Talk:Rayleigh–Jeans law

Untitled
Common notation should be used between this page and that on Wien's Approximation (Law) so that the results shown in the figure can be easily reconciled with the equations.

Energy densities
There is a potential confusion: Energy per unit volume, which is what one usually means by energy density, has different units from energy density per unit wavelength which, in turn, has different units from energy density per unit frequency. It is stated that the function given is the energy density which cannot be the energy per unit volume by dimensional analysis. Furthermore, the Plank law originally written had wavelength-cubed dependence in the denominator which I changed to wavelength-to-the-fifth. This is necessary to get the first equation as the short-wavelength limit. Which form of the energy `density' one uses is a matter of convention but because of non-trivial Jacobian factors which appear in going from one to the other, the functional dependence of these forms is quite different. —The preceding unsigned comment was added by Wdlinch3 (talk • contribs) 18:11, 22 March 2007 (UTC).

I could not agree more - one thing that you learn in physics is state your units - the article starts with a reference to spectral radiance - follow the link and you will see that it is power per unit area per rad - In most uses I would also add per unit bandwith. That is not the formula we have here - you can see that by checking the units. (let alone the per unit frequency, unit wavelength etc). I'm new to editing wikipedia so I will do nothing for a few days as I don't want to do things wrong - in fact I'm not sure that writing this here is the correct thing to do, but unless I hear different in a week or so I'll try and clean things up a bit. Part of the problem is that the language/conventions sub-fields of physics/engineering like to use is often different (let a lone the whole SI units/English units/CGS units/natural units mess - although that is not important on this page.)

Twodancer (talk) 01:46, 23 September 2008 (UTC)

energy density formula
on my school book the energy density formula is $$f(\lambda) = \frac{8\pi c k T}{\lambda^4}$$ instead of $$f(\lambda) = \frac{8\pi k}{c}~\frac{T}{\lambda^4}$$. light constant is in the upper side of the expression. right now i can't check on other sources.

I agree with the guy above, its proportional to kTc/lambda^4 according to the Oxford lecture notes

ok, I'm going to change it.

Electromagnetic modes
The stuff in the following link should be added: 68.145.103.0 (talk) 04:12, 8 January 2008 (UTC)http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/rayj.html

Alternative Form
Can someone please express the Rayleigh-Jeans law in its alternative form ( in terms of frequency as well as wavelength). It would be very helpful.JBcallOnMe (talk) 07:15, 17 January 2009 (UTC)


 * JBcallOnMe added such a form himself, but I reverted it because it was unsourced; I copy his response from my talk page:

The Blackbody spectrum is very commonly expressed in terms of the wavelength and frequency. A simple taylor expansion gives the rayleigh-jeans law, which can pretty obviously be done in terms of either. My addition to the Rayleigh-Jeans page was not "made up". I think a better course of action would have been to add a "citation needed" comment to the page, or to have posted something on the discussion board. Here's a citation ( http://scienceworld.wolfram.com/physics/Rayleigh-JeansLaw.html ), I'll leave the page alone and I'll leave it to you to change the page as you see fit... JBcallOnMe (talk) 07:16, 17 January 2009 (UTC)


 * Now that ref might be OK, but I'm not certain it's exactly right. I'm unclear how it relates to this book or this page, for example, which have a different constant but also a different power of c in the denominator.  Someone who understands this stuff better should try to reconcile.  Dicklyon (talk) 08:01, 17 January 2009 (UTC)

I'll write up a full derivation when/if I have time, but for now I'll try to briefly clarify. The confusion that your having comes from the fact that
 * $$B_{\nu}(T) \neq B_{\lambda}(T)$$

but rather :$$B_{\nu}(T) d \nu = B_{\lambda}(T) d \lambda$$. So, there are two ways to achieve the the "alternative" form of the Rayleigh-Jeans expression: Taylor expand the original Plank function expression in terms of either small nu or big lambda, OR, convert directly from the expression listed on the page following the equality listed above (including the differentials).

To be Perfectly clear, I'll do out part of it:
 * $$B_{\nu}(T) = B_{\lambda}(T) \frac{d\lambda}{d\nu}$$

where
 * $$\lambda = \frac{c}{\nu}$$

and so
 * $$\frac{d\lambda}{d\nu} = -\frac{c}{\nu^2}$$

Plugging in, we see
 * $$B_{\nu}(T) = B_{\lambda}(T) * \frac{c}{\nu^2} = \frac{2 c k T}{(\frac{c}{\nu})^4} * \frac{c}{\nu^2} $$

leading to a result of
 * $$B_{\nu}(T) = \frac{2 \nu^2 k T}{c^2}$$

If you have more questions, post them here and I'll try to respond. JBcallOnMe (talk) 02:12, 18 January 2009 (UTC)


 * Thanks for the detail; I don't want to try to check it, but would appreciate hearing how it relates to the formulas in the book and page that I linked above. Dicklyon (talk) 02:25, 18 January 2009 (UTC)

Looks like there is a difference in the definition of the Plank Function. Take a look at the Plank's law page. With no reference to back me up, I would claim that the most common colloquial use of Plank's law is the emitted power per unit area of emitting surface, per unit solid angle, per unit frequency ( that is units of [ergs sec -1 cm-2 ster-1 Hz-1] ). However, one can also define the plank function as emitted power integrated over all solid angles or even as an energy density per unit volume. If we take the later case, then one must include an extra factor of $$\frac{4 \pi}{c}$$ (which gives the answer in your book and on that webpage).

