# Talk:Planck's law/Archive 4

## Recently created opaque context problem

It occurs to me that the switch last week from I(ν,T) and I'(λ,T) to Bν(T) and Bλ(T) respectively creates the inflexibility that expressions can no longer reliably be substituted for either ν or λ without ambiguity. For example we could previously have written I(c/λ,T) and I'(c/ν,T) and no question would have arisen as to their respective meanings. But how are Bc/ν(T) and Bc/λ(T) to be interpreted? The sources we've used to justify this switch would appear to have overlooked this opaque context, aka a failure of referential transparency, which did not afflict the previous notation.

I therefore suggest retaining the prime in the case of the wavelength formula, without however making any other change to what we have now. This would mean writing Bλ(T) as B'λ(T).

Since the prime has been on this formula in the article for years, and since it solves the potential for ambiguity that we created a few days ago with this switch, I don't see any harm in putting the prime back. Comments? --Vaughan Pratt (talk) 09:15, 20 October 2011 (UTC)

Agreed, the old style works better for me.-- cheers, Michael C. Price talk 09:51, 20 October 2011 (UTC)
I agree that Bc/ν(T) is not good. There was suggestion expressed for notations such as ${\displaystyle I_{\lambda }(T)}$ said to be (though not actually) used by Rybicki and Lightman. I posted notation such as ${\displaystyle B_{\lambda }(\lambda ,T)}$, which is used indeed at times by Caniou, but my post was spoken against. I explained that one often enough needs to distinguish the functional form from a value of its spectral argument. No one seemed interested to defend it, so I put it back to ${\displaystyle B_{\lambda }(T)}$ as actually used by Rybicki and Lightman. The ${\displaystyle B}$ notes that we are talking about Planck's black body law. We have also seen notation such as ${\displaystyle B_{T}(\lambda )}$ used by some authors, which has at least the advantage that the spectral argument shown on the abscissa of many graphs is apparent as the spectral argument of the function, with the temperature, constant for the graph, appearing as a parameter indicated by a subscript. The notation that labels the functional form by writing ${\displaystyle I}$ and ${\displaystyle I}$ ′ has the disadvantage that it does not explicitly literally tell the reader which spectral argument is intended, so that the has to know it by heart; moreover it does not give the option of using a diversity of spectral arguments. Thus it makes no allowance for the options of such various possibilities as ${\displaystyle B_{\tilde {\nu }}({\tilde {\nu }},T)}$; perhaps this would have been an advantage in making it impossible to write such abominations as ${\displaystyle B_{k}(T)}$ ! Nevertheless I would like (when we have got rid of ${\displaystyle B_{k}(T)}$ ) to indeed post also ${\displaystyle B_{\tilde {\nu }}({\tilde {\nu }},T)}$ ), and so to retain a notation that gives that option. Although any first year physics student can safely transform these functions to different forms, I do not claim to be so clever, and I am not too proud to be spoonfed in that respect; perhaps I am not alone in that? The use of ${\displaystyle B}$ instead of ${\displaystyle I}$ conforms to the usage of several authors besides Rybicki and Lightman (such as Chandrasekhar, Mihalas and Mihalas, Goody and Yung, Liou) but does not literally tell that the value of the function is a specific intensity, nowadays called spectral radiance and written ${\displaystyle L}$. Some authors make the value of the function a spectral radiant exitance denoted by ${\displaystyle R}$ . If the prime notation is used I would think it more flexible and systematic at least to use not ${\displaystyle B_{\lambda }\ }$${\displaystyle (T)\ }$ but rather ${\displaystyle B\ }$${\displaystyle (\lambda ,T)\ }$ .Chjoaygame (talk) 11:29, 20 October 2011 (UTC)
How to choose amongst the options? I think that here we are concerned mostly to be clear and accurate, with some regard to flexibility. Brevity and convenience for particular uses are I think secondary to clarity and accuracy and flexibility. To me this means that notation such as ${\displaystyle B_{\tilde {\nu }}({\tilde {\nu }},T)}$ is best for our purpose. It is used by Caniou. To be more accurate, indeed Caniou uses not ${\displaystyle B}$ but rather ${\displaystyle L}$ to indicate spectral radiance and perhaps this is the most flexible way to go. Chjoaygame (talk) 17:16, 20 October 2011 (UTC)
We have also seen notation such as ${\displaystyle B_{T}(\lambda )}$ used by some authors Just noticed this (I'm a slow reader sometimes). (a) Is there any interest in having this article follow that style? It makes excellent sense to me. (b) Is there a consensus that the article would still faithfully represent how physicists understand Planck's law after switching to ${\displaystyle B_{T}(\lambda )}$? (c) What are the relevant sources? --Vaughan Pratt (talk) 05:35, 21 October 2011 (UTC)

## Referential transparency via strong typing

I agree with Chjoaygame about not going back to using primes. However I don't see any reason to write a variable twice when (now that I've had a chance to think about it) you can tell which function is intended from the parameter, even when it's an expression. In hindsight I think I was overestimating the referential opacity, in practice expressions tend to be referentially transparent as long as the types are clear.

One reason we're running into this problem is that we're viewing spectral radiance B(s,T) (where s is generically whatever spectral variable we're dealing with, ν, λ, etc.) naively as a function with domain ℝ2 (two reals), which is all that Fortran, MATLAB, and C know about. This limitation has been biting me for the MATLAB code I've been writing to generate Planck's-law graphs, and for each different version of Planck's law I use I've been using a separately named function, almost exactly as Chjoaygame proposes, writing Bν as B_nu, Bν̃ as B_tildenu, etc. In practice however B(s,T) is used with various domains, which more strongly typed languages like Haskell, object-oriented languages, and English handle in stride. Since this article is written in English we shouldn't have to suffer the limitations of those programming languages that can't be extended to have more than one type of real-valued scalar.

The second real can safely be left at Kelvin because spectral radiance is not a derivative with respect to temperature whence conversions from other scales like Celsius, Fahrenheit, and Rankine shouldn't create any problem for users. However spectral radiance B(s,T), and more generally spectral intensity I(s), is a derivative with respect to s (namely of (total) radiance or intensity over an interval [s0,s] where s0 is any convenient constant less than s, zero by default but close to s may give better accuracy when measuring spectral radiance). This complication is obviously creating problems even for the editors, so imagine the plight of the readers.

It is common to give s in a variety of units---MKS, CGS, FPS, etc.---and forms---frequency ν, wavenumber ν̃ = ν/c, wavelength λ = c/ν, or some function thereof such as log(s) (needed when covering more than two octaves of spectrum) or more creatively s/(s+p) (which fits the infinite spectrum into a finite interval with p a constant chosen to be near the spectral peak for optimal shape).

• The system of units impacts all constants and variables in Planck's law containing M or L in their dimension. (But not all combinations, e.g. k/h, which is 20.8366 GHz/degree in all systems, in contrast to k/hc which is .695 cm−1/degree in CGS but 69.5 m−1/degree in MKS.)
• The form of s on the other hand only impacts the influence of s on the law and not any of the constants or other variables (namely T).

One way of handling all this, either somewhere in this article or perhaps in a separate article since it's equally applicable to spectral emittance, spectral intensity independently of temperature, etc., would be as follows.

1. Point out that the system of units needs to be used consistently within the law, as always with scientific formulas.
2. Indicate the range of forms in which s can be given.
3. Point out that the form can ordinarily be inferred from a combination of notation and context. For example c/ν is obviously frequency whereas its reciprocal ν/c is recognizable as the same form as denoted by the variable ν̃.
4. State generally how changing the form of s influences the form of Planck's law independently of the form of s itself (frequency, wavelength, log(frequency), whatever), expressed in terms of the form being modified.
5. Illustrate these influences for the most commonly used cases, in particular wavenumber in units of cm−1, wavelength in units of μm and nm, and logarithmic spectrum in (dimensionless) units of octave (b = 2) and decade (b = 10). For each give the explicit form of Planck's law including the values of the constants. P&P and Caniou both use the notation c1 and c2 for the outer and inner constants, the latter being h/k for frequencies (4.799×10−11 in all systems of units based on the second including MKS, CGS, and FPS but not the furlongs-stones-fortnights system) and hc/k for wavelengths and wavenumbers (1.438775 in CGS units, 1% of that in MKS units), further divided by 2π for all angular counterparts, in particular angular frequency and angular wavenumber.

Typical expressions for items 4 and 5 could include the following. As noted above, s can be anything: wavenumbers, wavelengths, log thereof, etc.

• B(as,T) = B(s,T)/a (so B(ν̃,T) = cB(ν,T) given ν̃ = ν/c)
• B(1/s,T) = −s2B(s,T) (so B(ν̃,T) = −λ2B(λ,T) and νB(ν,T) = λB(λ,T))
• B(ln(s),T) = B(s,T)/s (more generally B(logb(s),T) = ln(b)B(s,T)/s)
• B(s/(s+p),T) = (s+p)2B(s,T)/p

If any of this is treated in this article, it would have to go somewhere after the formulas for B(ν,T) and B(λ,T) (or Bν(T) and Bλ(T) if that's what we prefer), since the Planck's law article should start out as straightforwardly as possible, without the distraction of the above gory details of the care and feeding of spectral variables.

Alternatively Wikipedia seems to like breaking up big articles into smaller ones and this seems like a fine candidate for its own article, especially given the lack of involvement of temperature T. Obviously item 5 (the parenthetical remarks after the examples for item 4) belongs to this article, so a link in this article to the more general article elsewhere, followed by how to handle the traditional constants c1 and c2 specific to Planck's law, might be one reasonable organization. --Vaughan Pratt (talk) 23:36, 20 October 2011 (UTC)

True, while you write ${\displaystyle B(\nu ,T)}$ , you can tell which function is intended, but when you get to want to write something like ${\displaystyle B(c/\lambda ,T)}$ , it may no longer be so obvious unless you have a good memory.Chjoaygame (talk) 00:32, 21 October 2011 (UTC)

Fair enough, but at least the ambiguity due to referential opacity has been resolved, which was my original problem.

I would be happy with either ${\displaystyle B(\nu ,T)}$ or ${\displaystyle B_{\nu }(T)}$, but I'm not yet convinced there's an urgent need for ${\displaystyle B_{\nu }(\nu ,T)}$. Assume the subscript form ${\displaystyle B_{\nu }(T)}$, and suppose you've written say ${\displaystyle B_{c/\lambda }(T)}$. Alert readers would deduce from the units of c being length/second and those of λ being length that the units of c/λ must be sec−1. But that's not good enough because not all your readers are that alert and you worry they may be unable to recognize ${\displaystyle B_{\nu }}$ in that form. In that case what you do is write it as "${\displaystyle B_{\nu }(T)}$ where ${\displaystyle \nu =c/\lambda }$."

