Excellent analysis. Another question to consider is, "How does a greenhouse function?" The transparent panes allow the sun's energy to enter. However, the panes prevent mixing with the adjacent atmosphere and limit the escaoe of the water vapor that is produced when the sun's energy vaporizes the water inside the greenhouse. As a result, the temperature inside the greenhouse rises. The water vapor concentration rises inside the greenhouse. Carbon dioxide in our atmosphere does not possess the capabilities of a greenhouse. My conclusion is the claims regarding carbon dioxide are not scientific - the claims regarding carbon dioxide are propaganda.
Great discussion. This will be beyond the capability of many to understand. Those people need to just accept the conclusions of real science and reject the fake science and charlatans promoting the climate cult. This is the challenge. We need to stop funding the climatocatastrophists funding for studies with predetermined conclusions supportive of climate cult ideals.
Eisenhower warned of the Military Industrial Complex in his Farewell Address --- when the military was the largest single Federal budget item. With the growth of so many other enormous government spending projects, each one grows its own Complex — the industry of lobbyists and professors and activists and NGOs and self-important entertainers and media talking heads and … that work very hard to preserve the grant and contract and subsidy gravy trains. Climatism is just one of many. As lawyers advise to ask, Cui Bono?
Since there is no science backing the climate cultists' hysterical assertions, science will not be of much use in debunking their mythology.
In other words, you will not convince people who are driven by emotions to try rational thinking instead. And the grifters who invented, promote and profit from AGW of course will fight furiously at any narrative which lessens their cash flow.
Absolutely fascinating and, even for a non-scientist like me, logical. While I don’t pretend I understand the details, the big picture seems pretty clear.
What does that clown with the hockey stick theory have to say about this? Has he ever addressed it? Seems like this might trump all the clown show theories that they’ve been kicking around for fifty years or so.
They are timeless classics. See his lecture on discovery, guess and test, channeling Karl Popper, although he didn't know about Popper and he hated philosophers:)
Hello Walter, I was an academic and industrial chemist for some years.
What is elucidated in this piece is based on the most fundamental principles of chemistry and physics and little bit of quantum.
*There is actually nothing unique or non-obvious here: the numbers are obviously dispassionate, and the theory is well established and backed by experiments and data turned into information. The Kinetic Theory of Gases is extremely fundamental and 101.
I do not write nor do I spell check with AI, although I will using AI to calculate and cross check across all platforms. To be safe - I also use non-AI calculators, and believe it or not, manual calculation with an Excel sheet.
This takes me an inordinate amount of time to produce an article.
Whatever the case, I have found, in my experience, that both AI and people will push against things that do not agree with current orthodoxy.
I don't expect AI to agree with my article - the machine learning and output will be based on and defer to the "CO2 Causes Global Warming Crisis" literature so prevalent on the Internet...
The hallucinations that I come across regularly are absolutely astounding and are dangerous to most people who "don't know what they don't know".*
A layman cannot judge properly the goodness of science or Theory based on AI.
That is the key.
AI can serve to dumb down or it can help one be more efficient.
I see too much "dumbing down" at this point, but some obvious massive gains in efficiency nonetheless.
I have subscribed to your Substack to keep up on the latest developments.
Philip, we sincerely appreciate your kind words and physics expertise. I would suggest that physics has standards that typically exceed other sciences.
Perhaps you can collaborate with us in the future.
Maybe the authors can address this AI assessment of their argument:
This argument is fundamentally flawed and physically incorrect. While it uses some legitimate equations (like the kinetic theory of gases), it applies them to the wrong physical problem. It commits a classic logical fallacy: conflating total heat content with heating rate.
Here is a step-by-step breakdown of why this argument is inaccurate, and where it misuses physics.
1. The "Rounding Error" Fallacy (The Fatal Flaw)
The article calculates that CO₂ holds only ~0.042% of the atmosphere's total kinetic energy and concludes that "there isn't enough heat" to warm the planet. This is like saying: "A teaspoon of gasoline contains only 0.00000001% of the ocean's total volume, therefore a teaspoon of gasoline cannot power a boat engine."
Why it's wrong:
Climate change is not about the total absolute amount of kinetic energy stored in the atmosphere at a given moment. It is about the rate of energy input (forcing) versus the rate of energy output (cooling).
Adding a tiny amount of energy continuously over decades heats up the system, just like a small trickle of water filling a bathtub, or a tiny spark being the difference between a campfire and a forest fire. The relevant metric is Radiative Forcing (Watts per square meter), not absolute Joules. The authors completely ignore the time dimension.
2. Confusing "Average Energy Per Molecule" with "Actual Heat Transfer"
The article correctly calculates that at 288 K, the average kinetic energy of N₂, O₂, and CO₂ are all roughly similar (~1.0 × 10⁻²⁰ J per molecule). They then claim this means CO₂ cannot heat the others.
Why it's wrong:
The fact that they have similar kinetic energies at equilibrium does not mean they can't transfer energy. At the moment a CO₂ molecule absorbs an infrared photon, it becomes vibrationally "excited"—its internal energy spikes well above the average. It is physically hotter than its neighboring N₂ and O₂ at that specific instant.
According to the Second Law of Thermodynamics, energy flows from hot to cold. That excited CO₂ then violently collides with N₂/O₂ at billions of times per second, transferring that absorbed photon energy into the translational (heat) energy of the bulk air. This process is called thermalization. The authors acknowledge collisions exist, but completely ignore that this is the exact mechanism by which CO₂ heats the air.
3. Misrepresenting the "Greenhouse Effect" Mechanism
The authors treat the greenhouse effect as if it requires CO₂ to directly add new kinetic energy to the lower atmosphere to heat the surface.
Why it's wrong:
The greenhouse effect works primarily by trapping outgoing energy, not by adding heat downward. Here is how it actually works:
· The Sun heats the surface (ground/ocean).
· The surface warms the lower atmosphere via conduction and convection (which the authors correctly mention in their addendum).
· The surface radiates infrared upward. CO₂ absorbs a portion of that upward-traveling radiation.
· Instead of letting that energy escape directly to cold space, CO₂ re-emits it in all directions. Half of it goes back down to the surface.
