Talk:Black body/Archive 6

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Dicklyon on "effective temperature"

According to this source, the "effective temperature" of a star is determined by its luminosity:

$L=4\pi R^{2}\sigma T_{eff}^{4}$

where, of course, the overall power output/unit area P is given by:

$P=\sigma T_{eff}^{4}$

In this edit Dicklyon has removed the wording saying "the radiation from stars and planets often is taken as a rough approximation to be that of a black body at an effective temperature fitted to the spectrum"

With the in-line comment "see effective temperature; that's not what it is", he has changed the wording to:

"the radiation from stars and planets often is taken as a rough approximation to be that of a black body at a temperature fitted to the spectrum"

What is this about? The original wording looks fine to me. Brews ohare (talk) 00:33, 18 February 2012 (UTC)

The sentence about "fitted to the spectrum" didn't seem compatible with the definition in terms of total luminosity. The spectrum is not relevant to effective temperature, but is very relevant to things like color temperature. Dicklyon (talk) 01:14, 18 February 2012 (UTC)

That is a fit to the spectrum - the total luminosity is an integral over the spectrum. Your change should be reverted. Waleswatcher (talk) 01:25, 18 February 2012 (UTC)

I changed it to be about that then. My impression had been that it was trying to say the emission of a star is spectrally approximately like a blackbody spectrum, but it didn't say that very well, either. Could say either thing; or both; but mixing them up isn't good. Dicklyon (talk) 06:09, 18 February 2012 (UTC)

I like your new wording. Waleswatcher (talk) 13:13, 18 February 2012 (UTC)

"must be rough" - seems dubious

The current language is

"The boundary of a body forms an interface with its surroundings, and this interface may be rough or smooth. A interface that is non-reflecting for general angles of incidence must be rough, because the laws of reflection and refraction governed by the Fresnel equations for a smooth interface require a reflected ray when the refractive indices of the material and its surroundings differ."

This seems dubious for several reasons. Is the surface of a hole in a large cavity rough or smooth? Seems pretty smooth to me - but it doesn't reflect. Same goes for black holes. Neither of those can be characterized by a changing refractive index - and in fact, neither can many physical materials.

So I suggest we either remove it or make it clear that "must be rough" applies only in certain cases. Waleswatcher (talk) 14:16, 22 February 2012 (UTC)

I believe this wording came out of one of Planck's papers. In any event, it appears you are not speaking of an interface in your example, but of a single medium that has a neck where it extends through the hole to the other side. There is no change in refractive index at the point where this medium goes from being "internal" to the cavity to being "external" to the cavity. So the statement appears to be OK to me. Brews ohare (talk) 15:09, 22 February 2012 (UTC)

I have no understanding of the black hole: do we need a theory of how gravity affects refractive index? How does the emission-absorption thing work in this case? It's not just electromagnetism. Brews ohare (talk) 15:23, 22 February 2012 (UTC)

I'm simply saying that the surface of a hole in a cavity is a black body, but it's hard to see how it's rough in any sense. The same goes for black holes - horizons are smooth. Waleswatcher (talk) 21:18, 22 February 2012 (UTC)

Maybe the issue is what constitutes an "interface". The language suggests a usage of "interface" as a surface that separates two different media with different refractive indices. You appear to want an interface to include a mathematically defined surface that may simply partition a medium into two regions without physical differences. Brews ohare (talk) 15:35, 23 February 2012 (UTC)

Maybe there is a discussion of the Fresnel equations for regions of gradually varying refractive index that suggests reflection occurs only when the index changes significantly over a wavelength of the radiation? Brews ohare (talk) 15:38, 23 February 2012 (UTC)

I think we can just change that so it says something like "when the body can be characterized by an index of refraction that differs from that of the exterior, the surface must be rough because....". Waleswatcher (talk) 16:23, 23 February 2012 (UTC)

OK, I made a change like that. Brews ohare (talk) 16:37, 23 February 2012 (UTC)

Thanks, that looks better. Waleswatcher (talk) 19:00, 23 February 2012 (UTC)

RfC: The role of photon-photon interactions in a cavity's approach to thermal equilibrium

In the subsection of the article Black body titled Cavity with a hole the simple general argument that the Second law of thermodynamics requires the cavity to reach thermal equilibrium eventually has been replaced by the suggestion that the minor (at best) mechanism of photon-photon scattering in the absence of matter is sufficiently significant to require mention. This assertion is supported only indirectly through references to the H-theorem of thermodynamics and technicalities about photon-photon events unrelated to the approach to equilibrium. The two texts are provided on the Talk page in the section RfC: The role of photon-photon interactions in a cavity's approach to thermal equilibrium. Comments upon their relative merits are invited. Brews ohare (talk) 15:16, 6 February 2012 (UTC)

Photon-photon text

Any interaction (for instance photon-photon interactions) will accomplish thermalization, but the time it takes to do so depends on the strength of the interaction and may be very long.

Second-law text

According to the second law of thermodynamics, any closed system eventually will reach thermal equilibrium; but notwithstanding this law, the time it takes to do so may be very long.

Comments

Comment 1

For the second-law text: The photon-photon text contains references that do not support its specific assertions, but only generalities. These very technical sources do not discuss the role of photon-photon interactions in the approach to equilibrium. Moreover, photon-photon interactions without engagement of matter are not known to be of significance in achieving thermal equilibrium, and certainly are secondary to many other mechanisms. For example, see Optics of waves and particles. Nothing suggesting their importance has been sourced.

On the other hand, the second-law text directly appeals to the well known second law and uses sources directly supporting the assertions. This form is understandable to the general reader, and is clearly supported by non-technical sources viewable through Google books. Brews ohare (talk) 15:17, 6 February 2012 (UTC)

Comment 2

My position on this: The Tolman reference proves explicitly, both in quantum mechanics and in classical mechanics, that a gas of photons (or any other Bose particle) will thermalize. The only conditions for the proof are the existence of interactions, specifically weak ones (although there is no doubt that the conclusion would be valid with strong interactions as well). Of course photons interact with each other, but in case there's any doubt, there are two references for that given. Note that the Tolman proof is simply a proof of the second law of thermodynamics applied to the specific case of a sealed box of weakly interacting Bose particles, so if you dispute its conclusion - that a sealed box with perfectly reflective wall containing only photons as an initial state will thermalize - you are disputing a fundamental law of physics. There are many, many other sources that do the same derivation and could be added, although I don't see why more are needed.

Why this physics is even slightly controversial is beyond me. The only argument I can see that one could make against its inclusion is that it's not relevant, because photon-photon interactions aren't the dominant interaction under "practical" circumstances. That's already mentioned in the article, but I think it's important as a point of principle to mention that interactions other than with matter will thermalize photons. That shows that matter is not necessary, it highlights that any interaction will thermalize, it's an interesting example of the 2nd law, and it's both relevant and important in some situations of great interest to physicists and current physics research (such as very high electric or magnetic fields or the very early universe). It's relevant, important, and might teach the reader something new and interesting. (For example: before this started several editors here apparently didn't know that photons interact, and still don't seem to have a grasp on the generality and importance of the 2nd law.) Waleswatcher (talk) 15:26, 6 February 2012 (UTC)

Comment 3

Waleswatcher, you write (above) "The Tolman reference proves explicitly, both in quantum mechanics and in classical mechanics, that a gas of photons" - I have not been able to get access to the title but if it contains the text that you cite it would indeed be an exciting new research result that "a gas of photons" could exist in classical mechanics. I attempted to explain the difference between classical and quantum mechanics above, I suggest it would be useful if you explained your understanding of the difference, such an explanation would surely reduce the possibility of misunderstanding. --Damorbel (talk) 16:08, 6 February 2012 (UTC)

He proves it for a classical gas of collisional particles, and then for weakly interacting bosons in quantum mechanics. You're correct that the former doesn't strictly apply to photons, but a gas of photons is the canonical example of the latter - and the proofs are actually more similar than different. Waleswatcher (talk) 18:18, 6 February 2012 (UTC)

"and then for weakly interacting bosons in quantum mechanics" Not so, he does not separate the interactions into two separate types, the interactions he is discussing are between classical particles and photons, not photon- photon interactions.

The matter was also dealt with by Einstein in his 1917 paper On the Quantum Theory of Radiation ( Zur Quanten-theorie der Strahlung) [unsigned comment made by Damorbel at 19:27, 6 February 2012; this attribution note made by Chjoaygame (talk) 21:17, 6 February 2012 (UTC)]

Nonsense. Tolman does precisely what I said, starting on p.436. Have you even looked? Waleswatcher (talk) 03:54, 7 February 2012 (UTC)

Comment 4

Brews ohare makes some very good points. May I add some details. A fuller quote from Waleswatcher's source Karplus & Neuman 1951 is:

   Finally, we may discuss the experimental significance of the results. Let us consider two photon beams of equal energy and of intensity n photons/sec colliding with each other; scattered photons are collected from a length L of their common path. Then the number N of collisions occurring per second is

N = (n²/A)L(σ/c) ≈ 10⁻⁴⁰n²(L/A) sec⁻¹,    (32)

where A is the area of the beam in cm², and σ ≈ 3×10⁻³⁰ cm² was taken as the cross section for scattering into a fair solid angle at an energy of about 1 Mev (see Eq. (7) and Fig. 5). For presently attainable values of the experimental parameters, therefore, it would seem that N is too small to be detected in the presence of the probable background radiation.

Waleswatcher is seeking to under-emphasize the number 10⁻⁴⁰ that appears in his source.

Another concern is that Waleswatcher is making a point of principle, and purely a point of principle, but offering only Tolman 1938 as source. Without prejudice as to its appropriateness here, such a point of pure principle deserves very well established reliable sourcing. A glance at the translation of Krylov, N.S, (1950/1979), Works on the Foundations of Statistical Physics, Princeton University Press Princeton NJ, and the appended commentary by Ya. G Sinai, a weighty authority indeed, shows that for such a profound matter of principle, something more up-to-date and thoroughly reliable than Tolman, respectable though he is, would be good. Krylov makes clear the importance of the relaxation time mentioned by Brews ohare above.

In simple terms, Waleswatcher is making bold claims, familiarly tossing off jargon such as 'thermo' and 'stat mech', but has not done his homework, as is manifest in his reliance on synthesis.Chjoaygame (talk) 15:57, 6 February 2012 (UTC)

Comment 5

Speaking as a non-physicist who has seen, second-hand, something of how treacherous a subject this sort of thing can become, I decline to discuss the technicalities. However, simply the fact that there can be serious disagreement on the matter suggests to me that the usual commonsense reliance on references where necessary, and the good understanding of the reader where they are not necessary, will no longer suffice. Either side might be right in part or ftm altogether, but in a case like this, the statement of each argument needs to be unusually tight, and the citations equally tight. Accordingly I go along with views such as those of Chjoaygame. Waleswatcher may be right in every detail, but here he needs to go the extra km to demonstrate it. Had that happened in the first place,there would have been no argument. As it stands, handwaving won't cut it. JonRichfield (talk) 17:47, 6 February 2012 (UTC)

The problem is, this is exactly what Tolman proves, and that's backed up by all sorts of other references (what we're discussing is just a special case of a fundamental law of physics, the 2nd law of thermodynamics). The disagreement is with editors who are manifestly not experts in this topic (for example, they didn't know that photons interact with each other). There is no disagreement in the literature, or in any published source at all that I'm aware of. Waleswatcher (talk) 18:20, 6 February 2012 (UTC)

• There is not only no disagreement in the literature, there is nothing in the literature about the role of photon-photon scattering in achieving equilibrium, except one source I found that says it is negligible in practice. I have proposed a compromise text above. Brews ohare (talk) 18:32, 6 February 2012 (UTC)
• Waleswatcher writes of "editors who are manifestly not experts in this topic"; since we are talking about an article on the black body, Waleswatcher's comment is like the pot calling the kettle black. He tosses off 'thermo' and 'stat mech' but an expert would produce estimates of relaxation times, not just handwaving about the second law of thermodynamics. And as for his claim that the editors "didn't know that photons interact with each other", the reader may check from this talk page the manifest inaccuracy of that statement and may judge Waleswatcher's intellectual honesty in making it. The work by Krylov is supported by a biographical note by V.A. Fock, and it is translated and commented on by Ya. Sinai; these are very well respected authorities, well aware of Tolman's work. Krylov writes in translation on page 3 of the above reference: "Despite the results, some of which are of exceptional value, obtained in attempting to overcome difficulties of either type, the problem of establishing the connection between statistics and mechanics should be regarded as being absolutely unsolved." So much for Walewatcher's view that "there is no disagreement in the literature" that he is aware of.Chjoaygame (talk) 21:09, 6 February 2012 (UTC)

