I just showed you how your misinterpretation does not come out of the theory. Look at the article I posted. If you don't understand calculus read the words. There is no hint that the SB equation has anything to do with the surrounding temperature.
No...you only demonstrated how much you don't know...and perhaps one of the prime reasons you have been duped so terribly.
That is not the fundamental form of the SB equation. Again, read the article.
It is the only one that matters...the other describes an idealized, probably non existent perfect black body alone in a vacuum with no other matter to emit to...the one I provided is for a radiator radiating into cooler surroundings with other matter.
I have to go with w on this one. Or rather, all the scientists and mathematicians that derived the relationships used to provide the proof.
The fundamental law is
j = sigma T^4
This describes the radiation produced by an object at a specified temperature. Regardless of its surroundings. One object, one temperature, one instant of time. It is the simplest and purest form of the S-B equations.
When you add other objects, emmisivity, or the passage of time the complexity explodes.
Every object radiates according to its temperature and emmisivity, all the time. It is the temperature that changes. A radiating object cools by emitting energy.
j = sigma T^4 is only valid for one instant of time, the next instant will have a lower temperature because of the energy loss of the previous instant.
If another object is nearby, the first object will be absorbing the radiation produced by the second object, and vice versa. Because temperature is a function of energy input minus energy output, the cooling (or warming) of the first object will be affected by the radiation received by the second object.
There is no 'cancelling out' of radiation. Both objects radiate fully at all times according to their temperatures. The temperature of either object will change, depending on the net radiation exchanged.
While you can calculate the individual energy flows coming off each object, it is only the net flow that causes change in the temperatures of the two objects.
ie. If an object at a temperature that radiates 300w is next to an object that radiates 200w, you cannot say that the cooler object is warming the hot one by 200w. At that instant of time, the cool object is receiving a net flow of 100w and the hot object is losing a net flow of 100w. At the next instant of time the hot object will be slightly cooler and the cool object slightly warmer. This exchange of energy will continue until they are both the same temperature, at which time they will STILL be radiating according to their temperatures but because there is no longer a net flow, the temperatures remain the same.