Evgeny (talk) 18:30, 14 March 2023 (UTC)
 * This article has a lengthy "History" section which discusses exactly that. The page is about a topic that reaches from the beginning of quantum theory to the present day, so it qualifies for inclusion in a list or category covering the early decades of the subject. If it doesn't belong in Category:Old quantum theory, it doesn't belong in any other history category either. XOR&#39;easter (talk) 19:21, 14 March 2023 (UTC)
 * The foundational category could be modified into Category:quantum mechanics previous to 1926 or something like that. Of course any historical treatment of quantum mechanics that you provide would include Planck's law as it was originally derived heuristically. However this is no longer the case and the formula is still the result you get from modern quantum statitical mechanics. It think I would agree to add it to the category if it was clear that the article is about the heuristic version and not the modern one, but that's not the case so it is kind of confusing to add it to the old quantum category. Why would it need to belong to more categories? --ReyHahn (talk) 21:05, 14 March 2023 (UTC)
 * If the point of the category is to gather together articles that one should read in order to understand the area, then this is one of them, and it belongs. I think the confusion is minimal; a brief skim of the article itself is enough to tell why it'd be sorted that way. But the total benefit to fiddling around with the categories is perhaps minimal, too. XOR&#39;easter (talk) 00:50, 15 March 2023 (UTC)
 * XOR'easter is right, old quantum theory is a term that refers to a period of physics, which does not imply obsolescence. Plank's law is one of the prototypical examples of old quantum theory, alongside the results of Debye, Sommerfeld, etc... See The Old Quantum Theory by Dirk ter Haar for an overview of topics, the very first one being Planck's Law. I've restored the category.&#32; Headbomb {t · c · p · b} 02:09, 15 March 2023 (UTC)
 * That book clearly addresses Planck's original paper (which is right away in the list of papers in section 2) not our current understanding of the formula. Note that contrary to the other items in the category, Plack's law is the only article that does not say it is obsolete or has been superseded right away by another theory. Does that mean that we also have to add Planck relation, the photoelectric effect and Compton scattering?. Also in one of the books cited earlier, Planck was a separate chapter from the chapter on the old quantum theory.--ReyHahn (talk) 02:37, 15 March 2023 (UTC)
 * "Does that mean that we also have to add Planck relation, the photoelectric effect and Compton scattering?"
 * To have a more complete category, yes. Rutherford scattering, Zeeman effect, Stephan-Boltzmann law, etc... and pretty much every other first quantization results/theory from roughly 1900-1926 (when Heisenberg/Schrodinger got around). You can check the index of that book for a more complete list of topics. &#32; Headbomb {t · c · p · b} 02:45, 15 March 2023 (UTC)
 * I sincerely think that it is not what people usually mean by old quantum theory. It was a theoretical framework and thus a set heuristic formulas that were used to predict some effects and that now it is rarely used. If we have a new version of it based on new quantum theory then it is certainly does not seem old quantum theory. As you currently put it sounds like we are going to end up with merge with Category:Foundational quantum physics and then it is going to remain as loosely defined as that category. Also Stefan-Boltzmann law is not quantum.--ReyHahn (talk) 02:52, 15 March 2023 (UTC)
 * "that now it is rarely used" well yeah. There's been many advances since the time of old quantum theory, specifically second quantization and being able to use Schrodinger's equation. Not everything from it is obsolete, but science moves on and no one uses the Bohr-Sommerfeld model anymore when we can instead solve the relativistic Schrodinger equation directly with many-body perturbation theory and similar techniques.&#32; Headbomb {t · c · p · b} 03:06, 15 March 2023 (UTC)
 * Even if you use second quantization you still get Planck's law for a gas of photons. There is a clear distinction also between articles like BKS, Bohr-Sommerfeld quantization and old atomic models. They are a set of heuristics and rules on how to use them, Planck law is just a formula. If we decide to go that route, please discuss if we should merge both categories and throw in any physics article between 1900-1925.--ReyHahn (talk) 03:20, 15 March 2023 (UTC)
 * @Headbomb, you write that "old quantum theory is a term that refers to a period of physics". I strongly disagree. I believe this is the main point of the discussion. I admit that the respective WP article is not entirely clear about it; if so, it should be (slightly) amended. But if you read it in its entirety, it becomes very clear what is meant. E.g., see the section "Limitations": nothing in it applies to the Planck law. Evgeny (talk) 08:35, 15 March 2023 (UTC)
 * You can disagree, but the sources back what I said, and Wikipedia goes by sources, not personal opinions. &#32; Headbomb {t · c · p · b} 10:59, 15 March 2023 (UTC)
 * Which source says that the Planck law is old quantum theory? Evgeny (talk) 11:02, 15 March 2023 (UTC)
 * See The Old Quantum Theory by Dirk ter Haar mentioned above. It's the very first chapter of the book. &#32; Headbomb {t · c · p · b} 11:05, 15 March 2023 (UTC)
 * Cite an exact sentence. On the contrary, the preface of that book has this very clear: "ALTHOUGH it is well known that for a proper discussion of atomic properties one needs wave mechanics and that the old quantum theory developed by Bohr, Sommerfeld, Kramers and many others between 1913 and 1926 is not a proper basis, there are many atomic phenomena which receive at least a qualitative explanation in the old quantum theory." Where do you see Planck's law in the context of old QM? Yes, of course, Planck's law was what caused the whole QM revolution in physics, that first went through the semi-empiric old QM. But the black-body radiation law is not part of that.