Actually, the very first thing I did when this conversation started is estimate the thermalization time due to photon-photon interactions. You can do it in your head, roughly. It scales like a high power of the final temperature, so it is very short for high temperatures and very long for low temperatures. But of course that estimate cannot be included in the article, since it would constitute "original research". Waleswatcher (talk) 03:56, 7 February 2012 (UTC)

I did not say thermalization by photon-photon interactions is unsupported, I said I could find no support - yet. Waleswatcher says there is support, and I cannot dispute that - yet. As I said before, the fact that it is a small effect under terrestrial conditions is not the point, it is irrelevant. It is an illustration of the fact that the old idea that matter is required is false. This is an important point, and so the illustration is an important one. PAR (talk) 20:01, 7 February 2012 (UTC)

PAR: The idea that equilibrium can be achieved without matter is a point that has neither theoretical or experimental support that can be located in the literature. On the other hand, support for thermalization in the presence of matter is easily found. My conclusion is that so far as the vast majority of the literature is concerned, thermalization of radiation without the presence of matter is not even a footnote, and one might well question how "important" this point can be when it is so universally neglected. Brews ohare (talk) 20:19, 7 February 2012 (UTC)

Comment 6

As long as there is a conceivable series of interactions which will allow every possible energy state of a system of photons to be populated, then equilibrium will occur. If not, then not. For example, if two photons always interact and randomly alter their momentum (while conserving it) but not their individual energies, then the energy distribution will not change and equilibrium will not occur. If two photons interact, but can never produce a photon with an energy below some threshold, then there are conceivable non-equilibrium energy distributions which will not equilibrate. Realizing that there are photon-photon interactions is not enough alone. It must be shown that every distribution of energies is conceivably accessible from any other distribution (while conserving energy) in order for the H-theorem to hold. In more technical terms, any point in the phase space of the system must be accessible from any other point. I believe, but cannot reference or prove that this is the case for QED photon-photon interactions, but that's only because I am not very good at QED photon-photon calculations. Maybe this needs to be looked into. If it is the case, then there is no obstacle in my mind to the statement that photon-photon interactions produce equilibrium. PAR (talk) 06:05, 7 February 2012 (UTC)

It is true, I can show you why if you want. The only constraints on what can be produced come from conserved charges - energy, momentum, and (since photons are massless spin 1) helicity. Also bear in mind that 2 into 2 scattering is just the beginning - there are all sorts of more complex interactions involving many photons as well (including 2 into many, which is sometimes called inelastic scattering). FYI, the only known (even theoretically) interactions that don't lead to thermalization are those in very special mathematical models that are called "integrable", with an infinite number of conserved charges. Light-by-light scattering is not in that class. Waleswatcher (talk) 12:14, 7 February 2012 (UTC)

PAR & Waleswatcher: As PAR points out, and as Waleswatcher's resort to personal estimates indicates, the statement that photon-photon interactions can produce thermal equilibrium of the radiation single-handed remains an unsupported assertion. Moreover, several sources indicate it is a very, very minor mechanism, and is dominated by interactions with matter wherever matter is present. The only case where photon-photon interaction is significant is at energies so large that charged matter is produced by the collisions. So what we have here is an unsupported allegation about an insignificant mechanism, and one has to ask why all the fuss? Brews ohare (talk) 16:12, 7 February 2012 (UTC)

Sorry - what? How does the fact that I did an estimate of the thermalization time "indicate" that something else - the fact that photon-photon interactions, like all others, thermalize - is an "unsupported assertion"? That makes no sense whatsoever, and moreover it's not true - the "assertion" is no more and no less than a specific example of the second law, one that's proven in detail in at least one reliable source. As for it being "minor", that's the case under laboratory conditions, but not at all in many other situations of interest to physicists and the public. Not to mention that this is important and informative as a point of principle. Speaking of which, didn't you already propose some compromise text that includes this? Did you now change your mind? Waleswatcher (talk) 16:19, 7 February 2012 (UTC)

Waleswatcher: My wording should read: "resort to personal estimates in place of a reference specifically addressing the calculation of thermalization based solely upon photon-photon interactions indicates... an unsupported assertion." As PAR points out, there are details that have to be established before any particular mechanism can be certain to lead to thermalization. It may be that systems always will drive toward equilibrium in nature, but the second law doesn't say that any mechanism will will have that result, particularly an idealized one singled out. The references on boson gases are models, and if they show thermalization, then one has to show that the photon gas satisfies the assumptions of the models. For WP, once challenged, such an assertion requires a source.

As per the revised text, I view it as containing an unsupported assertion. I do not choose to challenge it. However, someone else may do so, who knows? The question remains: why are you so insistent upon mentioning what is an unimportant mechanism that cannot be supported by a specific reference, but only by broad generalities that have not been demonstrated to apply to this instance? Brews ohare (talk) 17:39, 7 February 2012 (UTC)

You say the mechanism is not minor, but the only sources I can find say it is minor under all circumstances, not just in the lab, with the possible exception you have said in the article, of temperatures above several 10⁹K (another unsupported assertion). Brews ohare (talk) 17:59, 7 February 2012 (UTC)

I have fleshed out the Tolman reference to include a quotation that makes clear this source is a general derivation of the H-theorem. I confess to no understanding of how general this derivation is, or just how it applies here. The quotation probably will leave readers with the same uncertainty. Brews ohare (talk) 18:40, 7 February 2012 (UTC)

Perhaps you would consider improving the article H-Theorem and adding this example? Brews ohare (talk) 18:56, 7 February 2012 (UTC)

Even if that was your wording, you'd still be conflating two distinct things: whether or not these interactions lead to thermalization, and what the time-scale is. The latter is much harder to establish rigorously than the former, but rather simple to estimate (as I said, I did it in my head). I haven't seen an estimate like that published, but then again I haven't looked. Earlier Chojoyagame cited a source that discusses it in the context of the early universe, so that's at least one. Regarding whether photon-photon interactions satisfy Tolman's criterion, I've explained over and over again that they clearly do (just read what he writes). It seems that you cannot follow his derivation, which of course is rather technical. But as I've also mentioned many times, unless you think pure photons in a perfectly sealed box or periodic space are an exception to the 2nd law of thermodynamics, there is no question that they thermalize, and if so, it's manifestly photon-photon interactions that do so (since that's all there is). As such, the 2nd law itself suffices to "support" this statement, and here we have much more than just that. Waleswatcher (talk) 19:52, 7 February 2012 (UTC)

Waleswatcher: We are arguing over technicalities here. You are asking me to decide whether Tolman's derivation applies to photon-photon interactions, which I am unsure I have the background to do. I also view this work as a "derivation" of the second law, which is (in my view) a technical impossibility without assumptions that must be verified to apply in any real-world example.

The unanswered question remains: why bring this topic up? You claim it has some significance "in principle", but it seems that the significant point is that the second law applies, and not any specific mechanism. My conclusion is that so far as the vast majority of the literature is concerned, thermalization of radiation without the presence of matter is not even a footnote, and one might well question how "important" this point can be when it is so universally neglected. Brews ohare (talk) 20:09, 7 February 2012 (UTC)

I'm not asking you to decide anything. As for your "unanswered" question, it's been asked and answered repeatedly by both me and PAR. I see no reason to answer it yet again. Waleswatcher (talk) 21:25, 7 February 2012 (UTC)

Regarding gravitational photon-photon interactions, the thing that concerned me was the fact that the gravitational force is long-range (~1/r^2) so that each particle is in effect "colliding" with every other particle in the system, and I wondered if that was a problem. It is apparently not, since "infinitely large" globular clusters have been shown to achieve a Maxwellian distribution. The only problems with finite globular clusters is their "finiteness", resulting in "temperature" and density gradients and "evaporation". A quote from http://adsabs.harvard.edu/full/1954MNRAS.114..191W

The mathematical result that an isothermal gas sphere has infinite mass amy be compared to the physical idea that it is impossible to set up a finite isothermal body unless one provides it with an ideally non-conducting boundary...

In our case that "ideally non-conducting boundary" is the black body with perfectly mirrored walls. Is there anyone who can now believe that gravitational photon-photon interactions are incapable, in principle, of producing thermal equilibrium? PAR (talk) 07:07, 8 February 2012 (UTC)

Gravity will certainly thermalize photons as well. All the processes involving matter absorbing and re-emitting radiation also take place when photons interact via gravity - production and absorption of photons, scattering, even spontaneous creation of other particles. Waleswatcher (talk) 13:02, 8 February 2012 (UTC)

Comment 7

I don't understand why this relevant; you have to start with a photon gas coupled to a heat bath anyway to discuss black body radiation. If you have photon gas contained inside a cavity, then the photons interact with the atoms in the cavity wall. The cavity walls are at some temperature, so the photon gas reaches thermal equilibrium with the cavity walls. What would be interesting is to discuss corrections to Planck's law due to the photon-photon interaction. Count Iblis (talk) 00:12, 8 February 2012 (UTC)

"you have to start with a photon gas coupled to a heat bath anyway to discuss black body radiation" - no, you don't. The Planck spectrum is the unique equilibrium state for photons (i.e. it's the state with maximum entropy). That derivation is done in just about every stat mech book, often utilizing a periodic "box" (i.e. no walls and no bath, just photons). According to the 2nd law, any gas of photons left alone for long enough will approach a Planck spectrum, regardless of whether there are any walls or materials around. Thermodynamics doesn't care what the interactions are, or what the system is - that's why it's so incredibly powerful and useful, and that's a very important point to make, particularly in an article on black bodies. Waleswatcher (talk) 00:19, 8 February 2012 (UTC)

Yes, but this is done for mathematical convenience. So, because we already know that the nature of interactions don't matter, you can chose anything that is convenient mathematically to do the computations. In any realistic down to Earth situation, you can't confine a photon gas without it having to interact with matter, so this is moot issue. Count Iblis (talk) 00:38, 8 February 2012 (UTC)

That's true, and it's explained in the article. Waleswatcher (talk) 00:46, 8 February 2012 (UTC)

By the way, here's how it was worded: "Although the radiation in the cavity at any given time may not be in thermal equilibrium, if left undisturbed it will become so, typically by continual absorption and re-emission by material in the cavity or its walls.[6][7][17][18] Radiation entering the cavity will be "thermalized" (in other words, its energy will be shared with the rest of the radiation in the cavity in a Planck distribution). The time taken for thermalization depends on the nature of the matter in the cavity or walls. It is much faster with condensed matter than with rarefied matter such as a material gas, especially a Knudsen gas.[19] Any interaction (for instance photon-photon interactions[20]) will accomplish thermalization,[21] but the time it takes to do so may be very long.[22]"

Now, it says: "Although the radiation in the cavity at any given time may not be in thermal equilibrium, if left undisturbed the second law of thermodynamics guarantees that it will approach equilibrium,[12] although the time it takes to do so may be very long.[13] Typically equilibrium is reached by continual absorption and re-emission of radiation by material in the cavity or its walls.[5][6][14][15] Radiation entering the cavity will be "thermalized"; in other words, its energy will be shared with the rest of the radiation in the cavity until it achieves a Planck distribution. The time taken for thermalization is much faster with condensed matter than with rarefied matter such as a material gas, especially a Knudsen gas.[16] At temperatures below billions of Kelvin, photon-photon interactions[17] are usually negligible compared to interactions with matter,[18] but like any interacting gas, even in the absence of matter the radiation will come to thermal equilibrium eventually.[19]"

I think the old wording was better and emphasized photon-photon interactions less if anything, but other editors objected and forced the change. Waleswatcher (talk) 00:52, 8 February 2012 (UTC)

The "right" way to do this is:

"Although the radiation in the cavity at any given time may not be in thermal equilibrium, if left undisturbed the second law of thermodynamics guarantees that it will approach equilibrium,[12] although the time it takes to do so may be very long.[13] Typically equilibrium is reached by continual absorption and re-emission of radiation by material in the cavity or its walls.[5][6][14][15] Radiation entering the cavity will be "thermalized"; in other words, its energy will be shared with the rest of the radiation in the cavity until it achieves a Planck distribution."