Before I raised the possibility of writing ${\displaystyle B_{c/\lambda }(T)}$, that longer form was the only possibility with the ${\displaystyle B_{\nu }(T)}$ notation we adopted recently. So it's not like I'm proposing to tie anyone's hands by extending the language in this way. The point of the extended language allowing ${\displaystyle B_{c/\lambda }(T)}$ is not for more articulate communication with a broad audience, who will prefer "${\displaystyle B_{\nu }(T)}$ where ${\displaystyle \nu =c/\lambda }$" for its clarity, but for writing out relationships between functions, which is the sort of thing only a formalist interested in these definitions could love and certainly not a broad audience, as you say (if I understood you). --Vaughan Pratt (talk) 04:46, 21 October 2011 (UTC)

## Even simpler

Instead of the type-checking approach I was advocating above, it seems to me that an even simpler approach is possible, using just two elementary ideas.

1. Position in the spectrum is uniquely determined by either frequency or wavelength. Hence the total flux over any interval of spectrum is determined by that interval regardless of the form in which its endpoints are presented. If presented as frequency for example, we immediately know the wavelength, and therefore we can assume that whenever we are given one we have the other.

2. It is the horizontal scale that makes all the difference. The three main possibilities are that it is linear in frequency, linear in wavelength, or logarithmic in frequency and hence wavelength (or vice versa). This choice governs both the shape and the position of the peak relative to other features of the curve such as it median power.

Only the latter influences whether Bν or Bλ is the appropriate function. Whether it is ν or λ that is passed as the argument is irrelevant since either one determines the other. --Vaughan Pratt (talk) 09:41, 23 October 2011 (UTC)

## formula for wavenumber or angular frequency

The new edit by Vaughan Pratt is for an argument angular frequency ${\displaystyle \omega }$, but this is not the wavenumber formula that was requested by Q Science, and indeed is not a wavenumber formula at all. It is as stated a formula for angular frequency. This is for a section called common forms. It is an entire newcomer to the present conversation, and this doesn't look like evidence that it is in fact a common form. I think the formula that Q Science would be interested in (I trust I don't misrepresent him?) is about spectroscopists' wavenumber which Caniou lists with the symbol σ , while we have been writing ${\displaystyle {\tilde {\nu }}}$ till now, in agreement with the Wikipedia article wavenumber#In spectroscopy . Q Science has noted a difference in detail between σ and ${\displaystyle {\tilde {\nu }}}$ .Chjoaygame (talk) 00:47, 21 October 2011 (UTC)

It may help to note that Caniou has a rather special way of stating his formulas, and that when this is taken into account, Caniou's wavenumber formula does reduce to the one that I originally posted.Chjoaygame (talk) 00:52, 21 October 2011 (UTC)

Caniou p.117 (ref [4] in present version) has two formulas, one for angular frequency (units W/m2/sr/(rd/s)−1 and the other for wavenumber (units W/m2/sr/cm−1 if mixed MKS and CGS units are used, otherwise W/m2/sr/m−1 if straight MKS). The formula B_k labeled "wavenumber" seemed a better match to the former, so I corrected it to agree with that one. However it seems to me that most spectrograms use the latter (with mixed units making area m2 and spectrum cm−1), and that the latter should really be the one in the article (in which case "angular frequency" can go back to "wavenumber" which is defined in Caniou as 1/λ (= ν/c). Should we put both formulas in, or just Caniou's second one on p.117, the one for wavenumber, on the ground that this is the one more likely to be wanted? (Caniou's mention of ${\displaystyle B_{\omega }}$ is the first time I've ever heard of this form of Planck's law.)
Chjoaygame or Q Science, if you'd prefer the second one (for wavenumber) I'm 100% in favor, feel free to make the change. Except for his use of σ as the variable for wavenumber, which will need to be changed to avoid the conflict with the Stefan-Boltzmann constant, the formula in the book is exactly what you would expect it to be for wavenumber (as Chjoaygame observed just now, modulo "special way"). --Vaughan Pratt (talk) 00:56, 21 October 2011 (UTC)
Incidentally. if people do want the wavenumber formula, please feel free to change the first Caniou formula on p.117 to the second (wavenumber) one, which is the one standardly used in spectroscopy. I've seen thousands of spectrograms with wavenumbers of cm−1 for thermal energy spectra but never a single one with angular frequencies, which in the context of thermal energy is a novel unit for me, despite meeting a wide range of physicists at Stanford. A few days ago I gave a hypothetical scenario where angular units might be relevant, namely for thermal energy being routed through some sort of wave guide, but I've never actually seen anyone perform such an experiment or theorize about it. Such an experiment would certainly be the place to look for an example of the use of angular anything in conjunction with thermal emission.
Meanwhile anyone looking at a standard spectrogram with cm−1 on the horizontal axis is going to come away empty handed from the article as it presently stands. If you're serious about your customer, Chjoaygame, I'll support any action of yours on his or her behalf that you feel is warranted.
If no one wants the cm−1 formula I don't mind letting the formula with the interesting 8π4 denominator stand in its place for the time being as being the intended Caniou formula on p.117 cited by reference [4] (which could refer to any of the three formulas on that page). I like formulas for which there is only one source in the world, if only because of the statement they make about Wikipedia's ironclad sourcing policy, an interesting difference from every other major encyclopedia in the world. Not a great reason, but one I'll live with for now until someone decides there's a better formula from Caniou p.117 for this article, to which I will most definitely not object. --Vaughan Pratt (talk) 05:26, 21 October 2011 (UTC)
Done.Chjoaygame (talk) 07:40, 21 October 2011 (UTC)
Great, thanks. I suspect more than just your "customer" will be grateful for that, given that it's the gold standard horizontal axis in spectroscopy. --Vaughan Pratt (talk) 22:52, 21 October 2011 (UTC)

## Location of history section

I would have thought something about Planck's law itself should precede the history section. I checked a dozen Wikipedia articles on the major physics laws and principles of the last two centuries (Maxwell's equations, Stefan-Boltzmann law, etc.) and was unable to find a single one besides this one that started out with the history.

Who here would like the history section to be the first thing following the table of contents, and who would like it somewhere else?

If no one has any strong feelings either way on the location of the history section for a major recent law of physics, I propose to move it to somewhere closer to the average of where other such articles tend to put it. --Vaughan Pratt (talk) 05:59, 21 October 2011 (UTC)

It's pretty standard on wikipedia to start an article with the history. IRWolfie- (talk) 22:09, 22 October 2011 (UTC)
You mean no matter what kind of article? I can understand that about many kinds of articles, but this is an article about a recent (last two centuries) law of physics. What proportion of Wikipedia articles about recent physics laws would you say started out with the history? The first twelve I picked at random all had their history sections somewhere between the middle and the end. Do you have evidence to the contrary? --Vaughan Pratt (talk) 09:17, 23 October 2011 (UTC)
Which twelve? IRWolfie- (talk) 15:26, 23 October 2011 (UTC)
Vaughan Pratt led with two explicit and good examples and a number that he had checked. IRWolfie followed with an unsubstantiated "It's pretty standard ...". Now IRWolfie in two words is asking Vaughan Pratt for more detail, but has not told us about any research that he might himself have done. It's his turn to tell us some details of his findings. Vaughan Pratt has no duty to tell us more till IRWolfie does his stuff.Chjoaygame (talk) 15:40, 23 October 2011 (UTC)
This is childish. Large important articles like Electromagnetism, Nuclear_physics, Quantum_mechanics, Quantum_field_theory, Astrophysics, Optics and many more all have history sections at the front. IRWolfie- (talk) 16:40, 23 October 2011 (UTC)
General subjects tend to have history first, articles about specific equations, not. Electromagnetism, history first, but Maxwell's equations not. Quantum mechanics, history first, but Schroedinger's equation not. Quantum field theory, history first, Dirac equation not. etc. I could see the black body article having history first, but Planck's law not. PAR (talk) 15:15, 24 October 2011 (UTC)
Thank you IRwolfie for eventually giving us your findings.Chjoaygame (talk) 20:40, 23 October 2011 (UTC)

Explanation of what the law is should precede the history of it. Just commonsense. -- cheers, Michael C. Price talk 15:44, 23 October 2011 (UTC)

I agree. Especially such a detailed history section should not appear first, even if it were conventional to put the history section first. You don't want to go into details about e.g. the subtle differences between Planck's model and Bohr's model (both are historic now, being replaced by quantum mechanics), before explaining the physics as it is currently understood. Count Iblis (talk) 16:27, 23 October 2011 (UTC)
Sounds like strong support for moving the history section down. However before I do so, let me respond to IRWolfie, who reasonably enough asked me for the other ten articles on recent laws and principles of physics (besides Maxwell's equations and Stefan-Boltzmann law). Running down the Table of Contents for Vol. 2 of Halliday and Resnick and just picking out laws without first looking at their Wikipedia articles, how about Gauss's law, Coulomb's law, Ohm's law, Hall effect, Ampere's law, Faraday's law, Doppler effect, Bragg's law, Biot-Savart law, Lenz's law, and Poynting vector. That's it for the contents, but meanwhile I also thought of Wien's law, Rayleigh-Jeans law, Fick's law, Schroedinger's equation, Laws of thermodynamics, Pauli exclusion principle, and Le Chatelier's principle. Ok, that's 18, plus Maxwell and Stefan-Boltzmann make 20. Ok, now let's check the Wikipedia articles.
As it turns out, 2.5 of these do start with their history section, namely Hall effect, Rayleigh-Jeans law, and one of the two laws under Faraday's law. So if IRWolfie had looked at those first he might well have come away with the impression that all articles on laws of physics start with the history section, bearing out his claim that we're being "childish." However the other 17.5 don't. Furthermore there seems a strong sense here that one ought to explain the law itself before talking about its history.
So I will move it accordingly. --Vaughan Pratt (talk) 07:27, 25 October 2011 (UTC)
As I have shown above many physics articles do start with the history section. It is perfectly acceptable to do so. There is nothing that needs to be explained in the history section that is explained first in another section. No concensus has been reached for any move. Also you cherry picked your own articles for example it is not suprising that they do not start with a history section. I suggest an RFC be called on any move. IRWolfie- (talk) 08:57, 25 October 2011 (UTC)
What I said was "Running down the Table of Contents for Vol. 2 of Halliday and Resnick and just picking out laws without first looking at their Wikipedia articles." You accuse me of "cherry picking". How is the procedure I followed cherry picking? While I was doing that other laws kept occurring to me and I just wrote them down without first checking the Wikipedia articles, making my sample of 20 articles about physics laws reasonably unbiased. If anyone is vulnerable to that charge it is you, since you didn't give your procedure for how you chose your articles. Furthermore you chose articles of a kind likely to have the history section at the front instead of articles on physics laws, how is that not "cherry picking?" --Vaughan Pratt (talk) 03:03, 26 October 2011 (UTC)

