Talk:Planck's law/Archive 9

First lines
The first lines initiate the difficulties with this article:-
 * Planck's law describes the amount of electromagnetic energy with a certain wavelength radiated by a black body in thermal equilibrium (i.e. the spectral radiance of a black body)

Simply put, a body of any colour radiating energy is not in equilibrium; that is the reason Kirchhoff used his cavity with a very small aperture; the idea being that the aperture was negligibly small so that there was, effectively, no radiation.

This article is truly terrible! What is this supposed to mean:-
 * Physically, it means that any body held at fixed temperature will radiate something very close to a Planck spectrum of photons?

It is quite untrue, a body made out of coloured glass would do no such thing! --Damorbel (talk) 21:25, 13 December 2012 (UTC)


 * "a body of any colour radiating energy is not in equilibrium" - not exactly. If the body was also absorbing energy at exactly the same rate, it could be in equilibrium, and in that case the spectrum of EM energy around it would be Planckian.


 * Not remotely true. Let us imagine the body was a gas in a transparent container; it would, depending on pressure, absorb a rather narrow spectrum, centered on the molecular resonance(s); equally it would radiate, perhaps omidirectionally, only at these resonances, very, very far from a Planckian blackbody spectrum. --Damorbel (talk) 13:59, 16 December 2012 (UTC)


 * "a body made out of coloured glass would do no such thing" - it would if it was thick enough to be mostly opaque. But I agree with you that statement needs qualification.   Waleswatcher  ( talk ) 23:59, 13 December 2012 (UTC)


 * I agree, it needs qualification. But a body radiating energy can be at equilibrium as long as it is absorbing the same amount. The internal walls of a black body cavity are just such a case. A body has to be opaque, a sliver of colored glass does not qualify, nor does an optically thin gas in a transparent container. Optical depth DOES matter, in this context. Such bodies cannot absorb enough radiation to equilibrate. I think we should specify that the body is opaque, and leave it at that for the moment, and stay away from semi-transparent situations, because that brings in all the complications of the equation of radiative transfer. PAR (talk) 16:38, 16 December 2012 (UTC)


 * But a body radiating energy can be at equilibrium as long as it is absorbing the same amount.
 * Not true, I'm afraid. It depends what you mean by equilibrium, which really means uniform temperature. If you substitute energy balance, as above there will be a temperature gradient - somewhere! Energy balance is not a sufficient condition for equlibrium because there will be energy transfer along the temperature gradient - somehow! --Damorbel (talk) 18:10, 16 December 2012 (UTC)


 * Yes, by equilibrium, I mean the thermodynamic definition - the body and the radiation field form or are part of a closed system which is unchanging in time. This will imply a uniform temperature. PAR (talk) 19:43, 16 December 2012 (UTC)

I am not happy. The original situation was Kirchhoff's cavity which was effectively closed, the opening being negligible. He first proved the case when the enclosed bodies were black, i.e. did not reflect and had the same refractive index as the medium inside the cavity.

The radiation in this cavity is actually defined by the temperature of the walls, which is fixed, that is why he is able to develop the case where the contents are not black.

With such a cavity it doesn't matter what you put in it, when the temperature stabilises (this may take a long time if the cavity is full of reflecting material or even if the walls are only black in parts).

Sorry for this long winded explanation, but the subtleties are important.

The problems arise when the Sun, which is a powerful energy source, is said to approximate a black body. It comes no where near a black body, it has a massive temperature gradients because of the enormous energy output. The radiation from the Sun, because of its symmetry, has something that looks like the Planck spectrum but assumming, because of its spectrum, that it is a black body can lead to seriously incorrect calculations. --Damorbel (talk) 21:09, 16 December 2012 (UTC)

a work in progress
There is work in progress on the introduction. For passing motorists, the speed limit is 40 km per hour, drive carefully; actually there is also a traffic director with a lollipop sign. It would not be useful that I should try to second-guess the workmen on the job at this stage.

I would point out that the walls for the Wien process are explicitly intended in the source to be not thermalizing, in the sense that thermalizing means that they can absorb or emit radiation. They are theoretically perfectly reflective. In detail, I think some of them are white, that is to say, perfectly diffusely reflecting, while the piston that does the work and changes the wavelengths is a theoretically perfect specular reflector. The stability of the distribution derives from the change of wavelength due to the motion of the piston that does the work. As set out in the source, the motion is infinitely slow and therefore reversible, a so-called 'quasi-static' process. I do not know what happens if the motion is at finite speed. Perhaps someone can tell us that? (I think it reasonable to bear in the back of one's mind, though likely not to actually say here, that a theoretically perfect reflector may be difficult to realize in practice.)

I am unhappy with the idea that a body is a hole in a wall. I can live with the idea that a hole in a wall can represent or model a surface.

As the article appeared at the moment that I read it (perhaps already obsolete at the time I am writing this), it seemed to be a unclear whether there are two systems located in the same place, the system consisting of the radiative field, and the system consisting of material particles. Indeed the material particles seem to have appeared out of nowhere?

Bodies at room temperature emit mostly infrared radiation, but bodies much colder than that do not emit much infrared radiation; they emit mostly longer wavelengths. Extremely hot bodies, if they are really extremely hot, emit radiation of wavelengths shorter than ultraviolet. I am not sure what it means to say that a body emits "primarily" a certain radiation.

Planck's law describes not only how much but also in what direction a black body emits. Could we just say that it describes the radiation?

I would favour taking emissivity down a paragraph or two. The law for a black body is enough of a jump at the very beginning. Emissivity is quite a concept. I would also favour saying explicitly that the Planck radiation from a black body is the strongest possible thermal radiation for the temperature of the body.

I personally don't think of photons exchanging energy between each other in their interactions with material particles. I think of them as being created and annihilated mostly on separate occasions of interaction with material particles.

The traffic director with the lollipop has turned the 'stop' side around and now I see the 'slow' side. I should get going. Perhaps I will pass by again.Chjoaygame (talk) 06:11, 16 December 2012 (UTC)


 * Would you care to reduce the above to no more than five lines? Perhaps raising only one subject at a time. --Damorbel (talk) 16:15, 16 December 2012 (UTC)

response by PAR
I agree, lets go slow. Regarding your points:

point 1
''The photons have to be thermalized somehow. They have to be able to alter their energy so as to maximize their entropy and equilibrate. Absent photon-photon interactions, they must use the massive particles (i.e the black body walls) to accomplish this. I am not sure if perfectly reflecting walls will do that. If you are certain that they will accomplish this, then good. If they don't, then, absent photon-photon interactions, there is no thermalizing process.'' PAR (talk) 16:49, 16 December 2012 (UTC)
 * Planck says that the motion of the walls (through what we might call a Doppler-like effect) will make reflection change the wavelength of the light in just the right way to maintain the distribution as ideal; he gives detailed proof, taking into account the angle of incidence. He is emphatic that the carbon speck is not needed for this, though the walls are perfectly reflecting, neither absorbing nor emitting. I have not seen anyone contradict him on this.Chjoaygame (talk) 00:34, 17 December 2012 (UTC)


 * Planck says... Chjoaygame, could you cite this properly, please (book, page no. etc.)? It is not collegial to just state it! --Damorbel (talk) 10:09, 17 December 2012 (UTC)
 * Again for you.Chjoaygame (talk) 22:18, 17 December 2012 (UTC)


 * Well that is very interesting. I will change the sentence if you don't. PAR (talk) 04:02, 17 December 2012 (UTC)


 * My current plan is to let the workmen do their job. I love work; I can watch it for hours. To anticipate a later comment: Planck uses the carbon speck in other situations when he is using perfectly reflecting walls, but for this one, no; he emphasizes that it is not necessary. That's the point.Chjoaygame (talk) 04:38, 17 December 2012 (UTC)


 * Thinking about it, I have some doubts. Perfectly reflecting walls will conserve the number of photons, which, if I remember, will screw things up. The presence of mass renders the photon number non-constant. I will look into that. PAR (talk) 04:49, 17 December 2012 (UTC)


 * Photons, thought of as particles, are one way of thinking about it, but not the only way. The wave way of thinking does it safely with theoretically perfectly reflective walls. This reasoning was an important element in the historical progress that eventually led to Planck's law. I think it is notable physics.Chjoaygame (talk) 06:06, 17 December 2012 (UTC)

point 2
''Planck's law is generally for a "photon gas" in equilibrium with massive particles, so all are at the same temperature. A black body cavity is a particular way of realizing this, but it is not the only way. As Damorbel stated, a gas that is optically thick at a particular wavelength is a good candidate. Again, the massive particles are necessary so that the photons can thermalize, using the massive particles as intermediaries. We don't have to worry about the details, once we assume that there are massive particles and a radiation field that are each equilibrated and in equilibrium with each other.'' PAR (talk) 16:49, 16 December 2012 (UTC)
 * It's just the way it is written that I was referring to. It's not clear from the sentence sequence whether or how the "system" includes the particles of matter. As written, the system starts out as an apparently pure radiation field and then massive particles seem to appear unannounced. As a minor point, which you have noted, condensed matter is best for blackening. The thing about condensed matter is that it has lots of modes, practically a continuum of modes, while single particles are, as you have noted, not so well endowed. That's why Planck recommends a speck of carbon, so small that its internal energy is negligible in comparison with that of the radiation field.Chjoaygame (talk) 00:34, 17 December 2012 (UTC)


 * Wait - does Planck require a speck of carbon in his argument about reflecting walls?