The rest of the garbage in the present text is there because Waleswatcher wants to draw attention to radiation thermalizing without matter present, a situation possible in principle, but that hardly ever happens (if at all) in the Universe, and which is not discussed as such by any source, other than to discount this mechanism as negligible. Brews ohare (talk) 01:54, 8 February 2012 (UTC)

That "garbage" is what's actually in every source. Very few if any derive the Planck distribution or the H-theorem using any kind of remotely realistic model of interactions with matter. Instead, they arrive at both using collisions between particles or interactions between quantum states of the gas, i.e. photon-photon interactions in the case of cavity radiation, and often with periodic boundary conditions (such that there are literally no walls at all). As Count Iblis correctly points out, it makes no difference - all interactions increase entropy and systems tend to equilibrium. Bearing in mind that this paragraph is in a section titled "Idealizations", I have no idea what you are objecting to, especially considering that photon-photon interactions are actually the dominant effect in many physically relevant and interesting situations. Waleswatcher (talk) 04:20, 8 February 2012 (UTC)

It would be more convincing if you provided sources for these proclamations. Brews ohare (talk) 05:52, 8 February 2012 (UTC)

Already done. Waleswatcher (talk) 13:03, 8 February 2012 (UTC)

Waleswatcher: It has been a long discussion, and I recall no instance cited that would support your statement "especially considering that photon-photon interactions are actually the dominant effect in many physically relevant and interesting situations." If there are sources to support this remark, perhaps you could cite them again here to refresh my memory? That would go far toward meeting my objections. Brews ohare (talk) 17:34, 8 February 2012 (UTC)

At sufficiently high temperatures, photons interact very strongly. Chjoaygame posted a quote here http://en.wiki.x.io/wiki/Talk:Black_body#Kondepudi_.26_Prigogine_1998_on_matter_and_radiation . At such energies photon interactions will quickly produce matter, so it becomes a matter of semantics whether photon-photon or photon-matter interactions are more important, but regardless of semantics, a pure photon gas will rapidly come to equilibrium when the temperatures are high, and including matter in the initial state wouldn't change the time significantly. Such conditions are of great interest in early universe cosmology, possibly in astrophysics near pulsars and other objects where the electromagnetic fields are extremely strong, and in particle physics experiments. Waleswatcher (talk) 18:41, 8 February 2012 (UTC)

Maybe so, Waleswatcher, but still no sources. The thermalization of photons leading to the CMBR occurred when the photons interacted with matter, and the CMBR has a temperature established at the time of decoupling when matter became no longer ionized. Maybe there are astronomical objects that have no matter, but I don't know about them. This argument is not about the occurrence of photon-photon scattering but about its minor role in achieving thermal equilibrium of radiation, because in almost all circumstances there is matter present. Brews ohare (talk) 19:16, 8 February 2012 (UTC)

The source is right there - Kondepudi&Prigogine. Waleswatcher (talk) 21:08, 8 February 2012 (UTC)

Comment 8

Waleswatcher, the problem I have with this 'photon-photon' interaction arises from the fact that photons, according to Planck, Einstein and co., originate in accelerating electric charge and the terminate in accelerating electric charge. In a totally reflecting cavity by definition the photons do not interact with the walls. Do you have the mechanism by which the photons interact in these conditions? --Damorbel (talk) 07:17, 8 February 2012 (UTC)

This is classical viewpoint. Einstein's general relativity introduced gravitational attraction between photons, and QED, which came after Planck and Einstein, introduced photon-photon interaction via the creation of, e.g. virtual electrons and positrons. PAR (talk) 08:38, 8 February 2012 (UTC)

Thanks PAR. But can you tell me if photon-photon interaction (for pair production) takes place spontaneously i.e. in the absence of a third item? And if any of the possible interactions will change the momentum of massive particles (which are not there by definition) and (possibly) thermalise them?

PS It could be that the 'by definition' bit is impossible! --Damorbel (talk) 10:25, 8 February 2012 (UTC)

Yes, they take place in the absence of anything else. I don't know what massive particles you're referring to, but these interactions of course change the momentum of photons, as well as creating and destroying more photons and potentially other particles, i.e. there are both elastic and inelastic interactions involving only photons in the initial state. (Chjoyagame, take note.) Waleswatcher (talk) 12:58, 8 February 2012 (UTC)

• Check out "Photon-Photon Interaction in a Photon Gas" by Markus Thoma, along with associated references. I couldn't find where this has been mentioned before in this discussion, although I may be wrong. PAR (talk) 14:26, 8 February 2012 (UTC)

It is nice to return to sources and away from pronouncements. Two quotes from this paper are possibly relevant here:

"effects of the photon gas are expected to be very small due to the extremely weak photon-photon coupling"

"In QED, damping arises from the box diagram only above the threshold for electron-positron pair production."

Of course, above the threshold for real particle pair production, matter is present. This paper restricts itself to low order perturbation theory and finds no damping at this order, but suggests it will occur at higher orders (even weaker effects), not discussed here. All in all, this paper supports the view of all other sources found so far that the photon-photon scattering mechanism without mediation by matter is of little importance in forcing a photon gas to thermal equilibrium in realizable situations where matter is normally present. Brews ohare (talk) 16:37, 8 February 2012 (UTC)

This more recent paper suggests that the role of photon-photon scattering in a system near thermal equilibrium is yet to be established experimentally, and its importance still is rather conjectural. Brews ohare (talk) 18:22, 8 February 2012 (UTC)

By "damping" he probably means inelastic processes (i.e. processes that don't conserve photon number). It's true that below the e+/e- pair production threshold the interactions are elastic to lowest order, but elastic collisions thermalize, and higher order processes (like 2 photons->4 photons) are inelastic. Regarding the "extremely weak" comment, the sentence immediately preceding it says "As an application we consider the influence of the cosmic microwave background radiation on low energy photons." The CMB has today a temperature of around 2.7K, which is far below room temperatures, and photon-photon interactions are correspondingly much weaker than they are even at room temperature. Waleswatcher (talk) 18:55, 8 February 2012 (UTC)

• Thank you for thinking of me, Waleswatcher. But I may remind you that I have not proposed that photon-photon interactions do not occur. I have been pointing out that you are synthesizing their proposed power of thermalizing, based, you have now revealed, on your own research.

I wrote above and here copied:

If you have a reliable source that deals with walls and these kinds of thermal equilibria, here is the place for you to cite it. I hope it will not be some kind of original research or synthesis, but will explicitly address the matter in hand.Chjoaygame (talk) 21:54, 30 January 2012 (UTC)

You admitted that your post was based on your own reseach above and here copied:

Actually, the very first thing I did when this conversation started is estimate the thermalization time due to photon-photon interactions. You can do it in your head, roughly. It scales like a high power of the final temperature, so it is very short for high temperatures and very long for low temperatures. But of course that estimate cannot be included in the article, since it would constitute "original research". Waleswatcher (talk) 03:56, 7 February 2012 (UTC)

You are still not producing reliable sources according to Wikipedia policy.Chjoaygame (talk) 18:42, 8 February 2012 (UTC)

I never implied that you didn't - I wasn't referring to you. All the statements in the article are adequately sourced, so you'll need to be more specific about that. The fact that I did an estimate of the time is totally immaterial. Waleswatcher (talk) 18:45, 8 February 2012 (UTC)

If I may copy the immediately above comment from you as follows: "i.e. there are both elastic and inelastic interactions involving only photons in the initial state. (Chjoyagame, take note.) Waleswatcher (talk) 12:58, 8 February 2012 (UTC)", I trust you will forgive me for thinking you were referring to me.Chjoaygame (talk) 18:49, 8 February 2012 (UTC)

I was pointing out to you the evidence for my statement - that several editors (not including you) didn't know when this conversation started that photons interact. Waleswatcher (talk) 18:57, 8 February 2012 (UTC)

Waleswatcher: You say " By "damping" he probably means inelastic processes ". This author derives a real dielectric permittivity, which in my mind means no mechanism for thermalization. Your other remarks establish the restricted nature of this work. The point here is that this source is not an example supporting your thesis, but is simply one more author who agrees that thermal equilibrium of radiation by photon-photon interaction in the absence of matter is a very minor effect. Brews ohare (talk) 19:24, 8 February 2012 (UTC)

At this point I don't know what you're arguing about. You agree photon-photon interactions thermalize, but you also think they play a minor role in "practical" circumstances. But that's exactly what the article says, so...? Waleswatcher (talk) 21:08, 8 February 2012 (UTC)

Waleswatcher: I believe you are right: the article is no longer what this is about. I removed the RfC template. Brews ohare (talk) 22:21, 8 February 2012 (UTC)

Waleswatcher writes just above, with what I think is a valid ellipsis of quotation: "photon-photon interactions thermalize ... that's exactly what the article says". May we quote you on that?Chjoaygame (talk) 04:27, 9 February 2012 (UTC)

Chjoaygame writes "I...want...to....waterboard...you" (with equally "valid" ellipsis). That doesn't really seem in accord with wiki's policies, does it? Can we quote you on that? Waleswatcher (talk) 14:16, 9 February 2012 (UTC)

What is germane here is that the article says photon-photon interactions in the absence of matter will thermalize radiation. In my view, that is an unsupported statement. The various primary sources mentioned on this Talk page that explicitly treat photon-photon scattering in the absence of matter conclude (at most) that thermalization by this mechanism might occur, but calculations as yet do not extend this far. The Tolman reference cited in the article is to a certain derivation of the H-theorem, which might be germane, but does not specifically address this mechanism. Waleswatcher believes it does apply, and takes the view that his opinion is quite sufficient without any need for further support. Of course, his opinion may be correct, but WP policy allows such opinion to be challenged. I do not choose to do this, but others might. Brews ohare (talk) 14:59, 9 February 2012 (UTC)

That's not accurate. The article does not say that photon-photon interactions thermalize (although it could, since that's both true and sourced). Instead, the statements in the article are (a) at low temperatures photon-photon interactions are usually negligible, and (b) in the absence of matter radiation will come to equilibrium eventually. Point (a) doesn't seem to be in dispute, and point (b) is proved in Tolman (and other references) and in any case is a particular example of a fundamental law of physics, the 2nd law of thermodynamics. Waleswatcher (talk) 15:30, 9 February 2012 (UTC)

Maybe the text in the article is ambiguous. I don't read it the way you do. The wording is:

"At temperatures below billions of Kelvin, direct photon-photon interactions[17] are usually negligible compared to interactions with matter,[18] but like any interacting gas, even in the absence of matter the radiation will come to thermal equilibrium eventually.[19]"

It appears to focus upon photon-photon interactions in the absence of matter. If that is not your intention, this sentence could be dropped altogether, as the rest of this paragraph already encompasses the approach to equilibrium via the second law:

"At any given time the radiation in the cavity may not be in thermal equilibrium, but the the second law of thermodynamics guarantees that if left undisturbed it will eventually reach equilibrium[12] (although the time it takes to do so may be very long[13])."

Brews ohare (talk) 16:16, 9 February 2012 (UTC)

I agree with you that the lesson an intelligent and alert reader is likely to draw is that in the absence of matter, photon-photon interactions will thermalize the radiation. That's fine, because it's (a) a consequence of the laws of thermodynamics, (b) true, and (c) sourced. The wording at the moment does not explicitly state that, however, as a direct result of this discussion. Instead, it's more vague. In any case, I think this is the best we are going to do. For reasons stated multiple times I am not OK with removing this - I think it's important and interesting, and teaches a critical physics lesson. I'd prefer the language be changed back to what it was, but you seem opposed. So I think this is the best we can do, and further discussion seems pointless. Waleswatcher (talk) 18:14, 9 February 2012 (UTC)

I read that as a 'no'.Chjoaygame (talk) 18:23, 9 February 2012 (UTC)

the second law

According to Guggenheim (1949/1967) on pages 12–14 of the fifth edition, and other respected texts, the second law considers three types of process: natural, reversible, and unnatural, distinguished by their effects on the total entropy, which are respectively increasing, null, and decreasing. Another name for reversible processes is ideal or limiting processes. All processes that occur in nature are natural. No unnatural process occurs in nature. Ideal processes do not actually occur in nature, but can be approximated arbitrarily closely by allowing sufficiently slow progress in processes that might occur in nature. Such ideal processes are sometimes called quasistatic; they feature prominently in thermodynamics textbooks.