To summarize, there can be 6 equally valid forms of the Rayleigh-Jeans law. One can express the plank function in 3 fundamentally different forms, and then make a superficial change between the two variables of frequency and wavelength. Currently this page contains one of these forms. The expansion of one form of the plank function in terms of wavelength only. To avoid confusion, I believe this site should only include the one other form of the Rayleigh-Jeans law: the expansion of the same form of the plank function in terms of frequency. These are the two forms that people use most often. JBcallOnMe (talk) 03:05, 18 January 2009 (UTC)


 * I think that to avoid confusion we should include the other forms, and say how they relate, so that when people see them in sources they can interpret the discrepancy. Dicklyon (talk) 03:12, 18 January 2009 (UTC)

Maybe I'll try to express my opinion a different way: The first I've heard of the last 4 forms of the Rayleigh-Jeans law is when you directed me to that book and that website. I called them "6 equally valid forms" but they're really not equal at all. Standard text books on the subject such as An Introduction to Modern Astrophysics by Carroll and Ostlie and Radiative Processes by Rybicki and Lightman never reference these last 4 expressions at all. I'm not passionate enough to argue with you if you choose to include these last 4 expressions, but because I don't think they belong I won't write them up myself. Truthfully, all I want is the second form of this Rayleigh-Jeans law included on the site so that I can look is up when I need it. Beyond that I'm impartial. JBcallOnMe (talk) 03:33, 18 January 2009 (UTC)


 * I don't know that much about these formulas; these were just the first ones I found, and they didn't look like the one you were adding. I didn't notice any four, just noticed a difference.  Seems like an opportunity to try to clear things up, no?  Dicklyon (talk) 03:45, 18 January 2009 (UTC)

Rayleigh limit
I notice that Rayleigh limit redirects here. I think that is misleading: it should be set to Angular resolution instead. Any thoughts or objections before I proceed? CrispMuncher (talk) 19:19, 13 October 2009 (UTC)


 * Sounds fine. I think that the angular resolution thing is usually called the Rayleigh criterion (which does redirect to angular resolution), but a quick google suggests that the term "Rayleigh limit" is used both as an alternative name for Rayleigh criterion, or for the limit to the stability of charged droplets of liquid (see http://phd.marginean.net/rayleigh.html).  (Maybe both about equally?)  Neither of these have anything to do with the Rayleigh–Jeans law, so it definitely shouldn't redirect here!  Djr32 (talk) 20:20, 13 October 2009 (UTC)

Units of first plot
The units on the graph are given as J m^-2 Sr^-1 when radiance is given in W m^-2 Sr^-1. Is someone able to change this graph. Its either a mistake or at best a confusing abstraction. —Preceding unsigned comment added by Phuech (talk • contribs) 12:41, 9 July 2010 (UTC)

incompatible expressions?

 * $$B_\lambda(T) = \frac{2 c k T}{\lambda^4},$$

and
 * $$B_\nu(T) = \frac{2 \nu^2 k T}{c^2}.$$

seem to have different dimensions. mmkay mm? —Preceding unsigned comment added by 157.193.3.7 (talk) 17:14, 24 April 2011 (UTC)


 * Yes, conversion with nu = c/lambda was made incorrectly in entire article Dims (talk) 09:49, 1 December 2019 (UTC)

Rayleigh-Jeans law and the fatal error for the linear oscillator
It is believed that the Rayleigh-Jeans law strongly disagrees with experimental results at high frequencies owing to the inability to use classical concepts to describe the distribution of energy in the spectrum of the black body. In fact, the cause is incorrect use of the differential characteristics to describe the real processes. The Rayleigh-Jeans law contains three misconceptions. This law does not take into account the limitation of real processes in speed, it does not take into account the limitation of the real processes in energy and the uniform distribution of probability density (any oscillator can have any energy with equal probability) is not suitable to describe the processes that obey the normal distribution law. Reason of the error can be understood just from the classic concept of the linear oscillator. One picture is worth a thousand words. The most obvious explanation would look like with images. Energy of a linear oscillator is the sum of the kinetic and potential energy which changing in the opposite phase (on the image: Ek - kinetic energy, Ep - potential energy, t - time) and does not depend from time. Therefore, differential characteristics (instantaneous speed, instantaneous impulse and instantaneous energy) can be used for calculate the energy of a linear oscillator. In the Rayleigh-Jeans law is assumed that the energy of a linear oscillator is dependent only from temperature (on the image: E - energy, T - temperature, t - time). However, the energy of a linear oscillator can be completely consist only of kinetic energy, or only of the potential energy. Real time is needed for move from one energy state to another. For radiation of low frequency speed of transition is real and description in the Rayleigh–Jeans law is valid. But with increasing frequency time for the transitions between energy states must be less and less. Instantaneous speed (and instantaneous energy) of the such oscillator tends to infinity with increasing frequency. This is the fatal error for the linear oscillator. Therefore it requires a speed limit for transition of a linear oscillator from one energy state to another for high frequency radiation. Looks like nobody noticed how beautifully Planck introduced the dependence of the real process from time - the energy of the linear oscillator (kinetic energy) can not be greater than hν at any temperature. Such explanation could been done long ago (probably hundred years ago). In addition, one would assume (eighty years ago) that there is another solution when the distribution of energy in the spectrum of black body is described by Fermi-Dirac statistics /link/. Linear oscillator has limit by the energy (potential energy) directly in this case. Leonid 2 (talk) 06:19, 8 May 2011 (UTC)

