Question
Asked 5th Apr, 2014

Is Kirchhoff's law of thermal emission now dead?

Professor Pierre-Marie Robitaille has very recently presented a phenomenal conference presentation in which he has conclusively proven that Kirchhoff's Law of thermal emission is false. This will rock physics to its very core. It also eliminates the so-called Cosmic Microwave Background and hence the Big Bang Cosmology. Here is his talk, which follows up his series of papers published in the journal 'Progress in Physics':
Professor Pierre-Marie Robitaille, ‘On the validity of Kirchhoff’s Law’:

Most recent answer

25th Sep, 2021
Y.C. Zhong
ERICHEN Consulting
Stephen Crothers Indeed, this is an important issue to be discussed. It is know today that absorption and radiation can be either resonant or non-resonant, or both, as observed in the atmosphere. It seems unlikely the blackbody radiation formulated by Kirchhoff and Planck can be trusted.

Popular answers (1)

10th Apr, 2014
Kai Fauth
University of Wuerzburg
I have now taken the time to watch the entire talk. Not convincing, sorry.
I found interesting some of the early stuff like the thermal emissivity of gases (and its temperature dependence). But for a discussion of black body radiation, gases certainly fall short of the opacity that is required (as the speaker himself formulates it later, if I recall this correctly).
In my perception, Robitaille is not presenting a clearcut and really self contained, logically sound explanation of things.
When I present the rationale of cavity radiation, then it's all focussed on the radiation, radiation states (= modes of the electromagnetic radiation in the cavity), the notion that each mode (state) carries the same statistical weight, and that probabilities of states being "occupied" (excitations are being found to be active) follow Boltzmann statistics. Then, under the conditions of a canonical statistical ensemble (i.e. under the assumption that the cavity closely enough matches the conditions for such an ensemble to be realized), Planck's law follows....mathetematically in the limit of an infinitely large cavity only.
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All Answers (65)

8th Apr, 2014
Stephen Crothers
Alpha Institute of Advanced Study
It's very quiet out there. Are the Relativists unhappy? Without Kirchhoff's Law of Thermal Emission their CMB is dead and buried, along with their Big Bang fantasy, and much of physics is in trouble too. Strange - nobody game to offer arguments or even comments on the most important thing to happen in physics for 100 years or more.
2 Recommendations
8th Apr, 2014
Guoliang Liu
Independent Researcher
Dear Stephen,
I suggest that you link this question up to the maximum of six topics including cosmology and thermodynamic.
8th Apr, 2014
Stephen Crothers
Alpha Institute of Advanced Study
Dear Guoliang Liu, I have added as suggested. Thanks.
8th Apr, 2014
Guoliang Liu
Independent Researcher
Dear Stephen,
You are welcome.
Would you mind adding the link to Professor Pierre-Marie Robitaille's paper in the journal 'Progress in Physics' as well? Thank you.
9th Apr, 2014
Guoliang Liu
Independent Researcher
FYI:
A Critical Analysis of Universality and Kirchhoff's Law: A Return to Stewart's Law of Thermal Emission
An Analysis of Universality in Blackbody Radiation
9th Apr, 2014
Stephen Crothers
Alpha Institute of Advanced Study
Robitaille P.-M.
Kirchhoff's Law of Thermal Emission: 150 Years
Robitaille P. M. L. Blackbody radiation and the carbon particle, Prog. in Phys., 2008, v. 3, 36–55
Robitaille P.M.L. On the validity of Kirchhoff’s law of thermal emission. IEEE Trans. Plasma Sci., 2003, v. 31(6), 1263–1267
Robitaille P.M.L. An analysis of universality in blackbody radiation. Progr. in Phys., 2006, v. 2, 22–23
Robitaille P.-M.
On the Equation which Governs Cavity Radiation (Letters to Progress in Physics)
Robitaille P.-M.
A Critical Analysis of Universality and Kirchhoff’s Law: A Return to Stewart’s Law of Thermal Emission
Robitaille P.-M.
Further Insight Relative to Cavity Radiation: A Thought Experiment Refuting Kirchhoff’s Law
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9th Apr, 2014
Kai Fauth
University of Wuerzburg
I have just read into a couple of pages of two of Robitaille's papers. My impression is that there are severe flaws in his arguments.
(1) In the Letter to Progr. Phys. (Vol. 10, 2014, p.126), already in eq. 1, if we set epsilon equal to kappa (see eq. 2), then the left hqnd side is unity, and so would therefore have to be the Planck function, which it is not.
(2) All subsequent lines add nothing new, and I cannot see any progress in eq. (5) with respect to (1) which I believe to be wrong. (Following the authors argument to eliminate kappa, I can do the same with epsilon, since kappa=epsilon (remember eq. 2) and we fall back on f(T,nu)=1, which is not the case)
(3) I would think that eq. (1) is an improper rendition of Kirchhoff's law of radiation.
(4) all arguments resting on universally setting e.g. rho =0 and/or rho=1 violate known laws [well, I consider them known and understand/accept them] of interaction of matter with radiation (Kramers Kronig relations) and cannot therefore be expected to deliver universally true statements.
This latter point also applies to the paper in the previous issue of the same journal (ibid., p.38 ff).
His argument (applied to two cavities) lead the author to the conclusion that he can prove Kirchhoff's law to be false. My conclusion is different: under the (physically unreasonable & fundamentally impossible) conditions proposed by the authors, there is no mechanism to establish thermal equilibrium between the inner cavity and the radiation field it encapsulates. Kirchhoffs law of radiation therefore does not apply and cannot be proven wrong here.
I may be wrong in what I write but I actually don't believe I am. I'd tend to not take (these two, at least) Robitaille's papers very serious, on these grounds.
1 Recommendation
10th Apr, 2014
Kai Fauth
University of Wuerzburg
I have now taken the time to watch the entire talk. Not convincing, sorry.
I found interesting some of the early stuff like the thermal emissivity of gases (and its temperature dependence). But for a discussion of black body radiation, gases certainly fall short of the opacity that is required (as the speaker himself formulates it later, if I recall this correctly).
In my perception, Robitaille is not presenting a clearcut and really self contained, logically sound explanation of things.
When I present the rationale of cavity radiation, then it's all focussed on the radiation, radiation states (= modes of the electromagnetic radiation in the cavity), the notion that each mode (state) carries the same statistical weight, and that probabilities of states being "occupied" (excitations are being found to be active) follow Boltzmann statistics. Then, under the conditions of a canonical statistical ensemble (i.e. under the assumption that the cavity closely enough matches the conditions for such an ensemble to be realized), Planck's law follows....mathetematically in the limit of an infinitely large cavity only.
7 Recommendations
10th Apr, 2014
Guoliang Liu
Independent Researcher
Dear Kai Fauth,
Thank you for your comments. You found the stuff like the thermal emissivity of gases and its temperature dependence interesting, so do you agree his argument that the mechanism of black body radiations is not clear, and only solid lattice can produce black body radiations?
10th Apr, 2014
Kai Fauth
University of Wuerzburg
Well, unlike his opinion, mine is (in agreement with 'contemporary understanding', which Robitaille critisizes) that the details of production are not required as long that you can (i) sufficiently well rely on thermal equilibrium and (ii) accept the principles underlying Boltzmann statistics and their applicability to the present case.
I'll have to continue this later, got to head off and travel today, sorry.
1 Recommendation
10th Apr, 2014
Hugo Alberto Fernández
National University of Technology - UTN - Buenos Aires
Dear colleagues
I agree with Kai Fauth on incorrectness of Robitaile's article ("On the Equation which Governs Cavity Radiation"). Nevertheless, some aspects requires attention.
- The equation (1) is correct (Kirchhoff's law).
It would be convenient to express the law as:
e=k f(T,v)
- The first error is the assumption that emissivity is e=1 (for black body)
It must be: e= f(T,v)
- The second important error is considering that a perfectly reflecting cavity can be applied with Kirchhoff's law.
As Kai Fauth pointed, this (ideal) cavity do not admits thermal equilibrium, which is a necessary condition.
I believe that this particular paper has not scientific value.
1 Recommendation
10th Apr, 2014
Guoliang Liu
Independent Researcher
Dear All,
Even though there are some mistakes in the paper, Professor Robitaille's arguments against the universality of black body radiations are base on experiments.
Could anybody point out the flaws on those experiments, or provide even better experiment data?
10th Apr, 2014
Kai Fauth
University of Wuerzburg
Hugo, I agree that Kirchhoffs law can be written in that form, but then - as you state it - with a physically different meaning to epsilon than expressed in the paper.
Although I do not know this for certain, I would think that there is a specific reason why in the early years the idea of ideally reflecting (perfectly metallic) cavity walls was maintained. Such boundary conditions allow the most simple construction of the mode spectrum for the electromagnetic field in the cavity (*). As we said above, (i) neither is this physically possible (ii) nor does equilibrium then ever occur. The trick is then to insert the "piece of carbon" (or whatever).
Robitaille now appears to think that this combination is essential. It isn't, neither is it critical. That was understood later. Therefore I think Robitaille is criticizing idealizations which indeed are not entirely correct or possible physically but these idealizations do not hide anything nor are they responsible for the result.
(*) at finite size the mode spectrum ("density of states") does also depend on the shape of the cavity. Again this dependence is vanishing in the limit of (very) large cavities.
Finally, concerning the entire discussion of the topic, one has to be very, very careful not to intermix optical properties as we perceive them with absorptivity and emissivity in thermal equilibrium. Glas is transparent in the visible, but heat it to, say 1000°C and you will see that it does emit visible radiation!! But both, the observation of radiation from the hot body and the observation of light being transmitted usually relate to situations which are not representative of thermal equilibrium, unless you take particular precautions to approximate equilibrium conditions. The equilibrium we talk about is between the material in question and the electromagnetic radiation "ensemble" or field.