I have restored the original location of the history section. We do not need a new consensus to keep it there. You need a new consensus to move it to the beginning of the article. Q Science (talk) 09:04, 25 October 2011 (UTC)

To repeat what I said above, the articles you listed are general in nature. General subjects tend to have history first, articles about specific equations, not. Electromagnetism, history first, but Maxwell's equations not. Quantum mechanics, history first, but Schroedinger's equation not. Quantum field theory, history first, Dirac equation not. etc. Planck's law is in the second category. PAR (talk) 12:41, 25 October 2011 (UTC)
I agree with Vaughan Pratt and Michael C. Price and Count Iblis and Q Science and PAR.Chjoaygame (talk) 14:15, 25 October 2011 (UTC)
Given that only one quarter of the voters to date, namely 2 out of 8, want to move the history section to the beginning, it would seem preferable to leave it where it has been throughout the five years preceding last week's move of it to the beginning. But I admit I am impressed at the persistence of such a distinct minority, which does not seem at all in the spirit of Wikipedia. --Vaughan Pratt (talk) 03:03, 26 October 2011 (UTC)
Are you saying that the spirit of Wikipedia is that minorities should be silent?Chjoaygame (talk) 10:59, 26 October 2011 (UTC)

## History Section

I think the history section is too large for this article and should be moved to a new article "History of Planck's Law". The present section should be replaced by a condensed history and a "main article" link to the more complete history article. I will do this soon if nobody objects. PAR (talk) 03:22, 22 October 2011 (UTC)

Either way is fine by me. At 46 kB the article is not unreasonably long, but the history section is quite substantial. --Vaughan Pratt (talk) 08:59, 22 October 2011 (UTC)
Err a bit of discussion would be nice before you remove a large chunk of the article. The history section was a reasonable size, I see no reason for the splitting of the article. IRWolfie- (talk) 22:08, 22 October 2011 (UTC)
Agree with IRWolfie here. Planck's law does not have a history so large that it needs to be covered in a different article. It could perhaps use some subsections however. One subsection for the background and early attempts to characterize black bodies, one subsection for the postulation of Planck's relation + how it leads to Planck's law [aka what Planck did], one subsection with the implications to quantum mechanics (relation to photoelectric effect, development of photon statistics). 00:22, 23 October 2011 (UTC)
The vote looks like leave it where it is, so ok. PAR (talk) 02:07, 23 October 2011 (UTC)
I wasn't aware that we'd taken a vote. Headbomb was the one who claimed all articles have their history section at the beginning, and IRWolfie agreed with him. That's two in favor of the move. Chjoaygame moved the history section back to later in the article. I voted in favor of that move on the ground that, out of more than a dozen Wikipedia articles on major physics laws and principles of the past two centuries, this article is the only one to start with the history section. That's two against moving it to the front. Unless the tie is broken one way or the other, the original move is hard to justify if there's a tie in the voting. Any other voters, either way? However this turns out, there should be some uniformity in Wikipedia on this point, so if being at the front is the correct location we should make the same move in all the other articles on physics laws and principles. --Vaughan Pratt (talk) 00:41, 25 October 2011 (UTC)
History should come somewhere after a summary. It could come at the end as an appendix. The important thing is to have a link in the contents so the reader can find it. If I was to "vote", it would be to return the article to where it was in September before all this disruption and then to move forward with discussion and consensus. I particularly don't like the way the references were changed without any discussion at all. Q Science (talk) 06:39, 25 October 2011 (UTC)
Yes, that unilateral changing by Headbomb, of many things besides just the references, and his reverting of every attempt to undo his many changes without pausing and discussing it on the talk page as per WP:EW, was incredibly rude. Oddly enough it was not Headbomb that was threatened on his talk page with being blocked for his behavior but me for trying to find a way to cope with it without taking the easy way out by taking it to WP:ANI, who have quite enough on their plate already and also lack the expertise relevant to this article. I've been editing Wikipedia for years but this is the first time anyone's threatened to block me. --Vaughan Pratt (talk) 07:48, 25 October 2011 (UTC)
Don't feel bad, I've been threatened a couple of times for far less. I suggest trying your edits again. When we disagree, we can discuss why here. Q Science (talk) 08:56, 25 October 2011 (UTC)
Perhaps if you didn't try your best to make the conflict personal and take every opportunity to depict me in the least charitable light possible, such are you just did above, you wouldn't end up with threats of being blocked. 07:04, 26 October 2011 (UTC)

## we know better than Planck

The new version of Planck's archaic story uses ${\displaystyle N}$ because it is "more modern". But it is unsourced. Sources differ. For example, Eisberg, R.M. (1961), Fundamentals of Modern Physics, Wiley, New York, page 131, uses ${\displaystyle n}$, as does Ram, B. (1974), Presenting the Planck's Relation ${\displaystyle E=nh\nu }$, American Journal of Physics 42: 1092-1094, and as do Bransden, B.H., Joachain, C.J. (1963), Physics of Atoms and Molecules, Longman, London, on page 17, and as does Loudon, R. (2000), The Quantum Theory of Light, Oxford University Press, Oxford UK, ISBN 0-19-850177-3, on page 1. Perhaps there are others? Historical accounts, such as Stehle, P. (1994), Order, Chaos, Order, Oxford University Press, New York, ISBN 0-19-507513-7, page 122, and such as ter Haar, D. (1967), The Old Quantum Theory, Pergamon, Oxford, page 12, and such as Kangro, H. (1976), Early History of Planck's Law, Taylor and Francis, London, ISBN 0-85066-063-7, page 218, and such as Murdoch, D. (1987), Niels Bohr's Philosophy of Physcis, Cambridge University Press, Cambridge UK, ISBN 0-521-33320-2, page 2, struggle on with Planck's archaic ${\displaystyle P}$. I didn't find a source with ${\displaystyle N}$, but perhaps Michael C Price did?Chjoaygame (talk) 16:31, 23 October 2011 (UTC)

Why is it important if N or n is used or not if the meaning is just as clear? IRWolfie- (talk) 16:44, 23 October 2011 (UTC)
Chjoaygame, I should have thought you would have got it by now; you don't need sources for the symbols.-- cheers, Michael C. Price talk 17:08, 23 October 2011 (UTC)
Why is it important if P is used or not if the meaning is just as clear?Chjoaygame (talk) 20:37, 23 October 2011 (UTC)
Because it isn't. -- cheers, Michael C. Price talk 21:18, 23 October 2011 (UTC)

## time to act

Headbomb has restored the angular wavenumber version.

This version violates the rule against original research, because it is not the product of a mere routine calculation. It was apparently created by Headbomb himself, as shown by his statement quoted above "verify this one, since I might have done the conversion quickly." This comment by Headbomb, combined with with the statement in the article about conversion of forms (which requires differentiation), shows that indeed it is not the product of a mere routine calculation as defined by the Wikipedia article on the question.

Whether or not this version is original research, it is not suitable for entry in a section on common forms. That it is not a common form is shown by the failure of anyone to find it in the literature. Even if it were to be found in future, such a find would not make it a common form, because the delay in finding is good evidence of uncommonness.

One wonders did Headbomb read the above warning by Vaughan Pratt? Unless Headbomb himself removes this entry forthwith, surely some action seems warranted?Chjoaygame (talk) 20:11, 31 October 2011 (UTC)

If there is no serious disagreement, I think it is also time to restore the common symbol for the Boltzmann constant that is used in all the references. Q Science (talk) 20:25, 31 October 2011 (UTC)
The OR in here isn't a problem per se, it's more the fact that the lack of sources in this case points to the form not being notable enough for inclusion in this article. We should reserve the right to do the type of mathematical derivations needed to write this sort of an article, otherwise the derivation section should also be removed, as it uses techniques that differ a bit from the usual sources, like avoiding the use of the partition function for the full system that involves and infinite product and instead considering a partition function for a single mode.
If the B_k formula is removed, then we can replace k_{B} by k as Q Science suggests. To me k looks better than k_{B}, but that's more an aesthetic issue. What we should not do, is go to AN/I and ask for Admin intervention, because that only leads to behavioral issues being put under the microscope, which moves us further away from actually editing this article. Count Iblis (talk) 21:36, 31 October 2011 (UTC)
Vaguely agree with Count Iblis that to request Admin intervention is perhaps unlikely to be the best action.Chjoaygame (talk) 21:45, 31 October 2011 (UTC)
Expressing formulas in terms of different quantities is the very definition of a routine calculation. Expressing something in terms of 2π/λ is no more original research than expressing it in terms of 1/λ is. It's a rescaling by a factor of 2π for fuck's sake. I can't fathom how this could be even remotely construed as controversial... I asked for help at WT:PHYS to restore sanity on this article. 22:03, 31 October 2011 (UTC)
What Headbomb said. Multiplying through by the appropriate number of factors of 2π has to be close to the very definition of a routine calculation, as permitted per WP:OR and WP:SCG.
Now one can discuss, as a question of editorial judgement, whether including this version of the formula is either a valuable addition or is alternatively just unnecessary additional baggage. (Physicists tend to think in terms of wavenumber k, spectroscopists/chemists in terms of inverse wavelength; one thing that can perhaps be a gotcha, so may count towards giving the formula explicitly, is the extra factor of 2π that arises because you are giving spectral radiance per wavenumber, rather than spectral radiance per inverse frequency). That's a discussion we can have. But there's no way this counts as what WP considers OR: the example okayed at WP:SCG#Examples, derivations and restatements is explicitly of this type. Jheald (talk) 22:28, 31 October 2011 (UTC)
Having read through more of the discussion though, I am tending towards "unnecessary additional baggage", of limited real-world value. Maybe the formula using k could be dumped in a footnote? Jheald (talk) 22:58, 31 October 2011 (UTC)
Ideally, one would present Planck's law in terms of "plain jane" quantities with h, (${\displaystyle \nu ,\lambda ,{\tilde {\nu }}}$) and angular quantities with ħ, (${\displaystyle \omega ,y,k}$) [note: I'm using y because it seems Wikipiedia doesn't support \lambdabar], in a table similar to this one. 22:55, 31 October 2011 (UTC)
Updated with table. I also reduced unnecessary verbosity which were more similar to rambling rather than concise summary of properties. We could probably add the peaks of those distribution to the tables, but it's getting late here and I don't feel like crunching numbers at this hour. 05:31, 1 November 2011 (UTC)

I'm very impressed at just how incredibly complicated one can make Planck's original formula when one works hard at it. Let me argue here for getting the "Common forms" section back to its original simplicity.