8 mK
What is 8 mK supposed to be ?Eregli bob (talk) 07:18, 26 May 2011 (UTC)


 * Millikelvins, i.e. 8 mK = 0.008 K = -273.142 °C--SiriusB (talk) 12:46, 16 February 2012 (UTC)

Empirically
"In 1900 Max Planck empirically obtained an expression for black-body radiation" - Did he 'empirically' ...? --Gozo032 (talk) 15:53, 31 August 2020 (UTC)

Constants and Taylor series


Yesterday I modified the beginning of the article, with the edit comment "Put in numerical values for the constant terms, and added another term to the Taylor series." This gave:

In physics, the Rayleigh–Jeans law is an approximation to the spectral radiance of electromagnetic radiation as a function of wavelength from a black body at a given temperature through classical arguments. For wavelength $$\lambda$$, it is:

$$ \begin {align} B_\lambda(T) &\approx \frac{2c}{\lambda^4} k_\mathrm{B} T\\ &\approx 8.27816\text{ MW/m}^2\text{per steradian per micron}\times\left(\frac \lambda{\text{micron}}\right)^{-4}\times(T/1000\text{K})\\ \end {align}$$

where $$B_{\lambda}$$ is the spectral radiance, the power emitted per unit emitting area, per steradian, per unit wavelength; $$c$$  is the speed of light; $$k_{\mathrm{B}}$$ is the Boltzmann constant; and $$T$$ is the temperature in kelvins. For frequency $$\nu$$, the expression is instead

$$ \begin {align} B_\nu(T) &\approx \frac{2 \nu^2 }{c^2} k_\mathrm{B} T\\ &\approx 3.07236\times 10^{-22}\text{ W/m}^2\text{per steradian per Hz}\times\left(\frac \nu{\text{GHz}}\right)^2\times(T/\text{K})\\ &\approx 30723.6\text{ jansky per steradian}\times\left(\frac \nu{\text{GHz}}\right)^2\times(T/\text{K})\\ &\approx 0.0731681\text{ jansky per square arc second}\times\left(\frac \nu{\text{THz}}\right)^2\times(T/\text{K})\\ \end {align}$$

The Rayleigh–Jeans law agrees with experimental results at large wavelengths (low frequencies) but strongly disagrees at short wavelengths (high frequencies). This inconsistency between observations and the predictions of classical physics is commonly known as the ultraviolet catastrophe. Its resolution in 1900 with the derivation by Max Planck of Planck's law, which gives the correct radiation at all frequencies, was a foundational aspect of the development of quantum mechanics in the early 20th century.

Historical development
In 1900, the British physicist Lord Rayleigh derived the λ&minus;4 dependence of the Rayleigh–Jeans law based on classical physical arguments and empirical facts. A more complete derivation, which included the proportionality constant, was presented by Rayleigh and Sir James Jeans in 1905. The Rayleigh–Jeans law revealed an important error in physics theory of the time. The law predicted an energy output that diverges towards infinity as wavelength approaches zero (as frequency tends to infinity). Measurements of the spectral emission of actual black bodies revealed that the emission agreed with the Rayleigh–Jeans law at low frequencies but diverged at high frequencies; reaching a maximum and then falling with frequency, so the total energy emitted is finite.

Comparison to Planck's law
In 1900 Max Planck empirically obtained an expression for black-body radiation expressed in terms of wavelength λ = c/ν (Planck's law):

$$B_\lambda(T) = \frac{2 h c^2}{\lambda^5}~\frac{1}{e^\frac{hc}{\lambda k_\mathrm{B} T}-1},$$

where h is the Planck constant and $k_{B}$ the Boltzmann constant. The Planck's law does not suffer from an ultraviolet catastrophe, and agrees well with the experimental data, but its full significance (which ultimately led to quantum theory) was only appreciated several years later. Since

$$e^x = 1 + x + {x^2 \over 2!} + {x^3 \over 3!} + \cdots. $$

then

$$\frac 1 {e^x-1}\sim x^{-1}(1-x/2 \ \dots) $$

and in the limit of high temperatures or long wavelengths, $$x$$ is small, and the term is well approximated by the first-couple of terms of this Taylor series:

$$\frac 1{\exp(\frac{hc}{\lambda k_\mathrm{B} T})-1} \approx \frac{\lambda k_\mathrm{B} T}{hc}-\frac 12.$$

This results in Planck's blackbody formula reducing to

$$B_{\lambda}(T) \sim \frac{2 ck_\mathrm{B} T}{\lambda^4}-\frac{h c^2}{\lambda^5},$$ or, reducing even more, $$B_{\lambda}(T) \sim \frac{2 ck_\mathrm{B} T}{\lambda^4}$$

which is identical to the classically derived Rayleigh–Jeans expression.