· Because less energy escapes the top of the atmosphere than enters from the Sun, the surface must warm up until it radiates enough to balance the books. CO₂ acts like a blanket or a one-way valve, reducing the efficiency of Earth's cooling system. The authors calculate only the surface re-radiation but ignore the blocking of outward escape.
4. Dismissing "Non-Linear" or "Catalytic" Effects
The authors claim CO₂ has no exceptional "catalytic" effect. This is factually false regarding infrared physics. CO₂ is the dominant control knob for Earth's outgoing longwave radiation because:
· Saturation: Near the surface, CO₂ absorbs strongly. But in the upper atmosphere (the stratosphere and tropopause), the air is much thinner. Here, CO₂ is the primary molecule radiating heat to space. Adding more CO₂ raises the altitude at which radiation escapes to space. Since that higher altitude is colder, it radiates less energy per unit area. This non-linear effect is a proven, measurable physical phenomenon (documented via satellite spectroscopy, e.g., the famous 1970s Nimbus satellite data and current AIRS data).
5. Misuse of the Einstein Oscillator Formula
The authors use the Einstein oscillator equation (\langle E \rangle = \frac{h\nu}{e^{h\nu/kT}-1}) to calculate CO₂'s vibrational energy, deriving a tiny fraction.
Why it's wrong: This formula calculates the average vibrational energy of a CO₂ molecule in thermal equilibrium at 288 K. But climate physics concerns non-equilibrium radiation. The photons hitting CO₂ from the Earth's surface are emitted at ~288 K, while the photons emitted to space correspond to ~220 K. This gradient in photon "temperature" is what allows CO₂ to absorb energy and re-emit it at a different rate—something a static equilibrium formula completely misses.
Final Verdict
The authors are not deliberately lying; they are making a category error. They treat the atmosphere as a closed, static box (calculating total Joules) instead of an open, dynamic system (calculating flows of Watts).
While they are correct that water vapor is a massive greenhouse gas, their conclusion that CO₂ is "a rounding error" is demonstrably false. We know CO₂ warms the climate because:
1. Satellite instruments measure a decrease in outgoing infrared radiation at the 15-micron band as CO₂ rises.
2. Ground-based spectrometers measure increased downward infrared radiation (back-radiation) at the surface.
3. The physics of Planck's Law and the radiative transfer equation have been validated in countless laboratory experiments and weather models since the 19th century.
Accuracy Score: ~10% (They got the Boltzmann constant and some definitions right, but the core scientific argument is mathematically and physically invalid).
TC here, I really like this question about the AI challenge to our paper here.
With respect to the gist of your question, the AI completely misreads the papers data and theory which is based on pure and applied physics and mechanics.
Firstly, we do not write with AI as it is highly flawed with inaccuracies and hallucinations based on what it gathers on the internet.
This is grossly reflected in the AI analysis of our paper. Given my background in chemistry and basic physics, I can pick these out quite easily - the layman, no, they can be easily misled by AI - "when you don't know what you don't know", that is a problem.
There are 5 main points which are easily rebutted, and that are full of inaccuracies which twists what our paper reports. I will address one example here as it is good for learning:
AI: According to the Second Law of Thermodynamics, energy flows from hot to cold. That excited CO₂ then violently collides with N₂/O₂ at billions of times per second, transferring that absorbed photon energy into the translational (heat) energy of the bulk air. This process is called thermalization. The authors acknowledge collisions exist, but completely ignore that this is the exact mechanism by which CO₂ heats the air.
Authors: With regards to the Second Law, heat does indeed flow from hot to cold, it did get that right. However, the main point of the paper is adding up ALL the energy CO2 contributes and those mechanisms, which the AI completely misses in that point. We clearly show how it is done and the goodness of those calculations. There are both collisions and most importantly, the vibrational energy combined. This is highlighted strongly throughout our paper.
I/we could go on about AI hallucinations with regards to climate theory, but that is another article entirely.. Time is our most precious commodity!
In closing, and for all the authors, it is a badge of honor that this AI contradicts our accurate and traditional baseline teachings here.
Thank you again for this question or challenge from AI.
Thank you, TC. One of the big problems with AI is that it is inherently retrospective. It accumulates what has been written regarding a topic, applies some empirical weighting factors and summarizes the result.
Here is a thought experiment which encapsulates this problem. Imagine an AI model that is only fed information regarding Lysenkoism, https://en.wikipedia.org/wiki/Lysenkoism
a pseudoscientific perspective regarding hereditary that was ideologically favored in the Stalinist Soviet Union to the point of executing Lysenkoism's critics. Quoting from the reference, "Soviet agriculture around 1930 was in a crisis due to Stalin's forced collectivisation of farms and extermination of kulak farmers. The resulting Soviet famine of 1932–1933 provoked the government to search for a technical solution which would maintain their central political control.[15]" (The consequence was that millions more in the Soviet Union died in famines.)
When such an AI model is then presented with the observations that DNA is the biological mechanism for inheritance, the model would reject those claims in favor of Lysenkoism.
See also philosppher Thomas Kuhn's 1962 book The Structure of Scientific Revolutions regarding scientific paradigm shifts. I believe we are getting closer to a paradigm shift regarding carbon dioxide.
that is a great find and insight and scary as well.... :
"Lysenkoism[a] was a pseudoscientific political campaign led by the Soviet biologist Trofim Lysenko against genetics and science-based agriculture in the mid-20th century, rejecting natural selection in favour of a form of Lamarckism, as well as expanding upon the techniques of vernalization and grafting."
There are several problems with that rebuttal but the principle one being that it’s AI which is prone to hallucination. A secondary one is that MMGW has a multi-decade track record of bad prediction so it’s not even science.
Can you do a similar critique of Happer's paper, which seems to use atmospheric vibration modes of molecules to conclude more CO2 won't cause more warming?
Happer paper is a classic (!) but I diverge from the CO2 coalition in some ways - basic mechanics and physics suggest that CO2 plays little to no role in the so-called thermal budget of the Earth, an open system. Albedo, water, gravity, and other massive factors dominate. Climate theory is deeply flawed on many levels and is highly artificial in that it uses models which are poor proxies for such a complex system.