While i think there are more instances in Robitaille's talk where things get twists which appear incorrect to me, I'll leave it at that for the moment.
With respect to the question of black or grey body radiation from or in the (supposedly gaseous) sun I'd have to dig deeper to produce an opinion of my own. But I reckon that most of our every day experience is totally inadequate in discussing the realistic temperature and density range as well as the enormous length scales encountered in stars. I do not know whether Robitaille has calculated this stuff to substantiate his conclusions. In his talk I have not found any evidence for this being the case.
1 Recommendation
10th Apr, 2014
Kai Fauth
University of Wuerzburg
Dear Guoliang Liu,
I see your point. But then we should clearly enumerate each and every single experiment, and discuss them one by one, including their significance (esp. concerning equilibrium etc) and check out for the newest, hopefully most significant data. You're welcome to open that discussion.
4 Recommendations
12th Apr, 2014
Demetris Christopoulos
National and Kapodistrian University of Athens
Can somebody make a brief summary of the new results?Thank you.
1 Recommendation
12th Apr, 2014
Guoliang Liu
Independent Researcher
14th Apr, 2014
Kai Fauth
University of Wuerzburg
Dear Guoliang Liu & dear all,
since noone is actually forthcoming with specific experiments to be scrutinized critically, I propose a reading exercise to start with. Attention: this is not a short article, rather a long review. The link is given below. The reference is:
J. Hartmann, "High-temperature measurement techniques for the application in photometry, radiometry and thermometry", Physics Reports 469, 205–269 (2009). It contains a nice review of the historical development in the field.
Just to make it clear: J. Hartmann most probably does not contest the assumption of Planck's law being universal.
I have only partially read through the article, and I won't be able to finish reading it quickly, since this is not my primary occupation. What I like about the article and why I think it might be a good starter, is that it describes quite a few technical realizations of approximate black body cavity radiators. By no means is carbon/soot/graphite the only material used. By no means is a (very) high absorptivity/emissivity wall material required to achieve near unity effective emissivity of the radiation source. As an example, let me quote from the text, at some 60% of the article:
" The intrinsic emissivity of the cavity material, sandblasted and oxidised Inconel®, is approximately 0.75. Together with the geometrical dimensions shown in Fig. 25 an emissivity of 0.9996 is obtained."
It becomes also clear, that doing precision experiments is by no means trivial. Once again, my respect for those doing such painstaking work is growing. It is also very interesting to see that actually there is ample economic justification to do it since the lighting industry requires reliable standards.
I'll be happy to read your comments here.
1 Recommendation
15th Apr, 2014
Kai Fauth
University of Wuerzburg
Yet another link, this time to a solid material with negative differential thermal emittivity del(epsilon)/del(T) (in a small temperature range). The (indirect) link is included below.
With respect to the negative thermal emittance of gases I have a question, which PML Robitaille might answer (since he seems following the thread): the curves you displayed were obtained under which conditions (constant density, constant pressure....) ?
15th Apr, 2014
Guoliang Liu
Independent Researcher
Dear Kai Fauth,
Thank you for the links and comments.
Since the mechanism of black body radiation is not clear, as far as there is one exception will put the universality of Planck's law in doubt. If the negative thermal radiations of gases can be confirmed, then the standard solar model has to be revised.
15th Apr, 2014
Stephen Crothers
Alpha Institute of Advanced Study
Kai Fauth – You have not understood the issues. I number my replies in accordance with your initial numbered comments.
(1) Your remark is incorrect. We are dealing with emissivity here. An emissivity of 1 corresponds to a blackbody spectrum by definition, as emissivity is defined by the emission of the object in question divided by the emission of a corresponding blackbody (same surface area and shape). You get an emissivity of 1 across the entire spectrum. That is the Planck function in this context! If you want, you can multiply the emissivity by the blackbody function and convert it to emission. I refer you to Planck's book ‘Heat Radiation’ (see Section 26, where Planck uses the coefficients of emission and absorption, which correspond to emissivity and absorptivity, where he writes K_v = e_v/a_v). In Section 48 of his book Planck admits that his equation in Section 26 cannot be used when e_v = 0 and a_v = 0 because it results in 0/0 which is indeterminate, just as Robitaille has argued.
If you examine Planck's book (see Sections 26-44) you will see that Kirchhoff's law is defined in terms of emissive power and absorbing power (see Eq. 48 on page 40 in Planck's book). Now emissive and absorptive powers can be written simply as emissivity and absorptivity by dividing both the numerator and the denominator by the same factor. In so doing we do nothing to the fraction. The emissivity of a body is simply equal to its emissive power divided by the emissivity of a blackbody of the same dimension and shape. Likewise, absorptivity is simply equal to the absorptive power of the object divided by the absorptive power of a blackbody of the same dimension and shape.
Mathematically Robitaille has done nothing to Kirchhoff's equation. If you want, you can simply multiply both the numerator (epsilon) and the denominator (kappa) in Robitaille’s Eq. 1, by the blackbody function for an object with equal surface areas and shape, and you get the equation back exactly as Planck writes it. You would then have E/A = f(T,v) versus Robitaille's epsilon/kappa = f(T, v). The result is identical.
In terms of emissivity, Planck's function for a blackbody is equal to 1 - by definition - over the entire spectral range. Emissivity is defined as the emission of a material divided by the emission of a corresponding blackbody (same dimension and shape) at the same temperature! Whether one expresses Kirchhoff's law in terms of emissive power or emissivity, once again, the result is the same.
(2) You have not understood emissivity. Your arguments against Robitaille's paper again are not correct. For a blackbody, the absorptivity is equal to 1, so the Planck function is, I reiterate, equal to 1 over the entire frequency range. If you want to look at absorbance, you should multiply kappa by the absorbance function for a blackbody of the same shape and dimension at the same temperature.
(3) Your statement is simply false. In fact, Robitaille gives a proper representation of Kirchhoff's Law. I refer you to Eq. 42 in Section 39 of Planck’s book for verification, where he writes q^2K_v = q^2(e_v/a_v), which he says “does not depend upon the nature of the substance, and is, therefore, a universal function of the temperature T and the frequency v alone.”
(4) Contrary to your claim, Robitaille is allowed to set rho either to 1 or to zero, as even Planck uses the perfect reflector throughout his text (rho=1, kappa = 0). By your claim are you also arguing that Max Planck has also violated “known laws” in doing so? The point is that Kirchhoff's law claims to be applicable to all cavities irrespective of the nature of the walls. Obviously, a perfect reflector is a type of wall and when we use it, we end up with Kirchhoff's law becoming undefined. That is the entire point. A law cannot be applicable to all states if it has a limit which is not defined. Kirchhoff himself allows these scenarios by claiming that his law is applicable to all situations independent of the nature of the cavity walls. I refer you also to the original papers by Kirchhoff, cited in Robitaille’s papers. Kirchhoff’s Law of thermal emission is not universal. Robitaille will prevail.
15th Apr, 2014
Stephen Crothers
Alpha Institute of Advanced Study
Guoliang Liu - The solar model has already been thoroughly revised. The Sun is not a gas, it is condensed matter.
Robitaille P.-M.
Forty Lines of Evidence for Condensed Matter — The Sun on Trial: Liquid Metallic Hydrogen as a Solar Building Block
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15th Apr, 2014
Kai Fauth
University of Wuerzburg
Stephen, thanks for the comments above, I'll look into that.
Stephen & Guoliang, I have read a bit into this paper and can't help but not finding it not quit convincing. In my perception, Robitaille is relatively quick in critisizing some aspects to dismiss an ansatz or theory entirely. On the other hand I have not yet seen a single proof or calculation that conclusively demonstrates the superiority of his ansatz.
I may have missed that so far - in any case I am dearly missing it.
Back to materials properties: let's stick to condensed matter for now (avoiding the sun related discussion). We hopefully agree that the wall will be made up of normal matter, i.e. nuclei and electrons. We will then hopefully agree that the material will possess a nonzero, frequency dependent polarizability, the real and imaginary parts of which adhere to the Kramers Kronig relations.
No such material can possess a frequency independent reflectivity (be it zero or one or whatever other value). It is impossible. (This would be checked e.g. by determining the dielectric function from the polarizability, and the (complex, of course) refractive index next. Take Frenel's equations then to look at reflectivity, which takes its simplest form at normal incidence.)
Assuming a perfectly reflecting wall of a cavity is therefore an idealization. Now, idealizations are there to simplify our thinking, taking it away from problems which make an analysis (sometimes utterly) more complex, without really changing the heart of things.
Such idealizations may be misleading if they actually over-simplify the problem or take away the very core of it. Idealizations therefore need careful checking. I indeed do believe that Planck was aware of that idealization wherever he applied it. The conclusion would be that while describing the cavity system this way (illetigimately, if you like) reduces the complexity of the problem a lot, it does not destroy the adequateness of the physical picture emerging from this line of thought. The idealization eases the argumentation but does not change the essentials.
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18th Apr, 2014
Kai Fauth
University of Wuerzburg
Stephen, in (1) you write
a) The emissivity of a body is simply equal to its emissive power divided by the emissivity of a blackbody of the same dimension and shape.
I agree with such a definition, it causes no problems.
b) Likewise, absorptivity is simply equal to the absorptive power of the object divided by the absorptive power of a blackbody of the same dimension and shape.
I could also agree with that, but what you need to get there is different from what you do to get from emissive power to emissivity.