 * For some arguments with perfectly reflecting walls, Planck uses a carbon speck, but for the one about the moving ones, no. See above.Chjoaygame (talk) 04:40, 17 December 2012 (UTC)

point 3
''I agree, an extremely hot body could emit primarily x-radiation, an extremely cold one could radiate in the radio spectrum. This could be better stated.'' PAR (talk) 16:49, 16 December 2012 (UTC)

point 4
I think specifying that the radiation is independent of direction is the best way to express the directionality of Planckian radiation. PAR (talk) 16:49, 16 December 2012 (UTC)
 * Just as a matter of expression, it seems awkward listing energy and the directionality right here. I just meant that to say the law describes the radiation is enough for a start. The details of the description can be specified in due course.Chjoaygame (talk) 00:34, 17 December 2012 (UTC)
 * I think the introduction is an appropriate place to mention directionality using the link to isotropic, along with homogeneous, etc. but that's just my vote, let it be whatever the consensus says. PAR (talk) 04:10, 17 December 2012 (UTC)
 * It is right to put it into the introduction, and fairly early there. But is doesn't necessarily have to be right in the very first sentence or so, if it makes the sentence too clumsy.Chjoaygame (talk) 04:43, 17 December 2012 (UTC)

point 5
''I agree, any radiative transfer considerations should come later. Lets just deal with opaque bodies to begin with. Emissivity for opaque bodies is not that complicated. I agree that emissivity<=1 for such a body is a good thing to introduce early, which implies that Planck radiation is maximal.'' PAR (talk) 16:49, 16 December 2012 (UTC)
 * I think it desirable to emphasize explicitly that the Planck radiation is maximal, as an ideal natural characteristic in its own right, rather to leave it as a corollary of an arbitrary definition such as that of emissivity, to be worked out by the possibly naive reader. Emissivity of gases and of condensed matter are expressed in distinct ways.Chjoaygame (talk) 00:34, 17 December 2012 (UTC)
 * Yes but it has to be more carefully done than before. With regard to gases, transparent bodies, etc., it can be delving into radiative transfer. For opaque bodies, its simpler, and yes, I think it should be mentioned.

point 6
''Regarding photons "exchanging energy" mediated by the material, I think you are right. They don't have an "identity". The important point is that the photon energies must be able to change so that the energy can be spread out among various frequencies (thermalized). We have to have a short, succinct way of stating this without going into Einstein coefficients and all that detail.'' PAR (talk) 16:49, 16 December 2012 (UTC)


 * Once you are talking about photons at all, I don't think there is a problem about saying right away that they are created and annihilated, without need to mention the government of the rates of creation and annihilation. It makes sense of the Bose-Einstein statistics that they come about this way.Chjoaygame (talk) 00:34, 17 December 2012 (UTC)


 * Bose Einstein statistics for masseless particles does not directly give Planckian radiation. You also have to specify the chemical potential of the photons is zero, and that occurs because of the presence of matter. That should be left to another article, on the derivation of the Planck distribution. But my point is, its not that simple. My vote is to keep it the way it is more or less, but whatever consensus says. PAR (talk) 04:26, 17 December 2012 (UTC)


 * The chemical potential is zero in thermodynamic equilibrium. Surely it is enough to say that in thermodynamic equilibrium photons are created and annihilated in just the right numbers to sustain the Planck distribution, without further ado. The creation and annihilation is not too mysterious an idea for radiation. It came naturally before quantum mechanics in general. Don't worry now too much about consensus. You are the workman on the job.Chjoaygame (talk) 04:51, 17 December 2012 (UTC)

The intro is now very redundant
There are now three paragraphs in the introduction that contain material that substantially overlaps. I'll try to fix the problem.  Waleswatcher  ( talk ) 05:42, 17 December 2012 (UTC)

OK, done. AS it was, we had three successive paragraphs, all of which described Planck radiation in terms of the statistical mechanics of a photon gas in three slightly different but overlapping sets of words. I removed the detailed description of moving the walls, because it's just one specific example of equilibration when a change is made (and not a particularly physical one - there's no physical reason to move the walls slowly or have them be perfectly reflecting, it just makes the calculation easier). I removed "opaque" from "opaque body" in several places because it is superflous (emissivity makes perfect sense for transparent or partially transparent bodies). The "speck of matter" stuff is very 19th century, we now know that photons interact with each other, plus realistically there will always be interaction with the walls, and that thermalization is generic.  Waleswatcher  ( talk ) 05:59, 17 December 2012 (UTC)

Presence of mass
I know we have had this discussion before, but the presence of matter to equilibrate the photons is vital. The zero mass limit of the Bose-Einstein distribution is:
 * $$I_\nu(T)=\frac{ 2 h \nu^3}{c^2} \frac{1}{e^{\frac{h\nu}{k_\mathrm{B}T}-\mu} - 1}$$

This is NOT Planck's law, because of the presence of the chemical potential $$\mu$$. If photon number is conserved, $$\mu$$ is not zero and the distribution is not Planckian. That means that a photon gas enclosed by perfectly reflective walls, absent photon-photon interaction, will not be Planckian. Introduce matter and, when equilibrium occurs, it will be Planckian, because the introduction of matter renders the photon number unconserved, and the chemical potential becomes zero. Whether its a small speck of matter or whether the reflective walls are replaced by absorbing material walls, the result will be Planckian. If photon-photon interactions conserve the number of photons, the resulting distribution will not be Planckian. If they do not, the result will be Planckian. I don't know whether they do or don't. Please don't make edits which ignore the above considerations. PAR (talk) 20:58, 17 December 2012 (UTC)


 * Presence of mass? This has to be considered very carefully. Kirchhoff's original exposition on a blackbody says that there must be no change of refractive index in the cavity, otherwise there would be reflection (scattering). Yes, he subsequently considered the more general case of reflecting objects in the cavity but then the concept of a blackbody would no longer apply. --Damorbel (talk) 14:21, 20 December 2012 (UTC)


 * Further, what is this talk about the number of photons being conserved? Absolutely not! Photons are produced by accelerating charge and they (and their energy) are absorbed by the well-known PDQ quantum reaction. A photon lives from the moment it leaves the accelerating charge until it is destroyed by absorption. --Damorbel (talk) 14:21, 20 December 2012 (UTC)


 * Photon-photon interaction in the absence of matter is for the quantum theory of fields. I do not know the conventional view of quantum field theorists about the physical meaning of a perfectly reflecting wall. To physically realize a perfectly reflecting wall, perfectly enough reflecting to allow photons in general enough time to interact and reach their own mutual thermodynamic equilibrium in the absence of material inside the cavity, would, I suppose, not be very easy.


 * I have mentioned above that the idea of conservation of photon number is not required in my understanding of the usual wave-particle duality story. The idea of this story is that the choice of wave thinking or particle thinking depends on the problem at hand. Strictly, as I understand the doctrine, neither form of thinking, by itself, is uniquely necessary or sufficient.


 * Recalling the hotness of this topic, it is perhaps wise for me to note at this point that I think that the rates of photon creation and annihilation in the presence of matter or imperfectly reflecting walls far exceed the rates of directly thermalizing photon-photon interactions remote from matter, in most ordinary laboratory conditions. I think this because of what I read in texts such as Jauch, J.M., Rohrlich, F. (1955/1976), The Theory of Photons and Electrons. The Relativistic Quantum Field Theory of Charged Particles with Spin One-half, second expanded edition, Springer-Verlag, New York, ISBN 0-387-07295-0.Chjoaygame (talk) 22:04, 17 December 2012 (UTC)


 * "That means that a photon gas enclosed by perfectly reflective walls, absent photon-photon interaction..." Photon-photon interactions exist in the real world, so this statement is irrelevant.  We already had this discussion, references establishing that were added (and since removed).  Furthermore, "perfectly reflecting walls" are just as unrealistic as the absence of all particles in the cavity, if not more so.  I'm editing it back.   Waleswatcher  ( talk ) 00:15, 18 December 2012 (UTC)


 * We established that photon-photon interactions exist. We did not, as I remember, establish that the number of photons in these interactions is or is not conserved, nor did we establish that these interactions enable every energy level to eventually be populated. The presence of matter allows both. Until we establish that photon-photon interactions allow both, we should not simply assume that they do. Regarding your points above, I should have said "assuming photon-photon interactions are negligible" rather than "absent photon-photon interactions. The statement is then not irrelevant. Perfectly reflecting walls are unrealistic, yes, but so are quasistatic processes, reversible processes, equilibrium states, the thermodynamic limit of infinite number of particles, etc. etc. If you want to throw out every unrealistic concept in thermodynamics, you throw out the entire discipline. PAR (talk) 03:22, 18 December 2012 (UTC)


 * Strictly and exactly, I suppose cyclic processes are impossible or unrealistic. But perhaps not so very unrealistic, especially for gases. Cyclic processes are used for some thermodynamical considerations. They do not assume quasi-static processes, nor equilibrium states, nor reversible processes, nor do they talk of numbers of particles. We believe in the validity of the first law without too much reliance on extremely ideal processes, unless we count work as necessarily extremely ideal. In some sense I suppose we do the latter.Chjoaygame (talk) 04:12, 18 December 2012 (UTC)


 * We did establish that photon-photon interactions do not conserve photon number. The internal charged fermion line in the Feynman diagram can emit any number of photons (although of course momentum, angular momentum, and energy are conserved).   Same goes for gravitational interactions. Implying that the Planck distribution is only the equilibrium or maximum entropy distribution for photons if they are in equilibrium with something else is both false and WP:OR.   Waleswatcher  ( talk ) 07:19, 18 December 2012 (UTC)'


 * Ok, I will take your word for it. The statement that the Planck distribution is the "zero mass" limit of the Bose-Einstein distribution is still not true. You also have to specify that the chemical potential is zero as well. I see that this statement has not been restored, so that should end this thread. PAR (talk) 21:48, 18 December 2012 (UTC)


 * Referring particularly PAR's associated new edit, which reads: "with any interaction which does not conserve photon number". I agree with PAR's intention in his new edit. But I don't think his wording quite safely and exactly expresses his intention. I think he means to refer to 'any interaction that accords with the laws of physics, including such of those as involve non-conservation of photon number'. The actual words posted just say any interaction which does not conserve photon number; I think that an unreserved any is too wide; it wants the reservation that the interaction he refers to must also accord with the other laws of physics. I agree that this is a trivial point of wording, but while we are about it I think it would be wise to get it right. I think a slight re-wording would fix it.Chjoaygame (talk) 19:40, 18 December 2012 (UTC)


 * What I mean is that if you derive the Bose-Einstein distribution for massless particles whose number are conserved, the resulting distribution is a function of frequency $$\nu$$, temperature T, and chemical potential $$\mu$$. If you derive it WITHOUT the constraint that particle numbers are conserved, you get the same distribution but with $$\mu$$ set equal to zero. This latter distribution is just the Planck distribution. The derivation assumes that there is a thermalizing process such that every distribution possible is equally probable. Less precisely, there is some way in which the total energy can be continuously redistributed among all of the many particles.