 * Again, "old" is not about a specific time range, but about ideas and models that became outdated. If you write a paper based on those ideas and publish it in 2023 (assuming it passes the peer-review process...), it will still be the old QM. Evgeny (talk) 11:25, 15 March 2023 (UTC)
 * See also Pais (1979): Einstein's 1905 paper on light-quanta is the second of the revolutionary papers on the old quantum theory. The first one was of course Planck's paper (1900b) of December 1900. Helge Kragh is as much an expert on this period as anybody, and also puts Planck under that umbrella: Starting conventionally with Max Planck's work on black-body radiation in the 1890s, the book covers the development of the so-called old quantum theory until about 1923. So do da Costa and French: Thus, another striking example of inconsistency in the 'old' quantum theory is Planck's original derivation of the black body radiation law which involved contradictory classical and quantum hypotheses concerning the energy exchanges between the resonators of the black body and the radiation field itself. Likewise, Pié i Valls and Pérez write, The old quantum theory is considered to start with the appearance of the quantum hypothesis, in 1900, in Max Planck's hands. XOR&#39;easter (talk) 16:18, 15 March 2023 (UTC)
 * Let us avoid continuing to go back and forth between old quantum theory is this or that. Xoreaster and Headbomb have made it clear that Planck original papers on black body radiation are part of the old quantum theory per references: another striking example of inconsistency in the 'old' quantum theory is Planck's original derivation of the black body radiation law (emphasis mine). Evgeny and I have it tried to convey that it is about the original framework used to derive it and not about Planck law itself (see emphasisized line), which remains valid even if using advanced quantum mechanics. The articles currently on Category:Old quantum theory talk about models or heuristics to make calculations, except for Planck's law, which is about the law itself independently of the method used. I find that if we only keep old models and frameworks in that section we would have a more clear idea on what should go in there. If not please discuss how should we handle that category with respect to Category:Foundational quantum physics and if we throw every term pre-1926 in there.--ReyHahn (talk) 16:32, 15 March 2023 (UTC)
 * Here's what I'm failing to get, I think: This article isn't just about the law itself. It also goes into considerable depth about the history. So, why not include it in a category about history, as well as other categories? Conversely, is this article disqualified from any history-of-physics category because the topic reaches to the present day? Doesn't that just make topics essential for understanding the history of physics harder to find? If that is what we want, why is it in Category:Foundational quantum physics? Actually, I'm pretty much flummoxed by  Category:Foundational quantum physics, because that's not an established term, or rather, to the extent that it is established, it means something different. For example, take Tavakoli and Gisin, who derive simple Bell inequalities tailored to be maximally violated for measurement settings pointing towards the vertices of the Platonic solids. In this way, we connect beautiful mathematics with foundational quantum physics. Or Baggott, writing in Physics World: In the three decades since the publication of Bell's article in this magazine, we have witnessed a succession of extraordinary experiments designed to address issues in foundational quantum physics. It is an uncommon term, but when it does appear, it seems to be synonymous with quantum foundations. Bell's theorem would belong, for example, even though it was published in 1964. The Wikipedia category "Foundational quantum physics" was made up by a Wikipedian in 2005, and it has no real grounding in anything beyond Wikipedian whimsy. Is the intended scope really to have the plum pudding model at one end and hyperfine structure at the other? It's got Millikan's oil drop experiment and Dirac's transformation theory. The category description says that it's supposed to contain things that led to the development of quantum mechanics, but quantum mechanics was developed by the time of the Pocono, Shelter Island, and Oldstone Conferences. Is the category also intended to cover everything up through the maturation of QED? It also has some oddballs, like Sherman function and phase-space formulation, that don't fit with that remit either.  In contrast, old quantum theory is a term that scholars actually use, with a well-established time bracket. XOR&#39;easter (talk) 17:31, 15 March 2023 (UTC)
 * Ok I see, I think you are right about that category, it think it is ok we remove foundational quantum physics category. What is your proposal for the criteria for an article to be in Category:Old quantum theory? --ReyHahn (talk) 17:46, 15 March 2023 (UTC)
 * I agree that Category:Foundational quantum physics is very ill-defined. Whereas 'old quantum theory' goes very clearly from Planck (1900) to Heisenberg (1926), 'new quantum theory' being whatever came after Heisenberg (not a very useful category if you ask me), 'Foundational quantum theory', as it exists seems to mostly mean 'historically important things that are related to quantum mechanics from late 1800s (maybe the Zeeman effect is the start of this?) until circa end of WWII/start of Cold War when nuclear/particle physics took off hard and physicists stop caring about the spectra of gases because they had shiny new toys. &#32; Headbomb {t · c · p · b} 20:10, 15 March 2023 (UTC)
 * I give up. Do whatever you want. Evgeny (talk) 07:22, 16 March 2023 (UTC)
 * Why not kill 2 birds with one stone, and create a new article called History of Planck's Law (as the current history section is quite long) then add that article to Category:Old Quantum Theory instead of this one? 63.143.116.78 (talk) 23:14, 21 August 2023 (UTC)