Let me use capital letters (E,K) for emissive and absorptive power then in thermal equilibrium we'd argue that
E_v = K_v * S_v
Where S_v describes the spectral distribution of the radiation hitting the object. (From this, we can see that E and K do not share the same physical units. While E has energy in the denominator, the energy is contained in S on the right hand side, and K describes the fraction of the light being absorbed). Now let's divide both, left and right sides by (essentially) the Planck function (i.e. the bb emissive power, properly normalized, and at appropriate temperature) F_v, yielding
E_v / F_v = K_v * S_v / F_v
On the left side this will give emissivity in the above sense (hope you'll agree). On the right side it makes most sense to leave K as is and to divide S by F. Then (and only then) the normalized S function is equal to 1 if S already was the Planck function. But if we do that then there's nothing left to divide K with.
This does actually not change much to what you say above, besides that the fraction E/K is not unchanged due to division by the same factor. You *could* do this, but then the Sectral distribution function S is not changed (not unity).
Maybe we start by aggreeing on this?
Btw., if S_v =F_v then we get E_v / F_v = K_v. In this sense, if we would like to say emissivity=absorbtivity in thermal equilibrium, then K_v is already the absorptivity.
18th Apr, 2014
Kai Fauth
University of Wuerzburg
Stephen, I was just about to go back into one of Robitaille's recent papers and see what happens based on what You and I wrote above,
[P.-M. Robitaille, "On the Equation which Governs Cavity Radiation", Progr. Phys 10, 126 (2014)]
His equation (1) reads
e_v / k_v = f(T,v)
with e: emissivity, k: absorptivity, f: Planck function (later, r: reflectivity shall be used). As we saw above and as you also wrote in your post, in these terms the Planck function is equal to unity. In this case I would say the paper reveals nothing. Equation (5), for example
e_v = f(T,v) - r_v
reduces to the (trivial, after eqns (2) and (3))
e_v = 1 - r_v.
This already follows from the notions k_v + r_v = 1 (the limit of a sufficiently thick cavity wall to be entirely opaque) and e_v = k_v (following from thermal equilibrium). f(T,v) is neither needed nor do we learn anything about the cavity or the "equation which governs it".
Would we have divided K_v by F_v (see previous posts), then we would have retained the Planck function explicitely. But we would have lost another relation since
E_v / F_v is not equal to K_v / F_v, instead
E_v / F_v = K_v
(i.e. K_v of the previous post is equal to k_v in this one, as said before).
Can we agree on that?
Mr. Robitaille, since I've seen that you follow the thread, I'd appreciate if you voiced your opinion here.
1 Recommendation
22nd Apr, 2014
Kai Fauth
University of Wuerzburg
Stephen, concerning your point (4):
You write
Contrary to your claim, Robitaille is allowed to set rho either to 1 or to zero, as even Planck uses the perfect reflector throughout his text (rho=1, kappa = 0).
Planck using this is not per se a justification. In any case it is an idealization. Conclusions from idealizations can go wrong, but need not go wrong. It is important to check their purpose. The perfect reflector is certainly pathological (equilibrium cannot be established). At the same time it is physically impossible.
You ask:
By your claim are you also arguing that Max Planck has also violated “known laws” in doing so?
I have written before that I believed Planck to have been aware of the impossibility and thus the nature of this and related idealizations. Actually the point was raised by contemporary critics (this is mentioned in Schirrmacher's paper). But the Kramers-Kronig relations I have mentioned above might well not have been known the way we do know them today: the paper apparently dates from 1926.
You write:
The point is that Kirchhoff's law claims to be applicable to all cavities irrespective of the nature of the walls. Obviously, a perfect reflector is a type of wall and when we use it, we end up with Kirchhoff's law becoming undefined. That is the entire point.
A law cannot be applicable to all states if it has a limit which is not defined.
In principle you have a point here. However, if that singular point were the only shortcoming I could sleeep calmly - knowing that the perfect reflector is both, potentially pathological and physically impossible. Robitaille argues beyond that, however.
What I miss in all of Robitailles writings - as far as I have read them (still a minority) is that he actually computes the spectral density from a cavity of "material A" (and maybe some body inside it, from "material B") and how this spectral density relates to equilibrium properties of the material(s). And it would be nice to see a comparison of that to actual experimental data (to actually demonstrate that his approach leads to a better agreement with observations).
Would someone please point me to it in case I have missed it.
1 Recommendation
23rd Apr, 2014
Kai Fauth
University of Wuerzburg
Somehow, it feels lonely here. Never mind.
I have indicated above that I see problems with Robitaille's arguments pertaining to two cavities in one of his most recent papers (Progr. Phys., v.10, 2014, p.38-40)).
I find it sufficiently problematic to have decided it might be worth submitting a comment to the journal, which I hope to complete this week.
While doing this, another idea involving two cavities came to my mind. I believe that going through this gives rather more credence to universality of the thermal radiation spectral density than the opposite. The construction is so simple that I cannot believe it has not been considered by others before. Therefore, if you are aware of anything like this, please notify me. Also, it is so simple that arguments from it might be flawed. Discussion shall be most welcome.
The concept is enclosed as a figure. Consider two cavities (A,B), made from two different, real materials. Both are in thermal contact with a heat bath (defining a temperature T) and adjacent to each other. Actually there is a (magical :-) shutter device in between them, which may serve to connect the cavity volumina ("shutter open") and to separate them (shutter closed). While I don't believe the shutter material to play any role, we may find it convenient to assume that it is constructed such as to expose an opaque layer of material A to cavity A and an opaque layer of material B to cavity B.
In thermal equilibrium and with the shutter closed, cavity A will host electromagnetic radiation of some spectral composition, characteristic of material A, S_(A)(v,T). Likewise, cavity B will host electromagnetic radiation of some spectral composition, characteristic of material B, i.e. S_(B)(v,T).
Let us recall what that means: The energy uptake of material A from the radiation in cavity A is equal to the energy emission from wall of type A into cavity A (Stewart's law). Likewise, the energy uptake of material B from the radiation in cavity B is equal to the energy emission from wall of type B into cavity B. This is true for any spectral component v.dv (infinitesimal interval).
We may invoke the zeroth law of thermodynamics and say that the cavity volumina are in equilibrium with each other in this situation, despoite the fact that they are not interacting directly. This is because cavity housings A and B both are in equilibrium with the heat bath, with each other and - separately - with the cavity they host.
Cavities A and B being in equilibrium means (at least) that there will be no net energy flow between the cavities when they are allowed to "interact". Let us now open the shutter. If the spectral densities S_(A)(v,T) and S_(B)(v,T) differ in some interval (v,v+dv) then there will be a net flow of radiative energy from one cavity into the other. As soon as that happens, absorption and emission will get out of balance in this frequency interval and thus a situation of non-equilibrium is created. This opposes the initial assumption of equilibrium having been reached between all constituents of the system.
For the moment I can't see how to circumvent this by other means than assuming S_(A)(v,T) = S_(B)(v,T) [and hence universality for arbitrary real materials].
Opinions welcome, including objections.
23rd Apr, 2014
Guoliang Liu
Independent Researcher
Kai Fauth,
Because all cavities can only be constructed by condensed matter, so your argument can only prove that Planck's law can be applied to arbitrary condensed matter.
23rd Apr, 2014
Kai Fauth
University of Wuerzburg
Which would be much more than Robitaille is willing to concede.
He usually (and in my view incorrectly) insists on S(v,T) to explicitely depend on the material (its reflectivity, to be precise).
23rd Apr, 2014
Hugo Alberto Fernández
National University of Technology - UTN - Buenos Aires
Dear Kai Fauth
I think that your proposal needs some discussion on thermodynamic equilibrium.
In my opinion we have two different systems, both are in thermal equilibrium which is not the same as thermodynamic equilibrium (there are not initial interaction between them).
I will think some initial modifications of this experiment.
Regards
23rd Apr, 2014
Kai Fauth
University of Wuerzburg
Dear Hugo,
the "zero'th law of thermodynamics" states: be system A in equilibrium with system B. Be simultaneously system B *also* in equilibrium with system C. Then system A may be considered being in equilibrium with system C. As a consequence, no heat flow shall occur between systems A and C when brought into interaction. Now let system B be the heat bath and i believe you'll get to my result in few steps. Let me know where exactly you think otherwise. I'm interested.
Edit: it took me a moment to discern your distinction of thermal and thermodynamic equilibrium. I'll be interested to see what flows out of that.
5th May, 2014
Stephen Crothers
Alpha Institute of Advanced Study
Kai Fauth,
I suggest that you study this paper as well:
On the Equation which Governs Cavity Radiation II
5th May, 2014
Kai Fauth
University of Wuerzburg
I will, Stephen, but it sets out with the equation which I believe to be nonsensical. Nevertheless, I'll give it a go.
(Just as a reminder - why I believe it to be nonsensical: If we deal with thermal equilibrium, then emissivity = absorptivity. Therefore add r_v to both sides of eqn (1) to obtain 1=f(T,v). Imho it is at least utterly misleading to use a form of the equation in which f(T,v)=1, because there is no dependency left. Then I expect it to be next to impossible to derive any conclusion concerning the Planck function.)
And I'd suggest you seriously exchange arguments here. Above, at some point I asked whether you'd agree to some ideas of mine until a certain point. I'm still waiting for an answer.
3 Recommendations
7th May, 2014
Pradosh K. Roy
Independent Researcher
If Kirchhoff's Law of Thermal Emission is invalid , then Planck's Quantum Hypothesis Epsilon = h. Nu is also invalid. However , One of the famous papers of Einstein as well as numerous experimental evidences confirm that the quantum hypothesis is a valid law of nature. Hence , Kirchhoff's Law of Thermal Emission is valid. QED.