 * This is a physical model. If massive particles are in equilibrium with the radiation field, then photon numbers are not conserved and the interaction between the massive particles and the photons serves as a thermalizing process for the photons, therefore the model predicts that the Planck distribution will result. If photon-photon interactions do not conserve particle numbers and are "thermalizing" in nature (every distribution possible is equally probable), then a pure photon gas will have a Planckian distribution at equilibrium without the need for massive particles. So no, I don't mean 'any interaction that accords with the laws of physics, including such of those as involve non-conservation of photon number', I mean ONLY those interactions which do not conserve photon number. The rate of equilibration with massive particles will be enormously faster than without them. If you have a photon gas inside a box with perfectly reflecting walls, no mass present, and you can prove that the reflections are thermalizing, but DO conserve photon numbers, and you know that the photon-photon interactions equilibrate at a VERY slow rate compared to the equlibration rate provided by the reflections, then on a time interval of the order of the reflective wall equilibration time, the distribution will be very close to a non-Planckian distribution with a non-zero chemical potential. This distribution will not be stable on the long term. After a very long time, on the order of the equilibration time by photon-photon interaction, assuming they are thermalizing and non conservative of number, the distribution will become Planckian. That's what I am saying.


 * Waleswatcher's contention is that photon-photon interactions are both thermalizing and non-conservative of particle number, therefore a Planckian distribution is unavoidable. I have a hunch this is true, but I have not studied it in detail. What I object to is the idea that the zero-mass Bose-Einstein distribution is Planckian. It is not. You must also specify that photon numbers are not conserved, so that the chemical potential can be set to zero. PAR (talk) 21:48, 18 December 2012 (UTC)


 * But why should we single out photon number?  Photon number is not conserved, and so there's nothing special about it.  If photons carried any conserved charge (other than energy, angular momentum, and momentum) it would prevent a generic initial distribution of photons from reaching a Planck distribution.  But they don't.   Waleswatcher  ( talk ) 01:13, 19 December 2012 (UTC)


 * It is worthwhile to explain what it is about photons that cause them to equilibrate to a Planck distribution rather than, say, a Maxwell-Boltzmann distribution. The two properties that photons have which distinguish them from massive particles and the resulting MB distribution is that they are massless and that they are not conserved, and these two, independently true differences are what yields the Planck distribution rather than the MB distribution. Please help me to make that point, rather than reverting every attempt that I make to do so.


 * It is also worthwhile to explain that non-conservation and thermalization is almost always accomplished by the presence of massive particles in equilibrium with the radiation field. Again, please help me to make that point. Given that we have used the word "almost", we may want to keep the can of worms closed and carry on, or open the can of worms and mention photon-photon interactions and the fact that they are thermalizing and do not conserve photon number, and that the rates are much much slower than when matter is present, (with the required references to back that up) and thus yield a Planck distribution on a time scale very large compared to that when matter is present. PAR (talk) 03:13, 19 December 2012 (UTC)


 * You've been claiming that the massless limit of Bose-Einstein isn't Planck. That's not really correct.  The chemical potential isn't something you get to choose arbitrarily - it's determined by the physics.  In the case of massless bosons (or fermions), it's zero (it's true that under certain circumstances - like when photon number changing processes are really slow on the relevant time scales - one can pretend there's an equilibrium with non-zero mu, but it's never a true equilibrium).  By the same token, it's not true that the conservation of particle number in a massive Bose gas is independent of the fact that the particles are massive.  Massive particle number is approximately conserved because of the mass - it's because the energy to pair-create particles is far above the thermal energy.  There's also a question of stability (whether the particles can decay), but if they can decay there's no equilibrium for them at all.  In other words, chemical potential and mass are really not independent.
 * I agree with your second point if we restrict to laboratory experiments and/or ordinary life. But "almost always" is too strong - in the early universe, for example, the temperatures were high enough that photon-photon interactions were order 1.  The same might go for other regions of the universe too.  Waleswatcher  ( talk ) 11:17, 19 December 2012 (UTC)


 * Just to be clear, are you saying that the absence of chemical potential follows directly from the assumption of masslessness for the BE distribution? I have been going from the mathematical derivation of the Planck distribution in which I have always seen the argument as "since the presence of massless particles imply non-conservation...", but have never seen the argument that masslessness directly implies non-conservation. It has a ring of possible truth to me, and I would be interested in any references you can point to regarding this subject. This not said in the spirit of "gotcha" but rather of curiosity. PAR (talk) 23:39, 19 December 2012 (UTC)


 * Basically, yes. I am hedging a little  because masslessness alone isn't quite sufficient - for instance if you had exactly free photons in an expanding box you could get non-zero mu starting from Planck, or if you somehow had interactions that always preserve photon number (not sure that's actually possible quantum mechanically, apart from no interactions at all).  Adding charges doesn't conserve particle number for massless particles, because there's always an oppositely charged massless anti-particle by CPT invariance, so you can pair-create at arbitrarily small energy cost.  I don't have a reference off the top of my head.  Perhaps Zinn-Justin?   Waleswatcher  ( talk ) 00:55, 20 December 2012 (UTC)


 * I assume you meant "starting from Bose-Einstein". The presence of photon-photon interactions that conserve photon number is not what is required (except as a modelling exercise), what is required is the presence of non-conserving interactions which are unavoidable. Regarding the introduction, I am still, then, uncomfortable with the statement that the Planck distribution is THE equilibrium distribution for a photon gas in thermal equilibrium, unless we can reference the idea that non-conserving, thermalizing interactions are unavoidable in every case. I would not be astounded if that were true, though. PAR (talk) 20:35, 20 December 2012 (UTC)
 * No, I meant what I wrote. Starting from a Planck distribution, in the absence of any interactions, expanding the box will change the energy of the photons, but not their number.  Therefore, they'll have non-zero mu.  There are plenty of sources for the statement that the Planck dist is the equilibrium dist for photons.  As for thermalizing interactions, we have already established that they are unavoidable - you can't turn off (for instance) photon-photon interactions.  Waleswatcher  ( talk ) 20:56, 20 December 2012 (UTC)


 * Two points - One, we have not locked down the fact that they are unavoidable with an unambiguous reference. If I am wrong on this, please put in the reference. Two, I found a reference entitled "Light with nonzero chemical potential" by Hermann and Wurfel which addresses many of the points we have been discussing. It does not, as far as I have read so far, address the issue of the long term equilibrium distribution, but it does deal with many practical cases in which the chemical potential of light is not considered to be zero. I don't think it is worthwhile to go into the gory details in the body of the article, so I will add it as a referenced footnote. PAR (talk) 20:53, 21 December 2012 (UTC)


 * Was matter absent then?Chjoaygame (talk) 11:48, 19 December 2012 (UTC)


 * No, but photon-photon interactions were probably (I haven't checked to be certain) more important and common than photon-matter interactions. Certainly photon-photon interactions would suffice for thermalization.   Waleswatcher  ( talk ) 00:55, 20 December 2012 (UTC)


 * Perhaps the following secondary source may contribute to your purpose: Jauch, J.M., Rohrlich, F. (1955/1976), The Theory of Photons and Electrons. The Relativistic Quantum Field Theory of Charged Particles with Spin One-half, second expanded edition, Springer-Verlag, New York, ISBN 0-387-07295-0. They discuss at some length various primary sources, including the calculations of Karplus and Neuman.


 * Abridging so as not to breach copyright, they write in Chapter 13, starting on page 287: "Experiments for the observations of processes involving photon-photon collisions are extremely difficult to perform. ... the photon-photon cross section is at the present time still out of reach for the experimental physicist. ... The separation into virtual and real intermediate states is very basic and is neatly expressed in the general formalism. ... When two photons collide, they will not necessarily scatter, but may annihilate each other, thereby producing a negaton-positon [sic] pair. This absorption process for photons is actually much more probable that the scattering process, ... the basic principle of superposition is, in general, not violated to an observable degree."


 * Another secondary source that might be to your purpose is: Milonni, P.W. (1994), The Quantum Vacuum. An Introduction to Quantum Electrodynamics, Academic Press, San Diego, ISBN 0-12-498080-5.


 * On page 424, Milonni writes: " ... including photon-photon scattering and "photon splitting". Because of the extremely high field strengths required for such phenomena, however, there is still no prospect of ever observing them (Bialynicka-Birula and Bialynicka, 1970)."


 * In the light of these secondary opinions, I think it wise to take particular note of the Wikipedia policy of caution in referring to primary sources. Regrettably, I have failed to find any secondary source that explicitly mentions thermalization of the electromagnetic field in the absence of matter. Right now I also fail to recall any primary source that does so.


 * These two secondary sources seem more or less reliable, but obviously they are dated. Nowadays (as I seem to recall someone pointing out) there are considered to be future prospects, for the quantum field theory, of experimentally verifying the relevant interpretations of the mathematics and the consequent predictions for empirical observation. Presumably money will be found for them, in spite of the money problems of Europe and America. I will leave them for another occasion.Chjoaygame (talk) 11:47, 19 December 2012 (UTC)


 * Waleswatcher's cover note reads: "The Planck distribution is the maximum entropy distribution for photons, full stop. It is NOT necessary that they be in equilibrium with anything else." This is in agreement with Planck's story for the Wien displacement law. Planck says that in a cavity devoid of matter in its interior and with perfectly reflective walls, the radiation initially in thermodynamic equilibrium, with a black body distribution, at a temperature, when work is done on it by an external force that moves a wall, takes up a new black body distribution, with a new temperature. The redistribution is due to reflection in the moving wall, as a kind of Doppler effect. Planck was thinking in a wave picture. This was one of Planck's stepping stones.


