Russel Humphreys’ cosmology is trivially wrong

The starlight “problem”

Young Earth Creationist (YEC) claim the universe is 6,000 (or 10,000) years old. If it’s really that young, how can we see stars 30,000, light years away?


How YEC think General Relativity can help

In the movie Interstellar, Matthew McConaughey misses the teen years of his daughter for having spent too much time on a planet too close to the “Gargantua” Black Hole. Immersed in the formidable gravitational potential well of the Black Hole, one single hour on “Miller’s planet” is 7 years on Earth! Gargantua weights about 100 million times more than the sun, Miller’s planet orbits close to it, and yes, according to General Relativity (GR), a planet orbiting Gargantua like “Miller’s planet” does, would enjoy such a crazy time contraction [1].

According to his own wristwatch, Matthew McConaughey spends a little more than 3 hours in this planet. When he comes back to his mother ship, he finds he’s been away for 23 years.

What is then the idea? In Interstellar, 1 hour on the planet becomes 7 years out there. And 6,000 years? What would they give out there? 0.36 billion years! Could GR hold the key to thousands of years on Earth being like billions in the rest of the universe?


Russel Humphreys’ cosmology

I refer to the cosmology described here.

Humphreys imagine the Earth is at the center of a huge expanding spherical shell surrounded by water. “Using GR”, he derives the gravitational potential F inside the sphere, at a distance R from the Earth, and finds it behaves like

F = -GM/R

where M is the mass of the shell. This is equation (3) of the article.

Humphreys therefore recovers the kind of gravitational potential well you find around Gargantua, with a time contraction all the more intense than you get close to it.

What is the problem? Humphreys’ gravitational potential is wrong. And trivially wrong. According to the very GR equations Humphreys’ pretends he uses, the gravitational potential inside his sphere is just 0. And because of the Birkhoff theorem, there cannot be any other solution in the kind of spherical symmetry Humphreys uses. The potential inside the sphere is zero, and there is no other way it can be. No gravitational potential well. No time dilatation or contraction whatsoever inside the sphere.

There’s nothing more to it.



[1] See The Science of Interstellar by Nobel Prize Kip Thorne. The reader will also find more technical data on the same topic here.


Consensus. What’s that?

We often hear about scientific “consensus”. The thing seems quite misunderstood, sometimes seemingly considered as a gentleman agreement between researchers tired of getting headaches over a topic, or wanting to impose a conclusion. “Let’s say it’s like this, and that’s it!”.

No, it doesn’t work like that.

As an illustration, let’s see how a consensus was reached… on the sources of the Nile river. We will then make the comparison with the consensus reached on the Big Bang.

The sources of the Nile

The Nile delta has been known for millennia. Not the same for its source [1] which location remained a mystery for almost the same time. Let’s make this long story short [2]:

  • When Alexander the Great saw the Indus river around 325 BC, he thought he had found the source of the Nile. Still in the 6th century, the Byzantine historian Procopius of Caesarea wrote “the Nile flows from India to Egypt…”.
  • Egyptians contemporary of Herodotus saw the source at Aswan.
  • Juba II king of Mauretania (50 BC – 23 AD) thought he had discovered the sources of the Nile in the Atlas Mountains, northwest of Africa.
  • Ptolemy (2nd century) was perhaps the first to near reality by placing the source of the Blue Nile at Lake Tana, and that of the White Nile further south, in some legendary “Mountains of the Moon”.
  • The British explorer John Speke discovered Lake Victoria in 1858 and thought it would make an excellent source. Of course, his colleagues were not satisfied with his testimony only.
  • It was Henry Stanley who confirmed the discovery in 1875 during the expedition where he was to meet Livingstone and ask the famous and so British “Dr. Livingstone, I presume?”.

So was solved the enigma of the source of the Nile, after literally thousands of years of research. Long before satellite pictures, and, interestingly, long before someone navigated it from start to finish, which only happened in 2004 [3]!

The Big Bang

Well for the Big Bang, pretty much the same happened. On the Nile side, we had:

  • Competing hypotheses: India? Aswan? Mountains of the Moon? Atlas Mountains?
  • A discovery, that of Speke, is not enough.
  • Verification.

It would be difficult to imagine explorers of the 6th century complaining,

We’re fed up with this Nile business. Enough of it. Let’s choose a location for the source, and settle the case!

