What is the 2nd Law of Radiation 2?

The mysterious unphysical fictitious effect of "backradiation" underlying climate alarmism.

In the previous post I asked for a 2nd Law of Radiation, but could not find any such law in the literature. The first place to look for a 2nd Law is of course Stefan-Boltzmann's Law (SB)

• Q = sigma T^4

supposedly giving the heat energy radiated by a blackbody of temperature T and sigma is Stefan-Boltzmann's constant. In this form SB does not contain any 2nd Law because there is just one body and a 2nd Law is about transfer of heat energy between different bodies.

SB is derived by summation over frequencies from Planck's Law (P)

• R_f = gamma f^2 x C(f)

where f is wave frequency and C(f) represents an exponential cut-off to zero for large frequencies f scaling with T. The P and SB laws are derived for blackbody surrounded by a medium of temperature 0 K.

So what do we find as concerns radiative heat transfer between two bodies, body 1 and body 2 of temperature T1 and T2 (above 0 K)?

Well, Planck's derivation only concerns one body radiating into a surrounding medium at 0 K, and thus says nothing about two bodies. But in the engineering literature you find the formulas

• Q12 = sigma T1^4 - sigma T2^4, Q21 = sigma T2^4 - sigma T1^4 = - Q12

as the heat transfer Q12 from body 1 to 2 and Q21 the heat transfer from body 2 to 1, with different sign of Q12 and Q21. For example if T1 is larger than T2, then Q12 is positive and Q21 is negative.

But you don't find a derivation of these formulas along the lines of Planck's derivation of his one-body law based on statistical mechanics. The engineering formula for the heat exchange between two bodies appears to be ad hoc and as such mysterious. Anything ad hoc is mysterious.

The danger using mysterious ad hoc formulas is that it invites your defenseless mind into mysterious physics, as follows: If we stare intensively at the formula

• Q12 = sigma T1^4 - sigma T2^4

for a long enough time, assuming that T1 (hot) is larger than T2 (cold), then we could come to envision heat transfer in two directions: a major amount of sigma T1^4 transferred from hot to cold and a minor amount sigma T2^4 transferred from cold to hot. We could be (mis)led to the

mysterious concept of "backradiation" underlying climate alarmism, with a cold atmosphere

being capable of transferring heat energy to a warm Earth surface.

But this is all deception: The formula Q12 = sigma T1^4 - sigma T2^4 is incorrectly stated, and should be stated

• Q12 = sigma (T1^4 - T2^4) where T1 is larger than T2.

In this form, there is only a net transfer from hot to cold and there is no backradiation. This

formula can be seen as a 2nd Law of Radiation. A theoretical derivation without statistics is given in my article Computational Blackbody Radiation is the book Slaying the Sky Dragon

further exposed in the upcoming book Mathematical Physics of Blackbody Radiation.

How come then that the formula is stated in the form Q12 = sigma T1^4 - sigma T2^4 suggesting mysterious unphysical effects to the defenseless mind? Because it is an ad hoc formula without theoretical derivation, and for such a formula anything is possible as imagination.

Interpreting mathematical formulas without theoretical derivation opens to a form of scientific mathematical mysticism widely practiced in the modern physics of quantum mechanics and relativity theory:

The idea is to jot down a mathematical equation (formula) and then start to interprete it as physics. This is to be compared with classical rational physics, where you first envision some physics and then describe it by mathematical equations.

Examples of modern physics ad hoc mysticism:

• The Lorentz transformations of special relativity (weird unphysical physics).
• Schrödinger's linear multidimension wave function (statistical unphysical interpretation).

Example of rational classical physics:

• Maxwell's equations with electric and magnetic fields satisfying similar equations allowing electromagnetic waves.

In the next post I continue with an analysis of mysticism of modern physics.