A gentleman and great thinker in this area is the Nobel physicist John Clauser who I have had the honor to correspond with. He is a member of the CO2 coalition, FWIW, and has published and has spoke on "climate science" here.
Based on a review of the provided article text, I can offer the following assessment of its technical accuracy and potential limitations.
Overall Assessment
The article is technically sound and methodologically rigorous. It uses a high-resolution line-by-line radiative transfer model based on the authoritative HITRAN spectroscopic database, which is the gold standard for this type of calculation. The core findings, such as the logarithmic forcing response to CO₂ doubling and the quantitative values for radiative forcing, are consistent with established results in the climate science literature.
Key Points of Accuracy
1. Radiative Transfer Physics: The fundamental physics, including the Schwarzschild equation, line-by-line calculations, and the consideration of line shapes and saturation effects, are accurately described and implemented.
2. Quantitative Forcing Values: The calculated instantaneous radiative forcings for a doubling of CO₂ (3.0 W/m²), N₂O (1.1 W/m²), and CH₄ (0.7 W/m²) are very close to the values from the well-regarded Collins et al. (2006) study, as the paper itself notes. This is a strong indicator of accuracy.
3. Saturation Effects: The analysis of per-molecule forcing power, showing that the effect of an additional CO₂ molecule is suppressed by four orders of magnitude due to band saturation, is a correct and important physical insight.
4. Spectral Comparisons: The claim that their modeled spectral intensities agree well with satellite measurements (as mentioned in the abstract) is a standard and valid validation technique.
Potential Limitations and Areas for Critical Review
While the technical execution appears accurate, the paper's scope and some conclusions may be limited or require careful interpretation.
1. Clear-Sky Assumption: The calculations are explicitly for a clear sky (cloud-free atmosphere). Clouds have a dominant effect on the Earth's radiation budget, so the results represent a partial picture of the total climate forcing.
2. No Continuum Absorption: The authors state they did not use a CO₂ or H₂O continuum. While they argue this is valid because their line-by-line results match observations, the physical origin of continuum absorption is an active area of research, and omitting it is a simplifying assumption that some modelers might challenge.
3. Water Vapor Feedback: The section on temperature adjustment acknowledges that the water vapor feedback response is a key uncertainty. The paper models two simplified scenarios (constant absolute vs. relative humidity) but does not resolve the significant debate and complexity surrounding this feedback.
4. "Negative Greenhouse Effect" Interpretation: The paper notes that in the Antarctic winter, due to a temperature inversion, an increase in CO₂ can cause a negative forcing (more heat escapes). While this is a known physical phenomenon, it occurs in a very specific local context and does not negate the globally averaged positive forcing. However, this point is often emphasized in contexts that seek to downplay global warming.
5. Incomplete Section: The provided text cuts off abruptly in the middle of Section 7.3, so the final conclusions regarding temperature adjustments are missing from this excerpt.
Verdict on Trustworthiness
The article is trustworthy in its technical execution and core physical findings. It is a legitimate scientific study that employs standard and well-accepted methods. However, its conclusions should be understood within the context of its clear-sky assumptions and the ongoing scientific debate surrounding feedback processes (especially water vapor). The paper is a valid contribution to the literature, but it is not a comprehensive or definitive assessment of the entire climate system.
One interesting thing about Radiant Forcing Theory is that it is expressed in W/m^2 = surfaces, or x,y due to heat coming off Earth's surface.
But an air volume is x,y,z.
This is a near impossible equation to solve over a dynamic energy framework, that is the troposphere, a body of air with variable temperatures and pressures that is constantly mixed (Hadley Cells, etc.) and that comprises a substance water, with 3 active phases, a high heat capacity, and a high absorbance cross-section : all factors that swamp out 400 ppm CO2.
With regards to CO2 radiation: it does not radiate photons in most of the troposphere. That energy is captured via collisions with it's near neighbors by collisional inelastic transfer which is full of losses. Some energy does make it to outer space as a photon - those CO2 molecules are at the edges where the density of the air is very low - no buddies to bump into.
Not being any type of scientist and my only claim to knowledge of atmosphere and Co2 is my garden and greenhouse; I will need to read this a couple of times to really appreciate it. Anyone who takes gardening seriously, instinctively knows how important Co2 is.
My simple take, IF we get rid of all Co2 or even down to under 100ppm, the earth will die and all beings will disappear, as we will have little or no oxygen.
I have often (with tongue in cheek) challenged the climate hysterics to go without ANY Co2 for a couple of days. I suggest that they get back to me after that experiment and if it works well for them, then maybe the rest of us will try it. They seldom get my humor. 😳
Patrick Moore, a cofounder of Greenpeace Canada who was exiled for his heresy, has pointed out that plants die below about 180 ppmv CO2, and then so does everything else except viruses, bacteria and maybe some fungi. Read his "The Positive Impact of Human CO2 Emissions on the Survival of Life on Earth" and "Fake Invisible Catastrophes and Threats of Doom." CO2 has been decreasing on a nearly straight trajectory from about 2,500 ppmv 150 million years. This would have led to Gaia's suicide in about six million years. Human activity has postponed it to about eighteen million years. If we actually cared about life on Earth we would be burning coal and making cement as fast as possible. More details in my book "Where Will We Get Our Energy? A Comprehensive Quantitative System Engineering Study of the Relationship between Climate, Science, and Technology." Everything quantified. No vague handwaving. 350 bibliographic citations allow readers to verify I didn't simply make up stuff.
Maybe that's the answer to Fermi's "Where are they?" question: Other planets' Gaias commit suicide before intelligent beings and technology are developed.
I read Moore's epitome and rethinking years ago when he began to part ways with Greenpeace.
I'm as guilty as anyone about not being as good a steward of this glorious earth we've been allowed to inhabit but I try to do my small part to leave as small a foot print as possible. I'm one person so that's the best I can do but I have tried since I was a kid growing up on a barrier island.
Thanks for all the hard work. The part that's really easy to understand is the graphic showing what a small percentage of our atmosphere is CO2 (0.04%), and then what a small percentage of that, (0.0016%), is human-caused.