1 Recommendation
1st Feb, 2015
Stephen Crothers
Alpha Institute of Advanced Study
Robitaille P.-M., Crothers S. J.
"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,
1 Recommendation
18th May, 2015
Clifford Chafin
North Carolina State University
What an interesting discussion.  I've been trying to come to dynamical understanding of thermal equilibrium almost since I started studying it and have never come to any complete satisfaction.  The radiation spectrum of the sun outside the atmosphere is a pretty good black body which I've always found kind of shocking.  There is no cavity and it is a gas so I'm not clear what the value of such cavity arguments are here.  If one puts a set of gas atoms in a perfectly reflecting container in some excited states and wait for thermal equilibrium through photons one does not get a black body, at least based on quantum mechanics and how it handles absorption and emission.  Such a state often does not tend to anything like thermal equilibrium.  The hoped for effects of dynamic typicality and eigenstate equilibration hypotheses don't seem to work here.  
If we can resolve this problem we can resolve much of this dispute at a more microscopic level without the need for macroscopic notions and thermodynamic arguments.  
31st Oct, 2015
Lawrence Margulies
University of Guelph
This guy is a well known crackpot who attacks straw men in every theory he can. All his arguments can be summarized in this form: In reality there is no such thing as a perfect circle therefore any physical theory which uses the mathematically term Pi is invalid.  The only journal that publishes his nonsense is one which does violates the basic principle of open and transparent peer-review and which curiously he happens to be a member of the editorial board.
I looked into him because I got some unsolicited spam email from him about his quack theories and fake publications.
1st Nov, 2015
Stephen Crothers
Alpha Institute of Advanced Study
Lawrence Marguiles: You have not adduced a single scientific argument. No matter how vehemently or how often you employ irrelevant ad hominem drivel, it will never count as a scientific argument. 
Here is the proof that Kirchhoff's Law of Thermal Emission is false and that Planck's equation is not universal (hence there are no such things as 'natural units'):
Robitaille, P.-M., Crothers, S. J., “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, Progress in Physics, v. 11, p.120-132, (2015),
You are invited to explain to us all the means by which you think you can uphold Planck's false proof of Kirchhoff's false law.
1 Recommendation
1st Nov, 2015
Lawrence Margulies
University of Guelph
I don't waste my time debating the mentally ill. My only goal here is make sure others are aware of your history so they can avoid wasting their time.
1st Nov, 2015
Clifford Chafin
North Carolina State University
I have not come to a conclusion on Stephen's theory but I do respect the attempt find a better understanding of how this law arises from fundamental principles.  This seems like one of the most neglected fundamental results in physics.  I have taken a crack at explaining, from quantum dynamics, how it can arise.  The whole of quantum statistical mechanics is build on an ad hoc foundation.  A few are trying to do better, Goldstein, Popescu, etc.  I don't agree with their results but I think we need to keep a very open mind on this topic given the poor state of theory here.  
2 Recommendations
2nd Nov, 2015
Stephen Crothers
Alpha Institute of Advanced Study
Lawrence Margulies: As I said before, no matter how many times you resort to ad hominen drivel it will never count as a scientific argument. The only person your all consuming anger and malice will harm is yourself. Try instead to uphold Planck's false proof of Kirchhoff's false law. Here again is our paper:
Robitaille, P.-M., Crothers, S. J., “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, Progress in Physics, v. 11, p.120-132, (2015),
Kirchhoff's Law of Thermal Emission is false, and Planck's equation is not universal.  Planck's 'natural units' do not exist.
2 Recommendations
2nd Nov, 2015
Clifford Chafin
North Carolina State University
I have to admit that Planck's proof is not really a proof.  Stephen's claim should not really be controversial here regardless of how convincing his approach is otherwise.   There is a long history of such loose arguments to derive results in physics and the bar for them has declined during the history and introduction of quantum mechanics.  This is not to say that they serve no role just that we should not assume they are more than they are.  At best, they are evocative of a more decisive proof that is perhaps less general than the authors hoped. I am very interested in anyone that can explain why this "law" works so well and point out where it fails and quantify by how much.  I suspect that the dynamics of quantum theory will be unchanged but our understanding of how it involves "classical" matter will richer than it is now.  
2 Recommendations
4th Jul, 2016
Stephen Crothers
Alpha Institute of Advanced Study
When Penzias and Wilson assigned a temperature to their residual signal and the theoreticians assigned that signal to the Cosmos, they violated the laws of thermal emission. It is a scientific fact that no monopole signal has ever been detected beyond ~900 km of Earth. The signal is proximal (i.e. from Earth). 
Robitaille,P.-M., Crothers, S. J., “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, Progress in Physics,v. 11, p.120-132, (2015), http://viXra.org/abs/1502.0007 
NMR and MRI are thermal processes. That they exist is physical proof of the invalidity of Kirchhoff's Law of Thermal Emission and the non-universality of Planck's equation. If Kirchhoff's Law of Thermal Emission is true and Planck's equation is universal, then NMR and MRI would be impossible, because NMR and MRI utilise lattice-spin relaxation. The existence of clinical MRI proves that Kirchhoff's Law of Thermal Emission is false and that Planck's equation is not universal. This means that the 'CMB' does not exist because it requires the validity of Kirchhoff's Law of Thermal Emission and universality of Planck's equation. Hence, Big Bang Cosmology is dead.
1 Recommendation
4th Jul, 2016
Kai Fauth
University of Wuerzburg
Wait a minute: You write: "NMR and MRI are thermal processes".
Could you please specify exactly what is meant by this statement? I cannot on my own follow your conjecture that the existence of NMR/MRI disprove Planck's law, sorry. Thanks for your help.
Edit: I reckon there might be a connection to the article by PMR linked below. I have tried to understand its arguments by a question previously (see 2nd link) but unforunately enough, PMR cose to not discuss the issue in the public (= RG) nor did he provide an answer privately. My approach to thinking about NMR is that the signal detected reflects a response to an external stimulus and would therefore rqther qualify as a non-thermal process. I am interested, therefore, what kind of approach it takes to arrive at such a fundamentally different conclusion as does S. Crothers.
Edit2: for some reason, the links appear in reverse order.
1 Recommendation
4th Jul, 2016
Stephen Crothers
Alpha Institute of Advanced Study
Felix Bloch first showed NMR to be a thermal process. Robitaille has shown that MRI is a thermal process. Lattice-spin relaxation utilised by MRI proves Kirchhoff's Law of Thermal Emission false because there is energy in the walls of arbitrary cavities that is not available to thermal emission. Kirchhoff and Planck incorrectly made all energy in cavity walls available to thermal emission.
Robitaille, P.-M., Crothers, S. J., “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, Progress in Physics, v. 11, p.120-132, (2015),
4th Jul, 2016
Kai Fauth
University of Wuerzburg
Stephen, can you specify what is (or specifies) a thermal process (as opposed to a non-thermal one) in your understanding and language? Once I get that I'm certainly willing to get back to Felix Bloch on this (Or revisit Slichter...).
2 Recommendations
13th Jan, 2017
Clifford Chafin
North Carolina State University
I studied quantum gases in graduate school and the overwhelming opinion seemed to be that these gas clouds could be well treated as in thermodynamic equilibrium for the gas expansion and rotation experiments.  I was convinced and still am that this is nuts.  Too bad the density and T is too low to check the radiative signature.  This example is a good foil for what we mean by thermal and a thermal process.  I work on this problem regularly.  Hopefully something will convince me soon.  
14th Jan, 2017
Stephen Crothers
Alpha Institute of Advanced Study
Kai Fauth,
The production of a thermal spectrum requires a lattice. Hence only condensed matter can produce a thermal spectrum. Gases, be they 'optically thick' or not, ionised or not, cannot produce a thermal spectrum. Spin-lattice relaxation involves the spin of a proton and the lattice of the material. There is an exchange of energy in this process. This energy is within the walls of the material and is not available to thermal emission, but contributes to the temperature of the material. NMR and MRI are facilitated by spin-lattice relaxation. Hence their very existence proves that Kirchhoff's Law of Thermal Emission is false. It is not for nothing that Felix Bloch called T1 the Thermal Relaxation Constant. 
Robitaille, P.-M., Kirchhoff's Law and Magnetic Resonance Imaging: Do Arbitrary Cavities Always Contain Black Radiation?, Abstract: D4.00002, Bulletin of the American Physical Society, 2016 Annual Spring Meeting of the APS Ohio-Region Section Friday-Saturday, April 8-9, 2016; Dayton, Ohio,
What is Kirchhoff's Law of Thermal Emission? It is given in the paper I have already cited, but here is the paper again: 
Robitaille, P.-M., Crothers, S. J., “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, Progress in Physics, v. 11, p.120-132, (2015), http://vixra.org/pdf/1502.0007v2.pdf
According to Kirchhoff, the radiation within an arbitrary opaque cavity at thermal equilibrium is always black, dependent only upon temperature and frequency, totally independent of the nature and form of the walls of the cavity. Note that thermal equilibrium alone is not sufficient as enclosure is a required element of the setting of Kirchhoff's Law of Thermal Emission. By their theorising alone, Kirchhoff and Planck permitted all the energy in the walls of an arbitrary cavity at thermal equilibrium to be available to thermal emission and thereby made all cavities black. This is false. Arbitrary cavities at thermal equilibrium do not contain black radiation unless they are constructed from a blackbody material such as carbon. The nature of the material always determines the radiation within a cavity at thermal equilibrium. All materials other than an ideal absorber, possess reflectivity. Consequently, Planck's equation for thermal spectra is not universal. A thermal spectrum in general does not render the true temperature of the emitter, only an apparent temperature, unless the emitter is a known blackbody, such as soot. An immediate consequence of this, by way of example, is the temperature of the photosphere of the Sun.  According to solar physicists, by spectroscopic means, its temperature is 5,800 K. This is false. It is too low. The Sun is not a blackbody and is not at thermal equilibrium within an opaque enclosure. Although the thermal spectrum of the photosphere is Planckian in distribution, the temperature extracted from it by means of Planck's equation is only apparent. It also follows that the Sun is not a gas. It must be condensed matter.