The two notations I and I′, or the more trendy ${\displaystyle B_{\nu }}$ and ${\displaystyle B_{\lambda }}$ the article switched to a couple of weeks ago, get different names because they aren't linearly related, even though they're related by ${\displaystyle \nu B_{\nu }=\lambda B_{\lambda }}$. The analogous situation arises in trigonometry with sin and cos, which aren't linearly related and are notated separately, even though they're related by ${\displaystyle \sin ^{2}+\cos ^{2}=1}$.

That can't be said of the other ${\displaystyle B_{x}}$ notations that have been accumulating in this article over the past couple of weeks, all of which have been simply a constant times one of the above two forms. The notations and don't exist outside this article for the same reason there aren't separate notations for π sin(x) and e sin(x). Instead one simply sticks the appropriate constant in front of the formula. The same holds for the fifth and sixth formulas that Headbomb has just added.

For example what Chjoaygame has christened the "spectroscopist's wavenumber" is just ${\displaystyle cB_{\nu }}$. Furthermore spectroscopists accustomed to units of W/m2/sr/cm−1 will find the value of this formula in error by a factor of 100 with MKS units and 10000 with CGS units! (The article should point out that spectroscopists working with MKS units should use ${\displaystyle 100cB_{\nu }}$ for agreement with typical spectrograms.)

Likewise what Headbomb has denoted by ${\displaystyle B_{k}}$ is some constant times ${\displaystyle B_{\nu }}$, but in this case the question of whether it's off by a factor of 100 or 10000 does not arise because so far no one has produced an example of such usage to compare with. Not only is it not common in the literature, neither the concept nor the name ${\displaystyle B_{k}}$ has been seen anywhere in the literature, for the simple reason that no purpose is served by angular frequency, angular wavelength, or angular wavenumber (the entire right column of Headbomb's table) in the context of simple black body radiation. Are the formulas in the right column as easily derived as Jheald claimed? Judging by Headbomb's protracted difficulties in getting the formula for angular wavenumber right, apparently not. Are they notable? That Headbomb is the first to have noted Planck's law for either angular wavelength or angular wavenumber hardly seems sufficient grounds for notability.

The top left right entry for angular frequency does appear in Caniou's table of half a dozen forms of Planck's law. However I would claim that one appearance in a table listing six forms, that is not used elsewhere in either Caniou's book or anywhere else in the literature, is not enough to qualify it as notable.

My own preference FWIW would be to keep the article simple by not inventing new notations that can't be found anywhere in the literature, and not giving elaborate formulas that obscure the elementary fact that all the proposed "common forms" are nothing more than constant multiples of the two basic forms.

Responding to Headbomb's We could probably add the peaks of those distribution to the tables, but it's getting late here and I don't feel like crunching numbers at this hour, there is nothing to "crunch." Every spectrogram that has ever appeared in the last two hundred years of literature, predating Planck's law by a century, has depended either linearly or logarithmically on either frequency or wavelength, and these four combinations have only three peaks, not four, because the logarithmic peak is (very conveniently) the same for frequency and wavelength. The six formulas in Headbomb's table have only two peaks because none of his formulas include the logarithmic dependencies, which have been found useful for example when presenting the solar and terrestrial radiation curves together. A number of climate articles have taken advantage of this to plot the bimodal distribution of the 30% reflected sunlight and 70% terrestrial radiation from Earth, which is quite impractical with either of the two linear dependencies.

In the process of replacing the "Common forms" section with his table, he's also deleted a number of important facts in what was there before, and has replaced them with false statements such as "The emission does not depend on direction" which contradicts Lambert's cosine law.

I don't know about anyone else, but coping with Headbomb's habit of deleting other people's contributions (he's deleted all mine in the past two weeks on the ground that he's right and I'm wrong, with no constructive discussion entered into, merely flat contradiction) has been a giant timesink for me. Chjoaygame's title for the preceding section of the talk page seems very apt at this point. I believe Headbomb's insistence on charging ahead and editing instead of engaging in discussion when it's obvious he has a lot of opposition, combined with his evident lack of any deep understanding of the subject, meets Wikipedia's definition of disruptive behavior. Comments? --Vaughan Pratt (talk) 06:42, 1 November 2011 (UTC)

Agreed. We have been through this several times now and the consensus is pretty clear. Q Science (talk) 06:59, 1 November 2011 (UTC)

## spelling

As you rightly indicate,'in spite of' should be three words. Punctate is an adjective that means 'having the nature of a point', punctum, it is not the verb punctuate. Ponderable comes from ponderare, first conjugation, spelt with an a.Chjoaygame (talk) 06:39, 31 October 2011 (UTC)

Punctate, punctum, ponderable are all stupid words to use, if you're having to explain them here. (And of course, this isn't the first time you've been reminded of this.) Are they on Wikidictionary?-- cheers, Michael C. Price talk 06:52, 1 November 2011 (UTC)
Sorry Chjoaygame but I have to take MP's side on this one. Lawyers used to write in legalese until it dawned on them that obfuscation was counterproductive in the real world. Hopefully the medical profession will follow suit. Clarity of exposition should be a top level goal for Wikipedia. --Vaughan Pratt (talk) 07:14, 1 November 2011 (UTC)

## eponyms free for all

Never mind that it is not quite clear which relation we are talking about, or that we have no duty to promulgate or dictate dubious eponymous nomenclature. We started, in the history section, with the unsourced eponym "Planck relation". To cover up our lack of source, we talked about the "Planck-Einstein relation", again without giving a source. We have replaced that with the now posted unsourced "Einstein-Planck relation". Why stop there when we could add the "Planck-Einstein equation" used by Kirkpatrick, P. (1980), Confirming the Planck-Einstein equation ${\displaystyle h\nu }$=(1/2)mv2 , Am. J. Phys., 48: 803-806 ? Why should the Wikipedia provide information more selective than would a trip down Google books? Chjoaygame (talk) 21:27, 23 October 2011 (UTC)

This 1974 article by Budh Ram uses the term to refer to E = nhν, and it may well be the original source. So far I've been unable to find any reputable source other than Cohen-Tannoudji for the use of it to refer to E = hν. Once something is claimed in Wikipedia it ends up all over the web, making the web an unreliable source. Chjoaygame, do you have other sources for Budh Ram's usage? --Vaughan Pratt (talk) 00:52, 25 October 2011 (UTC)
Like you, my nearest thing to a source was the Ram article. Bearing in mind the general rule to try avoid eponyms, I wouldn't see that article by itself as a reliable source to establish or promulgate an eponym. My initial list of possible sources is
Ram, B. (1974), Presenting the Planck's Relation ${\displaystyle E=nh\nu }$, American Journal of Physics 42: 1092-1094 refers to Planck oscillators and does not mention photons.
Schwinger, J. (2001). Englert, B.-G., ed. Quantum Mechanics: Symbolism of Atomic Measurements. Springer. p. 203. ISBN 3-540-41408-8. Schwinger is quoted as calling the relation ${\displaystyle E=h\nu }$= ħω "Planck's energy-frequency relation". The context is simply wave-functions for force-free motions, with no mention of either photons or Planck oscillators.
French, A.P., Taylor, E.F. (1978), An Introduction to Quantum Physics, Van Nostrand Reinhold, ISBN 0-442-30770-5, on page 24 writes "the Planck-Einstein relation:
${\displaystyle E_{\mathrm {photon} }=E_{i}-E_{f}=h\nu }$ ." There is some genuine historical support for the latter relation being widely called 'Bohr's frequency condition' or the like.
On page 55, they write "the Planck-Einstein relation ${\displaystyle E=h\nu }$ for photons".
Razeghi, M. (2009), Fundamentals of Solid State Engineering, Springer, ISBN 978-0-387-92167-9, on page 77 writes: "Planck's relation for the irradiance of a blackbody ${\displaystyle I(\lambda )={\frac {2hc^{2}}{\lambda ^{5}}}{\frac {1}{e^{\frac {hc}{\lambda k_{b}T}}-1}}.}$ ".
Schumm, B.A. (2004), Deep Down Things: the Breataking Beauty of Particle Physics, Johns Hopkins University Press, Baltimore, ISBN 0-8018-7971-X, on page 34 writes of "Planck's relation ${\displaystyle E=hf}$", as pointed out by Headbomb. This particular citation of the eponym is in the context of tying Einstein and de Broglie together.
Mehra, J., Rechenberg, H. (1982), The Historical Development of Quantum Theory, Springer, ISBN 0-387-95174-1, uses the phrase 'Planck's relation' on page 102 in footnotes to refer to ε = h${\displaystyle \nu }$, and on page 125 to refer to the relation between ${\displaystyle \rho _{\nu }}$, the energy density of blackbody radiation, and the oscillator energy, which doesn't seem exactly to be our target relation. This makes it seem that the authors are using the term descriptively rather than as an established eponym.
But I don't find the eponym 'Planck's relation' widely and consistently used in what I generally find to be reliable sources. I haven't researched 'Einstein-Planck relation', but neither have I noticed it in my reading.Chjoaygame (talk) 05:01, 25 October 2011 (UTC)
LIGHT WEIGHS 2008, Progress In Electromagnetics Research B - Planck-Einstein equation - E=hν Q Science (talk) 05:41, 25 October 2011 (UTC)
I am not denying occasional use of names in various ways. I am just saying that we have no duty to promulgate eponymous nomenclature, and that in general, generation of eponymous nomenclature is to be frowned upon, and that most reliable sources do not make a habit of speaking of 'the Planck relation' or of 'the Planck-Einstein relation'. I have just now more or less read the paper by Puccini. I don't think my detailed comment would be valuable here.Chjoaygame (talk) 08:21, 25 October 2011 (UTC)
One reason for avoiding unnecessary eponymous nomenclature: in general it is frowned upon; Wikipedia should aim to set an example of good practice, not bad. Google for me gives top bill to "EPONYMOUS nomenclature for diseases has its advantages; it is a convenient cover for ignorance of the nature of a disease." Next is "In response to my example why eponymous nomenclature is bad..." A little further on "Authorities continue to recommend the suppression of eponymous nomenclature..." A little further on "in general the abolition of eponymous nomenclature is favoured." And tenth and last on that page "movement has been towards the elimination and discouragement of eponymous terms".Chjoaygame (talk) 19:04, 25 October 2011 (UTC)
A reason why it is not indicated here. This is an article about Planck's law, and the term 'Planck's relation' came up as something that this article is NOT about. The term is mentioned, unsourced, in the Wikipedia article on Planck's constant, if anyone wants an unreliable mention of it.
Another reason why it is not indicated here. It is in a section on the history of Planck's law. Historical sources do not use the term. For example, ter Haar 1967, Kangro 1976, Stehle 1994, Pais (Inward Bound 1986), van der Waerden (Sources of Quantum Mechanics 1967), Camilleri (Heisenberg and the Interpretation of Quantum Mechanics 2009), Kramers (Quantum Mechanics 1937). Need I go on?Chjoaygame (talk) 20:04, 25 October 2011 (UTC)
I reject the idea that the fact that a "movement has been towards the elimination and discouragement of eponymous terms" means that that is a good idea. Followed to a logical extreme, that would instruct us to quit using Joule, Hertz, and Watt even though the standards bodies say we should. If common textbooks and journal articles use a phrase, then we should also. When a phrase is used for several concepts, or several phrases are used for the same concept, then we should document the fact that there is no standard phrase. The fact that current terminology is different than older terminology does not mean that we should use the older terminology. Instead, we should use both to help the reader understand what the references are saying. Q Science (talk) 20:28, 25 October 2011 (UTC)
Thank you Q Science. Indeed, you are right that the mere fact that a "movement has been..." does not mean that it is a good idea. But there are more reasons against eponymous nomenclature than that mere fact. Many scientists have thought a lot about it and the said "movement" is only one manifestation of their thinking that it should in general be discouraged. No one is recommending taking things to logical extremes. The term Planck’s law is eponymous and I am not opposed to use of it.
Journals are considered primary sources and are not preferred as reliable sources. We are not obliged to follow others indiscriminately.
Common textbooks do not in general use the term as an eponym; it would be misleading to say that it is current terminology. It is one thing to use a phrase, another to use a term as an eponym. Here I am not trying to stop people using the phrase; they will use it as they think fit. I am saying that the present Wikipedia section on the history of Planck's law should not explicitly sanction the term as an eponym. The use of the term here will more likely confuse than clarify.
Perhaps indeed Wikipedia should document the use of the term 'Planck's relation'. Indeed, to some extent, it already does so in the article on Planck's constant. But I am proposing that the history section of the article on Planck's law is not the place for such documentation.
It is not just using eponymous terms that we are talking about here. No one so far has proposed to use the term ‘Planck’s relation’ here. Here we are talking about mentioning and endorsing , not about using. We are talking about generating or endowing eponyms with status as established, which they might not otherwise have.

