Says right there in the equation ian...i thought you were the brightest guy in the room....surprising that the smartest guy in the room would miss such a fundamental statement of the equations..and then base everything after on a terribly flawed understanding of the fundamentals...Here ian....
This equation represents a radiator...radiating into nothing...radiating according to its temperature...where might you find nothing...no background other than a vacuum ian?
This equation represents a radiator radiating into a background with some temperature....in order for the radiator to be radiating...(P=something other than 0), the background must be cooler than the radiator...the presence of a background with a temperature suggests somewhere other than a vacuum
This is something that I have been trying to point out to you for a long time ian, and you just don't seem to be able to grasp it...these aren't just numbers and symbols...they are sentences, structured to say something...structured to describe a physical reality...the words could be written out in english, or german, or yiddish, but the symbolism of math is more efficient...but it doesn't change the fact that they are statements written in a language describing a physical reality... one describes a radiator...in a vacuum, radiating according to its temperature...the other describes a radiator, not in a vacuum, radiating according to the difference between its own temperature and the background it is radiating into...you can't see that because you can't grasp that it is something other than math....you only see the equations and not the physical reality they are describing...which is precisely why you find that you had no idea that the radiator you love to describe radiating according to its temperature is sitting all by its lonesome in a vacuum...you are so busy being the smartest guy in the room that you have missed things that us guys who have to put an effort into thinking see pretty clearly. You apparently are under the impression that you know so much that thinking is no longer necessary.
It is a sad commentary on your intellect that you would have to have "special" mention made of a vacuum....the guys who wrote this figured that if you were interested, you would have already taken the time to learn to speak the language....where, other than a vacuum might you be able to put your radiator so that it remains unaffected by any background temperature?