This may be the heart of our disagreement ... radiation is emitted radially ... in all directions ... that what we mean by a radiator, something that emits energy radially ...
That may be what you mean by a radiator...but that is not what we mean by radiator, nor is that how the word is defined...the science dictionary defines a radiator as a body that emits radiation...the radial emission part is an assumption.
Unfortunately assumption has become an accepted means of logic in physics...it is rampant and becoming more rampant all the time.
CAUTION: HERETICAL SPEECH AHEAD. THE NATURE OF THIS SPEECH WILL CHALLENGE THINKING MINDS BUT WILL ONLY OFFEND THOSE HOLDING QUASI RELIGIOUS FAITH IN THE OMNIPOTENCE OF SCIENCE..IF YOU FALL INTO THE SECOND CATEGORY, TURN BACK NOW FOR YOU WILL SURELY BE OFFENDED....AND POSSIBLY OUTRAGED.
Now that my due diligence has been done.
Assumption. It has become part and parcel of physics and has led to a necessity of circular reasoning in which assumptions are accepted and lauded as true facts.
For example:
Suppose we make the assumption that a proton is made of three quarks. We can then theoretically derive a formula for the observed mass of a proton...therefore, a proton is made up of three quarks. It must be a true fact.
Suppose we make the assumption that light is made up of particles...lets call them photons. We can then theoretically derive a formula for photoelectricity which just happens to agree with certain observations that we have made...therefore light is made of photons. It must be a true fact.
Suppose we make the assumption that space time is curved. We can then theoretically explain observations of gravitation. Therefore space time is curved....It must be a true fact.
Suppose we make the assumption that there was a big bang. We can then theorize about the observed expansion of the universe. Therefore there was a big bang. It must be a true fact.
Suppose we make the assumption that there is a big old black hole at the center of a galaxy. Now we can theorize about the observation of the shape of a galaxy. Therefore there is a big old black hole at the center of a galaxy. It must be true fact.
Suppose we assume that the space time observations of different observers are connected by the Lorentz transformation of special relativity. Now we can theorize about the observation that the speed of light is the same for all observers. Therefore, all space time observations of different observers are connected by the Lorentz transformation.
Suppose we assume that the earth is sitting on the back of 4 invisible turtles. Now we can theorize about why the earth does not fall down even though everything else that is not supported falls down. Therefore, the earth sits on the backs of 4 big invisible turtles. It must be true fact.
A thinking person sees the possibility of flawed logic in those assumptions immediately. A thinking person sees that sort of thinking as pseudoscience...not actual science.
There is the fact that a particular phenomenon was observed...and the observation can be theoretically explained if certain assumptions are made. The fact that an observation was made is then used to support the claim that the assumption is not mere assumption, but true fact. Protons ARE made up of 3 quarks....light IS made up of photons.....space time IS curved...there WAS a big bang.....the Lorentz transformation MUST connect different observations....the earth IS sitting on the backs of 4 invisible turtles. CO2 IS a critical greenhouse gas....
In all of the examples above, it is not possible to directly check to see if the assumption is valid which is the pseudoscientific beauty of post modern physics...The assumption is exempt from direct experimentation and validation...it can only be tested indirectly. The assumption is correct because the theorized explanation of the observation supports the theorized cause for the observation...The assumption must be true because it is the only way the theoretical explanation seems to be possible...The inability to come up with a plausible alternative explanation is then presented as evidence ..and the more we restrict our creativity and perspective, the more sure we get that we are right...circular thinking at its best.
There are no direct observations and measurements of energy exchange between objects at equilibrium, nor are there observations and measurements of energy moving back and forth spontaneously between objects at different temperatures..
So without that ... then ... you say it's impossible for the cold Earth to transfer energy to the warm atmospheric gases through IR radiation...
Actually, I have never said that...I have said that the cold atmospheric gasses can not warm the warmer earth earth....except, of course in rare instances of temperature inversion where the atmosphere is warmer than the surface...
thus the greenhouse effect is non-existent ... you'll need to be more clever on how you algebraically manipulate SB than what you've posted ...
I have not manipulated anything...I only stated in plain english the energy exchange that the equation describes....You assume net, so you see net in an equation from which net can not be derived...therefore net must be a true fact...
And there can be no radiative greenhouse effect in a troposphere which is so completely dominated by convection and conduction..rare indeed, is the greenhouse gas molecule that actually gets to emit radiation...
In the troposphere, the mean time between molecular collisions through which an excited greenhouse molecule can trans for its energy to another gas molecule ) most often N2 is about a nanosecond. The mean decay time for an excited molecule in the atmosphere to emit that energy is about a second.
So when a greenhouse gas molecule absorbs some IR radiation, about 99.9999999% of the time, it will lose that energy via collision also known as conduction...
Therefore conduction and convection are the primary modes of energy movement through the troposphere..radiation is such a small player in the troposphere that it is hardly worth mentioning...and yet, we theorized about observations of energy in the atmosphere, and came up with one that seemingly explains the observations and therefore, by fiat, it must be true...even though observation with more and more sensitive instrumentation over the years have shown the original theorization to have been incorrect.
There is certainly a "greenhouse" effect if you like that term that keeps us warm at night, and from burning up in the day, but it is not radiative in nature.
I showed you how easy it is to demonstrate the equation you give is for net power ... try setting T(c) to 3 K ... see if that makes a difference ...
Actually, you theorized...you didn't show me anything..and you completely ignored the fact that you have your iron bar laying in the hot coals...and the underside of the bar, which is in contact with the coals is not radiating anything...AGAIN...the laws of physics state that there can be no radiation between objects that are in intimate contact...the underside of the bar is in intimate contact with the bed of coals...the iron bar is conducting energy through the side that is in intimate contact with the coals and radiating energy out into the cooler atmosphere precisely as both the second law and the SB law predict..
I guess I'm just a pansy for the past century's finest minds ...
I appreciate fine minds...but am acutely aware of the fact that even the finest minds can be wrong...and have been wrong throughout the evolution of science...there is no reason whatsoever to suspect that the minds of the present are the finest and that future fine minds won't find our notions on physics as quaint as we find the thinking of the finest minds of the past. It is arrogant in the extreme to believe that we have learned it all and are mistaken about nothing.....especially when physical evidence is lacking to support most of the true facts we accept today...as has always been the case, improvements in instrumentation, and the ability to look more deeply that those improvements provide will inevitably show us that the finest minds of today were certainly creative, but alas, wrong in far more cases than they will have been right.
We are constrained by what we can imagine...and nature has shown us over and over that our imaginations are very dim bulbs indeed when contrasted with the realities of nature....
