Trying to Shoot Down Cosmic Fine-Tuning, She Fires Only Blanks

There exist numerous cases of what look like very strong fine-tuning in our universe. Both fundamental constants and natural laws are arranged in a way that allows for us to exist. It seems that the probability of all of these favorable conditions existing by chance is incredibly low. It has been argued that the probability of you existing in a universe as fine-tuned as ours is like the chance of you surviving a firing squad (having 10 or more soldiers firing their rifles at you at close range). If you survived a firing squad, it is argued, you should assume there was some purpose involved in this, and that it wasn't just a lucky accident.

But physicist Sabine Hossenfelder disagrees. She has a recent post in which she attempts to debunk what she calls “the myth that our universe is 'finetuned for life.'” Her attempt, however, is a complete failure.

She starts out by giving a very general armchair argument:

The general argument against the success of anthropic selection is that all evidence for the finetuning of our theories explores only a tiny space of all possible combinations of parameters. A typical argument for finetuning goes like this: If parameter X was only a tiny bit larger or smaller than the observed value, then atoms couldn’t exist or all stars would collapse or something similarly detrimental to the formation of large molecules. Hence, parameter X must have a certain value to high precision. However, these arguments for finetuning – of which there exist many – don’t take into account simultaneous changes in several parameters and are therefore inconclusive.

This is not actually correct, as quite a few scientific papers about cosmic fine-tuning and the biological sensitivity of various fundamental constants do actually take into account the effects of simultaneous changes of more than one parameter. An example is the diagram below from a recent article by physicist Luke Barnes, in which he allows us to view simultaneous changes in the strong nuclear force and the fine-structure constant, showing only a tiny area that is compatible with living creatures such as ours.

Here's another example, a chart I created. The graph plots two different constants, the proton charge and the electron charge. Unless their absolute values match exactly (as they do in our universe to at least 18 decimal places),  planets cannot hold together.  You could actually expand this chart to be the size of a house, and it would still be appropriate to draw the green line as thin as it is here.

Then Hossenfelder claims to have found “counterexamples” that weaken the case for cosmic fine-tuning. But she's shooting blanks – her counterexamples are all duds.

The first “counterexample” she cites is a 2006 paper called A Universe Without Weak Interactions. She says that this paper describes a “universe that seems capable of complex chemistry and yet has fundamental particles entirely different from our own.” The paper actually talks about a universe without a weak nuclear force, one of the four fundamental forces of the universe. But the weak nuclear force has never been a very important part of arguments that the universe is fine-tuned. There are strong reasons for believing that all of the other three fundamental forces of nature (the strong nuclear force, electromagnetism, and gravitation) are very fine-tuned, but no one has claimed that the weak nuclear force is very fine-tuned.

Moreover, the 2006 paper she refers to was emphatically refuted by a later paper in 2006, a paper entitled “Problems in a Weakless Universe.” The paper concluded the following:

We point out, however, that on closer examination the proposed "weakless" universe strongly inhibits the development of life in several different ways. One of the most critical barriers is that a weakless universe is unlikely to produce enough oxygen to support life. Since oxygen is an essential element in both water, the universal solvent needed for life, and in each of the four bases forming the DNA code for known living beings, we strongly question the hypothesis that a universe without weak interactions could generate life.

So Hossenfelder's first “counterexample” doesn't do anything to undermine the case for cosmic fine-tuning. Her second “counterexample” is no better. She cites Abraham Loeb's paper “The Habitable Epoch of the Early Universe.” In that paper Loeb imagined that in the early universe, the cosmological constant (or the energy density of space) might have for a while been sufficient to bathe the whole universe with a warmth suitable for life. He imagined the following scenario:

1. The Big Bang occurs 13 billion years ago.
2. After about 400,000 years the universe cools enough for atoms to form.
3. About 10 million years later, planets and stars form.
4. For a few million years it is warm enough for life to exist, because of the cosmological constant, which fills all of space with a pleasant warmth.
5. Microbial life forms appear during this relatively brief period.
6. A few million years later, the continued expansion of the universe causes the universe to cool sufficiently so that the cosmological constant is no longer sufficient to keep space warm.
7. Any microbial life that may have arisen from the warmth of the cosmological constant then dies, as temperatures fall far below freezing.