We are here discussing an ideal situation, of light in a cavity with perfectly reflecting walls and no material content. The second law allows for reversible processes in ideal situations. In natural processes, it requires entropy increase, but the question here refers to an ideal, not necessarily natural situation. To make the second law prescribe thermalization, an entropy increase for the present situation, light must interact with itself in the absence of matter in a cavity with perfectly reflecting walls. The second law by itself does not say that light interacts with itself in that way. That is an additional requirement for the thermalization conclusion in the present situation.Chjoaygame (talk) 18:49, 9 February 2012 (UTC)

Chjoaygame: You've made an interesting point about three kinds of processes. Is it accurate to require only an unspecified interaction? For example, if all photons of energy E interact with each other, but not with those of energy ≠E, I don't think that suffices. If photons of energy >E interact only with each other and those with energy <E interact only among themselves, I expect that two temperatures might evolve, that of subpopulation <E and that with subpopulation >E. And so forth. In my mind the problem for Waleswatcher, aside from a proclivity for avoiding sources, is that nobody yet has shown that photon-photon interactions in the absence of matter fit the bill, and in addition, everyone agrees that it doesn't matter anyway because in any real-world situation these processes are always dominated by others. Brews ohare (talk) 19:25, 9 February 2012 (UTC)

Both statements in the last sentence are flat-out false. Since I've pointed that out over and over with no effect, I won't bother to do it again. Regarding Chjoaygame's quote, this is manifestly a "natural" process. The idealizations that lead to "null" processes require no interactions (or very, very specific interactions that conserve an infinite number of charges). Waleswatcher (talk) 19:42, 9 February 2012 (UTC)

I was trying to make the point that we are here considering an ideal situation with perfectly reflecting walls and no matter in the cavity. Without prejudice as to whether idealizations that lead to null processes require no interactions, the second law doesn't by itself say that light has self-interactions. That is required as another premise, beyond the second law.Chjoaygame (talk) 19:53, 9 February 2012 (UTC)

The second law applies to all such situations, because all particles and fields (in idealized containers or not, that isn't relevant, since it's just a question of whether more types of particles are present) interact. One could write down a mathematical theory in which there are literally no interactions, but it cannot describe anything in our world - certainly not light, which has multiple different types of self-interaction. Waleswatcher (talk) 20:25, 9 February 2012 (UTC)

• Waleswatcher: You are using a time-worn tactic of WP Talk pages: "Since I've pointed that out over and over with no effect...". The idea is to claim that suitable sources have been presented already and it is just the intransigence or pigheadedness of the rest of us that stands in the way of acceptance of the ideas claimed. Then there is the rhetorical device "Both statements in the last sentence are flat-out false." suggesting that the opposition is unreasonable and asserting obvious untruths.

None of these tactics would be necessary if you were on firm ground: you have only to cite your sources once more and deal with the reasons why they were not accepted as solid grounds for your assertions.

Failing that sensible approach, and resorting instead to the devices of debate, not discussion, discredits your position. Brews ohare (talk) 20:34, 9 February 2012 (UTC)

I have little experience with wikipedia, so I can't comment on whether my "tactics" are "time-worn". What I do know is that endless discussions of physics with anonymous people on the internet are quite useless. As I said before: "At this point I don't know what you're arguing about. You agree photon-photon interactions thermalize, but you also think they play a minor role in "practical" circumstances. But that's exactly what the article says, so...?" and your response "I believe you are right: the article is no longer what this is about." That sums it up nicely. Waleswatcher (talk) 20:44, 9 February 2012 (UTC)

• Waleswatcher writes above: "because all particles and fields (in idealized containers or not, that isn't relevant, since it's just a question of whether more types of particles are present) interact." That is the further premise, beyond the second law, that is needed for the desired conclusion.Chjoaygame (talk) 22:54, 9 February 2012 (UTC)

Here's the second law taken directly from a textbook: "If a closed system is in a configuration that is not the equilibrium configuration, the most probable consequence will be that the entropy of the system will increase monotonically in successive instants of time." That's precisely what a gas of photons with (say) periodic boundary conditions is - it's a closed system, as closed as you can get, and this law of physics states that its entropy will probably increase (the probabilities involved are of order one minus the exponential of minus the number of photons, and the number of photons in a human-scale box at room temperature is, at a guess, around 10^18). You're arguing against the laws of physics - often a losing proposition. Moreover, it makes it clear that you cannot be convinced no matter what, so there is no point in further discussion. Waleswatcher (talk) 23:43, 9 February 2012 (UTC)

I am concerned about logic here. The fallacy you are trying to sell here is a form of petitio principii, 'begging the question'. I am not denying the conclusion, but am analyzing its logical provenance. In writing "You're arguing against the laws of physics", you are accusing me of denying the conclusion.

You are offering a particular statement of the 'second law'. Many texts use the term closed system to mean one that can exchange energy, for example with a temperature bath, but not matter. Some, such as Callen, and quite likely yours, use the term 'closed' where many would use 'isolated'. It is not stated in your post which usage your unnamed source follows. In the currently more common usage, our concern here is with isolated systems, not closed systems.

A requirement for a system to reach thermodynamic equilibrium is that it have no internal constraints. The necessary added premise here is that light can interact with itself because its nature does not constrain it from doing so. Your statement implicitly includes that light does not have natural constraints that prevent the necessary self-interactions. That included implication is the further premise needed for the desired conclusion. There is experimental evidence for that further premise, that light does have self-interactions, but that is not part of the second law.

You write: "Moreover, it makes it clear that you cannot be convinced no matter what, so there is no point in further discussion." I am here concerned about the logic and reliable sourcing of the article, not only the physical questions to which you are here trying to narrow the discussion, avoiding the question of reliable sourcing. Indeed I will not be convinced that the article can dispense with logic and reliable sourcing.Chjoaygame (talk) 00:47, 10 February 2012 (UTC)

progress of physics

We are considering a matter of physical principle. We need to be careful.

Our presently cited text Tolman was published in 1938. It is a respected authority.

A glance at the translation of Krylov, N.S, (1950/1979), Works on the Foundations of Statistical Physics, Princeton University Press Princeton NJ, and the appended commentary by Ya. G Sinai, a weighty authority indeed, shows that for such a matter of principle as we are now considering, something more up-to-date and thoroughly reliable than Tolman, respectable though he is, would be good. Krylov emphasizes the importance of the relaxation time mentioned by Brews ohare above.

The revised version of the fourth edition of Dirac's 'The Principles of Quantum Mechanics' was published in 1967. It has a chapter on quantum electrodynamics not included in the first edition. Dirac is a respected authority. He was well and truly alive and active in 1967. Dirac in that chapter on page 312 writes: "Theories of [other kinds of interactions] have been set up and much developed and useful results have been obtained from them. But in the absence of equations of motion these theories cannot be presented as a logical development of the principles set up in this book." For our purposes, I read that as implying that Tolman does not have all the answers on quantum field theory.

There is a difference between the quantum mechanics (QM) of Dirac and the founders, and quantum field theory (QFT). The ordinary theory of quantum optics is in the realm of the quantum mechanics of the founders, but for photon-photon interactions, the current theory is quantum field theory. According to Blasone, M., Jizba, P., Vitiello, G. (2011), Quantum Field Theory and its Macroscopic Manifestations, Imperial College Press, London, ISBN 978–1–84816–280–8, on page 20: "In this sense, QM can only describe systems in a single specified physical phase. From such a perspective we may say that QFT is drastically different from QM and it provides a much richer framework than Quantum Mechanics." The main radical difference that they see is that QFT calculations have time running both forwards and backwards as ingredients in one and the same calculation; they say on page 188 that this doubles the number of degrees of freedom in QFT relative to QM, and that it "is not simply a mathematical tool" but "appears to be an essential feature of QFT". An account of quantum electrodynamics that has been cited here is Richard Feynman's 1985 QED. The Strange Theory of Light and Matter, Princeton University Press, Princeton NJ, ISBN 0691024170. It tells about calculations with both senses of time.

These developments make Tolman 1938 a source for historical studies but not by itself a currently reliable one for actual physics.Chjoaygame (talk) 19:39, 9 February 2012 (UTC)

Chjoaygame: I think your point is that science has advanced since 1938, and Tolman did not foresee these developments. Of course, that doesn't mean his arguments about the H-theorem do not apply, but rather that they must be shown to apply. That step is one Waleswatcher will not admit or attempt to source as regards the role in reaching thermal equilibrium via photon-photon interactions in the absence of matter. His reluctance may stem from other causes, but one impediment is that there exists at the moment no source, not even a specialized technical paper, that provides this information. Brews ohare (talk) 17:04, 10 February 2012 (UTC)

adkins as source

comment a

Adkins' third edition is currently cited in the article as the source for the proposal that the second law of thermodynamics guarantees that the radiation will come to equilibrium:

"At any given time the radiation in the cavity may not be in thermal equilibrium, but the the second law of thermodynamics guarantees that if left undisturbed it will eventually reach equilibrium"

I have here only the second edition of Adkins, not the third which is cited in the article. On page 156, in the section on thermal radiation, the second edition states that "with no body that can emit and absorb radiation in the container, we may consider the behaviour of individual rays or spectral components separately, knowing that there is no means of redistributing energy between them.³³ [footnote] ³³ In quantum terms, this means that there is now no coupling between the various modes of the container so that we may examine how each mode is perturbed by change of volume as if no other modes were present."

The internet doesn't show me in full the corresponding page (154) of the third edition. It just gives me the following quote: "(8.63) In quantum terms, this means that there is now no coupling between the various modes of the container so that we may examine how each mode is perturbed by change of volume as if no other modes were present."

Does someone who is interested have a full copy of the third edition handy?Chjoaygame (talk) 21:17, 11 February 2012 (UTC)

I don't have that book and didn't add it to the article. In any case, the quote you gave is flat-out false, and in direct contradiction to any number of other reliable sources, so we might want to find a better reference. Kittel&Kroemer would do. Waleswatcher (talk) 22:44, 11 February 2012 (UTC)

According to the present Wikipedia article:

"The cosmic microwave background radiation observed today is "the most perfect black body ever measured in nature"."

According to Kittel and Kroemer 1980 second edition page 98: "Most of the black body radiation energy was thus effectively decoupled from the matter. ... After the decoupling the evolution of matter into heavier atoms (which are organized into galaxies, stars, and dust clouds) was more complicated than before the decoupling. Electromagnetic radiation, such as starlight, radiated by matter since the decoupling is superimposed on the cosmic black body radiation." Much of it hasn't yet thermalized, it seems.Chjoaygame (talk) 05:33, 12 February 2012 (UTC)

That's accurate, yes. What do you find "curious"? Waleswatcher (talk) 05:49, 12 February 2012 (UTC)

I am curious to know when it will thermalize.Chjoaygame (talk) 05:58, 12 February 2012 (UTC)

Since the un-thermalized radiation is basically starlight, it will thermalize when the stars "thermalize" and the entropy of the universe reaches a maximum (the so-called "heat death" of the universe).

What Adkins is saying that during the time period of the "examining" of the modes (minutes? days? years?), the interaction between the modes is negligible. He did not mean to imply that the interaction between the modes is precisely zero on any and all time scales. He did not mean to imply that QED and gravitational interactions between photons are perfectly and completely nonexistent, in contradiction to the predictions of QED and general relativity. PAR (talk) 07:33, 12 February 2012 (UTC)

I suppose that even though light from remote galaxies has had trip times of billions of years and distances of billions of light years to reach us, so that we can resolve them in our telescopes, it has not suffered too many photon-photon collisions during the trip. So far as I know, we do not read reports of the thermal radiation that might have been produced by such collisions. It would then seem that the thermalization process has scarcely started, even over the present age of the universe.

According to the article on black holes:

"For a black hole of one solar mass ($M_{\odot }$ = 1.98892 × 10³⁰ kg), we get an evaporation time of 2.098 × 10⁶⁷ years—much longer than the current age of the universe at 13.73 ± 0.12 x 10⁹ years."

And larger black holes even longer. And perhaps some black holes will form in the future? Even in the remote future? So I suppose that if that is right, the "so-called 'heat death'" of the universe, and consequent on your answer the thermalization of light, should take at least that long to happen. Would it be fair to call such time scales "cosmological"?

"What Adkins is saying that ..." Looking through Adkins' second edition, I don't find him actually saying it. Perhaps he should have said it. For another purpose I had hoped to find such a statement in Adkins, but I couldn't find one. The nearest I can find is the following on page 11 of the second edition, where he is talking about hysteresis in a piece of iron in a magnetic field: "The potential barriers between these steps, however, are so large that the approach to equilibrium only proceeds at an extremely slow rate, one which is quite negligible on any normal time scale."Chjoaygame (talk) 12:25, 12 February 2012 (UTC)

"I am curious to know when it will thermalize." You realize it hasn't thermalized with the matter in the universe either - right? "I suppose that even though light from remote galaxies has had trip times of billions of years and distances of billions of light years to reach us, so that we can resolve them in our telescopes, it has not suffered too many photon-photon collisions during the trip." Nor has it suffered many photon-electron or photon-proton scatterings, despite the fact that space contains plenty of those in space. As for when it will happen - it's a continuous process happening all the time. Assuming dark energy is a cosmological constant, the time-scale is roughly the current age of the universe. That's also the time scale for matter to thermalize. And in fact, the primary mechanism is gravitational interactions.

As for Adkins, I hope you're not saying you think photons don't interact, after all? Waleswatcher (talk) 12:39, 12 February 2012 (UTC)

As for the plenty of protons. Kittel & Kroemer on page 110 tell me that "It is believed that the total number of photons in the universe is 10⁸ larger than the total number of nucleons (protons, neutrons). I had an idea that perhaps the bigger number might lead to more collisions?

As for when it will happen. It seems to me that the time scale for the evaporation of black holes would come into it, and that is according to the Wikipedia article far longer than the current age of the universe. If it has been happening all the time, I wonder where the radiation from it has been reported. Apparently Kittel & Kroemer are not overimpressed with the speed of thermalization. On page 110 they write: "We believe that the entropy of the photons is approximately constant, so that the entropy of the universe is approximately constant with time. Jim Steinman's song sung by Meat Loaf, Paradise by the Dashboard Light, has the following to say: "Boy: I swore that I would love you to the end of time! So now I'm praying for the end of time to hurry up and arrive."