### stating the case against

Copy-and-pasting from above in this talk page:

It's all over the web, but of course that's not reliable. I looked through a lot of physics textbooks on my shelf and finally found it in the following.
Cohen-Tannoudji, C, B. Diu, and F. Laloe, Quantum Mechanics, Wiley, 1977, ISBN 0-471-16432-1 (v. 1).
Section A.1 gives two equations collectively labeled (Planck-Einstein relations) (A-1):
${\displaystyle E=h\nu =\hbar \omega }$
${\displaystyle p=\hbar k}$
(p and k are bold in the text but latex barfs on {\bf p} and {\bf k}. Would love to know the fix.) As usual k is the wave vector. --Vaughan Pratt (talk) 08:10, 17 October 2011 (UTC)
Vaughan Pratt cites some formulas and a label, the "Planck-Einstein relations", without quoting a statement of the physical meaning of those formulas. Looking at the source, I see that they refer to photons as Einstein envisaged them. Planck did not refer to photons in this sense. The remark about the term 'Planck relation' in the present article does not refer to the formulas and physical meaning to which Vaughan Pratt's citation refers. Vaughan Pratt writes that he "looked through a lot of physics textbooks" and finally found what he cites above. This does not look like support for the use of the term 'Planck relation'. Vaughan Pratt has not cited a reliable source for the term 'Planck relation' that stands at present in the article on Planck's law.Chjoaygame (talk) 08:47, 17 October 2011 (UTC)

That Vaughan Pratt had to look through a lot of textbooks in order to find an instance is evidence that the terms "Planck's relation" and "Einstein-Planck relation" are NOT in common use in reliable sources.

The instance that he found was not of 'Planck's relation' E = nhν for Planck's virtual material oscillators. It was an instance of a bunch of formulas about photons, attributable to Einstein and perhaps to de Broglie. Just to head off one line of response, I am not saying that Cohen-Tannoudji is not a reliable source about quantum mechanics.

I am saying that Cohen-Tannoudji et al.'s text neither mentions nor uses the phrase 'Planck's relation', and is therefore not a candidate as a source for that term.

In the index, Cohen-Tannoudji et al. list under "Einstein" and under "Planck" the phrase "Planck-Einstein relations", and point to pages 10 and 18. On page 11 they list equations as shown above by Vaughan Pratt. Our current Wikipedia article writes of the "Planck-Einstein relation" in the singular, and does not include the last of the equations listed by Cohen-Tannoudji et al.. Though Cohen-Tannoudji et al. mention their eponym, so far as I see in their text, they do not actually use it. When they need them, they simply state the formulas again, as for example on their page 18. Thus they are an example of a text that does NOT use the eponym, as distinct from just mentioning it. This does not make much of a case why we should mention it too.

Another possible candidate source is French and Taylor as noted above. They do not mention or use the term ‘Planck’s relation’, and are thus no candidate as a source for that eponym. They mention and use the term "the Planck-Einstein relation", but in defining it they make it include what is generally called 'Bohr's frequency condition' or the like, and so they are an ambiguous source, and they do not refer to Planck's virtual oscillators. They are thus perhaps a source, but we are talking about common usage here, and one source, nearly isolated, does not establish common usage, which is crucial here.

To cite the article by Puccini would be to clutch at straws, as I guess you will agree when you read that article. They write of the "Planck-Einstein equation" as ${\displaystyle E=h\nu }$ and in the next line they get the dimensions of Planck’s constant wrong. They later use the term "Planck's relation" and do not seem to distinguish it from the "Planck-Einstein equation" which they define.

Another possible historical source is Mehra and Rechenberg cited above. But they use the same phrase with two entirely different meanings, only one of them applicable to our present question. Thus they would be a source of ambiguity.

Schwinger’s posthumous text was edited from lecture notes and from Schwinger’s hand is acknowledged to be a draft. I find the text weaker than papers definitely published by Schwinger that I have read on such matters, and therefore I find the text as edited to be dubiously from Schwinger. Schwinger’s text writes of "Planck’s energy-frequency relation", not of "Planck’s relation" simple, and what is offered is more usually attributed to Einstein than to Planck; it refers to photons, not to Planck's virtual oscillators. Thus I do not regard the Schwinger text as a reliable source for any of our terms. I have read an entirely other text authored by the editor, and that does not make me change my mind about this.

The only clean candidate so far that we have looked at that might seem to stand as a source for "Planck’s relation", Ram refers explicitly to ${\displaystyle E=nh\nu }$ , which does not appear in our article, and the fact that he has to state it explicitly is evidence that he does not regard it as a safely established eponym. The point about an established eponym is that it saves the trouble of explicit statement of the formula to which it refers.

Thus it seems that we have no good source for "Planck’s relation" which is where this thing is coming from. So it seems to me that we should remove the term from the body of our article.

Can we be rescued by the "Planck-Einstein relation"? We would have to move it from where it is in the article now to a place to which it might apply. We have scarce evidence for the view that it is commonly used, rather, our evidence is that it is NOT commonly used by reliable sources, and, we have, I think, only one candidate as a reliable source for it, French and Taylor, and their definition is ambiguous.

So I think it is inappropriate for our history section to refer to either eponym.Chjoaygame (talk) 03:28, 26 October 2011 (UTC)

If you think it needs a reference, then slap one of the thousands of books on quantum mechanics, or the history of quantum mechanics, such as PCW Davies (1986), The Forces of Nature, 2nd Edition, Cambridge University Press, p. 32. "E = (2.4)" and later on "Further evidence for the quantum nature of light comes from the photoelectric effect, which Einstein explained in 1905 in terms of the activity of 'particles' or photons of light obeying Planck's relation, Equation (2.4).". This is introduction to modern physics stuff, not something warranting huge walls of text on the talk page. 06:37, 26 October 2011 (UTC)
I am not saying that I think it needs a reference here. I am saying it should be, as you suggest, located in articles about introduction to modern physics, where the term is used, not here, in a section about the history of Planck's law.Chjoaygame (talk) 11:06, 26 October 2011 (UTC)
Are you suggesting Planck's relation has no relevance to Planck's law??? 17:17, 26 October 2011 (UTC)
Dear Headbomb, I am talking about the eponym.Chjoaygame (talk) 19:08, 26 October 2011 (UTC)
Checking the source to which you point above, I find that it refers to photons, which were not the subject of the relation in question. Planck did not believe in photons. This is an example of how the referent of the eponym is not distinctly recognized by those who use it. Personally, I am not impressed that Paul Davies qualifies as a reliable source for the present purpose.Chjoaygame (talk) 20:10, 27 October 2011 (UTC) (UTC)Chjoaygame (talk) 20:12, 26 October 2011 (UTC)
A respected text is Heitler, W. (1954), The Quantum Theory of Radiation, Oxford University Press, Oxford UK. On page 54, Heitler (in our notation) writes: "To avoid this difficulty Planck (and later Einstein) assumed that the energy of a monochromatic wave with [angular] frequency ω could only assume values which are an integral multiple of a certain unit proportional ot the frequency
${\displaystyle E=n\hbar \omega }$ ,              (1)
n being an integer, the number of light quanta or photons."
This is not the finest moment of Heitler.
• Planck in this referred to neither photons nor monochromatic waves.
• Photons in the sense of increments in stationary states of fields do not propagate as Einstein envisaged for his punctate quanta of energy. A travelling monochromatic wave is persistent and lasts for ever, and is not composed of a finite number of photons. This is explained by Kramers 1937/1957 (ter Haar transl., page 439 "one can not speak in particles in a radiation field as in the (non-relativistic*) quantum mechanics of sytems of point particles"), by Mandel and Wolf 1995 (page 480 "a plane wave has no localization in space or time") and by Loudon 2000 (on page 1 "The single mode photons are thus delocalized"); Scully and Zubairy 1997 are a bit less explicit (page 35 "“Photon” physics is very different from that of Schrödinger particles.")
Thus, although Heitler does not actually use the eponym "Planck's relation", his thinking in this is expressed in a muddled way, that is apparent in many users of it, and that does not call for gratuitous endorsement by a Wikipedia section on the history of Planck's law.Chjoaygame (talk) 22:08, 27 October 2011 (UTC)

### history of edits on "Planck's relation" and "Planck-Einstein relation"

In an edit of 21:38, 13 October 2011, Headbomb put in the sentence "This is known as Planck's relation" right after the formula

${\displaystyle E=h\nu .\,}$

No source was given, reliable or otherwise.