But this scenario is nothing like an alternate way for the universe to be life-friendly, because this “habitable epoch of the early universe” lasts way too short a time (as the expansion of the universe quickly causes those early warm temperatures to fade away, being replaced by deadly cold). It actually lasts (under Loeb's assumptions, as discussed here) only about two million years, as Loeb admits by saying that this epoch would last only “a few Myr,” using an abbreviation for megayears (a million years). Since there was supposedly billions of years (thousands of millions of years) between the appearance of earthly microbes and the appearance of man, it is clear that two million years is not long enough for any intelligent life to evolve. It is almost certainly not a sufficient time for any life at all to develop. So the possibility discussed by Loeb is irrelevant.

When discussing whether the universe is fine-tuned to allow for intelligent life, we don't care whether there might have been some brief two-million year window in the very early universe (a short-lived period of warmth) that might have allowed mere microbes to appear before being wiped out when the universe becomes super-cold again. We care about the possibility of intelligent life appearing. In fact, it is overwhelmingly likely that the higher radiation and asteroid concentrations in any early universe would not even allow microbes to have appeared in the early universe.

Loeb's paper (discussing something both extremely improbable and irrelevant) did nothing to upset the idea that the cosmological constant is fine-tuned. The fact that the cosmological constant is enormously fine-tuned is reaffirmed by a recent scientific paper noting that the cosmological constant is 10¹²³ times smaller than its “natural value,” and that “there is no satisfactory solution yet for this problem.” The paper's graphs suggest that there would no observers if the cosmological constant were a few hundred times smaller or larger. Given the natural value so much larger, having a cosmological constant within this range is like hitting the exact center of a target 1000 yards distant.

So Hossenfelder's second “counterexample” is a dud that does nothing to undermine the case for cosmic fine-tuning. Hossenfelder's third “counterexample” is no better. She cites a 2016 paper by Adams and Grohs discussing the “triple alpha process,” a case in which nuclear physics has to be just right in order for carbon to be produced, because of what is called a resonance fine-tuning. The authors imagine other universes that might not require this particular type of resonance fine-tuning.

Hossenfelder claims that this paper is a “demonstration that a chemistry complex enough to support life can arise under circumstances that are not anything like the ones we experience today.” That's wrong, because the paper actually describes universes very much like ours, but in which there are small changes in fundamental constants. And also, the paper does not actually describe an alternate universe with a chemistry complex enough to support life, because it fails to describe a universe in which oxygen is produced in sufficient quantities. This is made clear on page 26 of the paper, in which the authors say, “This set of simulations does not include nuclear reactions that produce oxygen, neon, and heavier elements.”

It has long been recognized that the fundamental constants have to be just right for nuclear reactions in stars to produce large quantities of both oxygen and carbon, both of which are requirements for life. By failing to discuss alternate reactions in which stars produce oxygen, the paper of Adams and Grohs does nothing to undermine that fine-tuning requirement. The fine-tuning requirement is stated in a 2014 scientific paper which tells us on page 16 that in order for you to have abundant quantities of oxygen and carbon, you need for the quark masses to be within 2 to 3 percent of their current values, and you also need for the fine-structure constant to be within 2.5% of its current value. You could therefore say nature has to hit two different “holes in one,” and these aren't the only “holes in one” nature has to hit in order to end up with intelligent life.

In short, all of Hossenfelder's “counterexamples” are empty duds. She has done nothing whatsoever to weaken the case that the universe is fine-tuned. Far from being a “myth” as she claims, the finding that the universe is incredibly fine-tuned for life is one of the fundamental achievements in the past 50 years of physics, and is something that has been acknowledged by many physicists and cosmologists.

As all of her “counterexamples” are failures, Hossenfelder doesn't actually succeed in providing even a single example of some alternate universe as life-friendly as ours. Even if she were to provide such a thing, it would do nothing to discredit the claim that our universe is fine-tuned for life. Arguments about cosmic fine-tuning never claim that there is only one possible universe consistent with life, but merely claim that it is incredibly improbable that any particular random universe would be compatible with the appearance of intelligent life. There are many possible universes that would allow intelligent life to appear, but the set of all possible universes that would allow intelligent life to appear is almost infinitely smaller than the set of all possible universes, making it almost infinitely improbable that any particular random universe would accidentally meet the many requirements for intelligent life. You do not damage such reasoning in the least by showing a few other possible universes that might allow intelligent life to appear.