Non-scientists relate more to pictures than to numbers and especially percentages.
I think I'll copy that graphic and put it in my Notes.
How did the idea that such an infinitesimal amount of man-caused CO2 have any significant effect on global warming get started, anyway? And why did so many people buy into such a ridiculous concept?
Al: The whole concept has been applied by Socialists to criticize the use of abundant and reliable energy by the industrial West. A prime example of the adverse consequences of this propaganda is to note the deindustrialization of Germany. (See also the U.K., Spain, and some states within the U.S.) Furthermore, Putin was able to weaponize the abundant Russians reserves of naturral gas as a means to minimize German objections to Putin's attempts to forcibly annex Ukraine with invasions in 2014 and 2022 because Germany was dependent on Russian natural gas to prevent its citizens from freezing during harsh German winters.
The political nature of this thought leadership is clarified with the observation that this campaign also grants a pass to the BRICS nations (Brazil, Russia, India, China, South Africa and others) to use as much raliable and abundant energy from fossil fuels and nuclear power as they desire. Nowhere is this seen more clearly than in the IEA's revelation that in 2024, the People's Republic of China consumed more coal than the rest of the world combined. See IEA's Coal 2025 report at https://iea.blob.core.windows.net/assets/113a8274-500c-4684-951f-947d25bef3c9/Coal2025.pdf
The graphic on page 13 of 128 shows China's annual consumption has been slowly rising to 4 gigatonnes per year in 2024. The projections of declining use are inconsistent with China's large capital investments in coal-fired power plants and steel mills. Any modest reductions in air and water pollution in the West are more than nullified by the lax environmental controls in China.
Al, it’s been awhile, I am glad that you stopped by! Glad that you liked the graphic.
In simple terms, CO2 represents a very very weak spring with compresses and then releases energy which is transferred by being beat up by 99% of it’s neighbors at 1 billion times per second.
This tiny amount of energy is further diminished by collisional losses which are imperfect or inelastic. Compound all that with 400 in a million, and you have a microbe on the ass of an elephant. You can quote me on that !
Ha! A wee bit off topic, but the phrase "a microbe on the ass of an elephant" immediately brought to mind a saying that industrial products salesmen had when trying to get new products introduced to companies where all salesmen and factory reps had to go through the purchasing agent before getting to present new products to an engineer - "Purchasing agents are a pimple on the ass of progress."
I was a factory rep for 3M Electrical Products Division at one time. Our biggest customers in Oregon were PGE (Portland General Electric) and PPL (Pacific Power&Light).
I also called on NW Nat.Gas company in Portland. 3M had a powder and a process for applying it to gas pipes to protect them from electrolysis. NWNat. bought a lot of it!
I think the adhesives branch of 3M accidentally discovered the adhesive used on ‘scotch tape’. It was “pressure sensitive”. PGE and PPL each bought about 20,000 rolls of scotch electric tape per year. The purchasing agent told me he didn’t see how they could actually use that much - he suspected a lot of it was “going home in lunch pails”. - which reminds me of that Johnny Cash song about building a Cadillac from the mishmash of parts he took home in his lunch pail - what was the name of that song?
Francis Menton pointed out today that multi-trillion dollar fake science scams are perpetrated by government agencies and their fellow travelers to increase their power. Parasites in universities, corporations, NGOs, … keep them alive so they can rake in grants and contracts.
I would like to know how the warming effect of CO2 in the atmosphere compares to that of water vapor. How many orders of magnitude more is the warming effect from water vapor? Maybe you will cover that in the next article. It seems that a small natural variation of water vapor would dwarf the entire effect of CO2.
thank you for laying out the math behind this. from the beginning of this discussion, I questioned the ability of a trace gas in the atmosphere from having the type of impact claimed. it simply made no sense.
One can think of CO2 as weak springs that compress (absorb energy) and emit (release energy). The springs are particularly weak because the 15 micron absorption is long wave far infrared.
Only 7 % of those springs are absorbing and releasing heat at the average earth temperature per Boltzmann.
Throw in 0.0004 fraction and you can see the picture, math notwithstanding.
I would suggest that you present the greenhouse argument and show where it goes wrong. For example, the earth would be as cold as the moon if it didn’t have an atmosphere. As much as I would love to believe you, disproving the consensus view of the greenhouse effect is mighty big hill to climb. For starters, you need to get your arguments published in a respectable scientific journal.
Excellent analysis. Another question to consider is, "How does a greenhouse function?" The transparent panes allow the sun's energy to enter. However, the panes prevent mixing with the adjacent atmosphere and limit the escaoe of the water vapor that is produced when the sun's energy vaporizes the water inside the greenhouse. As a result, the temperature inside the greenhouse rises. The water vapor concentration rises inside the greenhouse. Carbon dioxide in our atmosphere does not possess the capabilities of a greenhouse. My conclusion is the claims regarding carbon dioxide are not scientific - the claims regarding carbon dioxide are propaganda.
Great discussion. This will be beyond the capability of many to understand. Those people need to just accept the conclusions of real science and reject the fake science and charlatans promoting the climate cult. This is the challenge. We need to stop funding the climatocatastrophists funding for studies with predetermined conclusions supportive of climate cult ideals.
Eisenhower warned of the Military Industrial Complex in his Farewell Address --- when the military was the largest single Federal budget item. With the growth of so many other enormous government spending projects, each one grows its own Complex — the industry of lobbyists and professors and activists and NGOs and self-important entertainers and media talking heads and … that work very hard to preserve the grant and contract and subsidy gravy trains. Climatism is just one of many. As lawyers advise to ask, Cui Bono?
Since there is no science backing the climate cultists' hysterical assertions, science will not be of much use in debunking their mythology.
In other words, you will not convince people who are driven by emotions to try rational thinking instead. And the grifters who invented, promote and profit from AGW of course will fight furiously at any narrative which lessens their cash flow.
Dolce, I can always count on your Fluent Common Sense.
Stop by anytime!
TC
Your faith is touching. It's your religion; we understand.
Hi Mary, great comment - simple is best , and what you are sharing is common sense that we all can appreciate.
