The only reason to apply the Distributive property was to make it obvious that the Stefan-Boltzman equation unequivocally states that all bodies radiate according to their temperature and nothing else: that the resultant transfer of thermal energy at any point is simply the algebraic sum of all radiation passing by. To show the world - if it's possible to do so any more clearly than you do yourself - what an insane ******* idiot you actually are.
So you are saying that SB wrote the law wrong?
Do you not know what an equals sign means? There is no difference between the statements with and without the Distributive Property applied.
Are you saying that they weren't bright enough to write a physical law so that it showed what they found?
No.
If they intended to show a two way energy flow, do you really think that they couldn't have figured out a way to express that two way flow mathematically?
They did.
Is that what your argument has come down to now?
Hardly. As you've been told multiple times already your ideas violate numerous fundamental physical laws. Those violations would make up the content of my arguments. This sidebar on the Distributive Property was only an attempt to show you that the two temperatures included in that version of the S-B equation simply produce the algebraic difference between the radiation of each of two bodies. Each part produced by distribution is identical to an S-B description of an instance of one-body radiation. That is
P = (e sigma A T) is the one-body form
P = e sigma A (Ta-Tb) is the two-body form
and is equivalent to
P = (e sigma A Ta) - (e sigma A Tb) which is the simply the difference between the expressions describing two, one-body instances.
By the way, only the most basic form of the SB equation shows that all bodies radiate according to their temperature...if they are perfect black bodies, alone in a vacuum...
The equation says nothing of the kind. The equation's authors tell us that the simple form calculates the radiation of a single body. Can you find a statement from Stefan, Boltzman or ANY decent authority (and by decent authority I mean I am giving you
more than the usual latitude on their qualifications) that supports your contentions that objects cannot and will not radiate towards warmer objects, that the one-way radiation that does take place from a warmer object to a cooler object is proportional to the temperature difference between the two and that all objects are able not only to throttle their total emissions but possess directional control over their emissions so that they may simultaneously restrain all radiation towards warmer objects while radiating in a controlled manner towards cooler objects lying in a different direction? Eh?
Your claims are extraordinary. If they were true, such characteristics would be noted in detail in just about every work describing radiative heat transfer. Please find us one such description.
The rest of the law describes energy transfer and it is a one way transfer between a radiator and its cooler surroundings with the magnitude of that transfer being determined by the temperature difference between the radiator and its cooler surroundings....
You've now told us a dozen times that the S-B equation describes a one-way transfer of energy. Could you show us an instance of text accompanying a presentation of the S-B equation that says the same thing?