The same argument can be applied to the blackbody radiation expressed in terms of frequency ν = c/λ. In the limit of small frequencies, that is $$ h \nu \ll k_\mathrm{B} T $$,

$$B_\nu(T) = \frac{2 h\nu^3}{c^2}\frac{1}{e^\frac{h\nu}{k_\mathrm{B} T} - 1} \approx \frac{2 h\nu^3}{c^2} \cdot \left (\frac{k_\mathrm{B} T}{h\nu}-\frac 12\right ) \sim \frac{2 \nu^2 k_\mathrm{B} T}{c^2}.$$

This last expression is the Rayleigh–Jeans law in the limit of small frequencies.

This was immediately reverted by User:Headbomb, with only the edit comment "no units like that". I find this reversion to be unconstructive. If he thinks that the units I used are not suitable, then he should put better units. Frankly I think the units I chose were useful -- it doesn't matter whether there are "no units like that" (whatever that means!). And the addition I made to the Taylor series is quite interesting and is elementary math. Eric Kvaalen (talk) 07:13, 27 April 2022 (UTC)


 * The numerical values in specific units don't belong here. If a numerical value is to be provided, it should be in prefixless SI units, not in microns or GHz / THz, e.g.
 * $$B_{\lambda} (T) = \frac{2 ck_{\mathrm{B}} T}{\lambda^4} \approx \frac{T}{\lambda^4} \left( 8.278 \times 10^{-15} \mathrm{\frac{J \cdot m}{K \cdot s \cdot sr}} \right) $$
 * (though you could make a different choice of specific units, like using W instead of J/s)&#32; Headbomb {t · c · p · b} 15:01, 28 April 2022 (UTC)

Not obsolete physics
The Rayleigh-Jeans law is not obsolete physics, any more than Newton's laws of motion or Classical electromagnetism are obsolete. There are more modern versions of all three but people still use and research these 3 topics as well. Therefore I'm editing to remove the obsolete physics tag from this article.

A quick search of journal articles for the term "Rayleigh-Jeans Law" since 2019 reveals more than 7000 results. Here is a link to a Google Scholar search.

Here is a paper from 2019 describing using the Rayleigh-Jeans law to model radiation in nanoparticles: "Dimension Dependent Density-of-States Function and the Radiation Laws". The abstract of that paper clearly mentions the Rayleigh-Jeans law: "The concept of dimension dependent density-of-states function (DOS) is vital in the area of nanoscience and nanotechnology. In this paper we show that the same concept leads to the simple and compact derivations of the 3D, 2D and 1D Planck’s radiation laws in one hand and its two dimension dependent extremes namely Rayleigh-Jeans and Wien’s laws on the other hand. Besides we have also studied the 3D, 2D and 1D Stefan-Boltzmann laws in this context." [Emphasis added]

Another paper from 2022: Astrophysical information from the Rayleigh-Jeans Tail of the CMB

Another paper 2021: Energy and wave-action flows underlying Rayleigh-Jeans thermalization of optical waves propagating in a multimode fiber Dllahr (talk) 10:24, 8 March 2023 (UTC)