Here is another example; water. Water is a good absorber of microwave radiation, as microwave ovens and radio communications on submarines at sea prove without any doubt. It is well known that a good absorber is also a good emitter, and at the same frequencies. Hence, water is not microwave silent. Water has two bonds: (a) the hydroxyl bond, (b) the hydrogen bond. Most of the binding energy of water molecules is in the hydroxyl bond. The energy of the hydroxyl bond is not available to microwave emission. The energy in the hydrogen bond between water molecules however is available to microwave emission. The thermal spectrum from the hydrogen bond in the oceans renders a temperature of ~3K. This however is not the temperature of the oceans. It is only an apparent temperature of the oceans. The oceans are on average ~300K.  It is this ~3K signal that Penzias and Wilson detected and reported in 1965, from the ground, and which the theoreticians assigned to the Cosmos, calling it the 'Cosmic Microwave Background'. The 'CMB' is not cosmic in origin. It is from the oceans on Earth. The monopole signal of the alleged 'CMB' has never been detected beyond ~900km of Earth, because Earth is the source of the signal, via the hydrogen bond in water. Planck's equation yields ~3K for the oceans in microwave. It is not the temperature of the oceans. Planck's equation is not universal. 
The invalidity of Kirchhoff's Law of Thermal Emission and the non-universality of Planck's equation have deep consequences for physics and astronomy. 
1 Recommendation
14th Jan, 2017
Stephen Crothers
Alpha Institute of Advanced Study
Clifford Chafin,
You are right - it is "nuts".  Gases, quantum or otherwise, do not possess a lattice structure. Consequently they cannot produce a thermal spectrum. Only condensed matter can produce a thermal spectrum. Physics has never given a mechanism for thermal emission. Nobody knows how a thermal spectrum is produced. However, it is certain that it requires a lattice structure. Planck's equation for thermal spectra is not universal. It can only ever report a correct temperature for materials at thermal equilibrium within an opaque enclosure that are known blackbodies such as soot, or near to. Otherwise, temperatures cannot be ascertained by means of Planck's equation because they are then only apparent. The invalidity of Kirchhoff's Law of Thermal Emission and the non-universality of Planck's equation changes the very foundations of a lot of physics. 
1 Recommendation
18th Jan, 2017
Kai Fauth
University of Wuerzburg
Stephen,
without going in any detail now, let me try mentioning an analogy (not a particularly good one, maybe). Think of  gas in a container. We use the state equations to describe the state of the gas. And we do it such that the properties of the walls do not enter the problem: pV =NkT does not take notice of them. Now, if you construct the container from different materials, then the  details of the reflection processes at the wall (temporary adsorption, differences in momentum transfer to and from vibrations) do certainly change. However, for the gas it makes no difference.
If I draw an analogy, then - as I perceive them - you would argue that (at least at low density) the state of the gas (distribution of velocities/kinetic energies) should depend on the wall materials ?
Above, you mention that "thermal eqiuilibrium is not sufficient", but enclosure is required.
In my understanding, the enclosure is actually what assures thermal equilibrium. Constant temperature alone, for example, does not warrant thermal equilibrium. And, as I view it, this equilibrium is actually to be established between the cavity walls and the ensemble of excited electromagnetic modes ("the radiation"). I believe to remember that this view on the e/m radiation was questioned by PMR in one of his papers, I don't recall the details, however.
20th Jan, 2017
Stephen Crothers
Alpha Institute of Advanced Study
Kai Fauth,
Unfortunately you have not addressed any of the points I made in my previous post. Your analogy with gases within an enclosure has no relevance, and is false. Gases do not even emit a thermal spectrum under any circumstances. It is thermal emission that is the subject matter, not gas dynamics.
There is no theoretical proof of Kirchhoff's Law of Thermal Emission.  Planck's alleged 'proof' is a farce; exposed in the paper by Robitaille and Crothers, which I have already cited. No such theoretical proof even exists because Kirchhoff's Law is false, as explained in my previous post. 
Enclosure does not ensure thermal equilibrium. Any enclosure can be driven out of thermal equilibrium. When heat is injected into the walls of an arbitrary cavity the temperature of the walls increases. The injected energy is not converted in full to the emission field within the cavity. Cosmologists invoke thermal equilibrium without Kirchhoff's enclosure, for their big bang blackbody CMB. They assert that ~400,000 years after their big bang creation event, at what they call their time of 'decoupling', or 'recombination', their universe became transparent to radiation, setting their blackbody CMB free, and subsequently cooled by expansion of 'spacetime', down to ~2.725 K blackbody today (~13.8 billions years after their 'creation event'). However, at their 400,000 years, their universe was not within an opaque enclosure. Neither was it before their 400,000 years. The actual Universe is not within an opaque enclosure either. There is no means by which thermal equilibrium could have been achieved in their primitive big bang universe. That they say thermal equilibrium prevailed in their pathological 'early universe' does not make it so. At that 'time' their universe did not contain any condensed matter whatsoever, only exotic 'particles',  and protons and electrons, etc., they say. Only condensed matter however can emit a thermal spectrum because a lattice is required. The cosmologists have no lattice. Their application of Kirchhoff's Law of Thermal Emission violates Kirchhoff's Law, assuming it is even true. Their application of Kirchhoff's Law and universality of Planck's equation (also outside Kirchhoff's enclosure) not only violate Kirchhoff's Law, they violate the laws of thermal emission, because Kirchhoff's Law is false and Planck's equation not universal. Contrary to the cosmologists, no absolute temperature can be assigned to their so-called 'CMB' without violation of the laws of thermal physics. Consequently, their 'CMB' does not exist. 
Contrary to your allegation, neither Professor Robitaille nor myself contest that thermal equilibrium within an opaque enclosure is to be established with the emission field therein. The point is that at thermal equilibrium the emission field within an opaque cavity is never black unless the walls of the cavity are made of a blackbody solid such as soot. I have already made this point in my previous post. It is also made in the papers by Professor Robitaille, and in our joint paper. The radiation field within a cavity at thermal equilibrium always depends upon the nature of the material constituting the cavity walls, contrary to the assertions of Kirchhoff and Planck.
If you wish to contest the points I have made it is necessary that you actually address the points I have made. Otherwise, you can concede the points I have made, and join the rectification of physics, which is in a terrible state of intellectual decrepitude. In any event, Kirchhoff's Law of Thermal Emission is false and Planck's equation is not universal, despite 150 years or more of what theoretical physicists have believed.
3 Recommendations
20th Jan, 2017
Kai Fauth
University of Wuerzburg
Stephen,
we seem to be missing each other's points. I am not competent to talk about the CMB so I won't.
As far as the sun is concerned, equilibrium is certainly not given, so whether or not it might be a fair enough approximation to consider Planck's law (and disregarding your fundamental rejection of it) would certainly require thorough justification. Again, I am not sufficiently acquainted with the arguments presented by those who choose this description.
The point of whether some idealizations applied in reaching conclusions on a certain subject do actually help or spoil the problem is a very frequent one. I have so far concluded for myself that what Planck 'did' is certainly not on the level of a rigorous proof. The question to analyze then is, whether this lack of rigor renders the conclusion invalid. That need not be necessarily be so. (The harmonic approximation to vibrations in solids has its limited but still very useful range of applicability. I would not recommend dismissing the concept of phonons altogether 'just' because there are (i) no crystals of infinite dimension (ii) the true interatomic potentials are not harmonic or (iii) the model blatantly fails in describing thermal expansion).
I have not finished scrutinizing Planck's derivation myself in this respect. However, some 2-3 years ago I read into some of Robitaille's papers. My impression was that he actually "overused" the approximations of "ideal reflectors" or "ideal absorbers", which by vitue of the Kramers-Kronig relations of coursa cannot exist (I'll not go more into that at this time).
The analogy with the gas is the following: within classical statistical mechanics, the state of the (say, monoatomic) gas is sescribed by a distribution function for the energies/velocities/velocity components of its constituents, the Maxwell-Boltzmann distribution. The notion of thermal equilibrium has it, that this statistical distribution does not depend on the properties of the wall but on temperature (and atomic mass) alone.
The simplest way of "deriving" Planck's law is to proceed in analogous manner: you treat the e/m radiation as a canonical ensemble of quantum harmonic oscillators of a cavity. In this context, the notion of an ideal absorber surrounding vacuum simplifies determining the properties of the oscillators(*). The resulting distribution function for the oscillator modes is then the Bose distribution from which Planck's law follows in the thermodynamic limit (cavity size -> infinity). [this is calculation I have actually done myself]. This "derivation" does not make use at all of the arguments Planck advanced.
Applying this procedure, the resulting distribution is indeed universal and the question of which energy (in the cavity walls) is available what for (the importance of which I have so far been unable to comprehend) does not arise.
So again, the analogy would be that the equilibrium state of the subject of interest (the gas in one case, the e/m radiation in the other) is independent of the wall properties, while in both cases thermal equilibrium is established by virtue of (a huge number) of processes involving exchange of energy at the wall surface.