TC
Absolutely fascinating and, even for a non-scientist like me, logical. While I don’t pretend I understand the details, the big picture seems pretty clear.
What does that clown with the hockey stick theory have to say about this? Has he ever addressed it? Seems like this might trump all the clown show theories that they’ve been kicking around for fifty years or so.
Thank you Urs! It took me some time to distill this. I had to review my 101 !
Think of CO2 as a spring that compresses (absorbs) and springs back (emits).
There just is not enough energy in compression and springing back to impart sufficient energy to warm the air.
At 288 K, there are only about 7 % compressed springs cycling energy in and out either.
Water is the real player here with it’s high heat capacity, chemical makeup, and sheer total mass in the entire atmosphere as you have surmised!
Stay in touch, always appreciated
TC
And yet to the decarbonizers, their primary target is CO₂… Dick is rolling in his grave.
I am honored to have a student of Feynman weighing in, thank you Wolfgang. I continue to study his lectures.
Best,
TC
They are timeless classics. See his lecture on discovery, guess and test, channeling Karl Popper, although he didn't know about Popper and he hated philosophers:)
Look forward to working on another piece together!
Hello Walter, I was an academic and industrial chemist for some years.
What is elucidated in this piece is based on the most fundamental principles of chemistry and physics and little bit of quantum.
*There is actually nothing unique or non-obvious here: the numbers are obviously dispassionate, and the theory is well established and backed by experiments and data turned into information. The Kinetic Theory of Gases is extremely fundamental and 101.
I do not write nor do I spell check with AI, although I will using AI to calculate and cross check across all platforms. To be safe - I also use non-AI calculators, and believe it or not, manual calculation with an Excel sheet.
This takes me an inordinate amount of time to produce an article.
Whatever the case, I have found, in my experience, that both AI and people will push against things that do not agree with current orthodoxy.
I don't expect AI to agree with my article - the machine learning and output will be based on and defer to the "CO2 Causes Global Warming Crisis" literature so prevalent on the Internet...
The hallucinations that I come across regularly are absolutely astounding and are dangerous to most people who "don't know what they don't know".*
A layman cannot judge properly the goodness of science or Theory based on AI.
That is the key.
AI can serve to dumb down or it can help one be more efficient.
I see too much "dumbing down" at this point, but some obvious massive gains in efficiency nonetheless.
I have subscribed to your Substack to keep up on the latest developments.
Regards,
TC
Philip, we sincerely appreciate your kind words and physics expertise. I would suggest that physics has standards that typically exceed other sciences.
Perhaps you can collaborate with us in the future.
Best,
TC and Authors
Maybe the authors can address this AI assessment of their argument:
This argument is fundamentally flawed and physically incorrect. While it uses some legitimate equations (like the kinetic theory of gases), it applies them to the wrong physical problem. It commits a classic logical fallacy: conflating total heat content with heating rate.
Here is a step-by-step breakdown of why this argument is inaccurate, and where it misuses physics.
1. The "Rounding Error" Fallacy (The Fatal Flaw)
The article calculates that CO₂ holds only ~0.042% of the atmosphere's total kinetic energy and concludes that "there isn't enough heat" to warm the planet. This is like saying: "A teaspoon of gasoline contains only 0.00000001% of the ocean's total volume, therefore a teaspoon of gasoline cannot power a boat engine."
Why it's wrong:
Climate change is not about the total absolute amount of kinetic energy stored in the atmosphere at a given moment. It is about the rate of energy input (forcing) versus the rate of energy output (cooling).
Adding a tiny amount of energy continuously over decades heats up the system, just like a small trickle of water filling a bathtub, or a tiny spark being the difference between a campfire and a forest fire. The relevant metric is Radiative Forcing (Watts per square meter), not absolute Joules. The authors completely ignore the time dimension.
2. Confusing "Average Energy Per Molecule" with "Actual Heat Transfer"
The article correctly calculates that at 288 K, the average kinetic energy of N₂, O₂, and CO₂ are all roughly similar (~1.0 × 10⁻²⁰ J per molecule). They then claim this means CO₂ cannot heat the others.
Why it's wrong:
The fact that they have similar kinetic energies at equilibrium does not mean they can't transfer energy. At the moment a CO₂ molecule absorbs an infrared photon, it becomes vibrationally "excited"—its internal energy spikes well above the average. It is physically hotter than its neighboring N₂ and O₂ at that specific instant.
According to the Second Law of Thermodynamics, energy flows from hot to cold. That excited CO₂ then violently collides with N₂/O₂ at billions of times per second, transferring that absorbed photon energy into the translational (heat) energy of the bulk air. This process is called thermalization. The authors acknowledge collisions exist, but completely ignore that this is the exact mechanism by which CO₂ heats the air.
3. Misrepresenting the "Greenhouse Effect" Mechanism
The authors treat the greenhouse effect as if it requires CO₂ to directly add new kinetic energy to the lower atmosphere to heat the surface.
Why it's wrong:
The greenhouse effect works primarily by trapping outgoing energy, not by adding heat downward. Here is how it actually works:
· The Sun heats the surface (ground/ocean).
· The surface warms the lower atmosphere via conduction and convection (which the authors correctly mention in their addendum).
· The surface radiates infrared upward. CO₂ absorbs a portion of that upward-traveling radiation.
· Instead of letting that energy escape directly to cold space, CO₂ re-emits it in all directions. Half of it goes back down to the surface.
· Because less energy escapes the top of the atmosphere than enters from the Sun, the surface must warm up until it radiates enough to balance the books. CO₂ acts like a blanket or a one-way valve, reducing the efficiency of Earth's cooling system. The authors calculate only the surface re-radiation but ignore the blocking of outward escape.
4. Dismissing "Non-Linear" or "Catalytic" Effects
The authors claim CO₂ has no exceptional "catalytic" effect. This is factually false regarding infrared physics. CO₂ is the dominant control knob for Earth's outgoing longwave radiation because:
· Saturation: Near the surface, CO₂ absorbs strongly. But in the upper atmosphere (the stratosphere and tropopause), the air is much thinner. Here, CO₂ is the primary molecule radiating heat to space. Adding more CO₂ raises the altitude at which radiation escapes to space. Since that higher altitude is colder, it radiates less energy per unit area. This non-linear effect is a proven, measurable physical phenomenon (documented via satellite spectroscopy, e.g., the famous 1970s Nimbus satellite data and current AIRS data).