 * Planck carefully moved the wall quasi-statically. Thinking about the work done on a material body by rapid motion of the walls, I expect that a disturbance of an equilibrium distribution would arise mainly from friction inside the material body. I suppose there would scarcely be friction within the radiation, and so the speed of the movement of the wall could be finite without disturbing Planck's result.Chjoaygame (talk) 01:31, 18 December 2012 (UTC)


 * Waleswatcher's cover note reads: "The Planck distribution is the maximum entropy distribution for photons, full stop. It is NOT necessary that they be in equilibrium with anything else." The maximum entropy distribution is the distribution selected out of a class of distributions, the selection criterion being maximum entropy, the class needing explicit specification to make the problem definite. What is the specification of the class of distributions is being considered in this case? One answer to this question would be 'the distributions that can be reached by a set of specified mechanisms from a given distribution'. Perhaps one can suggest another way of answering the question? True, it is perhaps not logically necessary that the photons be in equilibrium with anything else; that doesn't have to be the way the specification is made. Nevertheless, some specification of the class considered is needed to make the problem a definite one.Chjoaygame (talk) 11:17, 25 December 2012 (UTC)

details not quite gory
I am impressed with the argument about photons. I think it may deserve more than a footnote. I am not familiar with the finer points of Wikipedia policy, but I seem to recall that footnotes are in general disapproved of. I think it likely that many readers will not notice this footnote when perhaps they would be interested in it. I think this amount of detail is probably not called for in the introduction, and that is why, I suppose, it is now in a footnote. I don't this detail is really gory, rather it is fine. Perhaps a briefer account of photons in the introduction and more detail about them in a separate new section?Chjoaygame (talk) 00:14, 22 December 2012 (UTC)


 * Unless we can find a reference for the statement that the Planck distribution is the ultimate equilibrium distribution for photons in equilibrium under any condition (which I believe is likely true), then the footnote is not sufficient. I am trying to find such a reference, any help would be appreciated. PAR (talk) 03:36, 22 December 2012 (UTC)


 * With respect, I am not impressed that it is likely that you will find a reliable source, not just a reference, for the statement that "the Planck distribution is the ultimate equilibrium distribution for photons in equilibrium under any condition". I for one would look very carefully at a reference to that effect.


 * As I understand it, the reason for the S-matrix formulation is that it makes direct reference to the directly observable, and its formalism distinguishes that from the only-indirectly-observable. I suppose its inventors were not too happy with extremely explicit and direct and uniquely determining statements about the only-indirectly-observable. With respect, photons belong to a particle picture, and many think that a purely and exclusively particle picture is not enough; they want to talk about waves sometimes too. In this sense, a statement couched in terms of photons is couched in terms of a particular picture, a picture that is not fully categorical, if I may abuse that word somewhat. I would expect a statement about an ultimate equilibrium to be more categorical, with the same abuse of the word.


 * The nearest I have found to an extensive discussion of this matter that does not take leave from ordinary language is in Jauch & Rohrlich (1955/1980). They write on page 297: "When two photons collide, they will not necessarily scatter, but may annihilate each other, thereby producing a negaton-positon [sic] pair. This absorption process for photons is actually much more probable that the scattering process." If this is intended to be as general as it seems, it means that photon-photon thermodynamic equilibrium will nearly always be in the presence of negatons and positons (to use their language!). This means that photon-photon thermodynamic equilibrium will practically never occur in the eventual absence of matter, though it might occur in the absence of matter in the initial conditions; again, how photons might arise in initial conditions of absence of matter is open to question. That might be a bit like talking about a charged particle that is for ever uniformly accelerated by some external force. The S-matrix approach seems to me to take process as the primary kind of actual reality. I don't see it as imagining a static situation of an isolating vessel with perfectly reflecting walls containing some photons that will find their thermodynamic equilibrium. A an actual process in general takes only finitely long. Thermodynamic equilibrium in these terms is an abstraction from a continuum of actual processes.


 * Milonni (1994) on page 427, for a chapter epigraph, quotes Feynman (1985, QED. The Strange Theory of Light and Matter, Princeton University Press, Princeton NJ,; my copy is a Penguin edition, and the quote is to be found there on page 149 in the last chapter). Feynman writes: "The theories about the rest of physics are very similar to the theory of quantum electrodynamics: they all involve the interaction of spin 1/2 objects (like electrons and quarks) with spin 1 objects (like photons, gluons, or W's) ..." I am not seeing there a signal that he is very interested in the case when the spin 1/2 objects are supposed to be entirely absent. One might say that the quantum vacuum includes fluctuations about its zero-point energy of the electron-positron field, or somesuch; one could then discuss whether this means absence or presence of matter.Chjoaygame (talk) 06:01, 22 December 2012 (UTC)

what worried me
Thinking it over again, I am wondering what worried me about your sentence "the Planck distribution is the ultimate equilibrium distribution for photons in equilibrium under any condition". I suppose what worried me was the proviso "under any condition". I suppose it seemed so wide as to make the whole sentence nearly meaningless, not the sort of thing a safety-regarding student would be likely to pronounce upon. I am still not sure what you intend by it.

An equilibrium is reached with the help of a mechanism of change. It is sustained or not under mechanisms of change. Perhaps you could say more precisely what you mean by the proviso "under any condition"? Or somehow otherwise clarify what you mean by it?Chjoaygame (talk) 09:37, 24 December 2012 (UTC)

the "zero chemical potential" of photons in thermal equilibrium
Following up your reference to Herrmann and Würfel 2005, I was led to Baierlein 2001, who writes on page 428: "There are several ways to establish that the chemical potential for photons is zero (though I find none of them to be entirely satisfactory)." I agree with Baierlein's reservation. If the chemical potential is defined as the measure of the tendency for diffusion between two bodies at the same temperature, the problem for photon diffusion between two bodies otherwise in thermodynamic equilibrium is that it is not a function of any variable other than the temperatures. The diffusion will be through a transparent but otherwise impermeable wall. The temperatures say it all. One can't take a partial derivative with respect to a non-existent variable. It is customary to say things such as the wording of Tolman at page 374: "This can be accomplished by setting the undetermined constant $α$ equal to zero in the final result (89.6)." The problem I see with that is that it is formalistic and has no physical meaning: there was no justification in the initial derivation for introducing the constant $α$, because there is no constraint on the number of photons. Again, it's like trying to take a partial derivative with respect to a non-existent variable. It is formally convenient to say "Oh, let's say $α = 0$ so that we can have a formally uniform derivation", but that's chatter, not physics.Chjoaygame (talk) 10:38, 24 December 2012 (UTC)

I have to infer that there is no chemical potential term in the distribution for photons in thermodynamic equilibrium. It is not that the chemical potential is zero. It is that there is no such term. This is simply because there is in the proper derivation no constraint on the photon number; no constraint means no undetermined multiplier, no term corresponding to chemical potential. In short, the reason why there is no chemical potential term for photons to get the Planck distribution is that photon number is not subject to a specified constraint in the process that leads to thermodynamic equilibrium for photons. It is not a matter of the photons' having zero rest mass, unless you like to say that their zero rest mass is the reason why their number is not subject to a specified constraint. I think this conclusion of mine nearly or partly agrees with Waleswatcher's comment above that "(it's true that under certain circumstances - like when photon number changing processes are really slow on the relevant time scales - one can pretend there's an equilibrium with non-zero mu, but it's never a true equilibrium)." I agree that one can pretend this or that. I agree that it's not a true equilibrium. I wouldn't like to actually say that $μ = 0$. I would just say that $μ$ is not a defined quantity in this problem.Chjoaygame (talk) 13:13, 24 December 2012 (UTC)Chjoaygame (talk) 00:25, 25 December 2012 (UTC)

Joule expansion of a light without the carbon particle as per Herrmann and Würfel 2005
Herrmann and Würfel point out that Planck considered an expansion so fast that the light became non-thermal. Planck opined that then the gas had no well-determined temperature. Herrman and Würfel opine that nevertheless it has a chemical potential. They do not further address Planck's view that it has no well-determined temperature. We are deep into non-equilibrium thermodynamics here. What is the chemical potential of a material that does not have a well-determined temperature? Herrmann and Würfel are not worried about that. They announce in their introduction on page 717: "We will show that the expansion of light without the presence of a ″carbon particle″ as described by Planck leads to a state in which the temperature of the light is the same before and after the expansion, and the chemical potential is negative." But in the body of their text in section ''IV. JOULE EXPANSION'' they say nothing about the temperature in the expanded state reached in the absence of the carbon particle. They didn't deliver on their promise. As I read it, Planck is right that then the gas has no well-determined temperature.Chjoaygame (talk) 10:38, 24 December 2012 (UTC)

constraining the particle number
If one wishes to consider a cavity with theoretically perfectly reflective walls and no matter inside it, one might also choose the particle picture for the light inside it, so that the particles are conserved on reflection and at other times. This would be a model in which there is a constraint on the particle number. Would it lead to a chemical potential for light?