(*) Having an ideal reflector/absorber has the stationary solutions of the harmonic oscillators being determined by the boundary conditions of zero amplitude at the wall surface. Certainly unrealistic for ANY material, but does it spoil the whole idea? Assuming it does not allows you to have a relatively simple problem. Going beyond would mean that the actual oscillators are coupled modes in which both radiation and movements of charges (electrons, ions) participate. That gets ugly and intransparent (certainly so for the novice). On the other hand, taking the idea of a radiation field with zero amplitude at the boundary overly serious might even lead some to apply that in this case there is actually no interaction between the radiatin and the cavity wall. (Resolving that "issue" would force us to again go into the details of interaction between matter and radiation.)
Another question is whether it is actually justifiable to subject excited states of e/m oscillators to the kind of Boltzmaniian probabilities exp (-En/kBT). Again, I believe to remember PMR to refute this idea in one of his papers but I didn't understand why he did so.
1 Recommendation
21st Jan, 2017
Kai Fauth
University of Wuerzburg
Stephen,
allow me one further remark. I haven't read all your and Prof. Robitaille's numerous papers on the subject. But in those I have, I only found the "one-way-expressions", Planck is wrong & the distribution function is not universal.
 I would actually consider it much more desirable to deliver a positive statement of the kind: "This is how you do it right, given a dielectric function of a cavity wall material, this is how to compute the proper distribution function from it." Maybe that was done somewhere. In case of "yes", I'd be thankful for a pointer.
1 Recommendation
27th Jan, 2017
Stephen Crothers
Alpha Institute of Advanced Study
Fai Fauth,
(A) “we seem to be missing each other's points.”
I'm not missing your points, but you are missing mine.
(B) “I am not competent to talk about the CMB so I won't.
I don't believe that you are not competent to talk about the 'CMB'. The 'CMB' is an alleged cosmic isotropic blackbody spectrum at 2.725 K, produced by matter that was not condensed at its alleged creation, not produced within an enclosure yet at 'thermal equilibrium', according to Planck's equation for thermal spectra by which the foregoing absolute temperature is assigned. This is an issue of thermal emission.
(C) “As far as the sun is concerned, equilibrium is certainly not given, so whether or not it might be a fair enough approximation to consider Planck's law (and disregarding your fundamental rejection of it) would certainly require thorough justification.”
Professor Robitaille has already dealt at length with the Sun. The Sun is certainly condensed matter, not a hot ball of gas. I don't believe that you do not have sufficient knowledge to understand the facts about the Sun.
(i) Robitaille P.-M., Forty Lines of Evidence for Condensed Matter — The Sun on Trial: Liquid Metallic Hydrogen as a Solar Building Block, Progress in Physics, v.4, pp.90-142, 2013, http://vixra.org/pdf/1310.0110v1.pdf
Planck was aware that the solar rays do not convey the temperature of the Sun:
Now the temperature of the sun is obviously nothing but the actual temperature of the solar rays, depending entirely on the nature of the rays, and hence a property of the rays and not a property of the sun itself.” [4, §101]
(D) “I have so far concluded for myself that what Planck 'did' is certainly not on the level of a rigorous proof. The question to analyze then is, whether this lack of rigor renders the conclusion invalid.”
What Planck did is not a question of insufficient rigor in his proof of Kirchhoff's Law of Thermal Emission. His proof is a travesty; a thorough violation of the physics of optics and thermal emission. Planck abused Brewster's Law, used polarised radiation for blackbody radiation when blackbody radiation is never polarised, permitted a purely geometrical entity to possess physical properties, and did not even test reflection in his 'proof'. Planck also omits absorption, but allows transmission and reflection. But absorption is a thermal process whereas transmission and reflection are not, because there is no exchange of heat by transmission and reflection. Moreover, Planck does not even permit absorption in his definition of a blackbody by transmission through a body of 'infinite thickness'. Professor Robitaille and I have exposed all this, and more, in fine detail, in our joint paper [1]. You cannot defend Planck for his violations of physics by claiming insufficient rigor in his proof. Planck's proof is unmitigated nonsense. There is no theoretical proof of Kirchhoff's Law of Thermal Emission, and there is no experimental proof of it either. In fact, experiments prove that Kirchhoff's theoretical Law is false.
(E) “... some 2-3 years ago I read into some of Robitaille's papers. My impression was that he actually "overused" the approximations of 'ideal reflectors' or 'ideal absorbers' ...”
Since Kirchhoff and Planck always utilsed the idealisations of the perfect reflector and the perfect absorber, both Professor Robitaille and I can do so too, especially when analysing Kirchhoff and Planck. You cannot allow Kirchhoff and Planck extensive use of the ideal but deny Professor Robitaille and me use of the same when analysing Kirchhoff and Planck. Furthermore, the ideal are still invoked regularly by textbook writers on heat and thermodynamics.
(F) “The analogy with the gas is the following: within classical statistical mechanics, the state of the (say, monoatomic) gas is sescribed by a distribution function for the energies/velocities/velocity components of its constituents, the Maxwell-Boltzmann distribution. The notion of thermal equilibrium has it, that this statistical distribution does not depend on the properties of the wall but on temperature (and atomic mass) alone.”
Your analogy with a gas is irrelevant. The radiation within an arbitrary cavity at thermal equilibrium is emitted, reflected and absorbed by the walls of the cavity. Any gas inside a cavity is not emitted or absorbed by the cavity. You digress here. Please stick to Kirchhoff's Law.
(G) “The simplest way of "deriving" Planck's law is to proceed in analogous manner: you treat the e/m radiation as a canonical ensemble of quantum harmonic oscillators of a cavity. In this context, the notion of an ideal absorber surrounding vacuum simplifies determining the properties of the oscillators(*). The resulting distribution function for the oscillator modes is then the Bose distribution from which Planck's law follows in the thermodynamic limit (cavity size -> infinity). [this is calculation I have actually done myself]. This "derivation" does not make use at all of the arguments Planck advanced.”
The assumption of an ideal absorber makes the absorber black. It is natural that the result of applying the Bose-Einstein distribution is then Planck's equation. But the form of Planck's equation is not the real issue. The real issue is: Is the radiation within an arbitrary opaque cavity at thermal equilibrium always black? In other words, is Kirchhoff's Law of Thermal Emission true? Professor Robitaille and I have proven that is is not true. Hence, any Planckian spectrum does not reveal the temperature of the emitter unless the emitter is a known black material such as soot. In general the temperature extracted from a Planckian spectrum is only apparent, without any way of determining the true temperature of the emitter by spectroscopic means alone. I previously gave two contrary examples, (i) the Sun, (ii) water. In general, other thermal modes are available than just thermal emission.
It is a scientific fact that NMR and MRI are facilitated by spin-lattice relaxation [2]. NMR and MRI are thermal processes [2]. This means that there is energy within the walls of an arbitrary cavity at thermal equilibrium that is not available to thermal emission. That NMR is a thermal process was known to Felix Bloch. As I said before, Kirchhoff and Planck, by theory alone, permitted all energy in the walls to be available to thermal emission. The clinical existence of MRI proves that Kirchhoff's Law is false. If Kirchhoff was right then MRI would not exist; but it does.
You also argue for “cavity size -> infinity”. This requirement is a serious problem. The only size issue is at the level of diffraction. And if a cavity is 'infinite' in size, can it emit any radiation? An 'infinite' cavity is always black because nothing can come out of it. Moreover, Kirchhoff's Law is independent of the nature and form of the thermally equilibrated (opaque) cavity. The size of the cavity is essentially irrelevant to Kirchhoff's Law. The size of the cavity is also irrelevant to Planck's equation. However, the nature of the cavity, contrary to Kirchhoff and Planck, is not irrelevant at all. The radiation within an arbitrary cavity at thermal equilibrium always depends upon the nature of the cavity walls. Consequently, such radiation is not always black [1, 2].
(H) “Another question is whether it is actually justifiable to subject excited states of e/m oscillators to the kind of Boltzmaniian probabilities exp (-En/kBT). Again, I believe to remember PMR to refute this idea in one of his papers but I didn't understand why he did so.”
Professor Robitaille has never made such a claim. One system can have energies in two different states at the same time and these states do not communicate with one another, e.g. water, where the system is composed of two different subsystems. I suspect you allude to this paper by Professor Robitaille:
Robitaille P.-M., Blackbody Radiation and the Loss of Universality: Implications for Planck's Formulation and Boltzman's Constant,
(I) “I only found the "one-way-expressions", Planck is wrong & the distribution function is not universal.
I would actually consider it much more desirable to deliver a positive statement of the kind: 'This is how you do it right, given a dielectric function of a cavity wall material, this is how to compute the proper distribution function from it.'”
Yes, it is desirable that a right and proper solution be found. That is the whole point. To know that a solution needs to be found it is necessary to first know that there is a problem requiring the solution. No scientist is obliged to provide a solution to a problem simply because he has revealed that there is a problem. The problem before us is the invalidity of Kirchhoff's Law of Thermal Emission, and consequently the non-universality of Planck's equation. To solve the problem of thermal emission the mechanism for thermal emission must be uncovered. In the meantime, Planck's equation is sound, but does not render the true temperature of the emitter unless the emitter is a known black material, such as lampblack.
(J) Professor Robitaille will be in Munich in late February. I'm sure he is open to discussion in person. All you would need to do is ask him.