It is obvious that they were going to seek until they’d find it, that competing hypotheses were going to arise, and that the end of the story would come by checking them all.

What about the Big Bang? Ditto, almost,

  • Competing hypotheses: Static universe or not? From Aristotle to Einstein in his 1917 article, the first option had strong supporters. The second, that of a dynamic universe, was mainly introduced by Hubble’s observations in 1929, but precisely…
  • Hubble’s observations didn’t settle the matter [4]. Einstein changed his mind in 1931 [5], but the controversy did not end there.
  • People wanted to check, which is perfectly normal. One check came from the solution of Einstein’s equations found by Friedmann, Lemaître, Robertson and Walker. The cosmic microwave background (CMB), predicted in 1948 and discovered in 1964, impressed many. The relative abundance of light elements did the same.
  • It was towards the end of the 1960s that the consensus arose, mainly the fruit of the discovery of the CMB [6].

Today, nearly all cosmologists think that some 14 billion years ago, the universe went through a very dense and hot phase and that it has been expanding since then. Other checks [7] have come to strengthen the picture which, ultimately, mainly owes its raison d’être to the expansion of the universe. Just rewind the movie.

Whether it be quantum mechanics, general relativity, plate tectonics, anthropogenic global warming or shockwaves in interstellar vacuum, consensus were established the same way. They don’t arise because people are fed up with not knowing, or fear any conclusion. They arise because years of study and checking have left no choice.

One only needs to make sure he/she doesn’t see consensus were there’s not (like on how the universe began – if it ever did).

But that is another story.


[1] Or rather its sources, since we have to distinguish the White Nile from the Blue, but let’s simplify.

[2] For the long version, see for example Terje Oestigaard & Gedef Abawa Firew, The Source of the Blue Nile: Water Rituals and Traditions in the Lake Tana Region, Cambridge Scholars Publishing, 2014.

[3] “National Geographic” produced in 2005 a documentary on this expedition entitled The Longest River.

[4] The main alternative to redshift as indicating receding velocities was Fritz Zwicky’s “tired light”. It has been discarded for many reasons (distant objects would be blurred, shift would depend on the frequency, etc. More here or here).

[5] Harry Nussbaumer, Einstein’s conversion from his static to an expanding universe, European Physics Journal – History, 39, 37-62 (2014).

[6] See for example Helge Kragh, Cosmology and Controversy, Princeton University Press, 1999.

[7] Temperature of the CMB at several epochs, structures of the universe and their distribution, baryonic acoustic oscillations, etc.

A few deniers’ (bad) habits

  1. Pretend there’s still a debate between experts. That there’s no consensus. If proved wrong, pretend consensus doesn’t mean anything anyway.
  2. Pretend the PhDs on your side are top notch, all time world class, scientists. If proved wrong, pretend expertise doesn’t mean anything anyway.
  3. Pretend your alternative theory is about to overcome the status quo, even though in reality, virtually no one knowledgeable cares about it.
  4. Discard any contrary evidences you’re presented. Then claim, “there are no evidences”.
  5. When cornered, never acknowledge. Don’t even wonder why you’re cornered. Just skip to your next argument. Next time you get, serve again the very argument you were cornered with.
  6. When cornered, never acknowledge. Instead, ask another question. That’ll let you deny you’re cornered, as you can argue you won’t pursue the discussion as long as the other doesn’t answer your question.
  7. When cornered, invoke (pseudo) philosophy. Pretend it’s all a matter of “worldview”, “interpretation”, etc. Postmodernism can be useful at times…
  8. Any peer-reviewed paper that seems to go your way, is dead right. The thousands which definitely don’t, are all dead wrong.
  9. Any peer-reviewed paper that seems to go your way… goes your way, even if it doesn’t.
  10. Any evidence that seems to go your way, is true. The thousands or millions of contrary evidences simply don’t exist.
  11. Any PhD who claims what you want to hear, is right. The thousands who disagree are all wrong.
  12. When opposed Wikipedia, ArXiv (you probably don’t know how it works, but don’t ask) or a pop science article, claim these are not serious sources (carefully ignore all the primary sources cited there). If opposed Nature or Science or Princeton, Cambridge, Harvard, Oxford… Presses, claim it’s all corrupted.
  13. Pretend Einstein, or equivalent, is on your side even if nothing supports that claim. When others disagree, tell them they have to prove you wrong.
  14. Find other pseudoscience(s) you can denounce. This will help you look scientific (ex: YEC denouncing geocentrism or flat earth).
  15. Frequently use pseudo-erudite vocabulary like “fallacy”, “strawmen”, “ad-hominem”, “non-sequitur”…  thinking it will help you look scientific (it doesn’t).
  16. Redefine “science” the way it fits your agenda (cite Popper to look erudite).
  17. Pretend you’re ridiculed because you’re the courageous-rebel-thinking-out-of-the-box, forgetting you can perfectly be ridiculed because… you are ridicule.
  18. Pretend what you claim is obvious, even if you have no idea why it should be obvious.
  19. Pretend the opposite views have been refuted many times, like flat earthers pretend globe earth has been refuted many times.
  20. Make any “scientific” claim you want without providing any reference. When asked for, tell others it’s their job to find it.
  21. Don’t try to learn correct science. Just bully it.
  22. Horribly distort correct science. It’ll be easier to criticize.
  23. The inner coherence of your arguments doesn’t matter. Feel free to argue today that fine tuning proves God, then pretend tomorrow that the laws of physics may have changed in the past.
  24. When really cornered, play the conspiracy trump card. It’s impossible to refute, so you’re on safe ground.
  25. When really cornered, play the assumption trump card, even of you don’t know which, or if your alleged assumptions are not assumed at all (of course, when proving your thesis, freely assume anything you wish, how absurd it may be).
  26. Be to science what DDR was to democracy. Butcher what you claim you own.

