It is not surprising that the people most confused about basic physics are the ones who can’t write down an equation for their idea.
The same people are the most passionate defenders of their beliefs and I have no doubts about their sincerity.
I’ll meander into what it is I want to explain..
I found an amazing resource recently – iTunes U short for iTunes University. Now I confess that I have been a little confused about angular momentum. I always knew what it was, but in the small discussion that followed The Coriolis Effect and Geostrophic Motion I found myself wondering whether conservation of angular momentum was something independent of, or a consequence of, linear momentum or some aspect of Newton’s laws of motion.
It seemed as if conservation of angular momentum was an orphan of Newton’s three laws of motion. How could that be? Perhaps this conservation is just another expression of these laws in a way that I hadn’t appreciated? (Knowledgeable readers please explain).
Just around this time I found iTunes U and searched for “mechanics” and found the amazing series of lectures from MIT by Prof. Walter Lewin. A series of videos. I recommend them to anyone interested in learning some basics about forces, motion and energy. Lewin has a gift, along with an engaging style. It’s nice to see chalk boards and overhead projectors because they are probably no more in use (? young people please advise).
These lectures are not just for iPhone and iTunes people – here is the weblink.
The gift of teaching science is not in accuracy – that’s a given – the gift is in showing the principle via experiment and matching it with a theoretical derivation, and “why this should be so” and thereby producing a conceptual idea in the student.
I haven’t got to Lecture 20: Angular Momentum yet, I’m at about lecture 11. It’s basic stuff but so easy to forget (yes, quite a lot of it has been forgotten). Especially easy to forget how different principles link together and which principle is used to derive the next principle.
What caught my attention for the purposes of this article was how every principle had an equation.
For example, in deriving the work done on an object, Lewin integrates force over the distance traveled and comes up with the equation for kinetic energy.
While investigating the oscillation of a mass on a spring, the equation for its harmonic motion is derived.
Every principle has an equation that can be written down.
Over the last few days, as at many times over the past two years, people have arrived on this blog to explain how radiation from the atmosphere can’t affect the surface temperature because of blah blah blah. Where blah blah blah sounds like it might be some kind of physics but is never accompanied by an equation.
Here’s the equation I find in textbooks.
Energy absorbed from the atmosphere by the surface, Ea:
Ea = αRL↓ ….[eqn 1]
where α = absorptivity of the surface at these wavelengths, RL↓ = downward radiation from the atmosphere
And this energy absorbed, once absorbed, is indistinguishable from the energy absorbed from the sun. 1 W/m² absorbed from the atmosphere is identical to 1 W/m² absorbed from the sun.
That’s my equation. I have provided six textbooks to explain this idea in a slightly different way in Amazing Things we Find in Textbooks – The Real Second Law of Thermodynamics.
It’s also produced by Kramm & Dlugi, who think the greenhouse effect is some unproven idea:
Now the equation shown is a pretty simple equation. The equation reproduced in the graphic above from Kramm & Dlugi looks a little more daunting but is simply adding up a number of fluxes at the surface.
Here’s what it says:
Solar radiation absorbed + longwave radiation absorbed – thermal radiation emitted – latent heat emitted – sensible heat emitted + geothermal energy supplied = 0
Or another way of thinking about it is energy in = energy out (written as “energy in – energy out = 0“)
Now one thing is not amazing to me – of the tens (hundreds?) of concerned citizens commenting on the many articles on this subject who have tried to point out my “basic mistake” and tell me that the atmosphere can’t blah blah blah, not a single one has produced an equation.
The equation might look something like this:
Ea = f(α,Tatm-Tsur).RL↓ ….[eqn 2]
where Tatm = temperature of the atmosphere, Tsur = temperature of the surface
With the function f being defined like this:
f(α,Tatm-Tsur) = α, when Tatm ≥ Tsur and
f(α,Tatm-Tsur) = 0, when Tatm < Tsur
In English, it says something like energy from the atmosphere absorbed by the surface = 0 when the temperature of the atmosphere is less than the temperature of the surface.
I’m filling in the blanks here. No one has written down such ridiculous unphysical nonsense because it would look like ridiculous unphysical nonsense. Or perhaps I’m being unkind. Another possibility is that no one has written down such ridiculous unphysical nonsense because the proponents have no idea what an equation is, or how one can be constructed.
No one will produce an equation which shows how no atmospheric energy can be absorbed by the surface. Or how atmospheric energy absorbed cannot affect internal energy.
This is because my next questions will be:
- Please supply a textbook or paper with this equation
- Please explain from fundamental physics how this can take place
Here’s my challenge to the many people concerned about the “dangerous nonsense” of the atmospheric radiation affecting surface temperature -
Supply an equation.
If you can’t, it is because you don’t understand the subject.
It won’t stop you talking, but everyone who is wondering and reads this article will be able to join the dots together.
The Usual Caveat
If there were only two bodies – the warmer earth and the colder atmosphere (no sun available) – then of course the earth’s temperature would decrease towards that of the atmosphere and the atmosphere’s temperature would increase towards that of the earth until both were at the same temperature – somewhere between the two starting temperatures.
However, the sun does actually exist and the question is simply whether the presence of the (colder) atmosphere affects the surface temperature compared with if no atmosphere existed. It is The Three Body Problem.
My Second Prediction
The people not supplying the equation, the passionate believers in blah blah blah, will not explain why an equation is not necessary or not available. Instead, continue to blah blah blah.