 * The Raleigh-Jeans law has been obsolete since 1900 or so when the Planck law came about. One may speak of the 1/&lambda;4 dependence at large wavelengths, but that is not the RJ law which claims to apply to all wavelengths. &#32; Headbomb {t · c · p · b} 02:35, 9 March 2023 (UTC)
 * Do you have any references that support your claim? I provided references to current scientific journal articles using RJ law. 2604:CA00:17A:2A1D:0:0:A61:2DC6 (talk) 03:29, 9 March 2023 (UTC)
 * Pick the first reference in this article. RJ Law agrees at long wavelengths, disagrees at short wavelengths, this is called the Ultraviolet catastrophe (or more pointedly, the Rayleigh–Jeans catastrophe), and was resolved by the Planck law in 1900. &#32; Headbomb {t · c · p · b} 03:32, 9 March 2023 (UTC)
 * It cannot have been obsolete since 1900. The Rayleigh-Jeans results were published in 1905, well after it was known that the it would not match the observed spectra. Rayleigh thought that the result meant that equipartition broke down for shorter wavelengths. There is nothing obsolete about the physics behind the Rayleigh-Jeans formula; it is an important classical derivation made with particular assumptions during the early development of quantum theory. We still use classical physics every day in the ranges for which it is appropriate. The 1900 letter that Rayleigh published was not about this law; instead he proposed substituting $\lambda^{-4}$ for $$\lambda^{-5}$$ in the Wien approximation while keeping the exponential term. StarryGrandma (talk) 05:50, 9 March 2023 (UTC)
 * Planck derived the correct law in 1900. The RJ law was obsolete from inception forward. Neither had theoretical basis at the time they were proposed. RJ found its theoretical footing in 1905, Planck in 1906, roughly. &#32; Headbomb {t · c · p · b} 06:00, 9 March 2023 (UTC)
 * This is tricky stuff, especially when the article itself is misleading. Rayleigh and Jeans were trying to figure out what was going on, not promulgating an accepted theory of nature. They believed the measurements were correct and that the relation they published did not match experiments for reasons they were trying to explore. What was going on was in question - Jeans thought the ether was absorbing the high frequency contributions, Rayleigh preferred to give up equilibrium and equipartition to find a relation that matched experiment. The relation they derived is not a theory of physics to become obsolete - they hadn't gotten that far. They were pointing out what didn't work. The relation is just an application of the classical physics of the time given certain assumptions, and still holds in the low energy limit. It ended up being called a law in the sense not of theory but, like Snell's law, a relationship between quantities. StarryGrandma (talk) 07:49, 9 March 2023 (UTC)
 * has argued elsewhere that this law is clearly obsolete. stated that this is cited in the article, but I do not see where. I am not taking a side here on whether or not it is obsolete, just ensuring that the information in this article is verifiable.      &mdash;&hairsp; Freoh 13:47, 9 March 2023 (UTC)
 * This is outside my area of knowledge. I based that opinion on Ultraviolet catastrophe. A "law" that doesn't match observations and the best models seems obsolete to me. I wouldn't really know how best to term that though so I will leave this to you guys. —DIYeditor (talk) 14:10, 9 March 2023 (UTC)
 * I told you multiple times, Ref 1. &#32; Headbomb {t · c · p · b} 14:15, 9 March 2023 (UTC)
 * Where is this described as obsolete? I also do not see where that source says that this law is, just that it disagrees with experimental results at high frequencies.      &mdash;&hairsp; Freoh 14:30, 9 March 2023 (UTC)
 * A law that doesn't replicate reality that's been supplanted by a more accurate law which does is obsolete by definition. &#32; Headbomb {t · c · p · b} 14:35, 9 March 2023 (UTC)
 * Do you have sources that explicitly say that this law was wholly supplanted by Planck's law?     &mdash;&hairsp; Freoh 20:29, 9 March 2023 (UTC)
 * Ref 1. Or any modern physics textbook of your choice. &#32; Headbomb {t · c · p · b} 20:31, 9 March 2023 (UTC)
 * By that criteria you would look in the modern physics textbook and declare Newton's Laws of Motion and Classic obsolete - but they are not, they are actively used by research scientist and engineers very heavily. You have the same exact situation for the Rayleigh-Jeans law - it is a useful approximation under certain conditions (long wavelength) and is used in that context, as in the current modern research papers I cited Dllahr (talk) 10:46, 10 March 2023 (UTC)
 * Neither the laws of motion nor classical electromagnetism are invalidated in any context. Rayleigh-Jeans fundamentally fails and is so physically untenable that its failure at short wavelengths is called the Rayleigh-Jeans catastrophe, spectral radiance goes to infinity, when it fact it drops to zero. There could not be a greater discrepancy between reality and theory. &#32; Headbomb {t · c · p · b} 11:32, 10 March 2023 (UTC)
 * Newton's laws of motion are not valid for small scales - they are superseded by Quantum mechanics, they are not valid for speeds near the speed of light, superseded by Special relativity, they are not valid for motion in strong gravity, superseded by General relativity. This is all stated in the first paragraph of the wikipedia article on the subject.
 * As stated in the intro paragraph to Classical electromagnetism, it does not work at small length scales and low field strengths where it is superseded by Quantum electrodynamics.
 * Rayleigh-Jeans is a useful approximation for long wavelengths that is actively used by scientists and researches as shown in the references above, the same way Newton's laws of motion and Classical electromagnetism are used despite not working under certain conditions. Dllahr (talk) 13:21, 10 March 2023 (UTC)
 * The three laws of motions are completely valid at small scales, within the Heisenberg uncertainty. They are also fully valid in general relativity. &#32; Headbomb {t · c · p · b} 20:15, 14 March 2023 (UTC)