As for Adkins. It is good to know that you care so much about my beliefs.Chjoaygame (talk) 19:08, 12 February 2012 (UTC)Chjoaygame (talk) 19:30, 12 February 2012 (UTC)

"I had an idea that perhaps the bigger number might lead to more collisions?" Really? Why? "It seems to me that the time scale for the evaporation of black holes would come into it" No, the timescale for black hole evaporation has absolutely nothing to do with starlight thermalizing. As for the entropy of the universe, K&K are probably wrong on that, because it seems that the entropy of the universe is dominated by black hole horizon entropy, specifically supermassive holes, not by CMB or starlight photons. I see we're back to the "let's discuss random physics facts" instead of "let's try to improve the article." Waleswatcher (talk) 20:21, 12 February 2012 (UTC)

comment b

Again, the Thoma paper deals with the role of photon-photon interactions in the cosmic microwave background:

Owing to the cosmic microwave background the velocity of light in the Universe is reduced compared to the vacuum. Actually it increases continuously with time as the temperature drops. Today at a temperature of 2.7 K it is given by (17) with γ = 4.7 × 10−43

In other words, photon-photon interactions result in a calculable (but not presently measureable) reduction in the effective speed of light compared to its vacuum value. PAR (talk) 03:24, 13 February 2012 (UTC)

Which has nothing to do with thermalization, BTW: the computed permittivity is real and allows for no energy exchange. Brews ohare (talk) 15:58, 13 February 2012 (UTC)

I only meant for that to illustrate the existence of photon-photon interactions, not thermalization. Check out http://meetings.aps.org/Meeting/DPP11/Event/152079. The abstract looks promising, but I cannot get the whole article immediately, I will get it in a day or two. PAR (talk) 22:32, 13 February 2012 (UTC)

Well, that is rather relevant, isn't it? Here's the abstract in full:

Thermally induced vacuum polarization stemming from QED radiative corrections to the electromagnetic field equations is studied. The physics of thermal radiation in the nonlinear vacuum first described by Heisenberg and Euler is a problem of some theoretical importance, in view of its relation to the cosmic microwave background, early universe evolution, and Hawking-Unruh radiation. In particular, the questions of the evolution toward equilibrium, stability, and invariance of thermal radiation under such conditions are of great interest. While nonlinear vacuum polarization effects in the photon gas had been previously studied, our analysis is presented in the framework of quantum kinetic theory. Within the context of the Euler-Heisenberg nonlinear QED vacuum, it is shown that a homogeneous, isotropic photon gas with arbitrary spectral distribution evolves toward an equilibrium state with a Bose-Einstein distribution. The transient evolution toward equilibrium of a gas of photons undergoing photon-photon scattering is described by the Boltzmann transport equation. Waleswatcher (talk) 03:38, 14 February 2012 (UTC)

I emailed Dr. Wu, the author of the above APS presentation, asking him to comment on our discussion and the idea of thermalization via QED interactions in general. Here, with permission, is his response:

Thanks for bringing this discussion to my attention. Although I am not an expert in QED, I can try to offer what I can and point you to pertinent sources. Firstly, the subject of photon-photon interaction in vacuum (absence of real matter) is much more than a matter of theoretical contrivance. Photon-photon scattering was much more prevalent in the early universe and may have played a role in the formation of the universe we know today; c.f. (Svensson et al, 1990). The topic of QED corrections in a photon gas has garnered some interest in the scientific community and is not an open and shut case as some readers/editors may believe. Below are some references. However, I feel these references may not adequately answer your questions or my own, which is why I’m also pursuing this problem using a different approach.

• Marklund, P.K. Shukla, “Nonlinear collective effects in photon-photon and photon-plasma interactions”, Rev. Mod. Phys. 78, 591–640 (2006)
• Partovi, “QED corrections to Planck’s radiation law and photon thermodynamics”, Phys. Rev. D 50, 1118–1124 (1994)
• Barton, “How close to ideal is the photon gas? corrections to Planck's laws at kT << me”, Annals of Physics, Volume 205, Issue 1, January 1991, Pages 49–69
• Kong, F. Ravndal, “Quantum corrections to the QED vacuum energy”, Nuclear Physics B, Volume 526, Issues 1–3, 24 August 1998, Pages 627–656

Secondly, the classical derivation of the fundamental laws of thermodynamics, e.g. Tolman’s book, has been revisited by numerous authors to include quantum kinetics. The ideas of detailed balance and the H-theorem remains applicable, with minor modifications due to the quantum nature of the particles. It indeed states that, with some caveats, interacting bosons will tend to Bose-Einstein equilibrium. My work (to be published) is based on this theoretical construct as well. My findings do not contradict the fundamental physics, but instead show the manner an isolated photon gas evolves to equilibrium and the timescale on which it does so -- a nontrivial quantity to define.

One point of interest to you is the above theory does not state that the equilibrium distribution has to be Planckian. Photon-photon scattering in vacuum, at least for the lowest order process (2->2), is a photon number preserving process. The constraint on the number of particles cannot be removed as typically done for blackbody radiation, for example:

http://en.wiki.x.io/wiki/Gas_in_a_box#Massless_Bose-Einstein_particles_.28e.g._black_body_radiation.29

Hence, the particular equilibrium distribution within the Bose-Einstein family is determined by the energy and photon number density of the initial system. Based on what has been described, low energy photon-photon scattering is sufficient in establishing equilibrium, though the resulting Bose-Einstein equilibrium distribution is not necessarily Planckian without some external interaction (wall absorption/emission, Compton scattering etc) or higher order QED effects. If you ever find a reference proving the Planckian claim, I’d appreciate it if you would drop me an email.

PAR (talk) 03:15, 24 February 2012 (UTC)

It seemed to me that "number conserving" implies non-zero chemical potential. So I asked Dr. Wu - "For a number-conserving process, I would think that the proper distribution would involve a chemical potential term in the usual Bose-Einstein derivation. Do you know if it is just that simple, would the addition of a chemical potential term to the exponential in the denominator of the Bose-Einstein distribution produce the proper distribution, or is it more complicated, or uncertain, than that?" - to which Dr. Wu replied (with permission) "In the interacting gas of bosons picture, you are correct in that a non-zero chemical potential could appear in the equilibrium distribution function. This number is uniquely determined by the energy and number densities of the particles. ... By the way, this reference looks interesting: Thermalization of a two-dimensional photonic gas in a ‘white wall’ photon box, Nature Physics 6, 512–515 (2010), doi:10.1038/nphys1680" The abstract is interesting in that it reports on an experimental non-zero chemical potential photon gas, but the thermalization is not via QED interactions.

The bottom line is that tentatively, low energy QED interactions tend to produce a Bose-Einstein distribution which is not Planckian simply because the chemical potential is not zero. It seems to me that the tail of this distribution would involve high-energy QED interactions which would. What the final equilibrium distribution would be, I don't know, but it seems calculatable. PAR (talk) 01:45, 29 February 2012 (UTC)

Let's be careful not to conflate two things - the effects of lowest order QED processes, which are 2->2 elastic scattering, and as such preserve photon number and cannot produce a Planck distribution from an arbitrary starting point - and QED processes in general, which do not preserve photon number and will produce a Planck distribution. Waleswatcher (talk) 12:30, 29 February 2012 (UTC)

Yes - I have asked Dr. Wu if, for a "low temperature" photon gas (well below the 2->2 cutoff energy), the fact that the high energy tail of the distribution is engaging in non-conserving collisions means that the non-Planckian distribution is a "metastable" distribution which is ultimately replaced by a Planckian distribution. PAR (talk) 21:18, 29 February 2012 (UTC)

I don't see how it can even be metastable - just long-lived. Waleswatcher (talk) 04:44, 1 March 2012 (UTC)

Well...yes - see http://en.wiktionary.org/wiki/metastable PAR (talk) 05:23, 1 March 2012 (UTC)

"metastable" in physics refers to a state that's stable under sufficiently small perturbations, but will eventually decay with a big enough or the right sort of stimulus. First order phase transitions and supersaturated fluids are examples. That's not the case here - there might be a relatively rapid thermalization to something close to a Bose-Einstein distribution with large chemical potential, followed by a slower, gradual change to a Planck distribution, but there's never any stability of any kind until the end. Just two time scales. Waleswatcher (talk) 12:50, 1 March 2012 (UTC)

That's in contradiction to the Wiktionary definition. If you are sure of that, and have a good reference for that statement, it might be time to edit the Wiktionary page. PAR (talk) 15:15, 1 March 2012 (UTC)

It's a term I use and hear used literally almost every day, and that's what it means. I can imagine someone using it loosely to mean just a long-lived state, but I can't imagine them using it to refer to a gradually changing state, as in this case. Waleswatcher (talk) 01:03, 2 March 2012 (UTC)

It seems to me that PAR has a good point. If a mass or quantity of energy of pure radiation in a perfectly reflecting cavity was sufficient only to produce an electron-positron pair after a very long time (supposing for the sake of argument without prejudice as to the real possibility), then the system would initially be trapped for a very long time in the no-electron-no-positron regime. But eventually, with the newly produced electron and positron, the process of thermalization would be very greatly sped up, until the electron and positron collide and perish again. This looks to me like two distinct enough rate regimes, such as is meant by 'metastable', not just a matter of two overlapping time-scales.Chjoaygame (talk) 04:15, 2 March 2012 (UTC)

• That's not the way it works. All QED photon-photon interactions are mediated by virtual electron-positron pairs, including both the lowest order and higher order processes, and all those processes take place even if there isn't enough total energy to create a real (non-virtual) electron-positron pair. Moreover, even if there is enough energy to pair-produce real electrons and positrons, inside a sealed box there is never any observation to collapse the wavefunction, so it's probably not correct to think of it as happening at any well-defined moment. Instead, there's a gradual evolution towards a wavefunction that's very close to a thermal density matrix. Waleswatcher (talk) 14:18, 2 March 2012 (UTC)

Thank you. I am glad to have this statement from you Waleswatcher. It wasn't clear to me till now that this is your position, and this now makes your position clear to me.Chjoaygame (talk) 14:44, 2 March 2012 (UTC)

• We have to do the calculations to determine the behavior. Until then, it's a semantic argument about the meaning of metastable - that's not going to shed any light onto the problem at hand, so I'm not too interested. I will adopt whatever definition the person I am talking to wants, unless it's logically cumbersome or contains a contradiction. Not the case here. PAR (talk) 04:35, 2 March 2012 (UTC)

comment c

Waleswatcher. Somewhere above you write "As for Adkins, I hope you're not saying you think photons don't interact, after all?" I suggest you are asking the wrong question. Let me ask you a question. - Is it your argument that photons interact in the absence of both matter and a gravitational field? --Damorbel (talk) 07:50, 14 February 2012 (UTC)

• It's impossible to have photons without a gravitational field. In classical general relativity all energy gravitates, hence all photons create a gravity field. By the same token, in quantum theory all gravitons have a non-zero amplitude to interact gravitationally. The situation for electromagnetism is analogous (replace "classical general relativity" with "Euler-Heisenberg Lagragngian", etc.). So to answer your question (at least I think it's your question) - photons always interact (although of course the interaction may be very weak). Waleswatcher (talk) 11:48, 14 February 2012 (UTC)

Great, so we have a talk presented at this meeting in November 2011. Supposing all is fine and this work passes scrutiny and gets published sometime in 2012 as a refereed paper in a professional journal, the view that photon-photon interactions cause equilibration eventually (maybe in the absence of matter - that isn't known yet to be part of this paper) has some support. So the statement in this WP article can be supplemented then by a citation to this primary source and is no longer an unsupported statement, although it remains a topic of current research and a very minor mechanism. Brews ohare (talk) 12:49, 14 February 2012 (UTC)

If that paper doesn't get accepted, it will be on the grounds that it is not interesting or new enough to warrant publication. Everyone knows this is true, it's an example of the second law/H-theorem, it's already proven in greater generality in old works on the H-theorem for weakly interacting Bose gases, and so proving it rigorously again is of somewhat dubious value. I suppose you can get an estimate for the thermalization time this way, but you can do that in your head (or at least on the back of an envelope). Waleswatcher (talk) 13:33, 14 February 2012 (UTC)

• Damorbel, we are here considering a section of the article about radiation in a cavity with opaque walls. The idea of 'no walls' with "periodic boundary conditions" is hardly directly relevant. The particular interest here is the case of perfectly reflecting opaque walls. Presumably the cavity walls consist of matter and so exert a gravitational field, or would it be zero because it is inside a cavity with spherical symmetry? We are then in the position of needing to enquire about the relative magnitudes of the gravitational effects of the cavity walls on the photons, and the photons on each other. Perhaps the cavity walls are made of very light perfectly reflecting materials, could I say lighter than light?Chjoaygame (talk) 17:23, 14 February 2012 (UTC)

".... radiation in a cavity with opaque walls." Please! I do understand your concern! The reason I made this intervention was to (try to) extract from Waleswatcher just what he wants to inroduce into the article. Kirchhoff introduced the concept of a black body as an abstraction, as such there can be no physical realisation of it. Kirchhoff needed (and Fourier did the same calculations but without the term 'black body') to distinguish between the thermal interaction that exchanges the photon energy with whatever charge carrier is involved and the scattering interactions (reflection, refraction etc.) that are non thermal. This is the whole (and only) point of the black body concept; it has two aspects that are symetrical, absorption of incident radiation and emission of radiation when >0K. The restof of the 'stuff' (equilibrium, Planck spectrum, black holes etc. are not really relevant and should be treated in separate articles with a link from a small paragraph.