How do we know it has to be possible to unify General Relativity and Quantum Mechanics?

We often hear about the unification of the two prodigy kids of the last century, namely, General Relativity (GR) and Quantum Mechanics (QM).

But, just why should they absolutely unite?

Couldn’t they eventually play separately, leaving the other alone? Granted, so far this unification-mania has borne much fruit, but hey, Mother Nature could have decreed,

“It’s enough, unification stops there, RG and MQ are the end of the story! Go home everyone!”

Actually, no. Mother Nature hasn’t decided that. And it’s easy to understand. Here is at least one reason for this (see another one here).

Cooking GR

When you derive the equations of GR, the famous Einstein equations, you manage to connect the deformations of space-time to the matter/energy it contains. In the mathematical salad that is being mixed, you have some stuff that describe the distortions of space-time (we call that the metric). And then you have other stuff that describe matter/energy. Once the salad is mixed, you get a mathematical relation between these two kinds of stuff: the equation of General Relativity.

Where’s the pb?

Now let’s see where the problem is: when you describe matter in the salad, you do it in a classical, non quantum, way. Basically, it means that if, for example, you have a proton wandering around, you pretend it’s a point of zero size. But we know that a proton, in the real world, is not a point. It’s not even a ball. It’s more complicated than that. And how do we know? Because of Quantum Mechanics, precisely.

Simply put, GR works “as if” my proton were a point, although it is not. And what happens if we do otherwise? What happens to Einstein equations if, instead of deciding the proton is a point, we let it be what QM tells it really is? Nobody really knows so far. This is precisely the problem of the unification of GR and MQ.

Conclusion, need for unification

We’re already there. Why do GR and QM must be able to merge? Because we know GR “cheats”. GR simplifies the description of matter. As long as space-time doesn’t see the trick, that is, as long as its curvature is much larger than the size of the proton, no problem. In fact, this approximation is almost always fully, abundantly, amply, thoroughly, justified.

Except in extreme circumstances where QM and GR cease to be valid because space-time does see the trick, like… near the Big Bang or in a black hole.

The limits of a theory

There is a concept in physics that is useful to follow the developments of contemporary cosmology, among others: it is the notion of the limits of a theory. Its validity domain.

Fluid mechanics is not valid over too short distances. Newton’s gravitation is not valid in too strong gravitational fields. Newton’s other law, which relates force to acceleration, is not valid when you go too fast. Just what does it mean? Let’s check it on an example.

Kinetic energy

Everyone knows about kinetic energy. A mass M at velocity V carries the kinetic energy,


Imagine an experiment where I measure the kinetic energy of a mass of 1 kg at various velocities. As long as it doesn’t go too fast, the formula above works very well. But as we step on the gas, our formula becomes progressively inaccurate. In fact, the formula above will give the blue curve below, while the experience will give the orange one,


The two curves gradually separate from each other, from about 5.0 × 108 km/h, that is, 500 million km/h. The orange curve goes to infinity when approaching 109 km/h (1 billion km/h), which is nothing else than the speed of light. Einstein’s Special Relativity gives the formula for the orange curve.