 * The given sources do not support the contention. For example, even the quoted passage from the first one explicitly treats both Wien and Rayleigh–Jeans as extremes of the correct Planck law. The second likewise discussed the Rayleigh–Jeans tail. The third is also discussing the physical implications of the breakdown of the Rayleigh–Jeans curve. (Although the physics of quantum gases and wave condensation are different, the underlying mathematical origin of the condensation process is similar because of the common low-energy divergence of the equilibrium Bose distribution for quantum particles and the equilibrium Rayleigh-Jeans (RJ) distribution for waves.) It makes sense to tag the article as covering an obsolete theory because most of what it's talking about is obsolete, and even adding more material based on more recent uses of the term "Rayleigh–Jeans" won't change that; a page belongs in Category:Obsolete theories in physics if it covers an obsolete theory, not necessarily if everything in it is about one. We don't expel the Caloric theory from that category just because it also discusses Joule and Clausius, or because people still talk about heat flowing like a fluid. XOR&#39;easter (talk) 13:37, 14 March 2023 (UTC)
 * Do you have sources that describe Rayleigh–Jeans as obsolete? The one provided by does not say that Rayleigh–Jeans is obsolete, only that it disagrees with experimental results at certain scales.  makes a good point: the same could be said about all of classical physics, even though it is not obsolete. (I do not think, for example, that conservation of energy should be in .) Wikipedia's verifiability policy requires that the obsolescence be verifiable, not the lack of obsolescence. The burden of proof is on those who wish to  the category to demonstrate that it is obsolete.      &mdash;&hairsp; Freoh 14:33, 14 March 2023 (UTC)
 * How about we remember the Rayleigh–Jeans law as an incorrect hypothesis superseded by that of Planck ? The problem is that the calculations which subsumed the Wien and Rayleigh–Jeans curves were themselves only what we would now call semiclassical approximations. Likewise, Jeans' attempt at avoiding the implications of the equipartition theorem assumed the existence of the luminiferous aether, which as hypotheses go is wrong, wrong, wrong. The Rayleigh–Jeans law is doubly outdated, surviving only as one regime of the Planck law. If there's a better way to express that fact in terms of Wikipedia categories, I'd go with that, but I don't know of one.  The status of the Rayleigh–Jeans curve is very different from the status of energy conservation. The latter holds true in quantum mechanics; it even holds true in general relativity, if you define energy using some scheme like pseudotensors. (The issue is not so much that the idea is wrong, but that it is not always useful, e.g., a mathematically nice definition of "energy" isn't always locally measurable. Historically, though, a pulsar spinning down because it radiates energy via graviational waves was an important confirmation of GR.) XOR&#39;easter (talk) 15:58, 14 March 2023 (UTC)
 * Pretty much yup. Obsolete premises lead to obsolete results. &#32; Headbomb {t · c · p · b} 20:17, 14 March 2023 (UTC)
 * , that looks like a good source to me. I would not be opposed to re-adding Category:Obsolete theories in physics along with a cited sentence to this effect., it seems like to show that this law is obsolete, you would need to show a context where physicists use the Rayleigh–Jeans law  of Planck's law—that is, not simply as an extreme or tail, as  pointed out in your sources.      &mdash;&hairsp; Freoh 01:08, 15 March 2023 (UTC)
 * What does the word obsolete mean? "no longer produced or used; out of date.".  The Rayleigh-Jean law is used, therefore it is not obsolete.  I'm confused why you would argue that it is not used when I have provided multiple references showing it is, and you can easily independently verify that it is being used in modern research.
 * @Headbomb is wrong when stating "The three laws of motions are completely valid at small scales, within the Heisenberg uncertainty. They are also fully valid in general relativity". The laws of motion fail when there is quantum tunneling, full stop.  It's not a matter of Heisenberg uncertainty - the particle that tunnels is directly violating Newtons laws of motion by moving "over" (through) a potential energy barrier that would be impossible by Newton's laws of motion.  There is the Ehrenfest theorem that is a useful guide and approximation under certain circumstances, that relates the center of a wavepacket to Newton's laws of motion - but that breaks down when there is tunneling.
 * Similarly for general relativity, there is no "force" of gravity that can be used with Newton's laws of motion to get the correct results. There are approximations that work well under certain circumstances.
 * If you're going to consider the Rayleigh-Jeans law obsolete you need to also label a large number of other physics and science articles as obsolete. Dllahr (talk) 12:38, 15 March 2023 (UTC)
 * "a potential energy barrier that would be impossible by Newton's laws of motion" Newton's laws of motions say nothing about particles being stopped by barriers. They say
 * A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.
 * When a body is acted upon by a force, the time rate of change of its momentum equals the force.
 * If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.
 * These things are true at all scales. "Out of date" bingo. RJ fails at short wavelengths and is completely superseded by Planck. That other physical models are also obsolete is both irrelevant, and a thing everyone's perfectly willing to accept. Wien is also obsolete. So is the Bohr model. So is the Dulong–Petit law. &#32; Headbomb {t · c · p · b} 19:54, 15 March 2023 (UTC)
