Talk:Planck's law: Difference between revisions

Kuhn citation for Planck's views on the UV catastrophe

In The Theory of Heat, Planck comments that the Rayleigh-Jeans law would lead to an infinite amount of radiation. Granted that was written in 1914, but if Planck's views on that changed over time that should probably be noted. Moreover, I read pages 151-152 of Kuhn, and I don't really see how they support the language in the article they are attached to. Chjoaygame, can you comment? Waleswatcher (talk) 00:09, 20 February 2012 (UTC)

The colourful term "ultraviolet catastrophe" was invented by Paul Ehrenfest in 1911. This invention is mentioned in the section of the article headed 'Subsequent events'. This heading means to indicate that there was a time lapse from (a) the discovery and initial explanatory efforts mentioned in the just previous section headed 'Trying to find a physical explanation of the law' to (b) the subsequent events. The section on subsequent events mentions a time lapse of five years, and then a development of Planck's thinking by 1908 and another by 1912 and another by 1919. There is in Kangro's rather detailed history of events no mention of any kind of catastrophe, and Kuhn writes on page 151: "Planck's model, in contrast, seemed free of such difficulties. On page 152 Kuhn writes: "The Rayleigh-Jeans law and what came to be called the "ultraviolet catastrophe" did not yet pose problems for more than two or three physicists." It seems reasonable to read this as meaning that Planck was not one of those two or three in those early days. The present Wikipedia article uses the past perfect tense: "But this had not been part of Planck's thinking, because he had not tried to apply the doctrine of equipartition: he had not noticed any sort of "catastrophe"." This indicates that the thinking of Planck that is referred to was prior in time to the invention of the colourful term by Ehrenfest, and was not in terms of a "catastrophe", specfically marked with quotation marks in the article. The word "catastrophe" does not appear in Planck 1914.

The Wikipedia article, of which I was unaware until I looked it up just now, on the Ultraviolet catastrophe has a section that reads as follows.

Historical inaccuracies

Many popular histories of physics, as well as a number of physics textbooks, present an incorrect version of the history of the ultraviolet catastrophe. In this version, the "catastrophe" was first noticed by Planck, who developed his formula in response. In fact Planck never concerned himself with this aspect of the problem, because he did not believe that the equipartition theorem was fundamental – his motivation for introducing "quanta" was entirely different. That Planck's proposal happened to provide a solution for it was realized much later, as stated above.

Though this has been known by historians for many decades, the historically incorrect version persists, in part because Planck's actual motivations for the proposal of the quantum are complicated and difficult to summarize to a lay audience.

It is common enough to read in unreliable sources implications that Planck's discovery was motivated by a concern to remedy the ultraviolet catastrophe.

For example, at http://physics.about.com/od/quantumphysics/a/blackbody_2.htm, we read: "In 1900, the German physicist Max Planck proposed a bold and innovative resolution to the ultraviolet catastrophe" and "Planck’s solution to the ultraviolet catastrophe is considered ..."

And at http://spiff.rit.edu/classes/phys314/lectures/planck/planck.html, we read about "Planck's solution to the Ultraviolet Catastrophe" and that "Max Planck was aware of the "Ultraviolet Catastrophe"."

And at http://www.egglescliffe.org.uk/physics/astronomy/blackbody/bbody.html, we read: "The failure of these formulae to account for the decrease in energy emitted at short wavelengths (the ultraviolet wavelengths) became known as the ultraviolet catastrophe. A major breakthrough was made by Max Planck who made a formula that agreed with experimental data, ...", as if Planck was working in an environment that spoke of an "ultraviolet catastrophe".

So it seems to me reasonable, in context, that our present Wikipedia article explicitly deny the suggestion that Planck at the time of his discovery was concerned about a "catastrophe".Chjoaygame (talk) 08:17, 20 February 2012 (UTC)

I think you're probably right, but I don't think the Kuhn reference establishes it at all clearly. In any case, by 1914 Planck seems to have known of this (it's not called "catastrophe", but he comments on it). So I think we need to make especially clear that the article is discussing his thinking around the time of 1901. Would you object to adding something like "at the time of XX paper" or "circa 1901" or something like that? Waleswatcher (talk) 11:49, 20 February 2012 (UTC)

No objection to that. Done.Chjoaygame (talk) 14:19, 20 February 2012 (UTC)

Is this correct for angular frequency?