Let’s now replot these two curves, but between 0 and 1 million km/h rather than 2 billion. You get that,


“Wait Antoine, you announced two curves and I see only one! Pay back!” Calm down… It just happens that the blue is almost exactly below the orange, so we can’t see it. They are almost superimposed. That’s why for the velocities at stake in our daily life, there is no need for relativity. Even a jet flying at 1 million km/h (Paris-Los Angeles in 32 seconds!), would hardly notice the difference.

Some remarks to conclude,

  • The transition is progressive, yet with a velocity of reference which is the speed of light. The orange curve progressively departs from the blue as we approach the speed of light.
  • There is therefore no particular speed of which can be said “before, it’s blue, after, it’s orange”. It’s progressive. Like a shade of grey that do not go abruptly from black to white, but gradually.
  • Imagine I don’t know the formula for the orange curve. Imagine I’m looking for it. Whatever it be, the fruit of my research must meet a requirement: it must smoothly connect to the blue curve for “small” velocities, that is, much smaller than that of light. Translated into mathematical terms, this “smooth connection” is therefore an acid test for any new scientific theory, since the blue curve at low velocities is consistent with experience.

Implications for cosmology (Big Bang theory)

I talked about cosmology to start with. What does it have to do with this?

According to General Relativity (GR), we come across a singularity with an infinite density when we rewind the movie of the universe.

But… is GR valid all this time? No. Just as the blue curve is only valid for small velocities, GR is only valid for small densities. What does “small” mean now? For the blue curve, “small” meant “much smaller than the speed of light”. For GR, “small density” means “much smaller than the Planck density”, that is, 1087 tons/cm3, or one thousand trillion of trillions of trillions of trillions of trillions of trillions of trillions of tons per cubic centimeter. Phew!

Even if this figure is gigantic, a density that goes to infinity will necessarily end up exceeding it. GR is therefore committing suicide, so to speak. In the movie played backward, as the density approaches that of Planck, GR tells us

“Stoooop! Rewinding further forbidden! I’m no longer valid. I’m no longer trustworthy in these waters”

That’s why the singularity of the Big Bang is not real. GR, that predicts it, is no longer valid at this stage, just as the blue curve tells nonsense for a speed doubling that of light.

In the case of the Big Bang, what is then the equivalent of the orange curve? What scientific theory would it take to know what happens prior to the “Planck wall”? We do not know yet, because we do not know how to marry GR and Quantum Mechanics (QM). But what we do know, is that at small densities, candidates must harmoniously connect with GR on the one hand, and with QM on the other hand, like the orange curve nicely lands on the blue at low speeds.


PS – Fluid mechanics and Newton’s gravitation

I mentioned at the beginning fluid mechanics, which is no longer valid for short distances. “Short” here means “smaller than the distance between two atoms, or molecules, of my fluid”. When fluid mechanics (without viscosity [1]) predicts something on this length scale, watch out! it’s probably talking nonsense.

What about Newton’s gravitation, also mentioned at the beginning? It is no longer valid in “strong” gravitational fields. “Strong” here means “of the order of the gravitational field felt when one approaches a mass at a distance of its Schwarzschild radius”. The Schwarzschild radius of the earth is 1 centimeter. That of the sun, 3 kilometers. Since these two are much larger than their Schwarzschild radius, we obviously cannot approach them so closely. However, as Newton’s law only gradually departs from reality as we approach the sun, very precise measurements have made it possible to detect small deviations from the Newtonian predictions for Mercury, the closest planet to the sun.


[1] For the expert, viscosity only rescues fluid equations for weak shocks. The problem comes back in the strong shock limit. See Zel’dovich & Raizer, Ch. 7.

I’d say math exist

Memory plays tricks, but I think I remember this moment quite well. It was 2 years after my Baccalauréat. In the midst of a massive ingestion of math and physics in “prépa”, I could not help thinking about it all after classes. My thoughts that night were on the laws governing electric and magnetic fields. The so-called Maxwell’s equations. They involve a mathematical arsenal called “partial derivatives”, discovered by Newton and Leibniz in the seventeenth century.

Lost in my Maxwellian dreams, I started to wonder: “How is it that abstract mathematical tools developed over millennia are suddenly perfectly adapted to describe something real?”

