## onsdag 18 mars 2015

### Schwarzschild, Chandrasekhar, Back Radiation and Ghost Detection

Non-physical two-way back-and-forth energy transfer with "back radiation". Notice that with N layers the "back radiation" to the surface increases like N x F into an absurdity for many layers. Nevertheless (or because of that), pretending to understand "back radiation" has come to be viewed as the sign of deep scientific knowledge acknowledged by all CO2 alarmists and quite a few (so called) skeptics, which differs the expert from the man in the street, who cannot understand how such a back-and-forth process can be real. See also posts under category "radiative heat transfer" connecting to the old controversy between Pictet and Prevost.

The notion of "back radiation" can be traced back to the Schwarzschild equations for radiative transfer from 1906, which formally mathematically decompose net radiative heat energy transfer into the difference of opposite two-way energy transfers, in order to faciliate symbolic solution by analytical mathematics. This method is also used by Chandrasekhar in his book on radiative transfer, and there correctly referred to as "formal solution".

Both Schwarzschild and Chandrasekhar thus use a formal mathematical decomposition similar to formally rewriting a physical Stefan-Boltzmann law
• $Q=\sigma (T_1^4-T_2^4)$                         (1)
for one-way net energy transfer $Q$ from a body with temperature $T_1$ to a body of lower temperature $T_2$,  into a non-physical form:
• $Q =\sigma T_1^4 - \sigma T_2^4$,                      (2)
formally expressing the net $Q=Q_1-Q_2$ as the difference of two opposite transfers with $Q_1=\sigma T_1^4$ from warm-to-cold and $Q_2=\sigma T_2^4$ from cold-to-warm, as if emitted to a background at 0 K (which is not the case).

Compare with Fourier's law of heat conduction $Q=\sigma (T_1-T_2)$ (or in differential form $Q=\sigma dT/dx$), which nobody would even think of splitting into $Q=\sigma T_1- \sigma T_2$ (or in differential form $Q=\sigma T_1/dx-\sigma T_2/dx$), not even a first year student, since a system acting like that with "back conduction", would be unstable and thus could not exist. "Back radiation" is as un-physical and unstable as "back conduction". Fourier would turn in his grave at the mere thought of such a horrendous concept.

Confusion arises if the non-physical form (2) is interpreted as a describing actual physics including the transfer $Q_2$ from cold-to-warm in violation of the 2nd law of thermodynamics. The confusion can lead to serious errors (as any violation of the 2nd law), with errors resulting from working with differences of gross quantities subject to perturbations (like all physical quantities), which easily may be unstable, instead of working with net quantities as being more stable.

In the setting of CO2 global warming alarm, gross two-way energy transfer between Earth surface and atmosphere is postulated to be about 350 W/m2, while net transfer is about 35 W/m2. As acknowledged by Henning Rodhe in the discussion we had, the difference is a factor 10 reduction of alarm from 3 C to 0.3 C = no alarm.

The lesson is: Do not confuse manipulations of symbols on a piece of paper with actual physical processes. Do not confuse the correct physical form of Stefan-Boltzmann's law (1) with the incorrect non-physical form (2). If you follow this lesson, then CO2 global warming alarm collapses to zero.

For an illuminating comparison of one-way and two-way equations for radiative heat transfer, see this article by Joseph Reynen.

Notice that another way of formally rewriting (1) is:
• $Q =\sigma T_1^4+GHOST_1 - (\sigma T_2^4 +GHOST_2)$,
where $GHOST_1=GHOST_2=GHOST$are equal (odorless, weightless) "ghost quantities" emitted by the bodies. By measuring $Q$ as the net energy absorbed by body 2 and postulating that body 2 is emitting $\sigma T_2^4 + GHOST$, one can argue that the measurement gives instrumental evidence of the existence of the quantity $\sigma T_1^4+GHOST$ and thus instrumental evidence of the existence of the quantity $GHOST$, which as you understand can be anything (odorless and weightless). The instrument is thus a perfect "ghost-detector" and as such potentially has a huge commercial market. Right? Anyway here is a handy instrument affordable to anyone in need of "ghost detection":

This is the way a pyrgeometer measuring DLR as atmospheric "back radiation" functions.

PS1 David Andrews states on p 84 of An Introduction to Atmospheric Physics, about two-way radaitive heat transfer:
• We find F-up and F-down by a sequence of tricks.
Yes, it is a "sequence of tricks" with no physical correspondence.

PS2 The fundamental error is clearly exposed in the above book:
• If the Earth is assumed to emit as a black body: $Q=\sigma T^4$...(page 5).
• The ground is assumed to emit as a black body (page 6).
But the ground does not emit as a black body emitting into a backgound at 0 K. The Earth-atmosphere system emits into a background at 3 K, and the ground emits into an atmosphere of about 255 K, thus vastly different form 0 K. The fact that physicists of today do not react to this fundamental violation of basic physics, can only be understood as a degeneracy of modern physics away from scientific principles into black magic. The day of reckoning is approaching and the verdict in the history of science to be written will be harsh. Assuming the Earth is flat is a small error in comparison.

