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.

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.


Peer-review is selective, but maybe not the way you think

Peer-review journals are the forum where professional scientists publish their research. That a journal is “peer-reviewed” does not mean everything it publishes is right. It simply means everything it publishes has been proofread by 1 or more knowledgeable people on the topic the paper deals with, before publication.

There are literally thousands of peer-reviewed journals, attached to all fields of human knowledge. What I’m about to share applies to the journals I’ve been dealing with personally [1]. It certainly applies to more, but I prefer talking only of what I’ve personally experienced.


From time to time, some complain about the peer-review system being discriminatory, for example on religious ground. So just in case, I want to make clear the following points,

  • Peer-review doesn’t care about your religion. Nowhere in the submission process, nor at any later stage, is any question asked about your religion. Nowhere.
  • Peer-review doesn’t care about your diploma or your position. You don’t have to be a Professor or a PhD to publish an article. I wasn’t a PhD when I published my first 5 papers.
  • Peer-review doesn’t care about your affiliation. You don’t have to be on a university payroll. Granted, you will be asked for an affiliation, but you can perfectly fill it with your personal address, as a friend of mine once did when writing an article between 2 contracts.
  • Peer-review doesn’t even care about you being a human! There’s a famous example of a physicist choosing his cat as a co-author for an article (he realized before submission that he was using “us”, “our” and “we” throughout the paper, while being single author. Instead of rewriting everything, he made up a second author). Full story here.

So if peer-review doesn’t care about your religion, your diploma, your position, and even your specie, just what does it care about?

Here’s what I’ve seen after having published more than 100 peer-review articles, be a referee even more times, and served 8 years as an Associate Editor [1] for a Cambridge Press peer-review journal:

On the long run, and even the medium one, peer-review eventually cares about your work teaching something new, and not being grossly inconsistent with logic, experiments and observations. That’s it.

Just try.


[1] Here they are:

  • Annales Geophysicae
  • Astronomy & Astrophysics
  • Astrophysical Journal
  • Astrophysical Journal Letters
  • Europhysics Letters
  • Fusion Engineering and Design
  • Fusion Technology
  • Journal of Plasma Physics
  • Laser and Particles Beams
  • Monthly Notices of the Royal Astronomical Society
  • Nature
  • Nature Scientific Reports
  • New Journal of Physics
  • Nuclear Instruments and Methods In Physics Research A, and B
  • Physica Scripta
  • Physical Review E
  • Physical Review Letters
  • Physics Letters A
  • Physics of Plasmas
  • Plasma Physics and Controlled Fusion
  • Reports on Progress in Physics
  • Science

Just Google the title to find their webpage and check the submission process.

[2] The Editors and the Associate Editors are the ones responsible for choosing the referees and eventually accepting the paper, rejecting it, or asking for revisions. As an Associate Editor, I don’t have to get anybody’s approval before accepting a paper.

Sure Einstein is on your side?

Almost everyone wants to have Albert Einstein on his/her side, which is quite understandable. And the science/faith debate is no exception. Quotes abound, not always authentic and seemingly contradictory, fired by each camp at the other. Of course, each side seems oblivious to the quotes opposing its views, which allows the “ping-pong quote” to keep on forever.

A book published by Princeton Press in 2010 may help. The Ultimate Quotable Einstein is the fourth edition of a collection of all the quotes Princeton’ people could gather on a variety of topics. Einstein stayed at the Princeton’s “Institute for Advanced Studies” from 1933 to his death in 1955, so it’s a good place to look for 1st or 2nd hand witnesses. The book has been compiled by Alice Calaprice, a German born expert on Einstein who’s been living in Princeton since the 1970 [1], when she started to work on the topic.

What do we find as “God quotes”? Here are few showing what Einstein was and wasn’t. It seems he doesn’t easily fit in any camp. I reproduce the references as they appear in the book. Some quotes are double edge, so I mention them twice. There are more quotes, but I think these capture the bottom lines.

Einstein was not a theist in the Abrahamic sense

“I cannot conceive of a personal God who would directly influence the actions of individuals”.

To M. Schayer, August 1, 1927. Quoted in Dukas and Hoffmann, Albert Einstein, the Human Side, 66, and in Einstein’s New York Times obituary, April 19, 1955. Einstein Archives 48-380.

“I [do not believe] in a God who concerns himself with the fate and the doings of mankind”.

In answer to Rabbi Harbert S. Goldstein’s telegram, published in the New York Times, April 25, 1929.