 * I do not know where is getting his information, but you are correct that Newton's third law of motion is not always valid. I get the sense that Newton's laws are not  because there are some contexts where they provide a very good approximation and are significantly easier to work with than the more precise theory. I am not sure if this is the case for the Rayleigh–Jeans law. To answer your definitional question, it is not clear to me whether your sources  the Rayleigh–Jeans law or simply  it (and this is admittedly not a clear-cut distinction). I do not have access to all of them, so I could be missing something. Are your sources  the Rayleigh–Jeans law to describe physical behavior and make predictions? If so, could you include quotes?      &mdash;&hairsp; Freoh 00:35, 16 March 2023 (UTC)
 * That paper is half nonsense that just gets by with its conclusion:
 * "As electromagnetic waves also carry momentum, their contributions must also be included in the evaluation of the total momentum of a system."
 * In each of the 3 supposed cases of "failure" of Newton's third law, the author neglects to consider the EM waves generated by the situations. That's like saying "When a bowl of soup sits on the table, mass is not conserved. But that's because you forgot to include the mass of the steam that escaped from the bowl." You can pick up any decent EM textbooks on this like Griffiths' or Feynman's. Or papers like which address the misconception. &#32; Headbomb {t · c · p · b} 00:47, 16 March 2023 (UTC)
 * This article contains (a) a brief summary of an argument among physicists in the early 20th century, made completely irrelevant two decades later; and (b), some elementary calculus that is mostly about how the Rayleigh–Jeans formula can be extracted from the Planck law. Honestly, it's not making a very good argument that this page needs to exist! We already have Planck's law, black body, and black-body radiation. Why have an entirely separate article for one tail of the Planck curve? But even setting that aside, the meat of this article is a discussion of how, exactly, the Rayleigh–Jeans law isn't just outdated, but known to be wrong from the start. Rayleigh knew it needed a high-frequency cutoff! Planck had the right answer by the end of 1900! Both Rayleigh and Jeans' suggestions for fixing their result were based on hypotheses that fell by the wayside, especially Jeans'. If we had a stronger word than "obsolete", this would be a good occasion to use it. Moreover, this is one reason why the comparison to Newton's laws isn't illuminating. We could get into hair-splitting about whether "Newton's third law" only includes massive bodies, like they say in high school, or if it includes momentum carried by fields, but that obscures the physics (the important thing is that momentum is conserved), and it's not even analogous to the situation at hand. People didn't spend two centuries thinking that the Rayleigh–Jeans law was right. It never was an idea with enduring validity. The only thing it's ever meant is the low-frequency regime of the Planck law. XOR&#39;easter (talk) 13:23, 16 March 2023 (UTC)
 * To @Freoh's question - and addressing other points - here is the ArXiv (free preprint) version of one of the articles using Rayleigh-Jean's law:
 * https://iopscience.iop.org/article/10.1088/1475-7516/2022/03/055/meta
 * On page 2: "Such a RBG is motivated by measurements with
 * the ARCADE [47] and LWA1 [48] which have found evidence for it towards the Rayleigh-Jeans part of the CMB.". That is the part of the CMB that is well-described by the Rayleigh-Jeans law.
 * Also on page 2: "We will follow the model of [50] where unstable dark matter particles decay into dark photons with a small mass and non-vanishing mixing angle with electromagnetism which increase the photon count at the Rayleigh-Jeans frequencies."
 * See also reference 50 in this paper: M. Pospelov, J. Pradler, J. T. Ruderman, and A. Urbano, Room for New Physics in the Rayleigh-Jeans Tail of the Cosmic Microwave Background, Phys. Rev. Lett. 121 (Jul, 2018) 031103, [arXiv:1803.07048].
 * This all agrees with what @XOR'easter you are saying - and th key point is that region is well described by the Rayleigh-Jeans law and furthermore scientists actively use the Rayleigh-Jeans law to model it. If it is used, it is not obsolete.
 * Newton's third law, as written, did not include momebtum carried by fields.. When you state that, you're patching the law to fit with modern discoveries. It doesn't change the fact that as it was originally written and used, Newton's third law is incorrect in some situations. That said, it is super useful in a large number of situations!
 * Lastly, as another example, Newton's laws of motion cannot be used to predict or model the behavior of an electron in a hydrogen atom. That is very well established physics.  If you think otherwise, please provide a reference. Dllahr (talk) 15:41, 19 March 2023 (UTC)
 * No, they use the Rayleigh–Jeans tail of the Planck curve. It's right there in the title of arXiv:1803.07048, and in the text just after their Eq. (1). The original physics of Rayleigh and Jeans is outdated, and indeed the original proposal of Rayleigh was outdated within a few months of his making it. No one is using their logic to try and understand the cosmic microwave background. Their names are just a convenient synonym for "low frequency". I'm more and more convinced that the problem with this article is that it exists. One warning sign is that there's not a clear indication of what we should call it. In the GS corpus, "law", "approximation", and "tail" are all about equally common, and "limit" is not far behind. More fundamentally, it doesn't stand on its own either from the perspective of modern physics or as a history topic. Our physics coverage in general has too many article fragments, divided up in ways that make no conceptual sense. This is bad for editors and for readers. It makes flushing out inaccuracies and all other routine maintenance much more laborious than necessary, while also making content just plain harder to find. XOR&#39;easter (talk) 16:04, 19 March 2023 (UTC)
 * I propose moving the content (minus the categories) of this R-J article to a section of the thermal radiation article. -- Ancheta Wis   (talk  &#124; contribs) 14:20, 20 March 2023 (UTC)
 * (I moved my comment from here to below) --Jähmefyysikko (talk) 13:01, 21 March 2023 (UTC)

