Talk:Black body/Archive 7

photon–photon interaction in the absence of matter
For the purpose of sourcing for photon–photon interactions in the absence of matter, the present Wikipedia article currrently contains the following: "direct photon–photon interactions ".

The 1951 article by Karplus and Neuman starts: "In an earlier paper1 the nonlinear interactions between electromagnetic fields were expressed in terms of the polarization of the electron-positron vacuum.

1 R. Karplus and M. Neuman, Phys. Rev. 80, 380 (1950)."

The 1950 article by Karplus and Neuman starts: "It has long been recognized that higher order corrections in quantum electrodynamics include non-linear interactions between electromagnetic fields.1

1 For a summary of the literature on this subject the reader is referred to A. Pais, "Developments in the Theory of the Electron" (Institute for Advanced Study and Princeton University, 1948), pp. 21–26."

Thus the 1951 article is about higher order correction calculations in quantum electrodynamics, not about direct physical photon–photon interactions in the absence of matter. It is a mistake to suppose that higher order interactions can be simply transferred to real physical processes. The non-linearities arise in the higher order calculations because there are several different fields with actual quanta present. There is no experimental evidence that the light field in the absence of matter has a non-linear character such as is considered for higher order correction calculations. The absence of such evidence is clear from the non-production of it on this talk page. It is true that speculations are made that in 2015 a facility will become available to test a presently untestable speculation that there may be non-linearity in the pure light field, but it is pure speculation without present-day experimental support. It is also true that it is planned at massive experimental facilities in future to make empirical studies of collisions of gamma rays in the absence of matter, but as is clear from the non-production of empirical evidence about it on this page, at present, non-linear gamma-gamma interaction in the absence of matter is also pure speculation.

According to the second edition (the first edition was cited above on this page) of Mandl, F., Shaw, G. (2010) Quantum Field Theory, Wiley, Chichester, ISBN 978–0–471–49683–0, on page 1: "The interactions between these particles are brought about by other fields whose quanta are other particles. ... These and other processes of course only occur through the interactions of fields." They clarify this on page 9 by saying: "For anything 'to happen' requires interactions with charges and currents so that photons can be absorbed, emitted or scattered." They are saying that, other than propagation of itself, a free field (in the absence of actual quanta of other fields) does not support any processes such as scattering. In particular this means that they are ruling out non-linear interactions of photons between each other in the absence of matter. The quantum vacuum implies the presence of matter. For example, the Casimir forces occur in a cavity so small that the distance between the material walls is of the order of the wavelength of the relevant light waves; that is to say, the quantum vacuum is derived from the presence of matter. Milonni, P.W. (1993) The Quantum Vacuum, Academic Press, Boston, shows how the quantum vacuum effects on an atom arise from the self-fields of the atom itself. Statements of principle like that of Mandl & Shaw 2010 just cited may be found in other reliable textbooks.

The article by Karplus and Neuman 1951 states on page 776: "The processes to be considered are the scattering of light by light,2 two-quantum pair creation,3 the scattering of light in an external field,4 and the creation of pairs in an external field.5

2 a H. Euler, Ann. Phys. 26 398 (1936). b A. Achieser Physik Z. Sowjetunion 11, 263 (1937).

3 G. Breit and J.A. Wheeler, Phys. Rev. 46, 1087 (1933)

The article by Karplus and Neuman 1951 in their section '''VI. FORWARD SCATTERING''' states on page 782: "This result is identical with that of Breit and Wheeler.3,9 [reference 9 is to a then unpublished article.]"

Breit and Wheeler are both well recognized physicists. The title of their cited article is 'Collision of two light quanta'. They are writing about "calculations for the production of positron electron pairs as a result of collision of two light quanta".