“I came to a deep religiosity, which, however, found an abrupt ending at the age of 12. Through the reading of popular scientifcs books I soon reached the conviction that much in the stories of the Bible could not be true”.

Writen in 1946 for “Autobiographical Notes”, 3-5.

“The idea of a personal God is quite alien to me and seems even naïve”.

To Beatrice Frohlich, December 17, 1952. Einstein Archives, 59-797.

Einstein was not an atheist

“I am not an atheist. I do not know if I can define myself as a pantheist. The problem involved is too vast for our limited minds.”

In answer to the question “Do you believe in God?” in an interview with G.S. Vierek “What life means to Einstein”, Saturday Evening Post. October 26, 1929. Reprinted in Viereck, Glimpse of the Great, 447.

“In view of such harmony in the cosmos which I, with my limited human mind, am able to recognize, there are yet people who say there is not God. But what makes me really angry is that they quote me for support of such views.”

Said to German anti-Nazi diplomat and author Hubertus zu Löwenstein around 1941. Quoted in his book, Towards the Further Shore (London, 1968), 156.

What Einstein said he was

“My comprehension of God comes from the deeply felt conviction of a superior intelligence that reveals itself in the knowable world. In common terms, one can describe it as “pantheistic” (Spinoza)”

In answer to the question “What is your understanding of God?”, December 14, 1922, posed by interviewers for the Japanese magazine Kaizo 5, no. 2 (1923), 197. Reprinted in Ideas and Opinions, 261-262.

“My religiosity consists of a humble admiration of the infinitely superior spirit that reveals itself in the little that we can comprehend of the knowable world.”

To M. Schayer, August 1, 1927. Quoted in Dukas and Hoffmann, Albert Einstein, the Human Side, 66, and in Einstein’s New York Times obituary, April 19, 1955. Einstein Archives 48-380.

“I believe in Spinoza’s God, who reveals himself in the lawful harmony of the world”.

In answer to Rabbi Harbert S. Goldstein’s telegram, published in the New York Times, April 25, 1929.

“I do not know if I can define myself as a pantheist. The problem involved is too vast for our limited minds.”

In answer to the question “Do you believe in God?” in an interview with G.S. Vierek “What life means to Einstein”, Saturday Evening Post. October 26, 1929, reprinted in Viereck, Glimpse of the Great, 447.

“My position concerning God is that of an agnostic”.

To M. Berkowitz, October 25, 1950. Einstein archives 59-215.


If you’re a Christian, like me, and want to enroll Einstein, you need to voluntarily forget he claimed “The idea of a personal God is quite alien to me and seems even naïve”, for example.

If you’re an atheist and want to enroll Einstein, you need to voluntarily forget he claimed “What makes me really angry is that they quote me for support of such views”, for example.

Unless you’re sort of cautious pantheist, not sure Einstein is on your side.


[1] Her husband, Frank Calaprice, is a physics faculty at Princeton.

The Big Bang raises many questions, and it’s perfectly normal

Discussions on the Big Bang often end up with the enumeration of the questions it raises: “How do you explain the matter/antimatter asymmetry  ? And the horizon problem? And the flatness problem? And the monopole problem? Huh? The Big Bang is a fraud!”

I fully understand how such objections can arise. And I would like to explain why they are unfounded.


Let’s first remember that as already explained on this blog, the Big Bang theory is not about the beginning of the universe (assuming the expression has any meaning). That’s why NASA cautiously defines it this way:

“12 to 14 billion years ago, the portion of the universe we can see today was only a few millimeters across. It has since expanded from this hot dense state into the vast and much cooler cosmos we currently inhabit”

The Big Bang does not tell how the universe began. It’s not in the beginning business. It’s just about a state the universe went through some billion years ago. And we have scores of evidences it did [0]. What came before this state is not accessible to us because we don’t know the physics that applies there [1].

And it is precisely this state that raises questions… considering the physics we know. Is this surprising? Not at all. Why? Precisely because this state comes from a previous era, governed by a physics we do not know.


To illustrate this point, let’s go back in time a little more than 100 years. We are in 1913. We are well aware of Maxwell’s equations, Newton’s laws, and Special Relativity (not yet with General Relativity, the one of gravitation). Rutherford has just done an experiment tending to show that an atom is a positive nucleus with some electrons turning around. And there, disaster, according to the physics known at that time, the atom cannot exist! Why? Because the electrons should spiral around the nucleus and eventually crash on it. Indeed, according to Maxwell’s equations, a rotating electron loses energy by emitting light [2]. Niels Bohr will show the way to the solution, Quantum Mechanics, in a famous 1913 article [3]. He describes very well the dilemma of the time,

“The inadequacy of the classical electrodynamics in accounting for the properties of atoms from an atom-model as Rutherford’s, will appear very clearly if we consider a simple system consisting of a positively charged nucleus of very small dimensions and an electron describing closed orbits around it.