I soon learned that I was far from being the first to wonder about this. Had not Galileo written centuries ago that “the book of nature is written in the language of mathematics”?

Albert Einstein also asked [1]:

“How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”

Finally, Eugène Wigner, physics Nobel in 1963, wrote in 1960 a text which title is as famous as explicit: The Unreasonable Effectiveness of Mathematics in the Natural Sciences.


A few thoughts later, an idea dawned on me: math exist. They are not invented. They are discovered. And here also, I realized many had came to the same conclusion. Cédric Villani for example Fields Medalist 2010 [2]:

“I am among those who believe that there is a pre-existing harmony… [it is] an unexplained intuition; a personal and quasi-religious conviction.”

Alain Connes, Fields Medalist 1982, is also worth quoting here [3]:

“Two extreme viewpoints are opposed in relation to mathematical activity. The first, to which I completely subscribe, is of Platonic inspiration: it postulates that there exists a mathematical reality, raw, primitive, which predates its discovery. A world which exploration requires the creation of tools, as it was necessary to invent vessels to cross the oceans. The second viewpoint is the one of the formalists; they deny any preexistence to mathematics, believing that they are a formal game, based on axioms and logical deductions, thus a pure human creation.”

Then he adds,

“This viewpoint seems more natural to the non-mathematician, who refuses to postulate an unknown world of which he has no perception. People understand that mathematics is a language, but not that it is a reality external to the human spirit. The great discoveries of the twentieth century, especially the works of Gödel, have shown that the formalist viewpoint is not tenable. Whatever the exploratory medium, the formal system used, there will always be mathematical truths that will elude it, and mathematical reality cannot be reduced to the logical consequences of a formal system.”

As Roger Penrose writes about math in general and the Mandelbrot set in particular [4],

“It is as though human thought is, instead, being guided towards some external truth – a truth which has a reality of its own…. The Mandelbrot set is not an invention of the human mind: it was a discovery. Like Mount Everest, the Mandelbrot set is just there.”

The Mandelbrot set, the Bernoulli numbers, the googolplex-th decimal of Pi [5], the non-trivial zeros of the Riemann zeta function, the Lorenz attractor… the list is endless, infinite indeed. All these things exist.

Could something else than math, exist? Seems Einstein, again, had some beautiful insights with respect to the music of Mozart [6],

“Mozart’s music is so pure that it seemed to have been ever-present in the universe, waiting to be discovered by the master.”

Einstein, Connes, Villani, Penrose… I was finally in good company. This “personal and quasi-religious conviction,” as Villani says, acquainted me with the possibility that something non-material might exist. It was probably, with the reading of Hermann Hesse, the beginning of my spiritual journey.


Further reading: I really recommend this conversation between the Platonicist Alain Connes and the neuroscientist and Formalist Jean-Pierre Changeux



[1] Einstein, Geometry and Experience, 1921.

[2] Pierre Cartier, Jean Dhombres, Gerhard Heinzmann, Cédric Villani, Mathématiques en liberté, La Ville Brûle, 2012, page 60.

[3] Alain Connes interviewed by Sylvestre Huet, Libération, december 1, 2001.

[4] Roger Penrore, The Emperor’s New Mind, Chapter 3 on Mathematics and Reality.

[5] A googolplex is 1 followed by 10100 zeroes. We’ll probabbly never know what is this digit, but it exists.


Climate change in 6 questions

Here are some briefs answers to 6 frequently asked questions on the topic. I also think that in the following order, these answers contribute to explain how we know there’s a climate change going on, and how we know it comes from us.

  1. How can we talk about the climate in 100 years if we don’t know if it will rain in 20 days?
  2. How do we know there is a climate change?
  3. How do we know it’s not the Sun?
  4. How do we know it comes from an increase of greenhouse gases (GHG)?
  5. How do we know these GHGs come from human activity?
  6. Do experts agree?

I will try to answer them as briefly as possible. Let’s go.

For Spanish speakers, my course on energy/climate is here.

How can we talk about the climate in 100 years…?

A very good question indeed. To answer it, let me ask two more questions:

  1. Will it be warmer in Madrid in July 2030 than in January 2030?
  2. Will it rain in Madrid on June 20, 2030?

I think anyone would answer “yes” to (1), and “no idea” to (2). How can we achieve certainty for (1) while it’s impossible for (2)?