The next edit, of 21:39, 13 October 2011, was by Headbomb, a tag that Planck's law is not to be confused with Planck's relation, which is a phrase used in the article Planck's constant, where no source is given for it.

In an edit of 06:05, 14 October 2011, Vaughan Pratt deleted the tag about Planck's relation.

In an edit of 07:07, 14 October 2011, Headbomb put the tag back.

In an edit of 05:23, 15 October 2011 Chjoaygame changed the formula to

${\displaystyle \epsilon =h\nu }$

In an edit of 05:30, 15 October 2011, Chjoaygame tagged a request for a source for the eponym "Planck's relation".

In an edit of 15:38, 16 October 2011, removed the tag request with the comment “remove silly tag”.

In an edit of 057:40, 23 October 2011, Michael C. Price added “or the Einstein-Planck relation”, with no source offered.

In an edit of 08:44, 25 October 2011, Vaughan Pratt changed “Einstein-Planck” to “Planck-Einstein”, with no source entered.

In an edit of 08:53, 25 October 2011, IRWolfie changed “Planck-Einstein” to “Einstein-Planck”, with no source entered.

In an edit of 09:00, 25 October 2011, Q Science reverted the foregoing edit by IRWolfie.

In an edit of 06:50, 26 October 2011 Headbomb removed the words “or the Planck-Einstein relation” with the comment “P-E is much rarer and doesn’t need to be mentioned here.”

In an edit of 06:56, 26 October 2011 Michael C. Price reverted the foregoing edit by Headbomb, with the comment “not that rare”.

In an edit of 07:24, 26 October 2011 Headbomb reverted the foregoing reversion by Michael C. Price, with the comment “still no point in mentioning it here.”

In an edit of 06:05, 29 October 2011 Michael C. Price put back the words “or the Planck-Einstein relation”, with the comment that it “is of interest to readers.”

These eponym statements are unsourced.Chjoaygame (talk) 22:37, 29 October 2011 (UTC)

Headbomb's statement “P-E is much rarer and doesn’t need to be mentioned here” is contradicted (i) by Google, which gives 16200 hits for P-E and 1890 hits for E-P when quoted (many more hits when unquoted but the ratio is still large) and (ii) by books: I've seen "Planck-Einstein relation" in books but never "Einstein-Planck relation." What is Headbomb's basis for his claim that E-P is more common, either on the web or in books? --Vaughan Pratt (talk) 04:53, 30 October 2011 (UTC)
Headbomb was not saying that E-P was commoner than P-E. He was saying that "Planck-Einstein relation" was rarer than "Planck's relation".Chjoaygame (talk) 05:41, 30 October 2011 (UTC)
My mistake. Meanwhile I notice that Google now gives only 13100 hits for P-E, down from 16200 yesterday. What could have caused that? Surely not the result of merely deleting "or the Planck-Einstein relation" from Wikipedia? Anyway, my bigger point is that Google gives 15200 hits for "Planck relation", slightly more than the 13100 (today, 16200 yesterday) for "Planck-Einstein relation", which doesn't bear out Headbomb's "much rarer." I would think a better argument for omitting one or the other is that either one should suffice to deal with any confusion, which is the only point of that hatnote. I would prefer "Planck-Einstein relation" myself but not strongly enough to spend time arguing for it. --Vaughan Pratt (talk) 16:36, 30 October 2011 (UTC)

### a reliable source proposed and retracted

I think several editors will be happy to see that I have found a source that I consider reliable for the eponym 'Planck's relation'. The eponym is not very widely used in reliable textbooks. Kuhn is a reliable historian, but not quite in agreement with all commonly held assumptions, as noted by Helge Kragh.Chjoaygame (talk) 12:18, 30 October 2011 (UTC)

Yes, Michael C. Price, on second thoughts, I have to agree that I went too far in my enthusiasm to please. Although Kuhn writes of the formula as a "mysterious formula" and several times in his extensive discussion calls it a "relation", it was inaccurate of me to imply that Kuhn actually used the eponym "Planck's relation" in those very words; he did not. Thus, I was mistaken to offer Kuhn as a source.

So, sad to say, the eponym still lacks a reliable source.Chjoaygame (talk) 16:59, 30 October 2011 (UTC)

I gave one above to PCW Davies' book. But it's becoming increasingly apparently that you're more interested in creating walls of texts about the most trivial of issues than make productive contributions. Want a reference for that? Just add it. 06:55, 1 November 2011 (UTC)
Agreed with the "walls of text" comment. Chjoaygame's verbosity is not constructive. -- cheers, Michael C. Price talk 07:02, 1 November 2011 (UTC)
I don't agree. Several editors are clearly pushing a single phrase as "correct" when the literature clearly does not support that. Q Science (talk) 08:06, 1 November 2011 (UTC)
Headbomb, I don't think Paul Davies is a reliable source for a history section on this point, as I indicated in my above response to your suggestion above. That you had to resort to him is evidence that the term is not widely used by reliable sources.
Mehra and Rechenberg use the eponym 'Kirchhoff's function' (page 26, volume 1, part1) and so does Kuhn on pages 8 and 28. But not ter Haar 1967. Kangro cites Paschen 1896 as referring to "Kirchhoff's emission function", but does not use it himself. I did not find a use of it by Planck. Sommerfeld 1923 does not use it. Stehle 1994 does not use it.
Kirchhoff did not actually know the form of, let alone explicitly specify, his function, but just asserted the necessity of its existence; this is perhaps a reason for referring to it by an eponym. I think the eponyn 'Kirchhoff function' is rarely used nowadays. I think that the eponym 'Planck's relation' is used loosely without much regard for precise meaning; a history section in a Wikipedia article has no duty to notice or to endorse that sort of thing.Chjoaygame (talk) 11:35, 1 November 2011 (UTC)
More walls of text. You satisfied yourself with the Kuhn souce, and felt the need to proclaim to the world that you've finally convinced yourself of something everyone encounters in an introduction to modern physics class. Yet, you did not add the source, but instead complained that something obvious was "unsourced". You were told Davies also covers this, but you're not happy with it for some unknown reason and won't add it either. It's resoundingly clear at this point that you're not interested in improving the article so much as you're interested in hearing the sound of your own voice. 18:23, 1 November 2011 (UTC)

## forms of expression of the law

The present section "Common forms" announces itself as about common forms.

Headbomb has recently put into this section a form which is perhaps the product of his own research and which has no source offered for it. I recall Headbomb saying that he would find and tell us of a source.

A form which is I think more commonly found in sources is the expression in terms of spectral emittance. To be found in reliable sources, there are other more or less common forms, such as the energy density as a function of wavelength. Would it be better to change the title of the section from "Common forms" to 'Forms of expression of the law' or somesuch less restrictive wording?Chjoaygame (talk) 19:39, 26 October 2011 (UTC)

No, it would be better to remove the original research. If there aren't at least 2 good references, it should not be here. Q Science (talk) 19:54, 26 October 2011 (UTC)
I agree. Disagree-ers please say.Chjoaygame (talk) 20:02, 27 October 2011 (UTC)
In an edit of 21:32, 13 October 2011, Headbomb asked for verification of the angular wavenumber formula which he had recently inserted, annotating his request "verify this one, since I might have done the conversion quickly." This seems like a res ipse loquitur case that the angular wavenumber formula is Headbomb's own research. No verification has been forthcoming. No reliable source has been shown for this formula. Eventually the formula was removed, with some support from various editors. I have found the formula in no source at all, reliable or not. Headbomb has recently put this formula back. I have proposed to delete it again, with support expressed by Q Science, but no others.Chjoaygame (talk) 20:19, 29 October 2011 (UTC)
Since it is not a common form (nor even one that exists anywhere in the literature), and moreover is unsourced, and obviously WP:OR, I've deleted it. If Headbomb puts it back yet again then it is time to take this to ANI, since it is clear by now that we have tried and failed to deal with this without ANI help. How many sections on this talk page are the direct result of Headbomb's approach to editing Wikipedia articles? --Vaughan Pratt (talk) 04:00, 30 October 2011 (UTC)
Headbomb's equation is a routine calculation, not original research. The proper objection to it is that it is not a "common form", if it is in fact not. PAR (talk) 21:43, 31 October 2011 (UTC)
For the record, here is a copy-and-paste from the article Wikipedia:No original research, edited to reduce header status:
Routine calculations
This policy allows routine mathematical calculations, such as adding numbers, converting units, or calculating a person's age, provided there is consensus among editors that the arithmetic and its application correctly reflect the sources. See also Category:Conversion templates.
comment signedChjoaygame (talk) 21:56, 31 October 2011 (UTC)

### routine calculation?

Headbomb did the formula manipulation himself. This seems clear from what he posted. A question is whether that was original research as defined by Wikipedia policy or not? It seems to be a matter of whether the formula manipulation was a routine calculation or not. The example cited by Jheald below refers to a multiplication of given constants, which may or may not be considered to be the same kind of thing as a manipulation of a formula which has attached to it a note about conversion of its forms.

In his initial input of the formula that he had manipulated, Headbomb offered a version of his work

${\displaystyle B_{k}(T)=2hc^{2}k^{3}{\frac {1}{e^{\frac {hck}{kT}}-1}}.}$

In a further edit he offered the version

${\displaystyle B_{k}(T)={\frac {hc^{2}k^{3}}{4\pi ^{3}}}{\frac {1}{e^{\frac {hck}{2\pi kT}}-1}}.}$

Subsequently he added a tag asking for verification, on the grounds that he "might have done the conversion quickly".