[If we] take the effect of the energy radiation into account… the electron will approach the nucleus describing orbits of smaller and smaller dimensions… It is obvious that the behaviour of such a system will be very different from that of an atomic system occurring in nature.”

According to the physics known in 1913, atoms cannot exist. The 40-year-old Mendeleev’s periodic table cannot exist. Molecules neither. And we neither.

The universe of the Big Bang is a problem for you? Well, 100 years ago, this was our current universe which was a problem.

Such are the walls we bang our heads against when we lack fundamental laws. We come across things that are really there, but which, according to our known but incomplete laws, should not exist.

The Big Bang universe is the fruit of an era which physics is unknown to us. It is therefore perfectly normal that it has aspects the physics we know cannot explain. It’s the opposite that would be amazing.


[0] See for example here and here.

[1] Which does not mean people like Steven Hawking, Alan Guth, Neil Turok, Paul Steinhardt, Martin Bojowald, Gabriele Venezianio, etc., can’t speculate with talent.

[2] This is why it is so difficult to accelerate particles in the LHC circular accelerator at CERN.

[3] A free version is available here.

Fine Tuning Argument or Young Universe, you have to choose!

The Fine-Tuning Argument (FTA) rightly states that given the laws of physics we know, you cannot even slightly change the constants within them without getting a universe improper for life. Contrary to the claims of some atheists, it is real. Cambridge Press recently published a great book on this topic. For those looking for more technical sources, here’s an article about it in the prestigious Review of Modern Physics (I give a link to the free version of the paper). Not really creationists sources…

As an argument for the existence of God, its usage is far from being restricted to creationist circles, as it can be found in the writings of people like Rodney Holder or Tim Keller.

In case you like it, here are a few consequences.

Mainstream scientists did a good job

For the FTA to hold, the laws of nature we know must be correct. If not, it makes no sense to claim our world could not sustain life if these laws were changed. Therefore, Maxwell, Planck, Einstein, Bohr, Schrodinger, Heisenberg, Dirac, Feynman, Yukawa, Salam, Weinberg and on and on, together with the thousands involved in refining theories and/or performing experiments, did a good job. They found the good laws. Besides, their findings were published in peer-review literature (check here), which may not be so corrupted after all.


The FTA requires the laws of nature did not change in the past. For if they changed and we’re still there, there’s no fine tuning at all. It is therefore surprising to see how young earth creationists use the FTA on the one hand, while claiming on the other hand that the speed of light, for example, could have changed in the past. The FTA implies indeed that if the speed of light had varied, we would not be here to talk about it. It the laws of nature and the constants within them changed in the past while we’re still here to comment on them, it means the tuning is so loose that you can do anything you want and still obtain a universe that works very well.

The universe is more than 6,000 years old

If General Relativity never changed, it means the expansion we currently observed started some 13.8 billion years ago. If Maxwell’s equations never changed, it means the speed of light was always the same in every possible direction, so that the light coming from stars 20,000 light years away took 20,000 years to come to us.

What about the distances measurements? We now have millions of stars measured farther than 6,000 light years by the Gaia satellite, through a purely geometrical method (parallax). So yes, they are really that far.

Fine Tuning Argument or young universe, you have to choose!


No, global warming did not stop in 1998

“The world hasn’t warmed since 1998”: so goes one of the many zombie arguments (dead but still walking) haunting the so-called debate on global warming.

Here is a series of graphs, from NASA for the most part, where I spotted the year 1998 (sometimes 2002) by a red line. Similar graphs can be found, for example, on the website of the UK MetOffice.

A picture is worth a thousand words, so let’s see if global warming stopped in 1998.

Has the Arctic sea ice stopped shrinking since 1998? No.

Diapositiva1And the mass of the Antarctic ice sheet, has it been stable since 1998? Niet.

Diapositiva2And the Greenland ice sheet, no losses since 1998? Ben non.

Diapositiva3And the volume of the world glaciers (Alaska, Alps, Himalayas …), flat encephalogram since 1998? Nein.


What about the oceans heat content? Nothing since 1998? Niente (source).

