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.
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 bluecurve below, while the experience will give the orangeone,
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’sgravitation
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.
Footnotes
[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.
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?”
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.”
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
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.
How can we talk about the climate in 100 years if we don’t know if it will rain in 20 days?
How do we know there is a climate change?
How do we know it’s not the Sun?
How do we know it comes from an increase of greenhouse gases (GHG)?
How do we know these GHGs come from human activity?
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:
Will it be warmer in Madrid in July 2030 than in January 2030?
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.
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”
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:
The extent of Arctic sea ice is shrinking.
The volume of Greenland ice is shrinking.
The volume of Antarctica ice is shrinking.
The volume of land glaciers is shrinking.
Let’s now continue with rising indicators,
The oceans’ heat content is rising.
Global temperature is rising.
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:
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.
Its upper value doesn’t even show an increase over the last decades, rather the contrary.
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:
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.
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.
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.I 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.
[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 CO2 goes 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.
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.
Footnotes
[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.
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.
Footnotes
[1] Her husband, Frank Calaprice, is a physics faculty at Princeton.
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.
[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.
I computed the blue curve starting with the concentration known in 1750, then adding each year what was emitted [6]. The red curve comes from 