Planck indeed considers that physical set-up (theoretically perfectly reflective walls, no matter inside the cavity), though he chooses a wave picture. He says that such a theoretically imaginable system would sustain a steady state, which one might call an equilibrium. But it would not be a thermodynamic equilibrium, because it is not stable against perturbations. Very brief exposure of such a steady state to a small speck of carbon would disrupt that theoretical equilibrium. Since the steady state, alias unstable equilibrium, is not a thermodynamic equilibrium, it has no temperature and does not qualify as a candidate to have a chemical potential. Simply formally constraining the particle number for photons does not bring about a thermodynamic equilibrium and therefore does not create a chemical potential for the photons. It is the mere possibility of disruption by a perturbation that precludes the theoretical steady state from being a thermodynamic equilibrium. If Planck had envisaged photon-photon interaction in the absence of matter, he would not have bothered to introduce the speck of carbon. In his day, the wave picture of light was dominant over the particle picture, and the experimental evidence seemed to point to the absence of interaction of light with itself in the absence of matter, and he worked from there.Chjoaygame (talk) 01:17, 25 December 2012 (UTC)


 * Yes. In short, you need a thermalizing process. Without a thermalizing process, any distribution whatsoever will persist. So Planck says that in a perfectly reflecting enclosure, with only photons, which do not interact with each other, the reflection process is not a thermalizing process? I wonder about that. Anyway, thats why he introduces the speck of carbon, to provide a thermalizing process. If photon-photon interactions are a thermalizing process, then yes, no need for the speck, but the equilibration time is huge at a few thousand degrees and below. PAR (talk) 03:47, 25 December 2012 (UTC)


 * Yes, as you say, you need a thermalizing mechanism. Planck's classical wave picture makes perfect reflection in motionless walls non-thermalizing. With very slowly moving walls, there is a wavelength changing process of reflection, that makes a pre-established black-body distribution lead to another black-body distribution, with a new temperature if work is done on the radiation by the wall motion; one might call this thermal stability though not thermalization. (I suppose that if the walls moved slowly and irregularly for a very long time, that would be a thermalizing mechanism.) No mention of photons by Planck in those days. With very rapid adiabatic changes, such as Joule-Thomson expansion, the pre-established black-body distribution can be broken, and the reflection process cannot be expected to restore it without motion of the walls. I think the eventual temperatures needed for reasonable thermalization times have to be in the very many millions of Kelvin, more than thousands. As far as I can see, such thermalization usually involves production of actual positrons and electrons in many or most cases.[Jauch & Rohrlich] Once that happened a little, it would of course speed things up by photon-matter interactions. For moderate radiation that will eventually produce a room temperature, to get a reasonable chance of photons energetic enough to produce actual positrons and electrons, one could very much enlarge the cavity. For very energetic starting radiation, one would need special care to provide a cavity with perfectly reflecting walls: walls that perfectly reflect x-rays and $γ$-rays would need special technology, unavailable today I think. Milonni gives an extensive discussion of the various ways in which the necessary background quantum field of matter vacuum fluctuations may be modeled. Some models, in particular proposed by Julian Schwinger, make the existence of effective vacuum fluctuations of the electron-positron field depend on the presence of the material of the walls. There is not a single unique model that does it.Chjoaygame (talk) 05:51, 25 December 2012 (UTC)


 * I would like to see removed the footnote reference to the Herrmann and Würfel 2005 paper. It is a primary source with seriously faulty reasoning.


 * The reasoning of the paper is faulty because it fails to provide a sound reason for its false claim that the perfectly-reflecting-wall-with-no-carbon-speck Joule-Thomson expanded radiation has a temperature. Mixed-frequency light has a temperature just when all its frequencies have the same frequency-specific temperature. This is not so for the expanded radiation. The Herrmann and Wŭrfel 2005 reasoning about water particle number again rests on particle number conservation and is therefore wrong for the same reason as its reasoning about light particle number. The existence of a chemical potential derives not from particle number conservation, but from particle number constraint, a different thing. This is discussed by Tisza 1966 on pages 79–80. A hint of this is provided by the Baierlein reference. The Baierlein argument, that photons are not conserved, is not worded exactly correctly, but making the wording exact makes it valid, but as a case for the non-existence of the chemical potential, not for its having a zero value. The exactly correct wording is that there is no constraint on the photon number, a stronger statement. Baierlein correctly expresses the physics: "Yes, a spatial gradient in the temperature field determines the flow of radiant energy and hence the ‘‘diffusion of photons.’’" This refutes Herrmann and Würfel's objection to the Baierlein argument.Chjoaygame (talk) 18:22, 9 January 2013 (UTC)

I don't have a copy of Tisza 1966. Can we wait until I find one, in a few days? PAR (talk) 07:31, 10 January 2013 (UTC)


 * Take your time. This is not remotely urgent.Chjoaygame (talk) 14:42, 10 January 2013 (UTC)

You don't need to go down this route. What you do is you take mirrors that are not perfect, they are themselves at the same blackbody temperature. But then the effect of these mirrors is almost identical to that of perfect mirrors, except that eventually things do thermalize. To make too much out of this issue is futile, because there are quite a few hidden assumptions in statistical physics (e.g. ergodicity etc.) that are not mentioned at all. It's a bit similar to the ideal gas, if you take the non-interacting molecules too seriously, it won't thermalize either. You don't deal with that by putting artificial entities in the gas, you deal with it in the standard modern physics way, which is to recognize that the interactions are not exactly zero, but close enough to zero to justify setting it to exactly zero for certain calculations. Count Iblis (talk) 11:07, 11 January 2013 (UTC)


 * In other words, a perfectly "white" wall, which reflects every incident photon, but not at the angle of incidence (except perhaps on a microscopic scale). Looking at the Herrmann and Wŭrfel paper, they do not contend that the perfectly-reflecting-wall-with-no-carbon-speck Joule-Thomson expanded radiation has a temperature, contrary to Chjoaygame's statement. They never speak about a perfectly reflecting wall, they only speak of the "white wall" you mention. I still don't understand Chjoaygame's statement that "The existence of a chemical potential derives not from particle number conservation, but from particle number constraint, a different thing.". Chjoaygame, could you expand on this? PAR (talk) 15:26, 11 January 2013 (UTC)

Relation to Gaussian distribution
I think in the non-relativistic case (where $$E\propto p^2$$), this distribution is a 3D Gaussian when expressed as a function of 3D momentum ($$B(p_x,p_y,p_z)$$). You can derive this by the fact that the convolution of a Gaussian with itself is another Gaussian, the convolution operation corresponding to scattering of photons in this case. Stephen J. Brooks (talk) 14:47, 9 January 2013 (UTC)

the topic was the footnote
As I saw it, the topic of the previous section,  details not quite gory , was the footnote.

The footnote reads: "A necessary condition for Planck's law to hold is that the photon number is not conserved, implying that the chemical potential of the photons is zero. While this may be unavoidably true on very long timescales, there are many practical cases that are dealt with by assuming a nonzero chemical potential, which yields an equilibrium distribution which is not Planckian."

I reached the point where it seemed to me that the footnote should go. My reason was that it rests on a primary source that has faulty reasoning.

(I do not see it as appropriate to appeal to "practical cases" in this situation; perhaps a new article on "practical cases" would be a suitable place for it.)

In more detail, my main claims are that in strict physics there is no chemical potential for photons. And that the key here is not precisely non-conservation; it is non-constraint.

It seems I am being asked to argue this case in full detail !!!

PAR refers to my having written: "The reasoning of the paper is faulty because it fails to provide a sound reason for its false claim that the perfectly-reflecting-wall-with-no-carbon-speck Joule-Thomson expanded radiation has a temperature." He says that this statement of mine is mistaken, because I mistakenly say they refer to a perfectly-reflecting wall when in fact they refer to a white wall. I have to guess that PAR thinks that a white wall is not perfectly reflecting.

The Herrmann and Würfel 2005 paper's introduction reads: "Planck did discuss the isoenergetic expansion of light, without realizing that the final state could be described by a nonzero chemical potential.3 [Reference 1, p. 68: ‘‘If the process of an irreversible adiabatic expansion of the radiation from the volume V to the volume V′ proceeds in the same way as described above, with the only difference, that no carbon particle is introduced into the vacuum, after the establishment of a uniform state of radiation, which will take place due to the diffuse reflection at the walls of the container after a considerable time, the radiation in the new volume V′ will not have the character of black radiation, and will consequently not have a well-determined temperature.’’] We will show that the expansion of light without the presence of a ‘‘carbon particle’’ as described by Planck leads to a state in which the temperature of the light is the same before and after the expansion, and the chemical potential is negative."

Now checking what Planck wrote, I see that H&W 2005 have quoted § 70 of Planck. Just prior to that, in § 69, Planck is translated as writing of "absolutely reflecting walls". In § 68, he writes of "the bottom of the cylinder ... as completely reflecting, e.g., as white".

I think for Planck perfectly reflecting includes white; I think it doesn't have to be specular. On page 9 he writes: "When a rough surface reflects all incident rays completely and uniformly in all directions, it is called ″white″."

Whatever. My reasoning does not hinge on whether the "perfect reflection" is specular or diffuse. It hinges on its not changing the wavelength. Planck thinks white reflection does not change the wavelength. If you want to say that Planck is wrong to think that, feel free, but that's what he thought.

If you want to say that perfectly white walls are thermalizing, then there is no question of introducing the carbon speck. But H&W 2005 are talking about introducing the carbon speck, and we are talking about their paper. They say that the perfectly white walls maintain isotropy, but it is essential to their argument that they are not thermalizing, and in this they agree with Planck. The whiteness versus the "perfect reflectivity" of the walls is not a decisive question here.

Now coming to the physics. What is wrong with H&W 2005 is that their argument assumes without sound reason that their no-carbon-speck-abruptly-expanded light has a temperature. They imply that because an ideal material gas does not change its temperature upon equilibration after an abrupt expansion into a vacuum, one can assume that a no-carbon-speck-abruptly-expanded light will also have a temperature that will be unchanged. They do not actually spell out that this step of their reasoning is an implication; evidently they hope the reader will find it 'obvious'. The ideal gas is by definition postulated to have a thermalizing interaction, but they have explicitly removed the thermalizing interaction from their photon gas. Yes, the newly expanded photon gas will be isotropic because of the white walls, but that still, in their account, explicitly leaves the wavelength distribution simply reduced by a factor the same for all wavelengths. A careful reading of Planck reveals that this reduction destroys the temperature; H&W 2005 do not deal with this part of Planck, which is carefully argued; H&W 2005 have not made their case. They do not cite right here their possible source 10, Würfel 1982, but seem to rely on the argument as just indicated.