And the global temperature? Stable since 1998? Que dalle.

Diapositiva6The data speaks for itself. All indicators are on the same track since 1998. Warming keeps on.

So, whence this zombie argument? Probably because the 1998 “El Niño” was quite strong, producing a year warmer than its neighbors.

Short term natural variability can veil deeper trends for a while, which is why it takes a step back to assess “climate”. April 4th 2017 in Lausanne, Switzerland, was much hotter than the following days [2], as shown on the graph below (this place and date have nothing special. I found similar patterns in Madrid, Paris, Nice, etc). Were our Helvetian friends entitled to decree that the earth stopped revolving the sun, paralyzing the cycle of the seasons? Of course not.

Daily temperature in Lausanne in 2017. Source.

As it appears, the two ingredients of the “1998 argument” are:

  1. Focus only on the few years of the global temperature curve following 1998, carefully forgetting the overall trend. Show for example, or pretend to see, only the orange part of the overall temperature curve below (it’s exactly the same as the one above)
  2. Forget all other indicators of global warming.

The amnesia of the “1998 argument” designers is remarkable. Unfortunately, their intellectual integrity is not.


[1] Cheng and co-authors (CHEN), Pacific Marine Environmental Laboratory (PMEL), Meteorological Research Institute (MRI), National Centers for Environmental Information (NCEI), and Atmospheric Potential Oxygen (APO).

[2] One had to wait for more than a month, May 15, to find a warmer day.

Why we do not know whether the Big Bang was the beginning of the universe, or not

“12 to 14 billion years ago, the portion of the universe we can see today was only a few millimeters across. It has since expanded from this hot dense state into the vast and much cooler cosmos we currently inhabit”

This is how NASA defines de Big Bang. A hot and dense state the universe went through long ago, rather than a beginning.

Why can’t we tell anything so far about the beginning (if any)? Because the laws we know break down before the Big Bang, this hot and dense state. Let’s see this.


Warm-up: Laws of nature have their limit

Newton’s law of motion (F=ma) is OK as long as you don’t go “too fast”.  What does “too fast” mean here? It means slower than the speed of light. So as long as you want to compute what happens to your car, this plane or this train, no problem, Newton is good. High speed trains in Spain run a best at 0.000028% of the speed of light. So yes, it’s slower.

But when you play with things approaching the speed of light, Newton progressively gets it wrong. In the equation “F=ma”, Special Relativity multiplies the mass “m” by a term which is 1 for small velocities, but progressively goes to infinity as you approach c (“c” is the symbol for the speed of light). No wonder its changes the math.

We know this thanks to Einstein’s theory of Special Relativity, and to the zillions of experiments which proved it right since 1905. In plasma physics for example, my field of research, there’s no way you can understand nowadays intense laser-plasma experiments, without Special Relativity.


Newton’s law of gravity also has allergies. It’s when the gravitational field becomes “too strong”. It wants it “low”. Here, “low” means you’re much farther from the central mass than its “Schwarzschild radius”. Important detail: this Schwarzschild radius is proportional to the central mass. It grows with that mass.

This radius is usually so small that it fits way inside the mass itself. For example, the Schwarzschild radius of the Sun is only 3 km. But if you’re close enough to the Sun, like Mercury, you can detect tiny, tiny, deviations from Newton’s law of gravitation. Einstein’s “General Relativity” (GR) solved this.

The bottom line? Every physical theory we know has its limits. Newton doesn’t like too fast a motion, or too close to the Sun. Maxwell’s equations also have their limits, etc. And GR Relativity, does it have limits? Yes. A little Thought experiment shows it. Here it goes.


General Relativity has its limit also

Take a mass M with the electric charge of a proton. Put an electron around. Quantum Mechanics (QM) tells the electron will settle from the mass M at a distance equal to the so-called “Bohr radius”. Then it can jump between energy levels and all that, but the Bohr radius is the typical distance it will orbit from the central mass M.

The Bohr radius does not depend on the central mass M. Only on its electric charge.

Now, increase the central mass. A lot. If M is an everyday proton, its Schwarzschild radius is so incredibly smaller than the Bohr radius that no one cares about gravity. But since the Schwarzschild radius grows with M and the Bohr radius does not, the Schwarzschild radius must eventually reach the Bohr radius, for a large enough M (see figure below).

Clearly, squeezing such a mass inside its Bohr or Schwarzschild radius implies an immense density. But in principle, it’s inescapable. As you push up density, both radii will eventually merge.