Kirchhoff made significant contributions to the undertanding of thermal radiation but Fourier had worked most of it out 50 years earlier, you can find it here Remarques sur la théorie mathématique de la chaleur rayonnante. I have translated some of it but only for my own purposes.

Waleswatcher's enthusiasm results in too many complications (e.g. interactions that only start to happen at gamma ray energies which have got nothing to do with the 100% reversible absorption/emission interactions). Waleswatcher needs to stick to the 'simplicity' of low energy interactions, they are far too obscure for most people, hence the need for a good (i.e. limited) Wiki article. --Damorbel (talk) 20:37, 14 February 2012 (UTC)

" The reason I made this intervention was to (try to) extract from Waleswatcher just what he wants to inroduce into the article." It might have been simpler just to ask! Anyway, the answer is "nothing", at least for now. Regarding photon-photon interactions, they take place at all energies, not just gamma ray and above, and they're essentially never reversible in the sense you mean that. Waleswatcher (talk) 00:53, 15 February 2012 (UTC)

response to Damorbel. He writes: "two aspects that are symetrical, absorption of incident radiation and emission of radiation when >0K. The restof of the 'stuff' (equilibrium, Planck spectrum ...are not really relevant ..." Does this mean what I read it to mean? I read it to be saying that absorptivity (absorbed / incident) and emissivity (emitted / Planck) are equal but the equality is not related to the equilibrium and the Planck spectrum?Chjoaygame (talk) 02:18, 15 February 2012 (UTC)

response to Waleswatcher. He writes: "they're essentially never reversible in the sense you mean that." I suppose this refers to what I have just written above about Damorbel's comment. But, apart from that, would Waleswatcher tell us his views about the possible reversibility, in other senses, of photon-photon interactions?Chjoaygame (talk) 02:18, 15 February 2012 (UTC)

As far as anyone knows, fundamentally all interactions are reversible (including photon-photon). But in the sense of thermodynamics, just about any interaction will lead to an increase in entropy, and so in that sense interactions (including photon-photon) are generally irreversible.

To give one example that makes it particularly clear, a possible interaction between two photons is 2-->4, where two photons turn into four. That's irreversible in the thermodynamic sense, because it's exceedingly unlikely that those four photons will ever re-converge and turn into two. But that reversed process is possible, and in fact has exactly the same amplitude - it's just very unlikely considering the larger phase space of four photons compared to two. The same holds (in a slightly less obvious but equally valid sense) for 2-->2 elastic scattering when the initial condition isn't equilibrium. Waleswatcher (talk) 04:07, 15 February 2012 (UTC)

• Thank you Waleswatcher for this answer.Chjoaygame (talk) 18:37, 15 February 2012 (UTC)
• "a possible interaction between two photons is 2-->4,". Has this been observed? How can I repeat the observation? --Damorbel (talk) 07:37, 15 February 2012 (UTC)

No, not directly. But the theory that predicts it is probably be most precisely tested scientific theory there is (quantum electrodynamics). Waleswatcher (talk) 12:34, 15 February 2012 (UTC)

"No, not directly". Well OK then, what about indirectly? If it hasn't been observed, it isn't scientific. My son is studying physics at Leiden University and he has observed double photon absorption by a molecule and also harmonic generation by non linear optics but these a well known interactions with matter and not (I understand) what you are suggesting. --Damorbel (talk) 15:59, 15 February 2012 (UTC)

It's been observed indirectly in many, many experiments. As I mentioned, QED is probably the most precisely tested theory in the history of science, and this (2-->4 photon processes) is a direct and basic consequence of it. I'd suggest reading about electroweak precision tests, or particle physics in general. Waleswatcher (talk) 17:03, 15 February 2012 (UTC)

"It's been observed indirectly in many, many experiments". Name one. --Damorbel (talk) 17:15, 15 February 2012 (UTC)

e+/e- scattering at LEP. Waleswatcher (talk) 00:58, 16 February 2012 (UTC)

The word 'indirectly' is important in Waleswatcher's comment. e+/e− scattering at LEP is interaction in the presence of matter. The virtual gammas are created and annihilated by matter but not observed as actual gammas.Chjoaygame (talk) 03:04, 16 February 2012 (UTC)

comment d

There is a new edit changing the word guarantees to the word states, with Adkins still as source. Adkins is not a good source for such a statement. He explicitly considers cases in which the approach to equilibrium is at a rate that is negligible on any normal time scale. That is non-committal as to what happens on abnormal time scales, while Adkins is used here to support a claim about what happens even beyond any normal time scale. As noted above, on page 11 of the second edition, where he is talking about hysteresis in a piece of iron in a magnetic field, Adkins says: "The potential barriers between these steps, however, are so large that the approach to equilibrium only proceeds at an extremely slow rate, one which is quite negligible on any normal time scale."Chjoaygame (talk) 23:13, 16 February 2012 (UTC)

Bhabha scattering

Waleswatcher, does you argument extend to Bhabha scattering? Are you suggesting that the (gamma) photons mediating the Bhabha interaction have got no connection with the electrons and the positrons that initiate the Bhabha scattering? My understanding of your argument is that photons interact to change their properties in the absence of matter. You quote QED as a theory supporting your argument but QED is the science of interacting charged particles (electrons, protons, positrons and antiprotons) by means of photons i.e. QED requires the presence of charged particles at its very basis. The argument that photons do not interact depends on the fact that the charge associated with the photons is remote i.e. the generation of a photon requires the presence of charge and the generation of a virtual photon which has a very limited lifetime and range. Your argument would seem to be that photons can be generated without the presence of charge in any manifestation e.g. within a massive particle. --Damorbel (talk) 07:55, 16 February 2012 (UTC)

Bhabha scattering is a prediction of QED. 2-->2 photon scattering is a prediction of QED. 2-->4 photon interactions are a prediction of QED. According to QED, photon interactions happen even when there is no charged matter in the initial state. Waleswatcher (talk) 11:52, 16 February 2012 (UTC)

"...even when there is no charged matter in the initial state". This really won't do, as it stands your statement is an unsupported opinion, this, according to Wikipedia rules, is an unsupported POV. Please support it. --Damorbel (talk) 12:32, 16 February 2012 (UTC)

Nonsense. It's fully supported by citations already in the article, and arbitrarily many more I could provide if there was any need (which there isn't, since you're just asking me questions about physics on a talk page). Waleswatcher (talk) 13:02, 16 February 2012 (UTC)

"...many more I could...". Waleswatcher, you keep making these promises about what you think should be in an article about a Black body, saying "It's fully supported by citations already in the article" without identifying which are relevant and, most important, why. I want to believe you are right but at present you are not turning up with the goods. --Damorbel (talk) 14:33, 16 February 2012 (UTC)

Huh? As I already told you, I'm pretty happy with what's in the article now. Waleswatcher (talk) 17:02, 16 February 2012 (UTC)

"I'm pretty happy with what's in the article now." I know that. But your happiness is scarcely relevant to a Wiki article. Your contributions have (as a minimum) the following problems 1/ you don't discuss why they are suitable, typically just stating they are correct, 2/ at least one of the links is hiding behind a pay wall. and 3/ you revert other contributions without discussion. --Damorbel (talk) 17:23, 16 February 2012 (UTC)

Your observations are accurate, but Waleswatcher has not absorbed previous advice of this nature. In this regard, he is a white body not a black body :-) Brews ohare (talk) 18:57, 16 February 2012 (UTC)

Damorbel - the purpose of a talk page is to discuss material in the article. If there's something you want added/removed, this is a great place to talk about it. But instead, you ask me general questions about physics. When I answer them, you demand sources. When I point out that I'm simply answering a question you asked and not adding material to the article, so no sources are needed, you accuse me of all sorts of other sins. I'm not really sure where this is going? Waleswatcher (talk) 00:42, 17 February 2012 (UTC)

"you ask me general questions about physics." That is exactly the problem. You claim they are general questions; they aren't, they are specifically designed to clarify your contributions, your contributions are confused and confusing and will only be useful if clarified. An obvious example was the 'black hole' contribution you made, you wrote as if it was an example of a 'black body' it isn't because it depends for it's existence on having an enormous gravitational field which is no part of the definition of a 'black body'. You have not, as far as I can see, made any response to this important difference; therefore I am driven to the conclusion that the difference means nothing to you i.e. you are, as yet, not sufficiently informed to contribute usefully on 'black bodies'. --Damorbel (talk) 07:24, 17 February 2012 (UTC)

Your questions are quite random, Damorbel, and the appropriate way to discuss material in the article is to discuss material in the article. As for black holes, you were wrong then, and you are still wrong now. You don't even seem to understand the concept of a definition. If a definition doesn't mention some property, then the presence of absence of that property is irrelevant to whether or not the object in question meets the definition. The whole point of definitions is to distill the subject to those properties that are necessary, and leave out those that are irrelevant. Black holes are black bodies because they are near-ideal absorbers of radiation, and that's the definition - full stop. Waleswatcher (talk) 12:26, 17 February 2012 (UTC)

" Black holes are black bodies ..., and that's the definition - full stop." Waleswatcher, you do not differentiate between the Kirchhoff definition of a 'black body' and something that 'looks black'. The article should be about the Kirchhoff definition of a black body, black holes, 'nearly' black surfaces such as black carbon, cavities with 'small holes' do not meet this definition; although referring to the differences should be OK. The Kirchhoff definition does not allow any reflection of incident EM radiation or there to be a gravitational field; so 'black holes' do not meet the definition, interestingly your assertion that black holes are 'near ideal absorbers' even admits this ('near ideal'). I understand that you are attached to your interpretaion (allowing black holes etc. to be included in the definition of a 'black body') but you have not cited any reliable source that agrees with you; the mere discovery of an author stating that something emits 'a blackbody spectrum' or 'absorbs almost like a black body' does not mean that it meets the requirements, don't you see? --Damorbel (talk) 15:46, 17 February 2012 (UTC)

" The article should be about the Kirchhoff definition of a black body" - Why? "The Kirchhoff definition does not allow...there to be a gravitational field" - Nonsense. "you have not cited any reliable source that agrees with you" - Nonsense. Waleswatcher (talk) 00:22, 18 February 2012 (UTC)

Kittel & Kroemer

Perhaps Waleswatcher may be right that Kittel & Kroemer (second edition 1980) are probably wrong about the entropy of the universe. It may be useful to look at their thoughts on the second law of thermodynamics. They say on page 49 of the second edition: "There are many equivalent statements of the second law." They then write a statement (the one given above by Waleswatcher) which they say is "looser" than the one they gave in their equation (36). They also give the "traditional" Kelvin-Planck statement. They say of equation (36) that it "is a statement of the law of increase of entropy: the entropy of a closed system tends to remain constant or to increase when a constraint internal to the system is removed." On page 29 they define: "A closed system will have constant energy, a constant number of particles, constant volume, and constant values of all external parameters that may influence the system, including gravitational, electric, and magnetic fields." Presumably they except the photon from their definition of a particle for that statement. They do not say whether or not a closed system is in contact with a heat bath, but presumably they mean that it is not.Chjoaygame (talk) 18:32, 13 February 2012 (UTC)

Feynman's lectures on Quantum Electrodynamics

First published in 1961 by Addison-Wesley. The version I am using was published in 1998 by Westview Press, ISBN 0–201–36075–6. The first section of the book is headed Interaction of Light with Matter—Quantum Electrodynamics. The first lecture starts: "The theory of interaction of light with matter is called quantum electrodynamics." The second lecture is headed Laws of Quantum Electrodynamics. It states the first law: "1. The amplitude that an atomic system will absorb a photon during the process of transition ... " and so on.Chjoaygame (talk) 17:09, 14 February 2012 (UTC)