On page 1087 they start their article: "Two simultaneously acting light waves with vector potentials

$$\mathbf{A}_j=\mathbf{a}_{j}^*\ \mathrm{exp} \{ -i( \omega_{j}t-\mathbf{k}_j\mathbf{r}) \}+\mathbf{a}_{j}\ \mathrm{exp} \{ i( \omega_{j}t-\mathbf{k}_j\mathbf{r}) \} $$  (1)

are considered as acting on an electron. Under the influence of the waves a single electron wave function $ψ^{(0)}$ is changed, ..." [I have inserted an $$i$$ which I think was omitted by misprint from the formula in the original Breit and Wheeler 1934 paper.]

Breit and Wheeler 1934 also remark: "It is also unnecessary to use quantized light waves in the pair production problem, since the results with quantized waves are known to be identical with those obtained by means of ordinary waves."

Breit and Wheeler 1934 are referring to a physical electron being present for their collision of two light quanta. Considering the general principle cited above as stated by Mandl & Shaw 2010 and considering the "identical" coincidence of results stated by Karplus and Neuman 1951, it seems hard to believe that this was not also implicit, though unstated, in the result of Karplus and Neuman 1951. Thus it seems that the paper of Karplus and Neuman 1951 is about photon–photon interactions in the presence of matter and is not suitable as a source for article entries about such interactions in the absence of matter.Chjoaygame (talk) 15:02, 3 March 2012 (UTC)


 * "Thus it seems that the paper of Karplus and Neuman 1951 is about photon–photon interactions in the presence of matter and is not suitable as a source for article entries about such interactions in the absence of matter." What in the world are you talking about?  In the abstract it says very clearly what they do: "The differential cross section for the scattering of light by light is calculated as a function of energy and angle..."  Do you know what a differential cross section is?  Do you know what "light" means?  They are computing the amplitude for scattering of photons by photons, not by matter, and (as I've tried to explain to you many times now) it's not zero even when the center of mass energy is below the threshold for e+/e- pair production.  Their calculations are done in a perfect vacuum, with an in state of two photons, and an out state of two photons.  Waleswatcher  ( talk ) 16:21, 3 March 2012 (UTC)


 * Here's a freely available recent paper that calculates some high order corrections to 2-->2 photon scattering. The first two paragraphs of the introduction give a nice overview.  I suggest you read them.  Waleswatcher  ( talk ) 16:59, 3 March 2012 (UTC)


 * Dear Waleswatcher, it seems you haven't read the body of the cited "source" article itself or its references, since you address only its abstract. Yes, they are computing the amplitude for scattering of photons by photons, but virtual photons by virtual photons, not as you mistakenly suppose actual photons by actual photons (perhaps though not explicitly in the presence of the quantum vacuum), as you would have noticed if you had done your homework by reading your supposed source and its references. Your "repeated" "explanations" are no counter to an actual reading of the article and its references. Your statement that your cited Karplus and Neuman 1951 calculations are done in a perfect vacuum (not actually explicitly stated in their article) might seem plausible if their results were not identical with results for the same problem done in the presence of matter as made explicit in the 1934 article by Breit and Wheeler to which they refer. It does not advance your argument to suggest that I don't know what a differential cross section or what light mean. To try to justify your supposed source, you need something a lot more convincing than a handwaving attempt at distraction such as that. The substantial matter here is not what I know, but what the sources say. The question is not as to what the scattering is by, as you try to suggest; it is as to whether it takes place in the presence of matter. Your suggestion that higher order corrections are relevant only compounds the fact that you haven't noticed that the article is about virtual photons in interactions between different fields. Well may you ask "What in the world are you talking about?" You have not attended to the physics, but have read only the mathematical formulas without their physical meaning. You have misread the abstract, and apparently left unread the main body and references, of your supposed source, instead of which the statement in the article needs a suitable and reliable one.Chjoaygame (talk) 17:17, 3 March 2012 (UTC)
 * Total and complete nonsense. I read the article, and unlike you, I understand what it says.  Equation (5) on page 777 is the differential cross section for 2-->2 elastic photon scattering, exactly as I said and the abstract says.  These are obviously not virtual photons, because this is (a) a cross section, and (b) they say so explicitly.   Waleswatcher  ( talk )
 * I have now read the arXiv article to which you refer. It doesn't come near addressing the problem of your not having read the Karplus and Neuman 1951 article or its references. In referring to an arXiv research article, a primary source, you are clutching at straws instead of producing a reliable source, which for a substantial matter of principle like this should be an established secondary one, or preferably several, since you claim that everyone knows it.Chjoaygame (talk) 17:26, 3 March 2012 (UTC)
 * "It doesn't come near addressing the problem of your not having read the Karplus and Neuman 1951 article or its references." You're obviously not posting in good faith, and I will ignore your future comments until you retract that and apologize.   Waleswatcher  ( talk ) 18:17, 3 March 2012 (UTC)