Now to the really physical case that I have to present, that light doesn't have a chemical potential. Not that the chemical potential is zero. That it doesn't exist.

I think I have presented above adequate arguments for this case. No one has actually explicitly responded to them. But still I am being asked to expand.

I have only limited explicit literature support for my case here. On page 58, Tisza 1966 says there is a chemical potential for each of the chemical components, while temperature gets its uniqueness from the uniqueness of energy. He adds that black-body radiation is a zero-component system, consisting only of energy. I read that to mean that it has no chemical component with respect to the concentration of which one could differentiate to get a chemical potential. Also, I have the cited article of Baierlein 2001, who writes on page 428: "There are several ways to establish that the chemical potential for photons is zero (though I find none of them to be entirely satisfactory)." I agree with Baierlein's reservation. I say that if they are far enough from satisfactory to elicit this comment from Baierlein, then they are not satisfactory as Wikipedia reliable sources. Baierlein is the author of a textbook on thermal physics.

H&W 2005 do not cite much literature that the chemical potential of light exists. Their main source is their reference 10, Würfel 1982. This does not get past the primary source hurdle, Würfel just citing himself. This article starts: "Electromagnetic radiation consists of photons which do not interact with each other. Their properties are therefore entirely determined by the interaction with matter, emitters and absorbers." Würfel 1982 goes on to invent his own definition of the temperature of radiation, simply repudiating the usual definition which he finds in the literature, which follows Planck. His new invention is not a temperature of radiation. His paper is a snow job; it is not a reliable source for Wikipedia.

I have to put my case for two approaches, the thermodynamic and the statistical mechanical.

The thermodynamic case is that light in thermodynamic equilibrium has its state fully defined by its temperature. The chemical potential is the partial derivative of the free energy with respect to the chemical concentration with other variables constant. But for light, one of the other variables is the temperature and that determines the chemical concentration; it would have to be held constant during the differentiation. For light, the chemical concentration is not an independent variable and thus one cannot differentiate with respect to it. It would be mere formalistic pretension, not physics, to try to deny this.

The statistical mechanical case is that the derivation of the Bose-Einstein distribution does not have a constraint on particle number to call on for the usual undetermined multiplier that will turn out to tell about a chemical potential. There is for photons therefore no such undetermined multiplier and therefore no reason to interpret it as a chemical potential. Expanding this, the derivation of the Bose-Einstein distribution is by the Lagrange method of finding constrained extremals by use of undetermined multipliers. There is one undetermined multiplier for each constraint. For chemical problems, the particular molecular species numbers are not conserved because chemical reactions are permitted, but they are tied together by a constraint. For chemical problems, there is a constraint on particle number and therefore an undetermined multiplier for that; that undetermined multiplier will turn out to be interpretable as the chemical potential. For photons there is no constraint on particle number, therefore no undetermined multiplier; therefore no chemical potential. It would be merely formalistic, without physical meaning for photons, to try to talk about a chemical potential that has a zero value.Chjoaygame (talk) 21:49, 11 January 2013 (UTC)


 * Regarding white walls, perfectly reflecting walls, etc. we have a semantic problem which is easily fixed. Lets just call perfectly reflecting white walls "white walls" and perfectly reflecting mirror-like walls "mirrored walls". I realize now that nobody is talking about mirrored walls, so we can all be on the same page by talking about "white walls".


 * Chjoaygame's argument against H&W's description of adiabatic expansion of a photon gas in a container with white walls is basically that the spectral energy distribution of the final state (volume V') will be equal to that of the original state (volume V) times (V/V') - i.e it will be reduced by a constant factor. H&W agree. However, Chjoaygame states that this is not an equilibrium distribution, that thermalization must occur in order for it to be an equilibrium distribution. Let's define $$B_\nu(T)$$ as the Planck distribution, and


 * $$\hat{B}_\nu(T,\mu)=\frac{ 2 h \nu^3}{c^2} \frac{1}{e^\frac{h\nu-\mu}{kT} - 1}$$


 * as the equilibrium distribution for non-zero chemical potential, which reduces to the Planck distribution for $$\mu=0$$. Chjoaygame's point is that


 * $$\frac{\hat{B}_\nu(T,\mu)}{\hat{B}_\nu(T,0)} = \frac{e^{h\nu/kT}-1}{e^{(h\nu-\mu)/kT}-1} \ne \frac{V}{V'}$$


 * and that is true, the volume ratio cannot be a function of frequency. In other words, unless somebody can talk me out of it, I agree, H&W's description of adiabatic expansion of a photon gas is junk, the final state is not an equilibrium state, it needs a thermalizing process, and Planck was right, a temperature cannot be assigned. Now the question remains, should the reference be discarded because of this, or retained because of some possibly valid points that it makes? H&W offer this as one example among others. Proving that H&W screwed up on one of their examples does not invalidate their other examples, and I still believe that the $$\hat{B}_\nu(T,\mu)$$ equilibrium distribution may have some practical validity. It is getting harder for me to defend keeping the footnote. I wonder if there are any followup articles by the same or other authors to the H&W paper? PAR (talk) 02:18, 12 January 2013 (UTC) (this signature copied by Chjoaygame (talk) 10:34, 12 January 2013 (UTC), with respect).


 * PAR has here considerately presented a careful and generous commentary, for which thanks.


 * Chjoaygame holds that it is not physically reasonable, without logical reservation, to define for photons "an equilibrium distribution for non-zero chemical potential". To do so without a logical reservation here would be what is often called petitio principii. The reasoning here presented by PAR can justly be described as a reductio ad absurdum and PAR's reasoning here is valid in that light as support for Planck's position against H&W 2005.


 * H&W 2005 didn't just "screw[] up on one of their examples". The argument that I presented above shows that they screwed up on the leading claim of their introduction, not far from being their fundamental general argument (if they had one), the validity of which they assume for their examples. A few examples don't in general prove a generalization. It seems I made a mistake in not directly adverting to every one of the arguments I noted in the section above. I should have also adverted to the argument about section 2 of H&W 2005, about conservation and constraints for water synthesis, on which PAR has asked for time for him to find a copy Tisza 1966, who on pp. 79–80 discusses the variables that appear in H&W's section 2 water synthesis argument; I agreed to wait for that. If it is established that H&W 2005 "screwed up" on one significant point in their paper, which was "junk", and it is agreed that they are an otherwise unsupported primary source, then the onus falls on a supporter of H&W 2005 to prove that the rest of the paper is valid, not on an opponent to go into detail to show that every example in H&W 2005 fails to prove their case.Chjoaygame (talk) 10:34, 12 January 2013 (UTC)


 * Regarding the distinction between "chemical potential is zero" and "chemical potential does not exist", I don't want to argue that. The mathematics is what it is, the interpretation is clear, and it sounds like a semantic argument to me, which I don't see as a big deal. PAR (talk) 02:18, 12 January 2013 (UTC)


 * I don't know exactly what PAR means by his words "the interpretation is clear". I don't agree that one can dismiss this as just a matter of semantics, not "a big deal". Semantics is about meaning, the interpretation of words and sentences. It matters very much. "The mathematics is what it is." Perhaps PAR will write down here exactly what is the mathematics for his derivation of the Bose-Einstein distribution for light in thermal equilibrium? Alternatively, one could just look at a textbook derivation to see why for photons there is no term that generates a chemical potential.Chjoaygame (talk) 10:34, 12 January 2013 (UTC)


 * It's basically the same idea as in the article on Maxwell-Boltzmann statistics. You have a set of energy levels with energies $$\epsilon_i$$ and a set of $$N_i$$ which specify how many particles are in the i-th energy level. You use Lagrange undetermined multipliers $$\alpha$$ and $$\beta$$ and form the function f:



f(\{N_i\})=\ln(W(\{N_i\}))+\alpha(N-\sum N_i)+\beta(E-\sum N_i \varepsilon_i) $$


 * The first term is the log of the number of microstates (dimensionless entropy), the second term corresponds to the requirement that the number of particles be fixed, and the third term specifies that the total energy be fixed. The f function must be at a maximum at equilibrium, and working it out, you can show that $$\alpha=\mu/kT$$ and $$\beta=1/kT$$ and you wind up with $$N_i/N=F(\epsilon_i,T,\mu)$$ which gives the fraction of the total particles in the i-th energy level for a specified T and µ. In the case of the Planck distribution, particles are not conserved, and it's a semantic argument whether you omit the particle conservation term or whether you set $$\alpha=\mu/kT$$ equal to zero, the mathematics are identical. PAR (talk) 15:32, 12 January 2013 (UTC)(with respect, signature copied byChjoaygame (talk) 21:35, 12 January 2013 (UTC))


 * Yes, that's the derivation I supposed you were using, and the textbook one I was referring to. But I make two points. First, the second term is not a "particle conservation" term; it's a particle number constraint term. Second, if there is no physical constraint on the particle number then there is no physical meaning for a corresponding mathematical term. I say that if there is no constraint then it is meaningless or nonsensical to put in a corresponding mathematical term. With respect, I think it is entirely improper and inadmissible to dismiss this as nugatory because it is semantic argument and to say that the mathematics are identical. If the term is admitted mathematically then one has a constant admitted, and that constant is either physically meaningless and nonsensical or it has a proper physical meaning. If there is no physical constraint on particle number then the constant is physically meaningless and nonsensical; it is improper and inadmissible to say that it has a zero value, which is a definite mathematical statement and in this context can be expected to have a definite physical meaning.Chjoaygame (talk) 21:35, 12 January 2013 (UTC)