Starting with:

$B_{\nu }(T)={\frac {2h\nu ^{3}}{c^{2}}}{\frac {1}{e^{h\nu /(k_{\mathrm {B} }T)}-1}}$

$B_{\omega }(T)={\frac {2(2\pi \hbar )\left({\frac {\omega }{2\pi }}\right)^{3}}{c^{2}}}{\frac {1}{e^{\hbar \omega /(k_{\mathrm {B} }T)}-1}}$

Doesn't that leave a 2 and a π² in the denominator as in:

$B_{\omega }(T)={\frac {\hbar \omega ^{3}}{2\pi ^{2}c^{2}}}{\frac {1}{e^{\hbar \omega /(k_{\mathrm {B} }T)}-1}}$

not

$B_{\omega }(T)={\frac {\hbar \omega ^{3}}{4\pi ^{3}c^{2}}}{\frac {1}{e^{\hbar \omega /(k_{\mathrm {B} }T)}-1}}$

? I'm tempted to fix this, but there are two other equations with ħ instead of h. Can someone check this and fix it please? I will take it to the expression at Planck units if it gets fixed here. 71.169.186.145 (talk) 22:12, 29 February 2012 (UTC)

See the remark just under the table, about converting Planck's law between different spectral units. Headbomb {talk / contribs / physics / books} 22:18, 29 February 2012 (UTC)

Okay, so we mean intensity per rad/sec vs. Hz, right? Looks like I might have jumped the gun a little at Planck units. 71.169.186.145 (talk) 22:47, 29 February 2012 (UTC)

Correct symbol for spectral radiance is L, not B

Most of the references I can find, as well as the IUPAC Gold Book and Wikipedia itself, use the symbol L for spectral radiance. Robert Hiller (talk) 02:20, 3 March 2012 (UTC)

• Yes, except for the spectral radiance of a black body. PAR (talk) 04:19, 3 March 2012 (UTC)

• I think that the Wikipedia is for reporting things, not arbitrating or deciding what is "correct". It is nowadays conventional to use the letter L for spectral radiance, but I don't think it is appropriate for Wikipedia editors to say that it is "correct" to do so, even in a talk page header. This is without prejudice as to whether the article should use L or B.

It so happens that I agree with PAR that the better symbol for this article is B.Chjoaygame (talk) 06:10, 3 March 2012 (UTC)

• B is the usual symbol for Planck's law, just as Γ is the usual symbol for the gamma function. L is the usual symbol for spectral radiance as the value of B at any given point of its domain, just as x,y are the usual symbols for a real as the value of Γ at any point of its real domain, and z as the usual symbol for a complex number as the value of Γ at any point of its complex domain.

My impression was that B originally stood for brightness, but that these days brightness as a radiation physics term is deprecated as per FS-1037C, so today it should just be considered the usual symbol for Planck's law. It may or may not be a coincidence that B also stands for both black and body. --Vaughan Pratt (talk) 18:44, 3 March 2012 (UTC)

reason for undoing good faith edit

The notation is not perfect, and is unlikely to become so. The edit that I undid was well intended and in some respects reasonable, but was not enough to make an actual improvement in the article. It was an attempt to prescribe for the article a particular notational convention as if it were somehow universal.Chjoaygame (talk) 16:27, 27 April 2012 (UTC)

Spectral Radiance as function of wavelength

Isn't B(lambda) wrong? hc^2/lambda^5 units are J/(m^3 s). Shouldn't it be hc/lambda^3 instead? — Preceding unsigned comment added by 194.65.138.120 (talk) 22:31, 30 April 2012 (UTC)

No, those are the correct. B(lambda) has units of energy/(time*area*wavelength). Waleswatcher (talk) 02:34, 1 May 2012 (UTC)