 * You refer to the first two paragraphs of the arXiv research article to which you give a link. The first paragraph has nearly the same old references as that of Karplus and Neuman 1951. The arXiv article references are (1) to 1935, 1936 papers by two authors with Euler, (2) to a 1951 paper by Schwinger not cited by Karplus and Neuman though they cite one by him of 1950 (3) to Karplus and Neuman 1951, and (4) the Akhiezer 1937 paper cited above. The second paragraph of thge arXiv research article to which you link confirms my above comment on the lack of adequate empirical evidence for photon–photon scattering. The arXiv authors write: "The direct experimental evidence for $γγ → γγ$ scattering is still scant, ..." Thus, your citation of this arXiv article does not advance your case, but just emphasizes that you have no Wikipedia-acceptable reliable source for your synthesized original research claim that in the absence of matter light will interact with itself to reach a Planck distribution.


 * You are avoiding the substantial issues by accusing me of bad faith and demanding an apology. If I thought you would really refrain from further comment I would expect to be able to edit the article without your intervention. Would I be so naive?


 * Your refusal to respond is just a word-game to cover your inability to produce reliable sources, which is what you need to do.Chjoaygame (talk) 18:43, 3 March 2012 (UTC)

Experimental Apparatus - Cavity with a Hole
Since the experimental apparatus of Lummer and Kurlbaum is central to real world attempts to create a blackbody, I feel this section should be expanded. Inclusion of a brief description of how the apparatus works and a figure would go a long ways to aiding reader comprehension. I am not knowledgeable enough about experimental physics to do this myself, so could someone with the background please expand this section? --BBUCommander (talk) 15:25, 19 August 2012 (UTC)

Definition of a white body
Why is a white body necessarily rough? Seems like this statement is not true and includes unnecessary detail. The roughness or smoothness of an ideal black body is not mentioned. neffk (talk) — Preceding undated comment added 15:24, 28 May 2015 (UTC)


 * A white body is necessarily rough in the sense that its surface is lambertian. It reflects every finite sized incoming pencil into every direction. A black body completely absorbs rays from every direction. If the "black" surface were not rough, but had a shine on it, it would not really be black. If a body that reflects is not rough, it is a specular reflector, and is even more shiny than polished silver, not white.Chjoaygame (talk) 11:30, 29 May 2015 (UTC)

undid faulty IP edit; reasons
I have undone a faulty IP edit.

There are two signs that a writer is cleverer than the reader: starting a sentence with 'actually'; and starting a sentence with 'however'. (Ordinary writers, however, use the word 'however' like this.)

The new material may perhaps, suitably re-written, be a useful addition to the article, but not as it was posted just now, directly in the lead. One guesses, perhaps mistakenly, that perhaps it was posted not by an ordinary Wikipedia editor, but by the enthusiastic author of the cited paper seeking self-promotion, with a risk of conflict of interest.

The material may perhaps, with some careful editing, be suitable to be posted in a section of the body of the article, and then may be considered for possible inclusion in a brief summary form in the lead.