Old quantum theory is not a period. Terminology speaking yes, all formulas and experiments delivered by quantum physics 1900-1926 gave origin or were derived with old quantum theory, even if many of those phenomena are not part of old quantum theory now. However, putting the definitions aside, I can agree with that categorization if we add everything quantum physics in that time window (not including Schrödinger's equation) to Category:Old quantum theory then we will at least be consistent.--ReyHahn (talk) 12:25, 16 March 2023 (UTC)


 * That sounds sensible. XOR&#39;easter (talk) 13:26, 16 March 2023 (UTC)

Equation errors?
It looks to me as though there are errors in at least one of the six "Different forms" equations. When I tried using the form that used wavelength instead of frequency, my answers were ridiculous. I'm not an expert so I don't want to change anything for fear of being mistaken, however a simple substitution of nu = c / lambda in the first equation yields an answer quite different than the equation right below it. I'm hoping someone knowledgeable will see this and take a look. 47.14.123.228 (talk) 18:23, 20 April 2023 (UTC)


 * There is no error. It is not the spectral densities that are equal to each other, but rather their integrals. For this reason e.g. frequency and wavelength forms are related by
 * $$ B_\lambda(\lambda,T)=-\frac{d \nu}{ d \lambda}B_\nu(\nu (\lambda), T),$$
 * which includes a factor from the change of variables. The relation between the different forms is discussed in the text after the table. Jähmefyysikko (talk) 18:59, 20 April 2023 (UTC)
 * Thanks for the clarification. I understand. 47.14.123.228 (talk) 14:47, 26 April 2023 (UTC)

Another Equation Error?
In the fractional bandwidth form for Planck's function, the numerator of the second factor is x4. I think it ought to be x3. The integral of Planck's function w.r.t. &nu; is the Stefan-Boltzmann law, and the coefficient of T4 after integration is the Stefan-Boltzmann constant &sigma;. With the numerator being x4, the constant is wrong, and contains a factor of &zeta;(5). With the numerator being x3 the constant after integration is the Stefan-Boltzmann constant. — Preceding unsigned comment added by Van.snyder (talk • contribs) 04:02, 5 November 2023 (UTC)


 * its distribution with respect to ln(x) so you have an extra x. EditingPencil (talk) 03:16, 6 November 2023 (UTC)
 * Also constants follow from Planck's spectral radiance law for frequency. B_ln(x) = B_nu d(nu)/d(lnx). Please don't mind my lazy reply ;p EditingPencil (talk) 03:22, 6 November 2023 (UTC)

Link to the CGS units
The link to the CGS units links to the page for Radiance rather than csg units. Lounls (talk) 21:46, 14 October 2023 (UTC)
 * Fixed, per WP:EASTEREGG .--ReyHahn (talk) 10:44, 15 October 2023 (UTC)

Bibliography for "Planck, M. (1901)" link not yet available
In Bibliography for "Planck, M. (1901)", as original Ando file is not yet available,

I propose to add a link to a new translated version on wikimedia, which respects as faithfully as possible the form of the german original:

https://upload.wikimedia.org/wikipedia/commons/4/4e/On_the_Law_of_the_Energy_Distribution_in_the_Normal_Spectrum.pdf

( https://commons.wikimedia.org/wiki/File:On_the_Law_of_the_Energy_Distribution_in_the_Normal_Spectrum.pdf ) Malypaet (talk) 21:47, 18 October 2023 (UTC)

Typo on graph
It seems there is a typo error on the ordinate-axis of the spectral radiance graph, namely, numeral 22 should be 2 and numeral 44 should be 4. Esem0 (talk) 06:03, 2 January 2024 (UTC)