 * When I say semantics, I refer to the meaning of words. If we say that the first three integers in order are one, two, three and if somebody else comes along and says, no, it's one, three, two, because three is one plus one and two is three plus one, then you realize that they are not wrong, they just have a different definition of the words "two" and "three". There is no proof that one is correct, one is not, its a matter of semantics. Once we agree on the meaning of the words, we can get on with the real problem. I am not massively interested in arguing over the meaning of words. If you say the first three integers in order are one, three, two, I say ok, whatever, but you better not tell me that one plus two is three, because then you are provably wrong. Semantic agreement is required for two people to converse intelligently and semantic arguments should be dispensed with quickly, so we can attack the real problem. I'm saying that I don't care whether you characterize the absence of the number conservation term in the above equation as the absence of chemical potential or as the chemical potential being zero. The mathematical equation does not change based on which characterization you choose, and so its a semantic distinction without a real difference. PAR (talk) 15:32, 12 January 2013 (UTC)


 * In the old language, semantics was part of the trivial syllabus, but that did not make it nugatory. No, it was essential and fundamental. I would say that you are improperly saying that semantics is nugatory. Such improper statements are unacceptable. Semantics is not just about how you define words. It's about the real meaning of the words and sentences, taking into account not only the verbal definitions and syntax but also the realities to which they refer. It's about testing sentences for truth, real truth, not merely syntactical or logical structure. I can't let you talk me into accepting that this doesn't matter. You try to make out that semantics is only about arbitrary definitions. Your example is a pure word game with no empirical reference, and is not a suitably general example such as would be needed to make your case. No, semantics proper is mainly about real meanings, usually with essential empirical reference. We are talking physics here, not just playing logical games. Meaning refers not only to syntactical and logical structure, but also to reality, which has an empirical aspect that cannot be dealt with entirely by word games such as you use as an example.


 * You say you don't care about the point at issue here. If you really didn't care, you would accept whatever I say just because I say it and you are a friendly fellow. So if you really don't care, you can demonstrate that by writing 'I agree that there is no chemical potential for photons'. If you were not happy to write that, then I say that would be evidence that you did care, and that the matter could not be dismissed as nugatory because merely semantic and that there was a real difference about which you did care. The real difference will emerge in this way: If I say 'Oh, yes, it's true that $μ = 0$', then surely I have to admit that it has a physical meaning for me to say 'Oh, I have changed my mind: now I think that it's false that $μ = 0$, indeed I think that $μ$ ≠ 0'. Then I have to start taking people seriously who tell me 'Ah, yes, I have a case where $μ = 1$.' Then our present discussion would have been entirely undone.Chjoaygame (talk) 21:35, 12 January 2013 (UTC)


 * Buchdahl 1966 writes on page 218: "... Wilson's excellent treatise." He is referring to Wilson, A.H. (1957), Thermodynamics and Statistical Thermodynamics, Cambridge University Press, London. On page 185 Wilson discusses radiation as composed of photons. He writes: "The parameter $μ$ must be omitted (or put equal to zero), since in deriving the distribution function we no longer have to impose any condition on the number of particles present." I contend that his first preference is to omit the parameter. On this contention, I agree with his first preference.Chjoaygame (talk) 22:07, 24 February 2013 (UTC)


 * I think it fair to say that your last comment does not seem to try to defend the H&W 2005 paper? That is one of the substantial questions here, beyond the semantics.Chjoaygame (talk) 21:35, 12 January 2013 (UTC)


 * The reference to the H&W 2005 paper is apparently undefended. The paper is primary research. I think it is time to delete the reference to it.Chjoaygame (talk) 23:04, 14 March 2013 (UTC)

Apparent Inconsistency Among Different Forms of Planck's Law
In the main article, different forms of Planck's law are summerised in a table. We know that frequency of photon is = the velocity-of-light/ wavelength. So, if i substitute c/ lambda for frequency nu in the expression in terms of frequency, then i should get the expression for lambda. But i get different formula when i substitute lambda for frequency nu and vis-a-vis. So, one of the formule seem to me not correct; or i am not correct?123.201.22.184 (talk) 11:22, 18 January 2013 (UTC)


 * It is not too surprising that you find a difficulty here. Perhaps one may explain it by saying that the notation is abbreviated in a way that may lead to confusion. The function name $B(·,·)$ is the problem. It is used in several senses without notational indication. The argument variable is left only implicit in this abbreviated notation, which is regarded as quick and efficient.


 * A more explicit naming would for example list the names $B_{ν}(·,·)$ and $B_{λ}(·,·)$. In this more explicit notation, the argument variable of the function is stated explicitly as part of the name of the function, leaving also place for insertion of a value of the argument variable. The two functions just named have different units and refer of course to different argument variables. This is indicated in the article with a temporary one-off use of the more explicit notation, in the section Corrrespondence between spectral variable forms, which I hope will answer your question.Chjoaygame (talk) 14:16, 18 January 2013 (UTC)


 * You write "So, if i substitute c/ lambda for frequency nu in the expression in terms of frequency, then i should get the expression for lambda.". That is incorrect, the correct expression is $$B_\nu\,d\nu=B_\lambda\,d\lambda$$, not $$B_\nu=B_\lambda$$ which you have used. PAR (talk) 16:16, 25 January 2013 (UTC)

a.k.a.
I undid the edit for formal reasons. It is not of a suitable form. But the substance which underlies it is in my opinion perhaps right.

The entry 'Planck's relation' is there in the article against my opposition. In my opinion it is there because it is aupported by some slipshod and inadequate arguments, pushed determinedly and insistently by a few editors. I think it should be removed.

There are a few uses of the phrase 'Planck's relation' in the reliable sources, but they do not in my opinion amount to the sources' giving the phrase the status of an eponym, and in my opinion not enough to justify its being promoted by the Wikipedia to the status of an eponym. True, a Google search also turns up some candidate sources, but most if not all of them are from low-weight writers, by which I mean writers who do not really know too much about the subject, and who are using the phrase as a label to cover their slipshod or lazy thinking.

This may morph into a case of a myth being created by Wikipedia editors, then being taken as a reliable source, when lazy writers rely on the Wikipedia's myth for the use of the phrase.

The editor who put up the a.k.a. edit was perhaps (I can't be sure) thinking of the formula $S = k log W$, which was originated by Planck, though known by the name of Boltzmann; this is the reasoning of history. The intention of the article's use of the phrase is, I think, to refer to the formula $ε = hν$.Chjoaygame (talk) 17:56, 3 February 2013 (UTC)

A Hair Cut is needed....
I propose to delete this text from the article because 1/ it is far too wordy for a Wiki article and 2/ contains too many contradictions:-
 * The surface of a black body can be well approximated by a small hole in the wall of a large enclosure which is maintained at a uniform temperature and volume. At equilibrium, the radiation inside this enclosure (and emitted from the hole) follows Planck's law. Planck radiation is isotropic, homogeneous, unpolarized, and incoherent. Just as the Maxwell–Boltzmann distribution for thermodynamic equilibrium at a given temperature is the unique maximum entropy energy distribution for a gas of many conserved massive particles, so also is Planck's distribution for a gas of photons, which are not conserved and have zero rest mass.[5][7] If the photon gas is not initially Planckian, the second law of thermodynamics guarantees that interactions (between the photons themselves or photons and other particles) will cause the photon energy distribution to change and approach the Planck distribution. In such an approach to thermodynamic equilibrium, or if the temperature is changed or work is done on the photon gas, photons are created or annihilated in the right numbers and with the right energies to fill the cavity with a Planck distribution at the eventual equilibrium temperature. For a photon gas, already having a Planck distribution, or any other given initial isotropic and homogeneous energy distribution, in a perfectly reflecting container devoid of contained material such as a speck of carbon, if adiabatic compression work is done on, or adiabatic expansion work is done by, the gas, so slowly that it is practically reversible, then the motion of the walls during the compression or expansion, combined with the reflection of the light with them, has the effect that the new distribution is also Planckian, or follows the given initial distribution.[8] The spectral radiance, pressure and energy density of a photon gas at equilibrium are entirely determined by the temperature. This is unlike the case for material gases, for which the pressure and energy density are independently determined also by the total number of particles and their properties, such as mass.

1/The assertion that "a surface" can be approximated by "a small hole in the wall of an enclosure" i.e. a hole in another surface must surely be unsustainable!

2/ Equally the radiation emmerging from a "small hole" cannot possibly be "isotropic"

3/ to say that: -
 * the second law of thermodynamics guarantees that interactions (between the photons themselves or photons and other particles) will cause the photon energy distribution to change and approach the Planck distribution

is a gross exageration. Interactions between photons in are discrete events that only occur in special circumstances (the proximity of other particles) so that both energy and momentum are conserved, circumstances generally found at energies far above the thermal energies discussed in the article (see pair production). So for this kind of interaction " between photons themselves ", the photon energy is not changed but the photons themselves disappear; thus the assertion that the interaction " will cause the photon energy distribution to change and approach the Planck distribution " is quite unsustainable. --Damorbel (talk) 07:56, 27 March 2013 (UTC)


 * As to 1/ above, I have rewritten this point to take account of this objection.


 * As to 2/ above, the text about which you complain does not say, as you mistakenly allege, that the radiation emerging from the small hole is isotropic. The text says that the radiation inside the cavity is so.


 * As to 3/ above, it is agreed by most that interactions between photons are relatively rare in ordinary laboratory and even many natural conditions, but we have an editor who is very keen to say that they can occur and therefore should be mentioned here. If you disagree with this, you might take it up as a separate specific concern, but it is not a reason for a "haircut".


 * I conclude that your proposed grounds for a "haircut" are inadequate. Consequently I have undone your removal of the section.Chjoaygame (talk) 08:39, 27 March 2013 (UTC)

I read:-
 * but we have an editor who is very keen to say that they can occur and therefore should be mentioned here

and I agree. We have an editor who wants to "own" or dominate the article, thus utterly against WP:POV. That there is one editor "who is very keen to say" is absolutely no reason for anything!