When we think of (1) we think about what should happen in July and January. And what should happen through one year is mainly related to the height of the Sun in the sky. The higher the hotter. But when we think of (2) we think about what will actually happen on that day, and here we find it impossible to answer more than a week or two in advance.

The graph below shows the daily temperature in Lausanne Switzerland, in 2017. It is obvious that the rather chaotic yellow line runs around a deeper tendency, shown by the blue line.

Climate Weather 2
Daily temperature in Lausanne Switzerland, in 2017 (Wolfram|Alpha Knowledgebase)

The blue line is about the climate. The yellow line is about the weather. Likewise, question (1) is about the climate, (2) is about the weather. As Mike Hulme puts it [1],

“Climate is what you expect, weather is what you get”

It is perfectly possible to forecast the climate. For this reason, travel guide books can inform about the average temperature in Madrid throughout the year, without the need for a crystal ball.

By contrast, predicting the weather well in advance is impossible. For this reason, unfortunate tourists may get rain when visiting Madrid in June, despite their travel guide book forecasting little of it.

How do we know there is a climate change?

The most well-known indicator is the global temperature (see the featured image above). It is an average of the temperatures over the surface of the planet. Global temperature has been rising for about a century. We have gained about 1°C since the XIX century (this figure of 1°C will play an important role in answering the next questions). However, it should be noted that it is not the only indicator. Let’s look at 6 more, see for example NASA or the UK MetOffice, all pointing to a warm-up.

Let’s start with some downward indicators:

  1. The extent of Arctic sea ice is shrinking.
  2. The volume of Greenland ice is shrinking.
  3. The volume of Antarctica ice is shrinking.
  4. The volume of land glaciers is shrinking.

Let’s now continue with rising indicators,

  1. The oceans’ heat content is rising.
  2. Global temperature is rising.
  3. Sea level is rising.

We then come to a total of 7 indicators, all pointing to the same direction: a warming. One can find a few more on the MetOffice web for example. Notably, the impact of global warming on fauna and flora is extensively studied, showing even more signs of a change.

Even before we know their origin, these observations lead us to the conclusion that global warming is occurring. Let’s see why.

How do we know it’s not the Sun?

Our planet is getting warmer. Why?

What does our climate depend on? It depends on the amount of solar energy that comes from the Sun, and of the composition of the atmosphere. Similarly, the temperature in my bed depends on the temperature in my room (the Sun), and of the numbers of blankets I have (the atmosphere). If I’m getting warmer under my blanket, it can only be for 2 reasons: it’s warmer in my bedroom or I have an extra blanket.

Could the Sun be responsible for the warming? It is obviously the first suspect. Does it have cycles that could change the climate? Of course. The last ice ages were the fruit of the so-called Milankovitch cycles. Yet, while they prompted ice ages, they cannot be held responsible for the current change. Why? Because the shortest of these cycles is 20,000 years long; far too long to explain a warming which has been going on for about a century.

So if the Milankovitch cycles are too long, are there shorter natural cycles? Yes. The Sun has a 11 years cycle. But it cannot be responsible either for at least 3 reasons:

  1. It is too short. We’re looking for a warming agent over a time scale of about one century. Here, it’s up, down, up, down, etc. every 11 years. Not an uuuuup lasting 100 years.
  2. Its upper value doesn’t even show an increase over the last decades, rather the contrary.
  3. Finally, a very simple calculation shows that this cycle can prompt variations of the global temperature of only 0.1°C [2]. We observe 10 times more (see previous paragraph).

It’s not the Sun.

How do we know it comes from an increase in greenhouse gases?

If it’s not the Sun, then it must be the atmosphere. No choice. It acts like a blanket which thickness depends on its composition. The most effective gases in this respect, the famous “greenhouse gases” are, in order of importance, water vapor (H20), carbon dioxide (CO2), and methane (CH4) [3]. Without them, the average temperature of the planet would be around -15°C  [4].

What about water vapor? It has something special. The amount of water vapor in the atmosphere depends only on the temperature of the atmosphere. What happens if there is too much? It just rains. This has a very interesting consequence: water vapor alone cannot be the cause of the warming. If there is more up there (and there is), that can only be the result of warming, not the cause. Something else must be warming the atmosphere.