Still uncited
I would like to point out that Category:Obsolete theories in physics is still unverified within the article. I have stated before that I am comfortable citing 's source about how this law was superseded by that of Planck, but there is no mention of it being obsolete or superseded, and the book that provided is not referenced in the article. Both of these things should be done for this category to be verified. Unfortunately, has protected this article in a version that includes the category which  has challenged and  has repeatedly added without citation. , could you explain this decision? &mdash;&hairsp; Freoh 18:12, 17 March 2023 (UTC)


 * Simple. See here. Daniel Case (talk) 18:15, 17 March 2023 (UTC)
 * Thanks for the clarification, I had not seen that essay before.     &mdash;&hairsp; Freoh 18:23, 17 March 2023 (UTC)

Seek first to understand, then to be understood
—Stephen Covey

Hi, perhaps we, all of us, might apply Covey's goal to settle down without the additional distraction of being widely watched.

--Ancheta Wis   (talk  &#124; contribs) 00:10, 19 March 2023 (UTC)
 * 1) I found an explanation of Gaslighting since I don't understand Gaslighting, but the fact that an editor has gotten to this state is not funny. If a reader is here, they probably want to help out, somehow.
 * 2) One issue is that 'physical law' has the connotation that we, all of us are somehow subject to this law, like gravitation, but the '§scale and scope' of a 'physical law' also needs to be stated before we might understand just where this law is applicable. This article (Rayleigh–Jeans law (R-J)) is silent on its scale and scope, so far. But, at least to me, a law (such as Newton's 2nd law) shifted in the 20th century; R-J can now also be understood as a model which we choose to apply in our respective situations. That means the R-J category could also be Category:Electromagnetic radiation, as Planck explained.
 * 3) Planck (1914) gives a clear explanation of black-body radiation, and subsumes R-J. One possibility might be to apply the R-J formula as a partial Taylor series expansion of Planck's law in its domain of applicability (as a model).
 * 4) In fact, the whole article could be a section of thermal radiation and its category would be moot.


 * I would be okay with merging this article into thermal radiation.     &mdash;&hairsp; Freoh 12:12, 21 March 2023 (UTC)


 * (I moved this comment here from above section to keep the discussion in one place) Can you justify why thermal radiation would be a good destination to merge to? I fail to see the relevance of this law for that article. In my opinion a natural destination would instead be Planck's law. The only problem I see with that merge is that the article is already quite long, and adding more content only makes the situation worse. But perhaps this could be solved by copy editing. Jähmefyysikko (talk) 12:56, 21 March 2023 (UTC)
 * That's a great suggestion. Thermal radiation is a substantial article with experienced editors, and I was trying to figure out how to keep our discussion there at the same level. I noticed that Kerson Huang's book was cited there; Huang's book has a portrait of Ludwig Boltzmann; using Boltzmann's method, Planck 1914 gives a great description (statistical picture) of the little oscillators in a gas, so alternatively, the parameters in the R-J equation are part of the machinery in statistical mechanics. I guess that would mean that a little bit of this R-J article might still survive, tucked away in an efn in its eventual home (maybe statistical physics if not Planck's law?). --Ancheta Wis   (talk  &#124; contribs) 14:05, 21 March 2023 (UTC)
 * So my proposal could be, in the Planck's law article, right after Ultimately, Planck's law of black-body radiation contributed to Einstein's concept of quanta of light carrying linear momentum, after the current refs, add an efn mentioning Rayleigh–Jeans.
 * The efn could mention Rayleigh's radiators, and might also mention how Rayleigh tried to solve his experimental mismatch problem using Regularization (physics). -- Ancheta Wis    (talk  &#124; contribs) 14:26, 21 March 2023 (UTC)
 * Works for me. &emsp;&mdash;&hairsp; Freoh 14:21, 22 March 2023 (UTC)
 * Planck's law seems like a more natural merge target for both this and Wien approximation; they're tails of the same curve. Thermal radiation is a more general concept, as not all thermal radiation is exactly Planckian. If Planck's law gets to be too long and unwieldy, I'd suggest first a copy edit and then perhaps splitting off its lengthy history section. XOR&#39;easter (talk) 01:17, 23 March 2023 (UTC)
 * Thank you for your suggestions for simplifying the problem; as I edit, please fell free to jump in; here is my plan of attack, so far:
 * reduce RJ to an efn in Planck's law; leave Planck's law article alone, including history; I'm depending on its previous editors as much as possible
 * Both tails of Planck's law, R-J equation and Wien approximation will be treated in separate efns.
 * I plan to lean heavily on Planck 1914 (internet archive), as my copy of Planck 1925 (Dover) lives in some box in the basement (I've been working from visual memory). The approximate layout would appear in the efns
 * use content of Wien approximation as the skeleton of the efn in #1, as it has a nice approach for 'scale and scope' of the efn. It uses natural units to emphasize what was known at the time, as well as the experimentally-based constants
 * -- Ancheta Wis   (talk  &#124; contribs) 14:09, 24 March 2023 (UTC)
 * Both RJ and Wien deserve way more than footnotes. At minimum, they deserve entire sections. &#32; Headbomb {t · c · p · b} 02:35, 28 March 2023 (UTC)
 * Both RJ and Wien deserve way more than footnotes. At minimum, they deserve entire sections. &#32; Headbomb {t · c · p · b} 02:35, 28 March 2023 (UTC)