REFERENCES
[1] Robitaille, P.-M., Crothers, S. J., “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, Progress in Physics, v. 11, p.120-132, (2015), http://vixra.org/pdf/1502.0007v2.pdf
[2] Robitaille, P.-M., Kirchhoff's Law and Magnetic Resonance Imaging: Do Arbitrary Cavities Always Contain Black Radiation?, Abstract: D4.00002, Bulletin of the American Physical Society, 2016 Annual Spring Meeting of the APS Ohio-Region Section Friday-Saturday, April 8-9, 2016; Dayton, Ohio, http://meetings.aps.org/Meeting/OSS16/Session/D4
[3] Robitaille P.-M., Forty Lines of Evidence for Condensed Matter — The Sun on Trial: Liquid Metallic Hydrogen as a Solar Building Block, Progress in Physics, v.4, pp.90-142, 2013, http://vixra.org/pdf/1310.0110v1.pdf
[4] Planck, M., The theory of heat radiation, P. Blakiston's Sons & Co., 1914
3 Recommendations
21st Sep, 2017
Clifford Chafin
North Carolina State University
I have struggled to even find a derivation of the emissivity of a material based on fundamental principles (or anything about the material for that matter). I always wondered why it wasn't in any of my EM or Quantum books.  Has someone got something like this?  
19th Nov, 2018
Julião João Cumbane
Eduardo Mondlane University
I've enjoyed this discussion on "the invalidity of Kirchhoff's Law of Thermal Emission, and[,] consequently[,] the non-universality of Planck's equation".
It seems to me that Robitaille and Crothers have made clear their point, and, be it wrong or right, it's a positive one: there's a problem with Kirchhoff's Law of Thermal Emission and Planck's Law of Black Body Radiation. It is the task of the whole world's physics community to proof them (Robitaille and Crothers) right or wrong. To some "physicists", Robitaille's, experiments seem convincing that his right. From what I learning from the discussion here and elsewhere on the subject matter of thermal radiation, apparently this isn't yet a well-settled physic's problem. There seem to be a need to readdress it and assess the consequences to the physics drawn from it (e.g. the Standard Model). That isn't to be feared. By the way, this is how science progresses. I see no point in challenging the ideas put forth by Robitaille with no strong and valid arguments but resorting to ad hominem. We learn more from our mistakes than from our denial of them. There is no doubt that the rest of physics works well in not so few cases. Otherwise, the technological advances that humanity enjoys today wouldn't have been possible. Let's then discuss constructively, reviewing our knowledge of the workings of the Universe and making the necessary corrections or adjustments where found reasonable to do so; or producing convincing proof that Robitaille is wrong with regard to Kirchhoff's law of thermal emission. Astrophysicists and cosmologists should not feel guilty or insulted by having their "standard theories" being challenged by so-called "outsiders". I'm hungry of a clear, sound and convincing argument Robitaille is wrong. Can someone feed me, please?
19th Nov, 2018
Stephen Crothers
Alpha Institute of Advanced Study
Dear Julião João Cumbane ,
Here is our paper on the subject:
Robitaille P.-M., Crothers S. J. "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,Progress in Physics, v. 11, p.120-132, (2015), http://www.ptep-online.com/2015/PP-41-04.PDF
Kirchhoff and Planck allowed all the energy in the walls of an arbitrary opaque cavity to be available to thermal emission and in doing so made all thermally equilibrated cavities black. However, not all the energy in the cavity walls is available to thermal emission. This is embodied in the fact that not all materials have an emissivity of 1. If all the energy within the cavity walls is available to emission then resonant cavities would not be possible because the radiant energy would be absorbed and converted to a thermal spectrum. Similarly, if Kirchhoff and Planck were right then MRI would not exist because MRI is facilitated by spin-lattice relaxation. This means that there is energy in the lattice that is not available to thermal emission. Such energy is not coupled to the thermally available energy in the lattice. A physical lattice is necessary for the production of a thermal spectrum. A gas cannot produce a thermal spectrum. This is one of many reasons why the Sun and stars are not hot balls of gaseous plasma but are in fact condensed matter. Only condensed matter has a lattice and the Sun and stars emit thermal spectra. Consequently, Planck's equation is not universal. It holds strictly only for black materials such as carbon. Arbitrary cavities do not all behave as a cavity lined with soot. The perfect reflector, for instance, cannot emit a single photon. Yet the theoretical perfect reflector is included by Kirchhoff and Planck as a blackbody cavity.
21st Nov, 2018
Julião João Cumbane
Eduardo Mondlane University
An alternative statement of Kirchhoff's and Stwart's ideas on thermal emission...
Recalling that the quest for the law of thermal emission was set forth by the need to fit and explain experimental data, I guess we can settle the ongoing "interesting" discussion by jointly restating Stewart's and Kirchhoff's ideas on the subject matter as follows:
Experiments show that there is a special class of materials that emit thermal radiation according to a special low, B = B(T,f), which is only a function of the emitted radiation frequency (f) and of the temperature (T) of the emitting special material, and NOT of material itself, such that for any other test material emitting or reflecting radiation according to a law L = L(T,f), of the same frequency (f) and at the same temperature (T) as the alluded special material, being the test material in thermal equilibrium with its surroundings, then it MUST follow that the ratio L(T,f)/B(T,f) is characteristic e = e(T,f) of the test material, which is also only a function of the frequency (f) and of the temperature (T) as the special material, and is dubbed "spectral emissivity" of the test material. The special material is dubbed "blackbody", and the functions B(T,f) and L(T,f) are dubbed "spectral radiance" of the blackbody and of the test material, respectively.
Clearly then,
L(T,f) = e(T,f)B(T,f).
From this restatement of Stewart's and Kirchhoff's ideas, it follows that:
1. For a perfect absorber [a=1], e(T,f) = a(T,f) ---> L(T,f) = a(T,f)B(T,f) = B(T,f);
2. For a perfect reflector [r=1], e(T,f) = r(T,f) ---> L(T,f) = r(T,f)B(T,f) = B(T,f); and
3. For a perfectly transparent medium [t=1], e(T,f) = t(T,f) ---> L(T,f) = t(T,f)B(T,f) = B(T,f).
Now, it clearly follows that the function B(T,f), proposed by Gustav Kirchhoff and discovered by Max Planck, is duly a limiting case of radiation emission by a material medium in thermal equilibrium. That is, in the theoretical limit, every material medium in thermal equilibrium emit black body radiation, independently of what it is made of, and whether it is or not condensed—and of course this includes "vacuum" filled with electromagnetic field or some other type of material field!
(To the best of my understanding, fields are forms of manifestation of matter; so that, rigorously speaking, there's no vacuum in our Universe, which also means that absolute zero is unattainable in our Universe, according to the 3rd law of Thermodynamics, meaning that there must be a minimal of thermodynamic temperature of the Universe, Tmin > 0. Cosmologists have since 1948 reported that such a minimal thermodynamic temperature of the Universe do actually exist and is approximately 3 K [references omitted for convenience]. )
If this proposal of restatement is sound and rationally well-grounded, then there is nothing wrong with Kirchhoff's law of thermal emission. Nor is there anything wrong with Cosmic Microwave Background Radiation (CMBR). (Of course, Kirchhoff may have not been so fortunate in using the right words as needed at exposing his ideas, but apparently his mind was clear as to what he intended to mean, I guess.)
To end this comment, I should make it clear that I'm a physicist specialising in Environmental Physics. I'm not astrophysicist nor astronomer or "thermodynamicist". Accordingly, I admit that my understanding of Kirchhoff's law may be erroneous too, but this is how I understand it. I'm open to corrections by, and to learning from, those who understand it better.
1 Recommendation
22nd Nov, 2018
Stephen Crothers
Alpha Institute of Advanced Study
Dear Julião João Cumbane ,
It seems that you did not study the paper I provided before making your comments. Here again is our paper on the subject:
Robitaille P.-M., Crothers S. J. "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,Progress in Physics, v. 11, p.120-132, (2015), http://www.ptep-online.com/2015/PP-41-04.PDF
23rd Nov, 2018
Julião João Cumbane
Eduardo Mondlane University
Dear Steve,
I studied all your papers before entering this discussion! I also studied the contents of all your videos posted on this platform (Internet). I'm have been following you for quite a while. My first and second comments build on what I learnt from your arguments since then. I'd love to learn from you on the suggestion I made to help clarifying Kirchhoff's Law of Thermal Emission. The enunciation of the law can be challenged, but its essence seems rational and clear.
10th Jun, 2021
Khan Hamza Saeed
Harbin Engineering University
Emissivity: Is the proportion of the radiation discharged by a surface to the radiation produced by a blackbody at a similar temperature. At the end of the day, Emissivity is a proportion of how intently a surface approximates the blackbody.
Absorptivity: Is the small part of radiation incident on a surface that is consumed by the surface. In real meaning absorptivity means the degree to which something absorbs energy, a liquid, or another substance.
The Kirchhoff’s law of radiation states that the emissivity and the absorptivity of a surface are equal at the same temperature and wavelength
25th Jun, 2021
Ivor Catt
The Northern Negros State College of Science and Technology (NONESCOST)
Why am I here?
Ivor Catt 25.6.2021
25th Sep, 2021
Y.C. Zhong
ERICHEN Consulting
Stephen Crothers Indeed, this is an important issue to be discussed. It is know today that absorption and radiation can be either resonant or non-resonant, or both, as observed in the atmosphere. It seems unlikely the blackbody radiation formulated by Kirchhoff and Planck can be trusted.

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Question on Lammps NVE ensemble Temperature increasing when calculating MOF thermal conductivity?
Question
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  • Jincheng ZhangJincheng Zhang
Hi, everone. I'm using lammps to calculate the thermal conductivity of Mg-MOF-74. I firstly perform NPT, NVT ensemble to get a stable equilibrium, with a total energy fluctuation within 0.5%. Then, when changing into NVE ensemble, the temperature strats to grow gradually at 230000 steps, and an error happened in 1639242 steps due to angle atoms missing.