What can that “something else” be? Only two suspects remain: carbon dioxide and methane. It has to be one of the two, or both. Let’s check it out. We can begin by plotting the concentration of these gases in the atmosphere over the last 1000 years:


As can be seen, these gases start rising at the beginning of the XIX century, with an acceleration in the XX century. Today, the CO2 concentration has reached 400+ parts per million (ppm), representing an increase of 42% over the pre-industrial era. As for methane, it has more than doubled. We have our heating factors, with the expected time scale. We already knew it from the previous elimination of suspects, and now we’re just checking. Our atmospheric blanket has been thickening for a century or two. Let’s keep checking: what is the increase in temperature that could be expected from such increases in these gases? Another simple calculation gives about 1°C, that is, what is observed [5].

Current warming comes from an atmospheric GHG increase.

How do we know these GHGs come from human activity?

Also a good question. Where do these CO2 and CH4 rises come from? From the volcanoes? They are often suspected. But we can exculpate them for at least 3 reasons:

  1. We have data for atmospheric CO2 and CH4 over almost a million years back and they never reached current levels. If volcanoes had been recently doing something they didn’t in a million years, we would notice.
    By the way, this point holds for any natural agent supposedly responsible for the current GHG rise: it should be doing something now that it hasn’t been doing in a million years.
  2. As shown in the figure above, CO2 and CH4 are rising steadily. Volcanoes would have to be very well in synch to cause such a gradual increase.
  3. Volcanoes emit about 0.3 Giga-tons (Gt) of CO2 per year. We emit 30 Gt, that is, 100 times more.

So where do these GHGs come from? The figure above gives us a clue: the rise began with the industrial revolution, which consisted in burning coal.

Could these GHGs come from human activity? To check this hypothesis, we can consider the amount of GHG emitted by humans every year since 1750, and reconstruct the evolution of the atmospheric concentration in CO2 and CH4, accounting only for human activity. The figure below is the result of this simple calculation for CO2.CO2_computedI computed the blue curve starting with the concentration known in 1750, then adding each year what was emitted [6]. The red curve comes from observations. Both fit remarkably. The difference between red and blue comes from deforestation.

There is no doubt. The rise of GHGs in the atmosphere has its origin in the massive use of fossil fuels. This can be checked in other ways [7], and all the tests are conclusive. These GHGs are “ours”.

Do climate scientists agree?

There is a climate change. It is due to human activity. And those who contribute to the progress of knowledge in this area, what do they say? What do experts say on the subject? They agree. Several surveys have been conducted in recent years. They concluded that more than 97% of experts agree.

I personally attended the American Geophysical Union Fall Meeting in 2015 and 2018. With more than 20,000 participants, this conference is the largest in the world for this field of knowledge. There, climate scientists present their latest research.

  • How many presentations questioned the existence of a climate change? Zero.
  • How many presentations questioned the role of human activity as the engine of change? Zero.

This can be checked browsing the scientific program of the last AGU 2018 for example.

It should be noted to conclude that what is happening is not a surprise at all. Almost two centuries ago, in 1824, Joseph Fourier already explained how an atmosphere warms its planet. In 1859, John Tyndall measured how some gases absorb radiation and concluded that without water vapour, the earth would be “held fast in the iron grip of frost”. In 1896, Svante Arrhenius calculated, by hand of course, the temperature increase that would come from a doubling of CO2 in the atmosphere. Applying his formula to the recent increase of 42%, one finds a warming of + 3oC. Not bad for someone who ignored the details of the interaction between the molecules of the atmosphere and the radiation sent from earth to space [8].

The current warming is not a surprise for the scientific community. It was expected. It is happening (it didn’t stop in 1998), and it comes from us.


[1] M. Hulme, Why We Disagree About Climate Change (Cambridge University Press, Cambridge, 2009), p. 1.

[2] See A. Bret, The Energy-Climate Continuum (Springer, 2014), p. 47.

[3] There are more, but these 3 are the most important.

[4] See Kendal McGuffie & Ann Henderson-Sellers, A Climate Modelling Primer (Wiley, 2005), ch. 3.

[5] The calculation can be done using equation (4.9) of my book, and this reference, which allows to evaluate the variation of parameter epsilon under a CO2 increase of 40%.

[6] About half of the emitted COgoes into the oceans (see here, p. 467).

[7] An example: if the excess CO2 comes from combustion, then the amount of oxygen in the atmosphere should go down. The observations confirm this perfectly (I designed an exam based on this in 2011). More conclusive evidences can be drawn from Carbon 13 or 14 atmospheric concentrations.

[8] He didn’t know about quantum mechanics.