It's rather like this. A man may point to a car, point out its fitness for a purpose, and say, “Wow, that sure is fine-tuned” or “that sure wasn't produced by some set of accidents.” You do not at all discredit such reasoning by demonstrating that there are other possible cars with a very different appearance.

The Dart of the Vacuum Miracle Hit the Distant Bullseye

Perhaps the biggest mystery in physics is why the vacuum of space has so little energy in it. Although it may seem intuitive to think of the vacuum of space as empty, quantum mechanics predicts that it should be something very different: something incredibly packed with energy, a dark energy caused by all kinds of quantum fluctuations. In a TED talk a physicist discussed this:

Now, if you use good old quantum mechanics to work out how strong dark energy should be, you get an absolutely astonishing result. You find that dark energy should be 10 to the power of 120 times stronger than the value we observe from astronomy. That's one with 120 zeroes after it. This is a number so mind-bogglingly huge that it's impossible to get your head around. We often use the word "astronomical" when we're talking about big numbers. Well, even that one won't do here. This number is bigger than any number in astronomy. It's a thousand trillion trillion trillion times bigger than the number of atoms in the entire universe.

Instead of the vacuum of space being filled with this kind of energy (which would give each square meter of empty space far more density than steel), we have a vacuum of space that is almost entirely empty of matter and energy. This discrepancy between reality and prediction is sometimes called the vacuum catastrophe. But for reasons I discuss here, it really should be called instead the vacuum miracle. Having a vacuum that is relatively empty is both exceptionally improbable and very fortunate in allowing our existence. The common term used for an extremely unlikely but highly fortunate event is the term “miracle,” as in: It was a miracle that she fell onto an open truck carrying pillows when she jumped off the high bridge.

The vacuum miracle is something that bothers many scientists, who would prefer to believe that the universe is not so well-arranged to favor creatures like us. One way they have tried to ease this discomfort is to suggest that perhaps there is some unknown reason why the vacuum of space has to be empty, resulting in a zero cosmological constant, or zero dark energy. But such reasoning doesn't work, because in the late 1990's it was discovered that the expansion of the universe is accelerating. This can only be true if there is a very small cosmological constant, which basically means that each square meter of the vacuum of space has a little bit of energy. Collectively this energy (the same as dark energy or the cosmological constant) is causing the expansion of the universe to accelerate.

A recent paper by five scientists suggests that a cosmological constant just like we have is actually necessary for the eventual appearance of creatures such as us. The paper states: “We find that we seem to live in a favorable point in this parameter space that minimizes the exposure to cosmic explosions, yet maximizes the number of main sequence (hydrogen-burning) stars around which advanced life forms can exist.”

The paper is discussed by this article in the journal Science, which states:

As it turns out, our universe seems to get it just about right. The existing cosmological constant means the rate of expansion is large enough that it minimizes planets’ exposure to gamma ray bursts, but small enough to form lots of hydrogen-burning stars around which life can exist. (A faster expansion rate would make it hard for gas clouds to collapse into stars.)

We can use the common phrase “threading the needle” to describe this type of fine-tuning. Or you might compare it to landing the golf ball in the golf hole, or hitting the distant bullseye target with an arrow. And given all the random quantum contributions to the vacuum, this should have been as improbable as a drunk blindfolded archer hitting the very distant target bullseye with his arrow.

But the journal Science is written for scientists, so it was quite predictable that the article author would try to ease the discomfort of any scientists who might be made uncomfortable by this extreme example of cosmic fine-tuning. This was in accordance with the standard principle that our scientists must be kept in carefully filtered information bubbles, like 1980 Moscow bureaucrats who would get all their news from Pravda. Heaven forbid that the tender ears of our scientists should ever be offended by something that does not match their expectations.

So the Science article cites a statement by physicist Lee Smolin:

However, he adds, all truly anthropic arguments to date fall back on fallacies or circular reasoning. For example, many tend to cherry-pick by looking only at one variable in the development of life at a time; looking at several variables at once could lead to a different conclusion.

It certainly is not true that “all truly anthropic arguments to date fall back on fallacies or circular reasoning,” a claim which is just a lazy kind of dismissal similar to statements such as “all Republican arguments use fallacies” or “all Democratic arguments rely on logic errors.” In fact, the particular example given does not hold up as an example of a fallacy.