Please desist. This editor (or editors) is (are) putting much unsourced and unsustainable material in the article and I suggest that all editors see to its removal. --Damorbel (talk) 09:48, 27 March 2013 (UTC)

Damorbel's latest
Dear Damorbel, you undid my edit, giving as your reason "I reversed the deletion because it gives the logical derivation of a blackbody, as defined by Kirchhoff."

The actions of my edit were two.

One was to separate a long paragraph into two, because the second part seemed to set on a fresh train of thought. But it did not alter the wording or delete anything. It just made it easier to read.

The second was to add a sentence emphasizing the special point of the second part, namely, that it was an insight by Kirchhoff; nothing was deleted.

Yet you characterize my edit as a "deletion".

I can see no rationality in your undoing. Most likely, you did not read the edit that you undid.Chjoaygame (talk) 13:58, 9 June 2013 (UTC)


 * Chjoaygame The deletion I restored contains one of the few valid concepts in the whole article:-
 * the spectral radiance, as a function of radiative frequency, of any such cavity in thermodynamic equilibrium must be a unique universal function of temperature. He postulated an ideal black body that interfaced with its surrounds in just such a way as to absorb all the radiation that falls on it. By the Helmholtz reciprocity principle, radiation from the interior of such a body would pass unimpeded, directly to its surrounds without reflection at the interface. In thermodynamic equilibrium, the thermal radiation emitted from such a body would have that unique universal spectral radiance as a function of temperature.


 * Which can be recognised as a consistent but not clear statement on thermal radiation.


 * Most of the rest of the article is very confusing and far too long and is in desperate need of complete revision. For example what is this (opening) statement supposed to mean:-
 * It is a pioneer result of modern physics and quantum theory. ?


 * When in fact it was Planck's radiation formula that initiated the whole business of quantum theory and signalled the start of the revolution that is modern physics. --Damorbel (talk) 20:40, 9 June 2013 (UTC)


 * Dear Damorbel, you undid my edit. My edit had changed this:

Spectral dependence of thermal radiation

 * There is a difference between conductive heat transfer and radiative heat transfer. Radiative heat transfer can be filtered to pass only a definite band of radiative frequencies.


 * It is generally known that the hotter a body becomes, the more heat it radiates, and this at every frequency.


 * In a cavity in an opaque body with rigid walls that are not perfectly reflective at any frequency, in thermodynamic equilibrium, there is only one temperature, and it must be shared in common by the radiation of every frequency.


 * One may imagine two such cavities, each in its own isolated radiative and thermodynamic equilibrium. One may imagine an optical device that allows radiative heat transfer between the two cavities, filtered to pass only a definite band of radiative frequencies. If the values of the spectral radiances of the radiations in the cavities differ in that frequency band, heat may be expected to pass from the hotter to the colder. One might propose to use such a filtered transfer of heat in such a band to drive a heat engine. If the two bodies are at the same temperature, the second law of thermodynamics does not allow the heat engine to work. It may be inferred that for a temperature common to the two bodies, the values of the spectral radiances in the pass-band must also be common. This must hold for every frequency band.    This became clear to Balfour Stewart and later to Kirchhoff. Balfour Stewart found experimentally that of all surfaces, one of lamp-black emitted the greatest amount of thermal radiation for every quality of radiation, judged by various filters. Thinking theoretically, Kirchhoff went a little further, and pointed out that this implied that the spectral radiance, as a function of radiative frequency, of any such cavity in thermodynamic equilibrium must be a unique universal function of temperature. He postulated an ideal black body that interfaced with its surrounds in just such a way as to absorb all the radiation that falls on it. By the Helmholtz reciprocity principle, radiation from the interior of such a body would pass unimpeded, directly to its surrounds without reflection at the interface. In thermodynamic equilibrium, the thermal radiation emitted from such a body would have that unique universal spectral radiance as a function of temperature.


 * into this:

Spectral dependence of thermal radiation

 * There is a difference between conductive heat transfer and radiative heat transfer. Radiative heat transfer can be filtered to pass only a definite band of radiative frequencies.


 * It is generally known that the hotter a body becomes, the more heat it radiates, and this at every frequency.


 * In a cavity in an opaque body with rigid walls that are not perfectly reflective at any frequency, in thermodynamic equilibrium, there is only one temperature, and it must be shared in common by the radiation of every frequency.


 * One may imagine two such cavities, each in its own isolated radiative and thermodynamic equilibrium. One may imagine an optical device that allows radiative heat transfer between the two cavities, filtered to pass only a definite band of radiative frequencies. If the values of the spectral radiances of the radiations in the cavities differ in that frequency band, heat may be expected to pass from the hotter to the colder. One might propose to use such a filtered transfer of heat in such a band to drive a heat engine. If the two bodies are at the same temperature, the second law of thermodynamics does not allow the heat engine to work. It may be inferred that for a temperature common to the two bodies, the values of the spectral radiances in the pass-band must also be common. This must hold for every frequency band.    This became clear to Balfour Stewart and later to Kirchhoff. Balfour Stewart found experimentally that of all surfaces, one of lamp-black emitted the greatest amount of thermal radiation for every quality of radiation, judged by various filters.


 * Thinking theoretically, Kirchhoff went a little further, and pointed out that this implied that the spectral radiance, as a function of radiative frequency, of any such cavity in thermodynamic equilibrium must be a unique universal function of temperature. He postulated an ideal black body that interfaced with its surrounds in just such a way as to absorb all the radiation that falls on it. By the Helmholtz reciprocity principle, radiation from the interior of such a body would pass unimpeded, directly to its surrounds without reflection at the interface. In thermodynamic equilibrium, the thermal radiation emitted from such a body would have that unique universal spectral radiance as a function of temperature. This insight is the root of Kirchhoff's law of thermal radiation.


 * You undid the insertion of the paragraph break that my edit had inserted, and you undid the addition of the sentence "This insight is the root of Kirchhoff's law of thermal radiation" that my edit had added.


 * The result of your undo was this:

Spectral dependence of thermal radiation

 * There is a difference between conductive heat transfer and radiative heat transfer. Radiative heat transfer can be filtered to pass only a definite band of radiative frequencies.


 * It is generally known that the hotter a body becomes, the more heat it radiates, and this at every frequency.


 * In a cavity in an opaque body with rigid walls that are not perfectly reflective at any frequency, in thermodynamic equilibrium, there is only one temperature, and it must be shared in common by the radiation of every frequency.


 * One may imagine two such cavities, each in its own isolated radiative and thermodynamic equilibrium. One may imagine an optical device that allows radiative heat transfer between the two cavities, filtered to pass only a definite band of radiative frequencies. If the values of the spectral radiances of the radiations in the cavities differ in that frequency band, heat may be expected to pass from the hotter to the colder. One might propose to use such a filtered transfer of heat in such a band to drive a heat engine. If the two bodies are at the same temperature, the second law of thermodynamics does not allow the heat engine to work. It may be inferred that for a temperature common to the two bodies, the values of the spectral radiances in the pass-band must also be common. This must hold for every frequency band.    This became clear to Balfour Stewart and later to Kirchhoff. Balfour Stewart found experimentally that of all surfaces, one of lamp-black emitted the greatest amount of thermal radiation for every quality of radiation, judged by various filters. Thinking theoretically, Kirchhoff went a little further, and pointed out that this implied that the spectral radiance, as a function of radiative frequency, of any such cavity in thermodynamic equilibrium must be a unique universal function of temperature. He postulated an ideal black body that interfaced with its surrounds in just such a way as to absorb all the radiation that falls on it. By the Helmholtz reciprocity principle, radiation from the interior of such a body would pass unimpeded, directly to its surrounds without reflection at the interface. In thermodynamic equilibrium, the thermal radiation emitted from such a body would have that unique universal spectral radiance as a function of temperature.Chjoaygame (talk) 21:23, 9 June 2013 (UTC)

Well, what is wrong with the blue section? The rest, where it goes on about temperature difference and heat engines, is not necessarily wrong but clearly superfluous when Planck's law applies only to an equilibrium condition. --Damorbel (talk) 05:26, 10 June 2013 (UTC)


 * So far as I can see, there is nothing much wrong with the blue section. My edit just marked the blue section off into a paragraph of its own because it expresses an idea more or less of its own. The blue section was not, as you seem to say, deleted by my edit; what has not been deleted cannot be restored, and therefore the blue section could not be restored by your undoing of my edit. A residual effect of your undo was to delete the sentence that my edit had added, "This insight is the root of Kirchhoff's law of thermal radiation."Chjoaygame (talk) 07:41, 10 June 2013 (UTC)


 * Chjoaygame, the details in your editing are not the principal defects in the article. The main problem is the many shortcomings in its technical content. In the opening section it claims:-
 * Planck's law describes the electromagnetic radiation emitted by a black body in thermal equilibrium at a definite temperature.
 * which is quite simply wrong. How can a body "emitting radiation" at the same time be in equilibrium? The whole point of Kirchhoff's cavity was that the cavity walls had a uniform temperature, ensuring equilibrium.


 * By this requirement Kirchhoff excludes all temperature gradients, gradients that would accompany any transfer of energy by emission.


 * Planck's law is about radiation in a thermodynamic system in equilibrium, in the case of the cavity it is the radiation inside the cavity.


 * I do think the opening section of the article should make the fundamental thermodynamics clear, at present it does not do that.


 * There are far too many fundamental errors in the article. Also it should be much shorter, the many errors arise mostly because the editors, as above, seem to have only a limited knowledge of the fundamentals of thermodynamics. --Damorbel (talk) 10:51, 10 June 2013 (UTC)


 * Can the tiger change his stripes, or the leopard his spots?Chjoaygame (talk) 12:34, 10 June 2013 (UTC)

Chjoaygame, such remarks do nothing to improve the article, you should bear this in mind when contribiting to Wikipedia. --Damorbel (talk) 13:23, 10 June 2013 (UTC)