This apparent strangeness (c^2/lambda^5 where one might expect c/lambda^3) arises from directly substituting wavelength for frequency in a derivative, namely spectral intensity, that has been taken with respect to frequency. One fix (not necessarily the best but it works) is to first undo the derivative by integrating $\nu ^{3}/c^{2}$ to give the radiant intensity $\nu ^{4}/4c^{2}$. Substituting $c/\lambda$ for $\nu$ then gives $c^{2}/(4\lambda ^{4})$, still radiant intensity, whose derivative, now with respect to $\lambda$, is $-c^{2}/\lambda ^{5}$ (back to spectral intensity, but with the sign changed reflecting the fact that $\lambda$ decreases with increasing $\nu$).

Incidentally the article used to draw these distinctions about spectral and radiant intensity. Did some editor find them too weird and confusing for this article? My bad, for "intensity" read "radiance" in the preceding paragraph. Intensity refers to the radiation from the entire radiator, radiance is area density of intensity (quotient of intensity by area of radiator). --Vaughan Pratt (talk) 09:10, 2 May 2012 (UTC)

Excessive complexity, nonstandard notation

Planck's law takes two distinct forms $B_{\nu }$ and $B_{\lambda }$, depending on whether it is expressed as a function of frequency or wavelength. Note that wavelength is not simply a different unit for frequency based on a change of scale but varies with the reciprocal of frequency, resulting in two qualitatively different laws having distinctly different shapes.

Six months ago Wikipedia invented the symbols $B_{\tilde {\nu }}$, $B_{\omega }$, $B_{y}$, and $B_{k}$, apparently by analogy with the notations $B_{\nu }$ and $B_{\lambda }$, in order to have separate laws for each of certain scales for each of frequency and wavelength, some in common use (e.g. cm⁻¹ instead of Hz for frequency) and others much less so.

The counterpart of this for Newton's law F = ma would be to have various subscripts for F and m according to the units used for force (newtons, poundals, etc) and mass (kilograms, grams, pounds, ounces, etc.). This is unprecedented: physics is never organized that way in standard physics texts used in accredited physics courses.

That these notations are nonstandard can readily be seen from the article's sources supporting the annotation "Planck's law expressed in terms of different variables" attached to the article's tabulation of these four trivial variants of the two basic forms of Planck's Law. The three sources are (i) Caniou (the English translation of a French engineering monograph about principles of, materials for, and applications of passive infrared detection devices, Amazon rank 2,832,875, price $381, i.e. ultraobscure); (ii) Kramm and Moelder (a paper by two climate scientists originally written for an Indian math journal that no longer appears on its authors' respective publication lists -- only the unpublished arXiv version seems to exist); and (iii) Sharkov (a monograph on passive remote microwave sensing of the Earth which Amazon ranks 3,433,164 at $345, i.e. at least as obscure as Caniou).

• None of these sources can be considered representative of how Planck's law is customarily taught in accredited physics courses.
• With the exception of Caniou, none of them tabulate a wide range of formulas for different units.
• None of them use these Wikipedia-invented notations.
• The fact that these were the best available sources highlights the inappropriateness of these invented notations.

The only versions of Planck's law needed for this article are those for the two forms of Planck's law, which is how the article was organized prior to the introduction of the six forms of Planck's law. Following universal practice in physics for formulas, these two forms should be given independently of the choice of units, just as F = ma is invariably given as a law that is independent of units. (It should however be noted that the differentials $d\nu$ and $d\lambda$ must be considered part of the respective formulas for the purpose of changing units, since the differentials themselves have dimensions of respectively frequency and length and therefore participate in that scale change.)

What support is there for continuing to introduce Wikipedia readers to Planck's law in the form of a table of six formulas, as done currently? --Vaughan Pratt (talk) 23:17, 3 May 2012 (UTC)

The table was introduced by a particular editor who does not right now need to be named. It was a trojan horse by which he bluffed or bullied people into allowing his fantastic inventions. The table was used because it has undesirable elements of one-size-fits-all inflexibility which suited the trojan horse purpose. Your criticisms of the referencing of the table are justified. I would like to see the table go.