5. Misuse of the Einstein Oscillator Formula
The authors use the Einstein oscillator equation (\langle E \rangle = \frac{h\nu}{e^{h\nu/kT}-1}) to calculate CO₂'s vibrational energy, deriving a tiny fraction.
Why it's wrong: This formula calculates the average vibrational energy of a CO₂ molecule in thermal equilibrium at 288 K. But climate physics concerns non-equilibrium radiation. The photons hitting CO₂ from the Earth's surface are emitted at ~288 K, while the photons emitted to space correspond to ~220 K. This gradient in photon "temperature" is what allows CO₂ to absorb energy and re-emit it at a different rate—something a static equilibrium formula completely misses.
Final Verdict
The authors are not deliberately lying; they are making a category error. They treat the atmosphere as a closed, static box (calculating total Joules) instead of an open, dynamic system (calculating flows of Watts).
While they are correct that water vapor is a massive greenhouse gas, their conclusion that CO₂ is "a rounding error" is demonstrably false. We know CO₂ warms the climate because:
1. Satellite instruments measure a decrease in outgoing infrared radiation at the 15-micron band as CO₂ rises.
2. Ground-based spectrometers measure increased downward infrared radiation (back-radiation) at the surface.
3. The physics of Planck's Law and the radiative transfer equation have been validated in countless laboratory experiments and weather models since the 19th century.
Accuracy Score: ~10% (They got the Boltzmann constant and some definitions right, but the core scientific argument is mathematically and physically invalid).
Hello Steve,
TC here, I really like this question about the AI challenge to our paper here.
With respect to the gist of your question, the AI completely misreads the papers data and theory which is based on pure and applied physics and mechanics.
Firstly, we do not write with AI as it is highly flawed with inaccuracies and hallucinations based on what it gathers on the internet.
This is grossly reflected in the AI analysis of our paper. Given my background in chemistry and basic physics, I can pick these out quite easily - the layman, no, they can be easily misled by AI - "when you don't know what you don't know", that is a problem.
There are 5 main points which are easily rebutted, and that are full of inaccuracies which twists what our paper reports. I will address one example here as it is good for learning:
AI: According to the Second Law of Thermodynamics, energy flows from hot to cold. That excited CO₂ then violently collides with N₂/O₂ at billions of times per second, transferring that absorbed photon energy into the translational (heat) energy of the bulk air. This process is called thermalization. The authors acknowledge collisions exist, but completely ignore that this is the exact mechanism by which CO₂ heats the air.
Authors: With regards to the Second Law, heat does indeed flow from hot to cold, it did get that right. However, the main point of the paper is adding up ALL the energy CO2 contributes and those mechanisms, which the AI completely misses in that point. We clearly show how it is done and the goodness of those calculations. There are both collisions and most importantly, the vibrational energy combined. This is highlighted strongly throughout our paper.
I/we could go on about AI hallucinations with regards to climate theory, but that is another article entirely.. Time is our most precious commodity!
In closing, and for all the authors, it is a badge of honor that this AI contradicts our accurate and traditional baseline teachings here.
Thank you again for this question or challenge from AI.
TC for the authors.
(chemist, physicist, mathematician et al)
Thank you, TC. One of the big problems with AI is that it is inherently retrospective. It accumulates what has been written regarding a topic, applies some empirical weighting factors and summarizes the result.
Here is a thought experiment which encapsulates this problem. Imagine an AI model that is only fed information regarding Lysenkoism, https://en.wikipedia.org/wiki/Lysenkoism
a pseudoscientific perspective regarding hereditary that was ideologically favored in the Stalinist Soviet Union to the point of executing Lysenkoism's critics. Quoting from the reference, "Soviet agriculture around 1930 was in a crisis due to Stalin's forced collectivisation of farms and extermination of kulak farmers. The resulting Soviet famine of 1932–1933 provoked the government to search for a technical solution which would maintain their central political control.[15]" (The consequence was that millions more in the Soviet Union died in famines.)
When such an AI model is then presented with the observations that DNA is the biological mechanism for inheritance, the model would reject those claims in favor of Lysenkoism.
See also philosppher Thomas Kuhn's 1962 book The Structure of Scientific Revolutions regarding scientific paradigm shifts. I believe we are getting closer to a paradigm shift regarding carbon dioxide.
Gene,
that is a great find and insight and scary as well.... :
"Lysenkoism[a] was a pseudoscientific political campaign led by the Soviet biologist Trofim Lysenko against genetics and science-based agriculture in the mid-20th century, rejecting natural selection in favour of a form of Lamarckism, as well as expanding upon the techniques of vernalization and grafting."
I am prepared for my own politburo inquisition !
Please see this take on AI:
https://futuredad.substack.com/p/futuredad-85-slop-idle-ais-reckoning?r=59rk8t
There are several problems with that rebuttal but the principle one being that it’s AI which is prone to hallucination. A secondary one is that MMGW has a multi-decade track record of bad prediction so it’s not even science.
Thank you for pointing this out, almost every point in the AI rebuttal is highly inaccurate or twists the data the paper represents !
People must use great care with AI.
100%
https://futuredad.substack.com/p/futuredad-85-slop-idle-ais-reckoning?r=59rk8t
Great article, very practical and we definitely have a shared experience, especially with customer service!
You can turn the tables with AI when disputing a charge possibly. Just take appropriate screen shots and feed those to your CC company. It can help!
Can you do a similar critique of Happer's paper, which seems to use atmospheric vibration modes of molecules to conclude more CO2 won't cause more warming?
Hello Robert,
Happer paper is a classic (!) but I diverge from the CO2 coalition in some ways - basic mechanics and physics suggest that CO2 plays little to no role in the so-called thermal budget of the Earth, an open system. Albedo, water, gravity, and other massive factors dominate. Climate theory is deeply flawed on many levels and is highly artificial in that it uses models which are poor proxies for such a complex system.