#### 19 kommentarer:

1. "Confusion arises if the non-physical from (2) is interpreted as a describing actual physics including the transfer Q2 from cold-to-warm in violation of the 2nd law of thermodynamics."

This looks as a very strange conclusion, since you only look at "half" of the processes taking place.

2. If half of the process is wrong then the whole is wrong is well. Two errors do not make it right.

3. It is relatively easy to show that for a black body, emission of radiation without accompanying absorption of radiation is an irreversible process.
The opposite, absorption of radiation without simultaneous emission of radiation is impossible, since it violates the second law of thermodynamics.

The question here is thereby not one of making one right from two wrongs, but to include all required processes to be able to make a correct statement at all.

4. No, it is two wrongs since both bodies are supposed to emit as if into a background of 0 K, but this is not the case for any of the two bodies.

Of course, absorption without corresponding emission is possible and occurs every time a cold body is being heated by a warm body. Your confusion is double.

5. "Of course, absorption without corresponding emission is possible and occurs every time a cold body is being heated by a warm body."

No, and as I wrote, the process that you describe here violates the second law thermodynamics. It quite simple to show this using basic thermodynamics. It only examines thermalized radiation impinging on a single black body surface.

Do you insist on creating free energy??

6. Your comments do not make any sense, and I think we have come to the end of this conversation.

7. Check out, for yourself, the derivation that Planck did in his treatise "The Theory if Heat Radiation" (Available at project Gutenberg http://www.gutenberg.org/ebooks/40030). Paragraph 102, page 116. Page 118 holds the conclusion.

"Generally we may say: Emission without simultaneous absorption
is irreversible, while the opposite process, absorption without emission,
is impossible in nature."

Please note that this is not in any way a violation of Clausius statement of the second thermodynamical law, as you seem to propose in your post. Heck, even Wikipedia got that one right ;-) (
http://en.wikipedia.org/wiki/Second_law_of_thermodynamics#Clausius_statement )

"The statement by Clausius uses the concept of 'passage of heat'. As is usual in thermodynamic discussions, this means 'net transfer of energy as heat', and does not refer to contributory transfers one way and the other."

This actually becomes evident if one takes the time to sort the matter out for oneself with the suitable models of heat engines in series and parallel.

So, in all honesty, we do not let first year students do that for themselves, but certainly third year students. There should not be a problem for you to do the same I hope ;-)

8. Planck compares the process of emission without absorption, which he claims to be irreversible, with the "opposite process" of absorption without emission, which he claims to be impossible. I must say that I do not understand the logic here. What is the "opposite process" of emission and not-absorption? Isn't it logically speaking not-emission or absorption. And what is the relation between "irreversible" and "impossible". Does it mean that reversing an irreversible process is impossible? Is so, then it is a tautology without physical content. If you can explain what Planck means, then you are welcome to post it as a comment.

9. what's wrong with the following?
- measure sigma*T^4 +GHOST at few different temperatures
- extrapolate to T=0
=> show if GHOST = 0 or not

10. Try it yourself with any ghost detector on the market.

11. I think it's pretty crystal clear, but sure.

The opposite of emission is of course absorption (opposite -> motsats, inte negering).

The conclusion, which by all means is pretty obvious from the derivation, says that

1. A body practising emission into 0K is an irreversible process. It seems that you don't know what this means from the perspective of thermodynamic nomenclature (otherwise there should not be any confusion). Irreversible may on this level be taken as thermodynamic lingo for "in accordance with the second law of thermodynamics" (you can also have reversibility as an limiting idealisation, and still make the second law "happy")

2. The opposite, a body in a thermal background, practising absorption, and at the same time don't practising emission, is neither irreversible nor reversible hence impossible according to the second law of thermodynamics.

That something is neither reversible or irreversible just means that it is not permitted as a thermodynamic process.

12. i tried, i got GHOST = 0

13. Then you are double fooled: First you buy an instrument pretending too detect ghosts, then believe the instrument when it reports GHOST = 0. To know that there are no ghosts is not easy since they always go in and out before you have catched them.

14. i agree with you, this time [*]. and this is one of the reasons why you should try to give us a key-experiment in which your theory gives different results from the standard one. all the discussions about instability and logic are GHOSTS.

[*] actually to say the truth i agree with you on your views about teaching mathematics

1. Instability is not a ghost. Balance a pencil upside down and you will understand the reality of instability. But you are right in saying that unstable systems tend to not exist. In this sense ghosts are unstable and difficult to catch.