On the other hand I do not accept your rejection of the wavenumber formulation. It was not invented by Wikipedia. One editor wrote that it was common in his line of work. True, it is notationally changed from its sources to conform with the present Wikipedia notation, but that is not "invention". The wavenumber formulation is explicitly stated in what I think is accepted as a reliable source, Paltridge and Platt 1976, and in Caniou 1999, which I think would qualify as reliable (there is no requirement for non-ultraobscurity, and the reference is directly linked to a valid internet source), though, as you say, in different notations.

The literature presentations of the formulas are not in some universal unique notation. It is up to Wikipedia to use what best suits it. I do not agree with the idea that the Wikipedia should limit itself to what is customarily taught in accredited physics courses.

Before the aforementioned unnamed editor's efforts, the article was not limited to two forms of the law. I think it reasonable to allow other forms, in particular forms for energy density, which occur commonly in the literature. And perhaps others.Chjoaygame (talk) 00:46, 4 May 2012 (UTC)

Excellent, 2 votes (counting mine) for eliminating the table, so far 0 for keeping it. Let's see how this progresses.

The possibility Chjoaygame raises of Planck's Law having more than two forms surely depends on the definition of "form." I would say that the unit sphere has the same form in MKS and CGS units, though obviously not the same size, but I'm open to alternative views on this question (though I notice that the sphere article does not list these separately).

There is no requirement for non-ultraobscurity. Let me recommend WP:RS as an excellent read on this topic. Without that guideline Wikipedia editors would be able to cite the most ridiculous sources! --Vaughan Pratt (talk) 03:58, 4 May 2012 (UTC)

I'm not sure what the problem with the table is; at first glance, it appears to be in agreement with the cited source [1]. What is it a Trojan horse for? Dicklyon (talk) 04:29, 4 May 2012 (UTC)

There's a considerable body of literature on Planck's law in the mainstream physics literature, including all the material standardly used in teaching Planck's law. How come Wikipedia has to go to a very obscure engineering monograph on passive infrared detection as its sole support for the idea that Planck's law needs a long table of trivial variants of the two standard formulas? The mainstream texts that treat Planck's law don't do this; for one thing it forces readers to plow through tons of formulas only to discover at the end that they're all describing the same thing at different scales. How can that be considered a clear exposition of Planck's law?

Regarding the "Trojan horse" Chjoaygame was referring to, he may have had in mind that HB had embarked on a major edit war in order to prevent the reversion (by at least two editors) of his replacement of k by k_B. HB came up with the idea of introducing the angular wavenumber k in order to create a notational conflict within the Planck's law article with Boltzmann's constant k so as to justify his k_B replacement. (Personally I'd be fine with k_B in place of k if that were standard in Wikipedia, but it's not, see e.g. Boltzmann's constant.) HB devised his massive rewrite of the article on October 13 for no other purpose than to justify his preferred notation for Boltzmann's constant. This can all be verified (by those with copious free time) by following the long history of the article step by step during that period, along with this supplementary discussion. --Vaughan Pratt (talk) 05:25, 4 May 2012 (UTC)

One cannot read others' minds. Maybe Vaughan Pratt is right, but I am not sure why the unnamed editor wanted to introduce the form of Planck's law that takes reduced wavenumber k as independent variable. But I think it's pretty clear that that's why he introduced the table.

I think there is a good case for prudent selection of reliable sources, not just any source will do; that's why the sources are required to be "reliable".Chjoaygame (talk) 06:26, 4 May 2012 (UTC)

It is very clear - the person wanted to force us to change the Boltzmann constant from k to k_B. Everything in his arguments was driven by that single goal. I support any change that fixes that.

As for $\nu$, in most references this represents frequency, therefore ${\tilde {\nu }}$ is used for wavenumber. When writing programs, it took a long time to get the equations correct because various references used the symbols differently. Therefore, I think it is useful to keep the 3 forms - wavelength, frequency, wavenumber. Q Science (talk) 13:27, 4 May 2012 (UTC)