No matter how much cleverer the poster than than the reader, the ordinary form of Kirchhoff's law does not need amendment. The law states the existence of a unique universal spectrum for thermodynamic equilibrium. That the posted material may contradict that would suggest that the posted material is not from a reliable source. Wikipedia does not admit in general that new research, in no matter how thoroughly peer-reviewed a journal, is adequately reliably sourced. The ordinary criterion for reliable sourcing is that the source be a secondary one, for example a respected textbook reporting other sources. At present, at a glance, it seems to me that the material is perhaps partly wrong because it does not agree with Kirchhoff's law; perhaps my first impression needs reconsideration.Chjoaygame (talk) 22:02, 20 January 2016 (UTC)

Ah, I see! My undo has been undone, 25 minutes after my undo. Evidently the undoer, the original poster, was so enthusiastic that he did not wait to read my talk-page reasons, which took me 32 minutes to write. Because that shows that the poster is new to Wikipedia editing, I will forbear for the moment from undoing his undo, so as to give him the opportunity to undo it himself. Anyhow, the original post will not stand. I suggest the poster, Editor IP 194.136.94.252, carefully read and consider my above talk-page reasons, and take advantage of my forbearance in not myself undoing his undo.Chjoaygame (talk) 22:17, 20 January 2016 (UTC)


 * I concur and have again removed the content from the lead. For something that necessitates the rewriting of long-standing, well-known laws of physics, we can wait until textbooks with the rewritten law have been published - or, at the very least, until secondary sources confirm the result. Huon (talk) 07:52, 21 January 2016 (UTC)

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Macdonald's model
The concept of black-body was formulated initially for size of it to be much less than the wave length. To say about diffraction the method of geometrical optics is valid then. To apply the Plank law for emitting of black body one has to regard the restriction:
 * $$ \lambda \ll\ L $$,

where $$ L $$ is the characteristic size of object. In 20-th age, the series of attempts was taken to find approach that is valid for any wave length - similar to ideal reflecting surface. In that case, an according mathematical condition has to be formulated on surface of black-body. As to be known, impedance matching is effective for the only angle of incidence. In 1911, Macdonald H.M. proposed nearly self-evident approach. He used two well formulated problems in electrodynamics- that of reflection from ideal metal:
 * $$ \mathbf E_{\tau} = 0 $$,

and that of reflection from ideal magnetic:
 * $$ \mathbf H_{\tau} = 0 $$.

Half-sum of solutions is the field around the black-body in Macdonald's model. The approach is clear in the scope of the geometrical optics. Two reflected rays have equal amplitudes of opposite signs and cancel each other. Therefore, the convex surface does not reflect rays at all. At the same time, surface forming convex and concave parts of surface allows double reflections. The second reflections have equal amplitudes of two rays what does not accord to black-body concept. Consequently, Macdonald's model is reasonable for the convex surface only. Diagrams of scattered fields around black ball for Macdonald's model are calculated on the base of Maxwell's equations in monography.

Adjunct space
Sommerfeld proposed to consider black flat screen as surface of continued space what is analogous to procedure in the theory of complex analysis. Therefore, the problem is got to be spacious instead of surface one.

The idea to continue physical space was developed later. In 1978, Sergei P. Efimov from Bauman Moscow State Technical University found that Macdonald's model is equivalent to that with symmetrical adjunct space. The spaces are connected formally on the surface of black-body. Actually, two problems are considered outside of the surface. One is with charges and currents, other is without that. Boundary conditions on the surface equate tangential components of electric and magnetic fields of two  problems with changing sign of the magnetic component. In such a way, electric field in physical space is equal to half-sum of solutions of two problems for ideal reflecting surfaces:
 * $$ \mathbf E= \frac{(\,\mathbf E_+ +\mathbf E_-)}{2} \qquad $$  (in physical space),

where $$ \mathbf E_+ $$ is field from problem for ideal metal and $$ \mathbf E_- $$ is the field from problem for ideal magnetic. In the adjunct space, where no charges and currents, the sought electric field is equal to the difference of the same fields:
 * $$ \mathbf E= \frac{(\,\mathbf E_+ -\mathbf E_-)}{2} \qquad $$  (in adjunct space).