Mandl & Shaw's Quantum Field Theory

I am looking at a copy of Quantum Field Theory, by Mandl, F., Shaw, G. (1984), revised 1993, reprinted 2002, John Wiley & Sons, Chichester, ISBN 0–471–94186–7. Chapter 1 states "In order to explain the spectrum of black-body radiation Planck, in 1900, postulated that the process of emission and absorption of radiation by atoms occurs discontinuously in quanta." That's not what is found by recognized research on what Planck actually wrote. But is typical of textbook misrepresentations. Mandl & Shaw then tell of the quantization of the electromagnetic field; then they say "The interactions between these particles is brought about by other fields whose quanta are other particles." They clarify this in Section 1.3: "In the last section, we quantized the radiation field. ... For anything 'to happen' requires interactions with charges and currents so that photons can be absorbed, emitted, or scattered."Chjoaygame (talk) 17:09, 14 February 2012 (UTC)

Chjoaygame, would you mind clarifying what it is that you are trying to establish? Are you trying to achieve consensus among the editors on some point? Searching for additional reliable sources for something? If so, what? The quotes you provide are interesting, but I'm unclear on the point of them. Thanks. Waleswatcher (talk) 17:31, 14 February 2012 (UTC)

Assessing the reliability of sources.Chjoaygame (talk) 17:36, 14 February 2012 (UTC)

"That's not what is found by recognized research on what Planck actually wrote." In 1901 Planck derived E=h nu per quantum, applied it to cavity radiation modes, and assumed that all electromagnetic energy (at least in an equilibrium cavity) followed that law, so....? Waleswatcher (talk) 13:00, 15 February 2012 (UTC)

Moreover, in 1914 (Theory of Heat p.153) that's exactly what Planck says: "Now, since in the law of absorption just assumed the hypothesis of quanta has as yet found no room, it follows that it must come into play in some way or other in the emission of the oscillator, and this is provided for by the introduction of the hypothesis of emission of quanta. That is to say,we shall assume that the emission does not take place continuously, as does the absorption, but that it occurs only at certain definite times, suddenly, in pulses, and in particular we assume that an oscillator can emit energy only at the moment when its energy of vibration, U, is an integral multiple n of the quantum of energy, e = hv." Waleswatcher (talk) 13:24, 15 February 2012 (UTC)

Planck expressed various views over time. So far as I know, the most thorough examination of this is by Thomas Kuhn (1978), Black-Body Theory and the Quantum Discontinuity 1894-1912, Oxford University Press, ISBN 0–19–502383–8, with a follow-up paper in 1984. Another close examination of some of Planck's writings about these matters is by Darrigol, O. (1992), From c-Numbers to q-Numbers. The Classical Analogy in the History of Quantum Theory, University of California Press, Berkeley, ISBN 0–520–07822–5.Chjoaygame (talk) 18:53, 15 February 2012 (UTC)

proposed definitions of a black body

Those arguing the black holes are blackbodies are just making up your own definitions.

Blackbody - An ideal object that is a perfect absorber of light (hence the name since it would appear completely black if it were cold), and also a perfect emitter of light. Light is emitted by solid objects because those objects are composed of atoms and molecules which can emit and absorb light. They emit light because they are wiggling around due to their heat content (thermal energy). So a blackbody emits a certain spectrum of light that depends only on its temperature. The higher the temperature, the more light energy is emitted and the higher the frequency (shorter the wavelength) of the peak of the spectrum.

John F. Hawley, Professor, Chair, Department of Astronomy, 2006- University of Virginia

Unless you can find multiple references saying that the above definition is wrong, I will stand by it and the related equations. Q Science (talk) 06:17, 21 February 2012 (UTC)

comment 1

Q Science is here proposing a definition of a black body, and offering a source for it. This is a rational, sober, and reasonable proposal. But I will oppose it, both on the grounds that the definition is not the most suitable one for this article, and on the grounds that the source does not make the grade as a reliable source.Chjoaygame (talk) 09:10, 21 February 2012 (UTC)

Balfour Stewart

Perhaps the first candidate as a definition of a black body may be supplied by Balfour Stewart (1858), Trans. Roy. Soc. Edin. 22:1–20. He writes: "The reason why lamp-black was chosen as the standard is obvious; for it is known from Leslie's observations, that the radiating power of a surface is proportional to its absorbing power. Lamp-black, which absorbs all rays that fall on it, and therefore possesses the greatest possible absorbing power, will possess also the greatest possible radiating power."

Stewart's name is not attached to what we now call Kirchhoff's law perhaps partly because of nationalistic reasons and partly because the level of logical abstraction of Stewart's 1858 paper did not reach that of Kirchhoff's 1860 paper.

Gustav Kirchhoff

The next candidate is Kirchhoff's 1860 definition in Annalen der Physik (Leipzig), 109: 275–301. He writes (as translated accurately by F. Guthrie): "The proof I am about to give of the law above stated, rests on the supposition that bodies can be imagined which, for infinitely small thicknesses, completely absorb all incident rays, and neither reflect nor transmit any. I shall call such bodies perfectly black, or, more briefly, black bodies. It is necessary in the first place to investigate the radiating power of bodies of this description."

Are you sure this is Kirchhoff? The text appears in my copy of Planck (Authorised translation by Masius).--Damorbel (talk) 14:22, 21 February 2012 (UTC)

Following your indication, I couldn't find it in my copy of Planck translated by Masius. I copied it from Phil. Mag. series 4, volume 20, page 2 of July 1860, where the translation is attributed to F. Guthrie. The original of Kirchhoff reads: "Der Beweis, welcher für die ausgesprochene Behauptung hier gegeben werden soll, beruht auf der Annahme, daß Körper denkbar sind, welche bei unendlich kleiner Dicke all Strahlen, die auf sie fallen, vollkommen absorbiren, also Strahlen weder reflectiren noch hindurchlassen. Ich will solche Körper vollkommen schwarze, oder kürzer schwarze, nennen. Es ist nöthig, zuerst die Strahlung solcher schwarzen Körper zu untersuchen."Chjoaygame (talk) 22:01, 21 February 2012 (UTC)

This is clearly intended as a logically defensible definition. It is I think the one that has been slightly adjusted but generally accepted by history; obviously here I will need to provide evidence and argument for that. The logical status of the definition is made clear by the next sentence of Kirchhoff: the radiating power will be considered as derived by analysis and development from the definition.Chjoaygame (talk) 09:34, 21 February 2012 (UTC)

But you should also include the part before your quotation where Kirchhoff says (my own translation):-

"according to the law of equivalence of heat and work, the amount of heat which must be transferred to a body in a given time to prevent cooling, which would occur in consequence of its radiation, is equivalent to the vis viva of the emitted rays; and the amount of heat which must be withdrawn in order to counterbalance the heating from absorption of radiations, is equivalent to the vis viva of the absorbed rays."

And:-

"Let a body which satisfies these conditions be surrounded by an enclosure, having the same temperature, through which no heat rays can penetrate, whose temperature is kept constant and which satisfies the same conditions. The body sends out heat rays and is encountered by such heat rays, which, in part, proceed from the enclosure, in part, are thrown back to the same by reflection from it, absorbing a part of them. Its temperature must thus remain the same, unless heat is withdrawn from it or communicated to it as follows on the principle from which Carnot's law results. For this reason, the vis viva of the rays, which it sends out in a certain time, must equal the vis viva of the rays which it absorbs in the same time."

Finally:-

"The proof that rests upon this conclusion requires the accurate investigation of the rays that travel back and forth between the body and the enclosure. This investigation will be much simplified if we imagine the enclosure to be composed, wholly or in great part, of bodies, which, for infinitely small thickness, completely absorb all rays that fall upon them."

This is clearly an abstraction so it is quite illogical to introduce the physical properties of real materials that are "nearly black" bodies arising from such effects as scattering etc. and gravitation into an article about a concept that should exclude them.--Damorbel (talk) 11:06, 25 February 2012 (UTC)

Your translation is admirable. I think your translation is from an 1862 book by Kirchhoff (reproduced in the Collected Discourses of 1882), while the quotes in the article are from 1860. But it remains the case that without good logic, as I have indicated below, trying to discuss this will be futile.Chjoaygame (talk) 16:45, 25 February 2012 (UTC)

Max Planck

The next major candidate definition will be that of Max Planck. His first considered version I suppose would be in his 1906 Vorlesungen über die Theorie der Wärmestrahlung, Johann Ambrosius Barth, Leipzig. I am not aware of a translation of this into English. The next edition, of 1912, was translated and published in English in 1914. Planck was a very leading physicist of that time, and his texts could be considered not only as primary but also as secondary sources. They are good candidates as Wikipedia reliable sources, subject to other requirements, of course. §10 of the first edition is hardly changed in §10 of the second edition. There Planck slightly modifies Kirchhoff's definition. He considers the black body to have, with its contiguous medium, a non-material, purely mathematical interface which reflects none and transmits all of the radiation that falls on it, and to have an interior which consists of material which absorbs all the radiation that reaches it. Planck follows Kirchhoff's logic, by analysing and developing the consequences of the definition as it applies to the adventures of the body.

Broadly speaking, this Planck definition is nearly the one the appears in the present version of our Wikipedia article.Chjoaygame (talk) 09:56, 21 February 2012 (UTC)

Why don't you quote Kirchhoff himself? You write this "...Planck definition is nearly the one the appears in the present version of our Wikipedia article." I have the impression from this that you regard your own contribution as a 'reliable source'! --Damorbel (talk) 13:51, 21 February 2012 (UTC)

The present article has a section as follows:

Definition

The idea of a black body originally was introduced by Gustav Kirchhoff in 1860 as follows:

...the supposition that bodies can be imagined which, for infinitely small thicknesses, completely absorb all incident rays, and neither reflect nor transmit any. I shall call such bodies perfectly black, or, more briefly, black bodies.

A more modern definition drops the reference to "infinitely small thicknesses":

An ideal body is now defined, called a blackbody. A blackbody allows all incident radiation to pass into it (no reflected energy) and internally absorbs all the incident radiation (no energy transmitted through the body). This is true of radiation for all wavelengths and for all angles of incidence. Hence the blackbody is a perfect absorber for all incident radiation.

Dear Damorbel, you flatter me! How many times do you want me to quote Kirchhoff?Chjoaygame (talk) 22:34, 21 February 2012 (UTC)

More recent sources

E.A. Milne (1930), Thermodynamics of the Stars, pages 65–255, Chapter 2, in Handbuch der Astrophysik, volume 3, part 1, writes on page 81: "A surface the material behind which absorbs all the radiation incident on it is said to be "black"." I would submit this as a reliable source for the present purpose.

Guggenheim (1949/1967) considers the Planck law without mentioning the black body. So does Chandrasekhar 1950. Callen (1960/1985) hardly considers even Planck's law and does not mention the black body.

J.R. Partington (1949), An Advanced Treatise on Physical Chemistry, volume 1, Fundamental Principles. The Properties of Gases, Longmans, Green and Co., London, on page 469 writes: "If a perfectly black body is one which absorbs all radiation falling on it and neither reflects nor transmits any, then: ..." I would submit this as reliable source to Wikipedia standards for the present purpose. Partington provides a rather good supply of basic references, which he has considered carefully, and which I have found to be accurately cited.

P.T. Landsberg (1978), Thermodynamics and Statistical Mechanics, Oxford University Press, Oxford, on page 209 writes: "... an enclosure (as described) with a small opening is a very good approximation to an ideally black body in the sense that radiation falling on to the opening is unlikely to be reflected out of the enclosure."

C.J. Adkins (1968/1983), Equilibrium Thermodynamics, third edition, Cambridge University Press, Cambridge UK, writes on page 149: "It is now convenient to define a black body as one which absorbs all the radiation incident on it." I would submit this as a reliable source for the present purpose.

Mihalas and Weibel-Maihlas (1984), Foundations of Radiation Hydrodynamics, Oxford University Press, Oxford, perahps depart from the absorption definition. On page 319, having given a brief derivation of the Planck law, they write: "... this distribution characterizes the radiation, usually called blackbody radiation, emitted by a perfect radiator or black body." They do not say that a black body is a perfect absorber of radiation, and they make no further use of the particular notion of a black body, that I found.

Goody, R.M., Yung, Y.L. (1961/1989), Atmospheric Radiation. Theoretical Basis, second edition, Oxford University Press, New York, on page 64 write: "The treatment of Kirchhoff's laws is nowhere more explicit and readable than in [the translation of the second edition of Planck 1912/1914]". They do not themselves actually define a black body.

M. Bailyn (1994), A Survey of Thermodynamics, American Institute of Physics, New York, on page 530 writes: "A black body is a perfect absorber and emitter of radiation, and can be approximated by a closed cavity of which the inner surface and the enclosed radiation are in equilibrium at some temperature T." He does not make any attempt to derive the emission property from the absorption property when there is thermal equilibrium.

