In his book ‘The Theory of Heat Radiation’, Max Planck adduced his theoretical proof of Kirchhoff’s Law of Thermal Emission. However, there are some problems with that approach, some of which we explain in

“The Theory of Heat Radiation” Revisited: A Commentary on the Validity of Kirchhoff’s Law of Thermal Emission and Max Planck’s Claim of Universality. Pierre-Marie Robitaille and Stephen J. Crothers. Progress in Physics 11 no. 2, 120-132 (2015).(edited by Anna V the link no longer works. the paper is here pdf page 121)

My question contains two parts. The first part is very easy: if 'yes' then its done, and Planck's proof is agreed to be false. So, is it false? The second part follows only if your answer to the first part is 'no', in which case I expect a scientific explanation in your answer to the second part. So, if 'no', why is Planck's proof not false? If you don't know anything about Planck's proof, then you can find the relevant information in the cited paper.

  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – David Z
    Feb 16, 2016 at 7:55

2 Answers 2


I'll start by saying that correctly stating Kirchhoff's law is quite tricky. "Emissivity equals absorptivity" in a certain sense, but they may depend on wavelength, and angle of incidence (or emission), and polarization. In magneto-optic materials, you can have high absorptivity from one direction balancing high emissivity into a different direction!! (This is called "Violation of detailed balance".) Kirchhoff's law can be stated in a correct and universal way, but it's more complicated than you may realize.

The second point is that most serious mathematicians / scientists / engineers don't spend time reading 100-year-old papers, and don't rely on or expect these papers to be fully correct. Important results (results that people continue to rely on) get re-derived in countless textbooks, lectures, homeworks, etc. And as time goes on people usually find better ways to explain, think about, and contextualize these concepts than did our pioneering forebears. (It can be fun and useful to read old papers, don't get me wrong, but the pioneers don't get the last word.)

As a matter of fact, I have not read Planck's paper and as far as I know it may have errors in it. But I know several airtight proofs of Kirchhoff's law from modern textbooks and papers, and that's why I believe it.

I have, however, looked at the Robitaille-Crothers paper, and they just seem so totally confused about basic aspects of thermal radiation that I'm embarrassed for them.

Here is a typical example from their paper:

It remains an experimental fact that good reflectors, such as silver, are never utilized to construct blackbodies, in direct contradiction to Kirchhoff’s claim that cavity radiation is independent of the nature of the walls from which it is comprised.

I encourage anyone reading this to borrow a thermal infrared camera and take it into a room with reasonably uniform temperature and no windows / lights / etc. Let's say a bathroom, which has a nice piece of silver in it---the mirror! Look at the wall with the camera - it has a certain glow. Now look at the mirror - you'll see the same glow with the same intensity. (Isn't that obvious? You're just seeing the reflection of the opposite wall!) In fact, anywhere you look (except your own warm body) will have the same glow from thermal radiation. That's what Kirchhoff, I imagine, was saying. The bathroom is a cavity, and indeed everywhere you look, you'll see the same uniform glow with the thermal infrared camera, whether it comes directly from a wall, or indirectly from one wall after multiple bounces off other walls, or even from the air if it's foggy.

So you can (and should!) check for yourself that having some silver walls does not prevent a closed cavity from having a blackbody radiation spectrum inside. At the same time, using exclusively silver mirrors would be a silly way to make a laboratory blackbody source! (It's not strictly impossible to do so, it just entails working unnecessary hard.) There's no contradiction here, unless you're hopelessly confused, as the authors appear to be!

  • $\begingroup$ Unfortunately you have not even addressed the actual question. Please read the question so that you answer the question instead of making a comment that is not an answer to the question. $\endgroup$ Feb 9, 2016 at 8:31
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    $\begingroup$ I believe Planck's proof because I never saw any reason to doubt it. And having read the linked paper, I still do not see any reason to doubt it. Additionally, I know that the result is right because I know several airtight proofs from reading modern textbooks, often crediting Planck. Admittedly, it is possible that Planck stated a true result but gave a false proof. But it suggests that is proof is probably by-and-large correct. Considering all these things, that is why I believe Planck's proof is not false. My belief is not an especially strong belief, but there you have it. $\endgroup$ Feb 10, 2016 at 14:04
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    $\begingroup$ Thanks for your admissions. I understand that you have in fact never studied Planck's proof of Kirchhoff's Law of Thermal Emission, and so you don't know it. Hence, unfortunately, you have still not addressed my question. I reiterate: is Planck's proof of Kirchhoff's Law of Thermal Emission false, and if not why not? to answer this question you will have to first study Planck. His book is free online, as in the references of the paper I cited. $\endgroup$ Feb 10, 2016 at 14:36

As an experimentalist, I know that black body is dependent on materials, which is taken into account by the emissivity . I always took the cavity model of the black body formula as an idealized tool to fit observed experimental distributions, the only contact with reality being the oscillators envisaged.

The formula fits , and the experimentally best fit is the CMB radiation . Even the sun's irradiance, which shows deviations, still follows the black body and not the rayleigh-jeans formula. .

I read the abstract of the link you give, and have no problem if you theoretically prove that reflections and what not, play a great role in the black body formula. Experimentally this true, as I said.

If you prove this theoretically, well done, particularly if you give a formula for emissivity. Lets see if a theoretically inclined user replies to your question.

I take objection to the last part of the abstract though and am puzzled if this was peer reviewed:

As a direct consequence, the constants h and k do not have fundamental meaning and along with “Planck length”, “Planck time”, “Planck mass”, and “Planck temperature”, lose the privileged position they once held in physics.

Actually when I think about it, it makes me laugh. The place in data from experiments of of h and k is supported by so many measurements , independent of black body radiation assumptions, that the claim from preposterous becomes funny. That "once" is really hillarious.

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    $\begingroup$ anna v: Unfortunately you have not addressed the question at all. Please read the question. $\endgroup$ Feb 8, 2016 at 16:27

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