The concept of adjunct space proves that Macdonald's model is physically correct for all frequencies. The causality holds in the approach and considerations of scatter of wave packs is acceptable. From symmetry of physical anf adjunct spaces follows two electrodynamical theorems: Macdonald's model and Efimov's consideration are valid for   equations of acoustics, to equations of hydrodynamics, to diffusion equation. It should be noticed that half-sum of two subsidiary solutions is valid for linear equations only. It is clear that theoretical model needs a way for realizations.
 * In state of the heat equilibrium, heat fluxes from surface in physical and adjunct spaces are equal to each other.
 * Scattered field from thin black disc is equal to that from hole in flat thin screen (Babine's principle).

The concept of adjunct space can be applied to the black hole in theory of gravitation. The famous Schwarzschild metric looks mathematically simple:


 * $$ \frac{\left (1-\frac{r_s}{4R}\right)^2}{\left (1+\frac{r_s}{4R}\right )^2}dt^2 + \left (1+\frac{r_s}{4R}\right)^2 (dx^2+dy^2+dz^2)$$,

where $$\mathbf R = (x,y,z) $$ is radius-vector, $$ r_s $$ is  the Schwarzschild radius i.e. radius of black-hole. From point of view of concept based on the adjunct space, it is useful to apply the following transformation  of physical space:
 * $$ \boldsymbol \rho = \frac{ a^2\mathbf R}{R^2} $$,

where $$ a $$ is radius of sphere that adjunct space is attached to. Radius $$ a $$ is taken to give the Schwarzschild metrics again:
 * $$ a =\frac{r^s}{4} $$.

Therefore, the black hole can be considered as the connection of two symmetrical spaces on the surface of ball with radius $$ a $$. In that case, well known peculiarity $$ R =0 $$ is disappeared.

Black-body of arbitrary form
Non-reflecting chamber has absolutely absorbing walls. Regarding physical picture, adjunct space now is simply the surrounding space as far as the walls are missed. Therefore, adjunct spaces for the totally convex surface and concave one are identical. The adjunct space is continued along normal directed into side of convexity of surface. Details are described in the paper. The equivalent electrodynamical problem can be formulated on the base of boundary condition. It analogous to the impedance matching. Nevertheless, the boundary condition binds tangential components of electric and magnet fields not in the point but on all surface. The condition is based on Stratton - Chu formula.

To demonstrate approach, it is useful to deduce boundary condition for scalar problem when Helmholtz equation is valid. Fields on the surface are bound by Green's function in two points - $$\mathbf x$$ and $$\mathbf y $$:
 * $$ G(\mathbf {x,y}) = \frac{\exp (\mathbf {\mid x-y \mid})}{4 \pi (\mathbf {\mid x-y \mid}) }.   $$

Let be charges (or radiation sources) are placed in non-reflecting chamber i.e. in free space. Green's formula defines field $$ u(\mathbf x) $$ in adjunct space by boundary values on the surface of non-reflecting chamber. Upon sending argument $$\mathbf x$$ on the surface, formula gives boundary condition:
 * $$ \frac {u(\mathbf x)}{2}= \iint\limits_{S,\, y \neq x   }\left[ { G(\mathbf{x,y})\frac { \partial u(\mathbf y)}{\partial n_y} -u(\mathbf y) \frac{\partial G(\mathbf{(x,y)}  }{\partial n_y  }       }\right]        \,dS_y   .$$

The surface integral   is calculated in the sense of Hadamard regularization. Normal $$ n_y $$ is directed outside of chamber i.e. in side of convexity of surface.

Boundary condition for convex black-body (for example ball) is the same. It is necessary however to take the normal directed outside of convex surface.

At last, boundary condition for arbitrary surface, containing convex and concave  parts, conserves its form under condition that normal is directed into side of convexity. Therefore, the normal changes its sign on different parts of surface. EfimovSP (talk) 18:57, 8 November 2020 (UTC)