Kondepudi, D., and Prigogine, I. (1998), Modern Thermodynamics. From Heat Engines to Dissipative Structures, John Wiley & Sons, Chichester on page 285 write: "For a perfectly absorbing body, a(T,ν) = 1. Such a body is called a blackbody; its emissivity is equal to the intensity, I(T,ν)." I would submit this as a reliable source for the present purpose. In a subsequent paragraph, they cite Planck 1906/1914.

K.N. Liou (1980/2002), An Introduction to Atmospheric Radiation, second edition, Academic Press, Amsterdam, on page 9 writes: "The term blackbody is used for a configuration of material where absorption is complete."

Bohren, C.F., Clothiaux, E.E. (2006), Fundamentals of Atmospheric Radiation: An Introduction with 400 Problems, Wiley-VCH, Weinheim, on page 13 write: "The definition of a blackbody as one that absorbs all radiation incident on it contains a trap for the unwary." Their "trap" relates to wavelengths that are too long. Nevertheless they use that definition.

As for John F. Hawley, he has a webpage at http://www.astro.virginia.edu/~jh8h/. I would count him as a specialist in astronomy. That neither automatically qualifies nor automatically excludes his opinions as reliable sources for Wikipedia. It is reasonable to say that he has not written a text specifically about thermal radiation. The cite that Q Science offers does not give references and has very limited context; it is thus a poor candidate as a source for a Wikipedia scientific article.Chjoaygame (talk) 12:02, 21 February 2012 (UTC)

Chjoaygame, very few, if any, of the references you give give above give the full definition of what defines a black body, they are authors using one or other of the properties of a black body. Waleswatcher might say that 'they allow black holes because the are not complete'; Waleswatcher's logic is frequently deficient because he places no restriction on what he allows to be black body, e.g. a grey body - soething that is completely outside Kirchhoff's concept; your refs. seem to have a similar problem - sorry!. --Damorbel (talk) 21:56, 21 February 2012 (UTC)

Dear Darmorbel, you continue to fail to distinguish between a definition and list of properties. The distinction is important as I have tried to explain to you. You seem not to have had a training in mathematical reasoning, or indeed in logic in general. Your viewpoint on this is so far from the normal way of conducting a logical discussion that it is hardly practical for someone to try to answer your puzzles. You will continue to have problems arising from this till you remedy it.Chjoaygame (talk) 22:41, 21 February 2012 (UTC)

Logic? Definition? This is physics we are (should be) talking about! Basically observation and measuring. Logic is useful but if there are, perhaps apparently, logcal inconsistencies between the logic and the observations, it is quite likely that the logic is faulty. Planck's discovery of blackbody radiation is a good example of this, the observed radiation spectrum did not fit (logically) with the classical (or wave) theory of radiation so a new theory was required, a theory which took at least 30 years to emerge. Planck, using Kirchhoff's model of 'a black body' conributed a great deal to this new theory. But don't forget, Kirchhoff's 'lack body' is only a model, any attempt tocompare it with reality is doomed to failure because a 100% 'black body' cannot exist and the article should explain this.

A 'Black body' is an abstraction used by Kirchhoff to distinguish the exchanging of EM radiation and thermal energy; chemical, gravitational energy are excluded by this concept, as is scattering (reflection, refraction, diffraction are some examples of scattering). Introducing 'grey bodies' and other black body 'approximations' is utterly illogical, because they are necessarily 'not black' bodies and really have no place in the article except to explain why they have no place i.e. that they are physically quite separate processes that do not involve absorption and emission.--Damorbel (talk) 10:32, 25 February 2012 (UTC)

Your response is not surprising. It is clear that like many who have been taught some physics, you have not been taught well; in particular, a reasonable grasp of ordinary logic is a necessary pre-requisite for a proper study of physics. For example, some physicists think that because they cannot see how ordinary logic applies to quantum mechanics, the ordinary logic is at fault, not the quantum mechanics. The real fault is their lack of knowledge of ordinary logic; neither ordinary logic nor quantum mechanics are at fault. Ordinary logic is about how to conduct a discussion; you can't properly discuss anything without logic, not physics, not football. It will be futile to try to continue to discuss these matters till you get a much better grasp of ordinary logic.Chjoaygame (talk) 16:14, 25 February 2012 (UTC)

comment 2

The first sentence is a reasonable definition of black body that agrees with the one already in the article (which is multiply sourced already). One quibble with Hawley's definition is that you don't need to require that the body be a perfect emitter in that sense, because that follows from perfect absorptivity.

In any case, black holes meet the above definition in every respect (apart for the "atoms and molecules" comment, which is explanatory rather than part of the definition), so I don't know why Q Science brings it up. Not only that, we have sources that say explicitly that "black holes are black bodies", so that cannot be disputed unless sources are found that explicitly say the opposite. Waleswatcher (talk) 11:44, 21 February 2012 (UTC)

I would say that it is not just a quibble, but is a substantial objection to Hawley's sentence as a definition, that it demands perfection both in absorption and in emission. Logically, an existence proof is needed when multiple properties are listed for a definition, because logically they might possibly be mutually inconsistent. The cited version of Hawley's sentence would need an existence proof, because it is a logical possibility that it is logically necessary that no body can be both a perfect absorber and a perfect emitter. It is bad enough that no perfect black body as a perfect absorber can really physically exist, but at least the notion makes sense as a limiting case.

A further very serious objection to the Hawley sentence as a definition is that it does not make it clear that for equality of absorptivity ratio (absorbed/incident) and emissivity ratio (emitted/Planck), in general, thermal equilibrium or some other related suitable condition is also required. This objection is very serious because the failure to note that requirement obliterates much of the important physics of Kirchhoff's law.Chjoaygame (talk) 12:21, 21 February 2012 (UTC)

I don't understand the absorptivity / emissivity ratio problem. Blackbodies absorb 100% of what is available and emit 100% of what is predicted which Hawley refers to as perfect absorber and perfect emitter. Hawley also makes it clear that emission depends only on its temperature. Q Science (talk) 19:35, 21 February 2012 (UTC)

• One doesn't need to include perfect emitter in the definition, because it can be derived from perfect absorber. One wants definitions to be as minimal as possible for many reasons. One of them (as Chjoaygame points out) is that otherwise you run the risk that your definition won't be self-consistent. In any case, everything Hawley says holds true for black holes in equilibrium (or even just in vacuum), so it's rather a moot point. Waleswatcher (talk) 19:41, 21 February 2012 (UTC)

• response to Q Science: With all respect, you seem to fail to distinguish between a definition and a list of properties. The distinction is one of logic, not of substance. It is generally and normally considered best to limit a definition to some least amount of stipulation that can be used for the purpose, and then to use that least amount of stipulation to derive, by analysis and development, further properties of the thing defined. The reasons for this are deeply embedded in the usual normal way of setting out logical conversations. The Hawley quote that you give would not normally be considered a definition. It would normally be considered a summary of properties, making no attempt to distinguish stages in derivation of them. There is nothing wrong with what Hawley writes, but by normal standards it is wrong to interpret it by trying to treat it as a definition proper. The point here is not as to substance; we agree about that. The point here is as to logical structure of presentation of argumentation; with all respect, I think you are misled in that.Chjoaygame (talk) 22:52, 21 February 2012 (UTC)

Wolfram

A hypothetic body that completely absorbs all wavelengths of thermal radiation incident on it. Such bodies do not reflect light, and therefore appear black if their temperatures are low enough so as not to be self-luminous. All blackbodies heated to a given temperature emit thermal radiation with the same spectrum, as required by arguments of classical physics involving thermal equilibrium. However, the distribution of blackbody radiation as a function of wavelength, known as the Planck law, cannot be predicted using classical physics. This fact was the first motivating force behind the development of quantum mechanics. Wolfram - Referenced to Eisberg, R. and Resnick, R. "Thermal Radiation." §1-2 in Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, 2nd ed. New York: Wiley, pp. 2-6, 1985.

I think this also supports the "must emit" part of the definition. Q Science (talk) 19:37, 21 February 2012 (UTC)

• No, it quite clearly does not - just the opposite. The first sentence is the definition. What follows are consequences of that definition. In any case, I suggest you review the impressive number of reliable sources (Wolfram is not among them) that Chjoaygame collected. Waleswatcher (talk) 19:43, 21 February 2012 (UTC)

• A quote from Wolfram does not come near being a reliable source for a Wikipedia article on the present subject. In general, the internet is an aid but not an authority. Also, here recurs the same logical problem as I have just observed to you above under comment 2.Chjoaygame (talk) 23:00, 21 February 2012 (UTC)

back to a section in Archive 4

Copying from Archive 4 at Talk:Black body/Archive 4#Kondepudi & Prigogine 1998 on matter and radiation:

Kondepudi & Prigogine 1998 write on page 293: " ... we conclude that the chemical potential μ = 0."Chjoaygame (talk) 18:14, 24 January 2012 (UTC)

Yes. Your point?? As I explained just above, mu=0 means particles can be created and destroyed with no thermodynamic cost (i.e. no energy change with all else held fixed). Physically, that's either because the particles in question are massless (photons, for instance) or because the temperature is so high that the mass is not relevant (electrons etc. in the very early universe, for instance). Waleswatcher (talk) 18:55, 24 January 2012 (UTC)

Now I see more clearly how Waleswatcher was mistaken. He was presuming that the formula μ = 0 was from his own context in quantum electrodynamics in which the symbol μ denotes the virtual mass of the virtual photon, when in the context in which I cited it from Kondepudi & Prigogine 1998 as they say it refers to the chemical potential, an entirely distinct concept. An example of the use of the symbol in Waleswatcher's context is as follows, from A. Zee (2101), Quantum Field Theory in a Nutshell, second edition, Princeton University Press, Princeton NJ, ISBN 978–0–691–14034–6, on page 150: "The resolution of course is that as the coupling of the longitudinal mode vanishes as μ → 0 the time it takes for the longitudinal mode to come to thermal equilibrium goes to infinity. Our crafty experimentalist would have to be very patient." This is the relaxation time for the photon-photon interactions beloved of Waleswatcher and PAR.Chjoaygame (talk) 14:17, 23 February 2012 (UTC)

I wasn't mistaken, and I was referring to the chemical potential when I said "mu=0 means particles can be created and destroyed with no thermodynamic cost". The chemical potential divided by the temperature is the energy cost to create a particle (as can be easily seen from the form of the grand canonical ensemble). For a photon, that energy cost depends on the frequency, and it goes to zero for zero frequency because photons are massless. As for your quote from Zee, you'll need to provide more context for me to be sure what he's talking about, but it sounds like the longitudinal mode of the photon - which doesn't exist on-shell and is irrelevant to the arguments regarding thermalization we had (it's the transverse modes that thermalize). Waleswatcher (talk) 14:29, 23 February 2012 (UTC)

Good to know you weren't mistaken. Not so clear about what you mean by "no thermodynamic cost". It might mean "with no entropy production". We are hoping that thermalization will indeed be a process with entropy production. But it seems from what you write that you mean "no energy consumption"? Indeed photons are massless as to their rest mass, but they have an energy, and that energy usually has to come from somewhere; things can be transduced with no energy consumption. So why were you worried about what Kondepudi & Prigogine 1998 had so say? As to Zee, indeed he is, as he says in the quote, talking about the longitudinal mode of the photon, but all virtual photons have that, being as you say off-shell. You need to show that your thermalization by photon-photon interaction does not require thermalization also of virtual photons, if you want to avoid what Zee is saying.Chjoaygame (talk) 17:07, 23 February 2012 (UTC)

I meant at no energy cost, not no entropy production. In the limit of zero momentum photons have zero energy, and that's what zero chemical potential corresponds to. As for Kondepudi&Prigogine, I don't recall being "worried" about what they had to say.

"You need to show that your thermalization by photon-photon interaction does not require thermalization also of virtual photons, if you want to avoid what Zee is saying."

I can't make sense of what you are saying. Virtual particles aren't thermal or non-thermal, physical modes are. Thermality is tested by (for example) putting a thermometer into the system and seeing what it says. Because the thermometer will never absorb or emit a longitudinally polarized photon, the state of such photons (to the extent that phrase even makes sense) is irrelevant. In any case, none of this has anything to do with the particular interactions that thermalize the photons. If we had to worry about the thermality of longitudinal photons (we don't), we'd have to worry about it even when the approach to equilibrium is brought about by interactions with matter. Waleswatcher (talk) 18:53, 23 February 2012 (UTC)

edit of insulated enclosure

The enclosure is said in this caption to be 'insulated' for good reasons. You may read the article for a fuller explanation of why the enclosure is 'insulated'. In a nutshell, the walls must not be transparent to thermal radiation and must not allow matter or energy to flow in or out so as to destroy the steady state of the contents of the enclosure. The word 'insulated' in the caption intends to briefly indicate these necessary things.Chjoaygame (talk) 05:15, 3 March 2012 (UTC)