Later he removed the verification tag and offered a version

${\displaystyle B_{k}(T)={\frac {hc^{2}k^{3}}{2\pi ^{2}}}{\frac {1}{e^{\frac {hck}{2\pi k_{\mathrm {B} }T}}-1}}.}$

Then he referred to the talk page and offered a version which is at present in the article

${\displaystyle B_{k}(T)={\frac {hc^{2}k^{3}}{8\pi ^{4}}}{\frac {1}{e^{\frac {hck}{2\pi k_{\mathrm {B} }T}}-1}}.}$

which he had reached as he showed on the talk page:

Weird, I set up to show my work my work was right and turns out all I achieved by doing that was prove that I was wrong (I think I multiplied by 2π rather than divide by 2π at some point, which would explain the difference of 4π2). Anyway, starting point, we all agree on
${\displaystyle B_{\lambda }=B_{k}|{\frac {dk}{d\lambda }}|}$
From ${\displaystyle k=2\pi /\lambda }$, we have
${\displaystyle |{\frac {dk}{d\lambda }}|=2\pi /k^{2}}$
So we have
${\displaystyle B_{k}=B_{\lambda }|{\frac {dk}{d\lambda }}|={\frac {2hc^{2}}{\lambda ^{5}}}{\frac {1}{e^{\frac {hc}{\lambda k_{\mathrm {B} }T}}-1}}{\frac {2\pi }{k^{2}}}.}$
Substituting ${\displaystyle \lambda =2\pi /k}$, we get
${\displaystyle B_{k}={\frac {2hc^{2}}{32\pi ^{5}/k^{5}}}{\frac {1}{e^{\frac {hck}{2\pi k_{\mathrm {B} }T}}-1}}{\frac {2\pi }{k^{2}}}.}$
Or simplified,
${\displaystyle B_{k}={\frac {hc^{2}k^{3}}{8\pi ^{4}}}{\frac {1}{e^{\frac {hck}{2\pi k_{\mathrm {B} }T}}-1}}.}$
I should have gotten this right the first time, so apologies for the trouble and extra work. 23:33, 16 October 2011 (UTC)

A trivial adjustment to this was pointed out by Q Science.

This is not a mere multiplication of constants. Does it seem wise to make it a precedent for a "routine calculation" for the Wikipedia?Chjoaygame (talk) 02:10, 1 November 2011 (UTC)

To restate what I said above: Headbomb's equation is a routine calculation, not original research. The proper objection to it is that it is not a "common form", if it is in fact not. Just because Headbomb initially messed up a routine calculation does not disqualify it as a routine calculation. Chjoaygame's statement of the relevant policy reinforces this, but additionally requires a proper source for the routine calculation. The routine calculation is simply ${\displaystyle |B_{\nu }d\nu |=|B_{x}dx|}$ where x is any monotonic function of frequency ${\displaystyle \nu }$. If we are intent on improving this article, we will search for such a source and make this important point, rather than shooting ourselves in the foot trying to remove Headbomb's calculation for the wrong reason. PAR (talk) 03:19, 1 November 2011 (UTC)
It's trivial substitution and derivation per the method mentioned in the article. If that's not a routine calculation, nothing is. You have no real argument, you just don't like k. 03:20, 1 November 2011 (UTC)
Also agree with PAR on the need for a source for conversions in general. 05:32, 1 November 2011 (UTC)
Thinking about it instead of worrying about it, its just the chain rule and the requirement that energy is positive. PAR (talk) 06:12, 1 November 2011 (UTC)
It'd be better with a source, but I can live with the explanation as given (not really sure were really should mention the energy requirement, since it's rather obvious, but as I said, I can live with that). 06:23, 1 November 2011 (UTC)
Added one. Hopefully we can now move on from this issue into something actually meaningful now. 20:16, 1 November 2011 (UTC)

## Gustav Kirchhoff

I find it a considerable deficiency in the article that Gustav Kirchhoff is not mentioned as the originator of the concept of a blackbody. I will be adding relevant material shortly. --Damorbel (talk) 09:17, 2 November 2011 (UTC)

Great minds think alike. I have just posted a start to a history section in the article on the Black body. I wrote about Balfour Stewart and about Gustav Kirchhoff. (As a trivial point, I think the noun phrase is often 'black body' and the adjective is often 'blackbody'.)
I agree that something more is needed in the history section of the present article on Planck's law, but I thought it might be easier, in the present climate, to start the work in a more sheltered environment. Putting in material about Kirchhoff will probably mean dividing the present history section with subheadings, a task that might take some time and care. I would be glad of your further comment.Chjoaygame (talk) 10:02, 2 November 2011 (UTC)

I agree, this is a difficult matter for some, I'm thinking about it! --Damorbel (talk) 10:11, 2 November 2011 (UTC)

## Ribaric and Sustersic 2008

This paper cited in the article writes on its page 8: "So parts of Planck's law are practically untestable, cf. e.g. [7]." And for reference [7] we find "Planck's law, En.wikipedia."

I propose that the reference to this article should be deleted from the Wikipedia article, together with the whole paragraph in which it is cited, namely "Planck's formula predicts that a black body will radiate energy at all frequencies, but its intensity rapidly tends to zero at high frequencies (short wavelengths). For example, a black body at room temperature (300 K) with one square meter of surface area will emit a photon in the visible range once every minute or so, meaning that for most practical purposes a black body at room temperature does not emit in the visible range. Significance of this fact for the derivation of Planck's law from experimental data, and for the substantiation of the law by the data, is discussed in Ribaric & Sustersic 2008.".Chjoaygame (talk) 06:15, 27 October 2011 (UTC)

Why? The statements seem valid to me. PAR (talk) 02:45, 28 October 2011 (UTC)

Surely Wikipedia is not a repository for statements with little to recommend them beyond that they that seem valid? Some notability is needed. A reliable source is needed. Isolated unrefereed research does not generally qualify as a reliable source. Unrefereed research that relies essentially on a statement in Wikipedia that refers to the said unrefereed research is hardly deserving of special exemption from the policy. You say that the statements seem valid to you. Have you done some original research to verify that? What is being said here is hardly so pressing that the general policy should be overruled.Chjoaygame (talk) 02:59, 28 October 2011 (UTC)

Ah, ok, your problem is not with the statements themselves, but rather that they use an arXiv reference. It would have been helpful if you had mentioned that in the original post. What is the Wikipedia policy on arXiv references?
As for the statements themselves, it is important to realize that Planck's law treats electromagnetic radiation as a classical field and assumes the spectral radiance can be measured for arbitrarily low values. It does not account for the fact that the radiation energy arrives in packets (photons) and when the spectral radiance is sufficiently low, the classical field assumption breaks down and Planck's law becomes invalid, or must be re-interpreted as a probability density for arriving photons. If arXiv references are unacceptable, then we need to find an acceptable reference which makes this point. 04:36, 29 October 2011 (UTC)
My feeling, FWIW, is that quotations from arXiv references are acceptable provided they're not contradicted by an equal or higher authority. But I'm open to arguments against that. I do however agree with Chjoaygame about circular references to Wikipedia; I believe I've seen WP guidelines recommending against that, I forget where. --Vaughan Pratt (talk) 05:04, 30 October 2011 (UTC)

My concern is not specifically about arXiv. This particular source relies on this very Wikipedia article itself. I suppose one might call it a circular reference.Chjoaygame (talk) 04:50, 29 October 2011 (UTC)

What exactly is in dispute here? That Planck's law drops off exponentially with frequency on the high-frequency side of the peak? Who here disputes this? That and the fact that it drops off polynomially on the low-frequency side are important characteristic properties of the law that are clearly visible in a semilog plot of the law (which the article needs, btw -- Goody and Yung have a suitable one that can be used as a source justifying a similar plot usable on Wikipedia). --Vaughan Pratt (talk) 04:23, 30 October 2011 (UTC)
The point that I am making here is that the sentences in question do not say something very notable and that they are sourced circularly through this very Wikipedia article and I think that is reason to delete themChjoaygame (talk) 05:47, 30 October 2011 (UTC)
Sorry, replace "important" by "notable" in my preceding comment. The point of my "what is in dispute" was to replace troublesome circular sourcing with (hopefully) less troublesome editorial consensus. If no editor disputes the obvious, worrying about whether a source for the obvious is circular is like worrying about how many angels can dance on a pinhead. --Vaughan Pratt (talk) 05:59, 30 October 2011 (UTC)
The paragraph and the reference are saying that Planck's law is put at risk by a certain fact.
That fact is that the intensity drops off at high and low spectral values. The point being made by the paragraph is not the fact that the intensity drops off at high and low spectral values. The claim made by the paragraph, that the the law is put at risk by this essential and obvious fact, is indeed like counting angels that dance on the head of a pin. The paragraph is not making a point about the form of the law. The form of the law is dealt with very well in other parts of the article. The paragraph and reference are making a point about the safety of the law, and, I say, a point that is not notable, indeed a point that is hardly plausible.Chjoaygame (talk) 08:36, 30 October 2011 (UTC)
Sometimes one might say that an obvious thing should be omitted just because it is obvious. That something is agreed by editors to be obvious is not a reason to put it Wikipedia.
The empirical verification of Planck's law is a serious matter. The law arose in stages because the methods of spectral analysis and of detection gradually improved. The methods have improved considerably since then. If we are serious about the validity of the verification of Planck's law, we should say some of the basic things about it before going into questions of what happens when the law predicts very small effects. For example, should we regard the measurement of the cosmic microwave background, for a 'body' at 2.7K, as problematic for the law, on the grounds that the intensities are small? The article of Ribaric and Susteric 2008 is an exercise in triviality when it comes to considering Planck's law, and therefore does not deserve a place in a section on physics where the basic things have not been stated.Chjoaygame (talk) 20:11, 30 October 2011 (UTC)

Planck's law supposedly tells you the energy E arriving in a small frequency band ${\displaystyle \Delta \nu }$ at frequency ${\displaystyle \nu }$ in a time interval ${\displaystyle \Delta t}$: ${\displaystyle E\propto B_{\nu }\Delta \nu \Delta t}$. That energy will arrive as photons, each photon having energy ${\displaystyle h\nu }$. So the number of photons arriving in time ${\displaystyle \Delta t}$ will be ${\displaystyle E/h\nu }$. What happens when the spectral radiance given by Planck's law is so low that ${\displaystyle E/h\nu =1/1000}$?. Will you measure one one thousandth of a photon? No. On average, one out of a thousand times you will measure a photon with an energy a thousand times greater than that predicted by Planck's law, the other 999 times you will measure zero. Planck's law only holds in the limit of large numbers of photons. This is a fundamental, and therefore VERY notable limitation on Plancks law if you interpret it as a spectral radiance of a classical EM wave. PAR (talk) 20:14, 30 October 2011 (UTC)