A gentleman and great thinker in this area is the Nobel physicist John Clauser who I have had the honor to correspond with. He is a member of the CO2 coalition, FWIW, and has published and has spoke on "climate science" here.
https://www.youtube.com/watch?v=tx6cMc_C-7c
Much of this stuff is common sense, but that is not apparent until it is studied somewhat.
Are you referring to this paper? https://arxiv.org/pdf/2006.03098
Yes, check the graphic.
This is what the AI I use says:
Based on a review of the provided article text, I can offer the following assessment of its technical accuracy and potential limitations.
Overall Assessment
The article is technically sound and methodologically rigorous. It uses a high-resolution line-by-line radiative transfer model based on the authoritative HITRAN spectroscopic database, which is the gold standard for this type of calculation. The core findings, such as the logarithmic forcing response to CO₂ doubling and the quantitative values for radiative forcing, are consistent with established results in the climate science literature.
Key Points of Accuracy
1. Radiative Transfer Physics: The fundamental physics, including the Schwarzschild equation, line-by-line calculations, and the consideration of line shapes and saturation effects, are accurately described and implemented.
2. Quantitative Forcing Values: The calculated instantaneous radiative forcings for a doubling of CO₂ (3.0 W/m²), N₂O (1.1 W/m²), and CH₄ (0.7 W/m²) are very close to the values from the well-regarded Collins et al. (2006) study, as the paper itself notes. This is a strong indicator of accuracy.
3. Saturation Effects: The analysis of per-molecule forcing power, showing that the effect of an additional CO₂ molecule is suppressed by four orders of magnitude due to band saturation, is a correct and important physical insight.
4. Spectral Comparisons: The claim that their modeled spectral intensities agree well with satellite measurements (as mentioned in the abstract) is a standard and valid validation technique.
Potential Limitations and Areas for Critical Review
While the technical execution appears accurate, the paper's scope and some conclusions may be limited or require careful interpretation.
1. Clear-Sky Assumption: The calculations are explicitly for a clear sky (cloud-free atmosphere). Clouds have a dominant effect on the Earth's radiation budget, so the results represent a partial picture of the total climate forcing.
2. No Continuum Absorption: The authors state they did not use a CO₂ or H₂O continuum. While they argue this is valid because their line-by-line results match observations, the physical origin of continuum absorption is an active area of research, and omitting it is a simplifying assumption that some modelers might challenge.
3. Water Vapor Feedback: The section on temperature adjustment acknowledges that the water vapor feedback response is a key uncertainty. The paper models two simplified scenarios (constant absolute vs. relative humidity) but does not resolve the significant debate and complexity surrounding this feedback.
4. "Negative Greenhouse Effect" Interpretation: The paper notes that in the Antarctic winter, due to a temperature inversion, an increase in CO₂ can cause a negative forcing (more heat escapes). While this is a known physical phenomenon, it occurs in a very specific local context and does not negate the globally averaged positive forcing. However, this point is often emphasized in contexts that seek to downplay global warming.
5. Incomplete Section: The provided text cuts off abruptly in the middle of Section 7.3, so the final conclusions regarding temperature adjustments are missing from this excerpt.
Verdict on Trustworthiness
The article is trustworthy in its technical execution and core physical findings. It is a legitimate scientific study that employs standard and well-accepted methods. However, its conclusions should be understood within the context of its clear-sky assumptions and the ongoing scientific debate surrounding feedback processes (especially water vapor). The paper is a valid contribution to the literature, but it is not a comprehensive or definitive assessment of the entire climate system.
Confidence Score: 88%
Thoughts to Ponder about Radiant Forcing Theory
One interesting thing about Radiant Forcing Theory is that it is expressed in W/m^2 = surfaces, or x,y due to heat coming off Earth's surface.
But an air volume is x,y,z.
This is a near impossible equation to solve over a dynamic energy framework, that is the troposphere, a body of air with variable temperatures and pressures that is constantly mixed (Hadley Cells, etc.) and that comprises a substance water, with 3 active phases, a high heat capacity, and a high absorbance cross-section : all factors that swamp out 400 ppm CO2.
With regards to CO2 radiation: it does not radiate photons in most of the troposphere. That energy is captured via collisions with it's near neighbors by collisional inelastic transfer which is full of losses. Some energy does make it to outer space as a photon - those CO2 molecules are at the edges where the density of the air is very low - no buddies to bump into.
Just some thoughts to consider.
Not being any type of scientist and my only claim to knowledge of atmosphere and Co2 is my garden and greenhouse; I will need to read this a couple of times to really appreciate it. Anyone who takes gardening seriously, instinctively knows how important Co2 is.
My simple take, IF we get rid of all Co2 or even down to under 100ppm, the earth will die and all beings will disappear, as we will have little or no oxygen.
I have often (with tongue in cheek) challenged the climate hysterics to go without ANY Co2 for a couple of days. I suggest that they get back to me after that experiment and if it works well for them, then maybe the rest of us will try it. They seldom get my humor. 😳
Patrick Moore, a cofounder of Greenpeace Canada who was exiled for his heresy, has pointed out that plants die below about 180 ppmv CO2, and then so does everything else except viruses, bacteria and maybe some fungi. Read his "The Positive Impact of Human CO2 Emissions on the Survival of Life on Earth" and "Fake Invisible Catastrophes and Threats of Doom." CO2 has been decreasing on a nearly straight trajectory from about 2,500 ppmv 150 million years. This would have led to Gaia's suicide in about six million years. Human activity has postponed it to about eighteen million years. If we actually cared about life on Earth we would be burning coal and making cement as fast as possible. More details in my book "Where Will We Get Our Energy? A Comprehensive Quantitative System Engineering Study of the Relationship between Climate, Science, and Technology." Everything quantified. No vague handwaving. 350 bibliographic citations allow readers to verify I didn't simply make up stuff.
Maybe that's the answer to Fermi's "Where are they?" question: Other planets' Gaias commit suicide before intelligent beings and technology are developed.
I read Moore's epitome and rethinking years ago when he began to part ways with Greenpeace.