Here are some details about my input file and log file. Hope anyone can help me or give some suggestions.
minimize 1.0e-4 1.0e-8 100 1000000
neighbor 2 bin
neigh_modify delay 0
variable T equal 300
variable V equal vol
variable dt equal 1
variable p equal 10000
variable s equal 1
variable d equal $p*$s
variable kB equal 1.3806504e-23 #[J/K] Boltzmann
variable kCal12J equal 4186.0/6.02214e23
variable fs2s equal 1.0e-15
variable A2m equal 1.0e-10
variable convert equal ${kCal12J}*${kCal12J}/${fs2s}/${A2m}
thermo $d
thermo_style custom step elapsed time temp pe ke etotal press vol xlo xhi ylo yhi zlo zhi density
thermo_modify flush yes line one
timestep ${dt}
dump dtrj all custom 10000 Mg-MOF-74.lammpstrj id type element x y z
dump_modify dtrj element O O C H Mg O O O b b b
dump_modify dxyz element O O C H Mg O O O b b b
restart 100000 restart/Mg-MOF-74.restart
velocity all create $T 135790 mom yes rot yes dist gaussian
fix NPT all npt temp 300.0 300.0 100.0 iso 1.0 1.0 100
run 2000000
unfix NPT
fix NVT all nvt temp $T $T 100 drag 0.2
run 2000000
unfix NVT
fix NVE all nve
reset_timestep 0
compute myKE all ke/atom
compute myPE all pe/atom
compute myStress all stress/atom NULL virial
compute flux all heat/flux myKE myPE myStress
fix JJ all ave/correlate $s $p $d &
c_flux[1] c_flux[2] c_flux[3] type auto file J0Jt.dat ave running
variable Jx equal c_flux[1]/vol
variable Jy equal c_flux[2]/vol
variable Jz equal c_flux[3]/vol
variable scale equal ${convert}/${kB}/$T/$T/$V*$s*${dt}
variable k11 equal trap(f_JJ[3])*${scale}
variable k22 equal trap(f_JJ[4])*${scale}
variable k33 equal trap(f_JJ[5])*${scale}
variable kall equal (v_k11+v_k22+v_k33)/3.0
thermo $d
thermo_style custom step temp v_Jx v_Jy v_Jz v_k11 v_k22 v_k33 v_kall
restart 100000 restart/Mg-MOF-74.restart
run 2000000
variable k equal (v_k11+v_k22+v_k33)/3.0
variable ndens equal count(all)/vol
print "average conductivity: $k[W/mK] @ $T K "
log:
NPT(last 0.1ns):
Step Elapsed Time Temp PotEng KinEng TotEng Press Volume Xlo Xhi Ylo Yhi Zlo Zhi Density
1900000 1899924 1899924 300.19589 -72370.237 3864.7575 -68505.48 299.43364 61487.115 0.54900172 51.848998 0.47544944 44.902551 0.28871887 27.267281 0.943907
1910000 1909924 1909924 304.39345 -72373.125 3918.7974 -68454.327 569.0023 62045.487 0.47159199 51.926408 0.40841065 44.969589 0.24800925 27.307991 0.93541241
1920000 1919924 1919924 296.47968 -72332.43 3816.9145 -68515.515 -1001.0074 61854.713 0.49798744 51.900013 0.43126978 44.94673 0.26189056 27.294109 0.93829743
1930000 1929924 1929924 300.84356 -72258.982 3873.0957 -68385.886 -532.9097 61938.096 0.48644389 51.911556 0.42127278 44.956727 0.25581984 27.30018 0.93703426
1940000 1939924 1939924 300.69654 -72261.493 3871.2029 -68390.29 1354.783 61796.867 0.50600174 51.891998 0.43821037 44.93979 0.26610527 27.289895 0.93917574
1950000 1949924 1949924 294.40876 -72216.855 3790.2533 -68426.601 -116.07429 61438.444 0.55577131 51.842229 0.48131209 44.896688 0.29227899 27.263721 0.94465475
1960000 1959924 1959924 298.22917 -72236.965 3839.4377 -68397.527 467.83331 61744.472 0.51326511 51.884735 0.44450063 44.933499 0.26992506 27.286075 0.9399727
1970000 1969924 1969924 300.94669 -72282.289 3874.4233 -68407.865 2188.0688 61582.774 0.53570686 51.862293 0.46393576 44.914064 0.28172713 27.274273 0.94244079
1980000 1979924 1979924 299.61245 -72340.45 3857.2463 -68483.204 662.75969 61799.319 0.50566188 51.892338 0.43791604 44.940084 0.26592654 27.290073 0.93913847
1990000 1989924 1989924 298.56203 -72204.753 3843.723 -68361.03 330.52411 61829.602 0.50146577 51.896534 0.43428211 44.943718 0.26371981 27.29228 0.9386785
2000000 1999924 1999924 300.84392 -72332.003 3873.1003 -68458.902 114.02159 61177.299 0.59215519 51.805845 0.51282145 44.865179 0.31141319 27.244587 0.94868716
2000076 2000000 2000000 300.77454 -72260.156 3872.207 -68387.949 -195.10172 61447.341 0.55453353 51.843466 0.48024013 44.89776 0.29162804 27.264372 0.94451797
NVT(last 0.1ns)
3900000 1899924 3899924 303.16078 -72306.041 3902.9278 -68403.113 -2245.6907 61447.341 0.55453353 51.843466 0.48024013 44.89776 0.29162804 27.264372 0.94451797
3910000 1909924 3909924 297.23095 -72357.734 3826.5866 -68531.147 -1626.6059 61447.341 0.55453353 51.843466 0.48024013 44.89776 0.29162804 27.264372 0.94451797
3920000 1919924 3919924 307.35255 -72388.507 3956.8932 -68431.614 1089.8766 61447.341 0.55453353 51.843466 0.48024013 44.89776 0.29162804 27.264372 0.94451797
3930000 1929924 3929924 305.8046 -72358.423 3936.9646 -68421.459 189.14304 61447.341 0.55453353 51.843466 0.48024013 44.89776 0.29162804 27.264372 0.94451797
3940000 1939924 3939924 303.90881 -72381.89 3912.5581 -68469.332 3028.6707 61447.341 0.55453353 51.843466 0.48024013 44.89776 0.29162804 27.264372 0.94451797
3950000 1949924 3949924 304.507 -72381.785 3920.2593 -68461.526 -230.57069 61447.341 0.55453353 51.843466 0.48024013 44.89776 0.29162804 27.264372 0.94451797
3960000 1959924 3959924 301.92666 -72228.085 3887.0397 -68341.045 91.686489 61447.341 0.55453353 51.843466 0.48024013 44.89776 0.29162804 27.264372 0.94451797
3970000 1969924 3969924 304.5679 -72424.318 3921.0433 -68503.275 1519.0109 61447.341 0.55453353 51.843466 0.48024013 44.89776 0.29162804 27.264372 0.94451797
3980000 1979924 3979924 301.65781 -72297.044 3883.5784 -68413.466 -271.48268 61447.341 0.55453353 51.843466 0.48024013 44.89776 0.29162804 27.264372 0.94451797
3990000 1989924 3989924 307.00495 -72360.954 3952.4181 -68408.535 -2521.9574 61447.341 0.55453353 51.843466 0.48024013 44.89776 0.29162804 27.264372 0.94451797
4000000 1999924 3999924 299.67001 -72401.719 3857.9873 -68543.732 -1943.6075 61447.341 0.55453353 51.843466 0.48024013 44.89776 0.29162804 27.264372 0.94451797
4000076 2000000 4000000 302.62485 -72438.022 3896.0282 -68541.994 893.07637 61447.341 0.55453353 51.843466 0.48024013 44.89776 0.29162804 27.264372 0.94451797
NVE(part of it):
Step Temp
0 302.6249
10000 297.02
20000 298.0575
30000 299.9917
40000 300.5121
50000 300.1069
60000 295.1424
70000 301.0109
80000 304.1412
90000 298.6296
100000 306.4158
110000 305.5104
120000 302.2589
130000 302.5609
140000 302.2362
150000 308.1364
160000 300.0563
170000 299.8534
180000 301.2992
190000 300.5985
200000 297.9644
210000 306.8841
220000 301.2316
230000 309.1059
240000 308.7167
250000 308.4066
260000 312.7306
270000 312.1801
280000 309.4838
290000 307.1806
300000 311.2416
310000 309.7554
320000 305.7033
330000 309.8235
340000 306.4184
350000 314.2227
360000 308.5119
370000 309.2281
380000 311.6083
390000 313.6745
400000 310.9765
410000 310.7669
420000 309.8643
430000 311.8931
440000 312.4852
450000 312.7968
460000 308.2947
470000 313.6332
480000 317.9289
490000 316.7104
500000 316.3063
510000 313.6752
520000 314.1453
530000 319.4908
540000 316.4856
550000 315.7817
560000 322.8026
570000 318.0926
580000 321.9529
590000 319.9658
600000 321.1059
610000 317.1512
620000 321.6389
630000 316.6208
640000 327.5142
650000 326.9689
660000 320.0033
670000 318.9957
680000 324.4062
...
1530000 390.3848
1540000 392.2057
1550000 394.7468
1560000 394.4621
1570000 391.4525
1580000 396.4241
1590000 397.9968
1600000 403.3611
1610000 405.7124
1620000 408.3486
1630000 407.2747
and here is the wrong message
ERROR on proc 3: Angle atoms 307 2702 2704 missing on proc 3 at step 1639242 (../ntopo_angle_all.cpp:68)
Last command: run 2000000
any help will be appreciated!

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