Thank you PAR for this account of what Planck's law supposedly tells you. Pray tell us, do you think the cosmic microwave background obeys Planck's law, and pray tell us how you think this question has been handled by empirical workers, and how they should have handled it? They use radio aerials with baselines of thousands of kilometers sometimes, and they do wait a long time. Does this mean that Planck's law is threatened? I wish I had a way of making the detectors that you cite, that have a dark current so small that they will return a zero count 999 times out of the thousand that are expected to return a single count; perhaps you can tell us how to make such a detector? Is there some principle that one must not run an experiment for a long time to collect suitable samples? Right beside me I have an account of a relevant experiment that had an exposure time of 336 hours. Does this mean that Planck's law is at risk?
The cited article in question does not make clear the point you make. It does not mention photons. The Wikipedia article talks only about most practical purposes: but surely the testing of Planck's law is not bound by what holds for most practical purposes? This is a very special practical purpose, as you say.
The empirical verification of Planck's law is very important, but this paragraph in this section ignores the main empirical aspects of it, and focuses on a very fine theoretical point instead, a point that Vaughan Pratt finds obvious, and that, in context, I find nearly trivial. Something better is needed, and a start to that is to delete the present paragraph.Chjoaygame (talk) 23:33, 30 October 2011 (UTC)
Chjoaygame - I can't tell whether you are being sarcastic or polite, but I will assume the latter and return the favor. I said that ${\displaystyle E\propto B_{\nu }\Delta \nu \Delta t}$ which means that the number of photons ${\displaystyle E/h\nu }$ increases as ${\displaystyle \Delta t}$ increases. For a sufficiently LONG time interval ${\displaystyle \Delta t}$ (perhaps as high as 336 hours), Planck's law will hold, it is for very short time intervals that it breaks down. With regard to the cosmic microwave background measurements you are referring to, I bet that if you calculate the number of photons captured in a single measurement, it will be rather large and Planck's law will hold.
I don't understand what an experimental complication (i.e. subtracting dark current) has to do with Planck's law, so I won't respond to that.
If the cited article does not make the point clear, then I agree, it cannot be used to make this important point. I also agree that this point should be made after the essence of Planck's law has been explained, not before or during. Since it is a rather important point, neither trivial nor obvious, it should be made eventually, and rather than simply delete it, we should try to come up with a valid reference for it. Your knowledge of the literature is far better than mine, perhaps you can find it more quickly than I. PAR (talk) 01:56, 31 October 2011 (UTC)

I got stuck at these two sentences: On average, one out of a thousand times you will measure a photon with an energy a thousand times greater than that predicted by Planck's law, the other 999 times you will measure zero. Planck's law only holds in the limit of large numbers of photons. Where is the inconsistency when one makes a million measurements? I would have thought a thousand photons was a "large number." If not, then let's consider a billion measurements or whatever it takes to get to a "large number." (I do believe in the law of large numbers, in case that was in any doubt.) --Vaughan Pratt (talk) 05:17, 31 October 2011 (UTC)

For ${\displaystyle E/h\nu =1/1000}$ photons, where E is total energy predicted to be measured according to Planck's law, if one made a million measurements, one would measure one photon a thousand times, 999 thousand times nothing. Whether you measure a thousand or a million photons, the average would be what was predicted by Planck's Law, but the individual measurements would not be. If you collect ${\displaystyle E/h\nu =1/1000}$ photons for a one-second long collection time, then for a million-second collection time, E will become a million times greater, and you will collect 1000 photons. Now the amount of energy measured will be what is predicted by Planck's law. Note that photon arrival rates are a Poisson process and I am being kind of sloppy with my description, for the sake of simplicity. PAR (talk) 09:58, 31 October 2011 (UTC)

Yes, that was how I understood it. But at all frequencies photons are being emitted discretely. For every frequency there is a rate of sampling such that one sees only one photon in every thousand measurements. Or so I understood the usual view of photons.

However the rate rises exponentially with decreasing frequency (or increasing temperature), so it quickly becomes infeasible to sample at that rate. Enter the proverbial unheard falling tree. If the photons are being emitted in such quantities as to make it infeasible to observe them individually, can one really subdivide time finely enough that only one photon is emitted every thousand divisions? This presumably becomes impossible if lots of photons are emitted in one Planck time unit, in which case I see your point. --Vaughan Pratt (talk) 18:27, 31 October 2011 (UTC)

What I mean to say is that for Planck's law, there are frequency bands, temperatures and areas (e.g. visible frequency, room temperature, one square meter) for which measurement times on the order of seconds will yield an energy that is a fraction of the emitted photon energy - in other words, Planck's law breaks down in the way described above. PAR (talk) 19:04, 31 October 2011 (UTC)
Planck's law is about a body in thermodynamic equilibrium, for which measurements are allowed to take a long time. A measurement made in a short time is not a reliable test of the law.Chjoaygame (talk) 21:09, 31 October 2011 (UTC)

The way you put it above was "the classical field assumption breaks down and Planck's law becomes invalid, or must be re-interpreted as a probability density for arriving photons." Both of these puzzled me because the classical field assumption gives the Rayleigh-Jeans law and Planck's law is a consequence of the radiation being emitted as discrete photons. So neither "classical field assumption" nor "reinterpreted" seems appropriate, the former because it gives a different law and the latter because the law averages over photons to begin with (it's all done with the sort of statistical mechanics pioneered by Maxwell and Boltzmann) so there's no reinterpretation needed. I thought by "breaks down" you must have meant in some numerical way but it turns out you merely meant a transition from continuous to discrete. What confused me was that in my view of what was happening there was no such transition, and it hadn't occurred to me that anyone including you would see such a transition.

Perhaps your concern is a legitimate one and that some readers may be thinking of the radiation described by Planck's law as continuous rather than discrete. However if that's the case it might be better to clarify earlier on that it's always discrete, otherwise those readers that already have the always-discrete view will find it confusing to be told it's sometimes continuous, as I did. --Vaughan Pratt (talk) 20:45, 31 October 2011 (UTC)

To be a little more precise, whenever you make a spectral radiance measurement, there is a certain amount of photon "noise", equal to the square root of the number of photons. This is true of any spectral radiance measurement, not just Planck's law. So the root mean square error in a spectral radiance measurement due to photon noise will be ${\displaystyle \Delta E={\sqrt {Eh\nu }}}$ where E is the energy predicted by e.g. Planck's law. This is the consequence of photon arrival rates being a Poisson process. There are a number of ways of stating things:
1. If you define ${\displaystyle B_{\nu }}$ as the spectral radiance of a classical EM wave, then Planck's law will "break down" when ${\displaystyle \Delta E}$ becomes "unacceptably large" (e.g. of the order of experimental error due to other sources). There is no transition point fixed in stone, the transition point is the point at which ${\displaystyle \Delta E}$ becomes "unacceptably large".
2. If, as Chjoaygame has suggested, Planck's law is only to be defined as valid over those situations where ${\displaystyle \Delta E}$ is "negligible", then sure, that is a second way of stating things.
3. Another way is to interpret Planck's law as expressing the average, or expected value, of the energy for a given measurement. If you make M identical measurements and average the energies you measure, then in the limit of large M, that average will coincide with the value predicted by Planck's law. That is a third way of stating things.
I think that the way to develop the article is to describe it as a classical EM wave, without going into the quantum problems until later. After the theory has been laid out, it should then be added that due to the discrete nature of photons, option 1, 2, or 3 is the proper way to look at things. I am not adamant that Planck's law be described as "breaking down", only that the complications due to the discreteness of the energy measured be adequately described. PAR (talk) 02:53, 1 November 2011 (UTC)

Do we have a source justifying describing thermal emission as a classical EM wave? My impression was that thermal emission is the canonical example of photonic emission, which is naturally broadband, as distinct from a classical EM wave, which is naturally narrowband, in fact sinusoidal when one draws it on the blackboard. For this reason I have great difficulty picturing thermal emission as a classical EM wave. Do you have a source supporting your viewpoint? (Same question to Headbomb, whose angular wavenumber stuff is coming out of left field by making a claimed connection between broadband thermal and narrowband classical EM waves for which there seems little to no support in the literature.) --Vaughan Pratt (talk) 07:06, 1 November 2011 (UTC)

The question of whether EM radiation can be treated as a classical EM wave or as a collection of photons is entirely dependent upon whether the number of photons collected in a measurment is large or small. If its large, then the classical treatment (i.e. spectral radiance over infinitesimal frequency bands ${\displaystyle d\nu }$) will apply. Planck's law as stated in the article, calls ${\displaystyle B_{\nu }}$ a spectral radiance, which immediately implies a classical EM wave, no reference needed. Photonic emission is for any EM radiation where the number of photons collected is small, including Planck's law in certain cases. "Broadband" means the radiation is spread out over a relatively wide bandwidth, "narrowband" means it is not. Broadband is not necessarily photonic, nor is narrowband necessarily classical EM. Its not a matter of how spread out the radiation is, its a matter of how many photons are collected in a measurement. Broadband can be classical EM if many photons are collected, narrowband can be photonic if only a few are collected. PAR (talk) 15:48, 1 November 2011 (UTC)

### promotion?

The cited Ribaric and Sustersic 2008 article does not make the point clear; it is moreover a circular reference. It was put in in an edit of 14:15, 7 November 2008, by Spancek. It was deleted at 19:26, 7 November 2008 by 2over0 who commented that it looked like promotion. It was restored by Spancek at 10:51, 20 November 2008 with no comment; this was reverted without comment at 17:19, 24 November 2008; it was restored without comment by Spancek at 08:18, 25 November 2008. I did not find further removals or restorations to the present Wikipedia article.

The cited article was cited also in the Wikipedia article on Empirical formula, put in there by Spancek at 14:01, 7 November 2008. It was removed from the body of that Wikipedia article to its Empirical formula#External links section by editor 58.7.8.182 at 14:02, 29 April 2010, with no comment; and it remains there to this day.

I think that the allegation of promotion is probably supported by the way the cited article is referred to in the arXiv entry, which refers to the two Wikipedia articles. Is there some way of checking this allegation of promotion?Chjoaygame (talk) 21:09, 31 October 2011 (UTC)

While the present company is assembled, I would like to ask again, is there some way of checking this allegation of promotion?Chjoaygame (talk) 07:05, 6 November 2011 (UTC)

Is there anyone who will oppose my removing the citation of the Ribaric and Sustersic 2008 article from the Physics section of the present Planck's law article?Chjoaygame (talk) 17:07, 8 November 2011 (UTC)

Did you ever find out about Wikipedia thoughts on arXiv articles? If the source is questionable, then it should not be used and, without researching it, it appears that it is. If it is agreed that the source is questionable, I oppose removing the information itself, replacing the source with a "citation needed" tag, while we go looking for a source for this information, which is both notable and valid. PAR (talk) 18:28, 8 November 2011 (UTC)
Dear PAR, I respect your concern to keep the statements themselves, and accordingly I proposed only to remove the citation. I do not object to the citation on the ground that it comes from arXiv, but on the ground that it is circular, in the relevant part citing this very Wikipedia article. I do not myself propose to hunt for a valid citation, but will be content to put up a "citation needed" tag as you propose. So now my question is again is there anyone who will oppose my removing the citation, provided I put in the "citation needed" tag at the same time?Chjoaygame (talk) 19:45, 8 November 2011 (UTC)