I'm as guilty as anyone about not being as good a steward of this glorious earth we've been allowed to inhabit but I try to do my small part to leave as small a foot print as possible. I'm one person so that's the best I can do but I have tried since I was a kid growing up on a barrier island.
Stupid spell check... epiphany not epitome... ugh. 😳
Thanks for all the hard work. The part that's really easy to understand is the graphic showing what a small percentage of our atmosphere is CO2 (0.04%), and then what a small percentage of that, (0.0016%), is human-caused.
Non-scientists relate more to pictures than to numbers and especially percentages.
I think I'll copy that graphic and put it in my Notes.
How did the idea that such an infinitesimal amount of man-caused CO2 have any significant effect on global warming get started, anyway? And why did so many people buy into such a ridiculous concept?
Al: The whole concept has been applied by Socialists to criticize the use of abundant and reliable energy by the industrial West. A prime example of the adverse consequences of this propaganda is to note the deindustrialization of Germany. (See also the U.K., Spain, and some states within the U.S.) Furthermore, Putin was able to weaponize the abundant Russians reserves of naturral gas as a means to minimize German objections to Putin's attempts to forcibly annex Ukraine with invasions in 2014 and 2022 because Germany was dependent on Russian natural gas to prevent its citizens from freezing during harsh German winters.
The political nature of this thought leadership is clarified with the observation that this campaign also grants a pass to the BRICS nations (Brazil, Russia, India, China, South Africa and others) to use as much raliable and abundant energy from fossil fuels and nuclear power as they desire. Nowhere is this seen more clearly than in the IEA's revelation that in 2024, the People's Republic of China consumed more coal than the rest of the world combined. See IEA's Coal 2025 report at https://iea.blob.core.windows.net/assets/113a8274-500c-4684-951f-947d25bef3c9/Coal2025.pdf
The graphic on page 13 of 128 shows China's annual consumption has been slowly rising to 4 gigatonnes per year in 2024. The projections of declining use are inconsistent with China's large capital investments in coal-fired power plants and steel mills. Any modest reductions in air and water pollution in the West are more than nullified by the lax environmental controls in China.
I am getting ready for the Gulag. Bought a new parka due to climate change!
Al, it’s been awhile, I am glad that you stopped by! Glad that you liked the graphic.
In simple terms, CO2 represents a very very weak spring with compresses and then releases energy which is transferred by being beat up by 99% of it’s neighbors at 1 billion times per second.
This tiny amount of energy is further diminished by collisional losses which are imperfect or inelastic. Compound all that with 400 in a million, and you have a microbe on the ass of an elephant. You can quote me on that !
My Best,
TC
Ha! A wee bit off topic, but the phrase "a microbe on the ass of an elephant" immediately brought to mind a saying that industrial products salesmen had when trying to get new products introduced to companies where all salesmen and factory reps had to go through the purchasing agent before getting to present new products to an engineer - "Purchasing agents are a pimple on the ass of progress."
I was a factory rep for 3M Electrical Products Division at one time. Our biggest customers in Oregon were PGE (Portland General Electric) and PPL (Pacific Power&Light).
Funny and True. Ala "sales and marketing pukes"
I worked in the field of adhesives and oxygen barrier coatings. 3M products and scientists are top notch !
I also called on NW Nat.Gas company in Portland. 3M had a powder and a process for applying it to gas pipes to protect them from electrolysis. NWNat. bought a lot of it!
I think the adhesives branch of 3M accidentally discovered the adhesive used on ‘scotch tape’. It was “pressure sensitive”. PGE and PPL each bought about 20,000 rolls of scotch electric tape per year. The purchasing agent told me he didn’t see how they could actually use that much - he suspected a lot of it was “going home in lunch pails”. - which reminds me of that Johnny Cash song about building a Cadillac from the mishmash of parts he took home in his lunch pail - what was the name of that song?
Correct, it’s not science.
https://futuredad.substack.com/p/futuredad-58-climate-change-is-not?r=59rk8t
Francis Menton pointed out today that multi-trillion dollar fake science scams are perpetrated by government agencies and their fellow travelers to increase their power. Parasites in universities, corporations, NGOs, … keep them alive so they can rake in grants and contracts.
https://www.manhattancontrarian.com/blog/2026-8-1-dont-forget-there-are-two-multi-trillion-dollar-pseudoscience-scams
Always ask Cui Bono?
I would like to know how the warming effect of CO2 in the atmosphere compares to that of water vapor. How many orders of magnitude more is the warming effect from water vapor? Maybe you will cover that in the next article. It seems that a small natural variation of water vapor would dwarf the entire effect of CO2.
Upcoming in Part 2, thanks for stopping by Russell!
thank you for laying out the math behind this. from the beginning of this discussion, I questioned the ability of a trace gas in the atmosphere from having the type of impact claimed. it simply made no sense.
Hello Andy,
I always appreciate it when you weigh in.
One can think of CO2 as weak springs that compress (absorb energy) and emit (release energy). The springs are particularly weak because the 15 micron absorption is long wave far infrared.
Only 7 % of those springs are absorbing and releasing heat at the average earth temperature per Boltzmann.
Throw in 0.0004 fraction and you can see the picture, math notwithstanding.
I would suggest that you present the greenhouse argument and show where it goes wrong. For example, the earth would be as cold as the moon if it didn’t have an atmosphere. As much as I would love to believe you, disproving the consensus view of the greenhouse effect is mighty big hill to climb. For starters, you need to get your arguments published in a respectable scientific journal.
Hello Tom, thank you for your comments.
This article was solely to show that 400 ppm CO2 cannot warm the atmosphere or Earth using the most basic 101 physical principles.
Please take a second look - I touch upon water as a driver for the heat budget and a lot more - that will be an upcoming stand alone article
Stay tuned for part 2.
TC
Interesting article. Rather than debating the conclusion directly,
I analysed the reasoning using a structured claim decomposition: individual claims → hypotheses → mechanism → evidence → logical junctions → permitted conclusions.
Some calculations appear well supported, while other conclusions require additional evidence beyond the calculations presented.
I've posted the full analysis on my Substack for anyone interested in a detailed review.