Rs and a0

For a large enough central mass M, the Schwarzschild radius must catch up with the Bohr radius. The left figure is absolutely not to scale.


Now, for such a huge mass, what do QM and GR say? The Bohr radius was computed forgetting about gravity. And the Schwarzschild was computed forgetting about QM. But now that both radii are equal, we can no longer be so forgetful. How should we then modify QM and GR to describe the motion of the electrons?

No one knows.

GR is no longer valid when QM effects must be accounted for, and vice versa. Like Newton’s law of motion is no longer valid when you approach the speed of light. Like Newton’s law of gravity is no longer valid when you’re too close to the Sun.

But while Einstein found how to extend Newton if you go to fast, or you’re too close to your sun, we still don’t know how to extend GR when QM has a word.

In case you’re familiar with the double slit experiment in QM, here’s another thought experiment which shows the same: GR has its limit, which we could write “GR+QM=?”.

Now we can talk about the Big Bang.


What does it have to do with the Big Bang?

I won’t elaborate too much on the Big Bang here. Let me just remind that the idea was born with the observation of the expansion of the universe. That some have tried to interpret these observations otherwise, without success. And that such observations are perfectly in line with GR.

Since the universe is expanding today, we just have to rewind the movie to find any 2 points of it must have been closer to each other in the past. That’s precisely what GR tells us. In addition, GR provides the mathematical description of how this distance changed with time (see the famous “FLRW metric”).

It just happens that at time t=0, the distance between any 2 points goes to 0. This is called the “Big Bang singularity”. So the question comes: is it physical? In other words, can we trust GR it really happened, like we trust GR when our GPS tells we’re or there?

No. The reason for this is simple. As we approach t=0, the universe squeezes matter in an ever-decreasing volume. So the density goes up, together with the temperature. Not only they go up, but they mathematically go up to infinity at the singularity. Now, if the density goes to infinity, sooner or later you must reach a point where our thought experiment describe above applies. You must reach a point where GR and QM have to work together. Where GR can no longer ignore QM effects. That is, when GR fails.

There’s no way around. The FLRW metric fails before it reaches t=0. We cannot trust it down to t=0. GR alone cannot tell whether the BB singularity really happened, or not. It becomes blind before.


Any way out?

To resolve the singularity, that is, to know what really happened instead of these mathematical infinites at t=0, we need to marry GR with QM. Many bright people have been working on this for decades (Einstein included), so far without success, probably in part because it is extremely difficult to make experiments or observations that could help discriminate between various options.

The good old days when you could test GR with Mercury’s orbit and QM in your kitchen, are gone. It took billions of dollars to test de Standard Model and to find the Higgs boson at CERN, and still, the accelerator they used for that is way too small to test any proposal of GR/QM unification.

So there are candidates out there, like String Theory or Loop Quantum Gravity, all of them untested, be it through observation or experiment. Interestingly, both String theory and Loop Quantum Gravity could give a “Big Bounce”.  Other kinds of “bounce cosmology” are also proposed. Some models feature a past eternal universe, like Turok and  Steinhardt’s endless universe, or  Penrose’s conformal cyclic cosmology. Stephen Hawking also had a proposal, this one with a real beginning. But again, nothing certain, for nothing successfully tested like GR or QM. A review (jan 2017) of all the candidates currently out there, nicely titled “What We (Don’t) Know About the Beginning of the Universe”,  is available here.

One last word about the “BGV theorem“, frequently cited in this context. It is classical, which means it does not account for QM. Just GR here. Its conclusions are therefore very useful, but we know they do not describe the real world (it’s always useful to know the behavior of a model, even if you know it does not describe the real world). That’s what Sean Carroll tries to explain to William Lane Craig around min 58 of this debate. He even shows the picture below, where Alan Guth, the “G” of BGV, writes on his laptop screen “I suspect the universe didn’t have a beginning. It’s very likely eternal, but nobody knows“,


We may close further this case with this text from Avi Loeb, who teaches cosmology at Harvard, and Paul Steinhard who does the same thing at Princeton. Toward the end, we find this sentence,

“Although most cosmologists assume a bang, there is currently no evidence—zero—to say whether the event that occurred 13.7 billion years ago was a bang or a bounce”

Finally, those who worry about entropy can rest assure that Alan Guth, Avi Loeb, Neil Turok or Paul Steinhard, to name a few, also know about it and for example, read this.

The current scientific answer to the question “did the universe had a beginning?” is therefore simple, and for simple reasons.

Current science simply doesn’t know.