Let's imagine if you found a case in which one cosmic parameter seemed to be extremely fine-tuned for life. Would it be wrong to form an opinion based on that parameter, without considering all other parameters? It might be if you were examining some external universe, and you didn't know whether life existed in it. Because the overall situation might be like this:

1 parameter with just the right value for life to exist

5 parameters inconsistent with the existence of life

But we know that no such situation can exist in our universe, because we know that life does exist in our universe. So given the discovery of a single parameter that seems to be fine-tuned for life, the worst situation that could exist is:

1 parameter with just the right value for life to exist

All other parameters consistent with the existence of life

Even if you found such a situation, the evidence would still be pointing to a fine-tuned universe. You would have one “thumbs up,” and zero “thumbs down.”

In fact, we know the situation is much better than that. We know that there are quite a few parameters and fundamental constants which are fine-tuned for life, as discussed here and here. So we know that the situation is really: lots of thumbs up, and no thumbs down (if there were any thumbs down, we wouldn't exist). We know of lots of parameters that are very fine-tuned, and there is no chance that we will discover some other parameter that will cancel out such evidence (because if such a parameter existed we could not). The darts of nature known as the universe's fundamental constants have most improbably hit not just one distant bullseye, but lots of them.

Cosmic fine-tuning

So Smolin's reasoning here has no weight. In fact, Smolin himself showed that he is extremely impressed by the evidence that the universe is fine-tuned. This is because Smolin wrote a whole book called The Life of the Cosmos in which he advanced an elaborate theory designed to explain the fine-tuned features of the universe. It was a pretty goofy theory, involving the idea that universes magically pop into existence whenever black holes collapse. But at least it showed that Smolin thought that cosmic fine-tuning is something very important we need to explain.

In general, we should not pay particular attention when physicists lecture us about errors in logic, as physicists have no training in logic. You can get a PhD in physics without ever taking an introductory course in logic.

Far from involving some fallacy, the fact that our universe is incredibly fine-tuned is one of the most important things discovered by science in the past hundred years. If your philosophy doesn't mesh with such a fact, your philosophy needs to be revised. 

Postscript: This post included this snarky comment: "This was in accordance with the standard principle that our scientists must be kept in carefully filtered information bubbles, like 1980 Moscow bureaucrats who would get all their news from Pravda." I didn't expect to see another example of that so quickly. Shortly thereafter news arrived that a flood of complaints by scientists caused the PLOS One journal to retract a scientific paper dealing with the great amount of coordination in the human hand -- solely because the authors made three one-sentence references to "the Creator" -- for example, "The explicit functional link indicates that the biomechanical characteristic of tendinous connective architecture between muscles and articulations is the proper design by the Creator to perform a multitude of daily tasks in a comfortable way." Again, we see the Pravda principle at work -- the tender ears of our scientists must not be offended, the information bubble must be carefully filtered from contaminating deviations of thought, and the sociological taboos of the tribe must be rigidly enforced.

The Professor's Fallacious Critique of Cosmic Fine Tuning

A recent article in the Wall Street Journal was entitled “Science Increasingly Making the Case for God.” The article seems to have mixed up some solid points based on modern physics with some dubious arguments based on a misguided idea that the Earth or earthly life is some possibly unique cosmic miracle. The article was rebutted by physicist Lawrence Krauss in this New Yorker article. But in rebutting an opinion piece that seems to have had some logic errors mixed up with a good deal of truth, Krauss has given us a rebuttal that itself is a mixture of some truth and some serious errors of fact and reasoning.

Krauss discusses the origin of life, and he assures us that the building blocks for the first living things are abundant in space. “We have continued to find in space the more sophisticated components associated with the evolution of life on Earth.” This statement includes a link to a news article. But when I follow the link and read the article, I don't find anything that backs up the claim. The linked article refers to the discovery of space chemicals, and says, “Chemicals they found in that cloud include a molecule thought to be a precursor to a key component of DNA and another that may have a role in the formation of the amino acid alanine.” But that's a giant leap away from finding “the more sophisticated components associated with the evolution of life on Earth.” The article merely discusses the discovery of distant precursors of some of the parts of the key molecules of life – rather like finding sand that is a distant precursor of the silicon chips in your computer. In fact, we have not actually found in space "the more sophisticated components associated with the evolution of life on Earth," but only some relatively simple precursors. Krauss is also on very weak ground when he discusses some speculative theory of an MIT scientist, one that has neither experiments nor observations to back it up.

Krauss attempts to rebut arguments that the fundamental constants of the universe are fine-tuned, as if some cosmic designer had chosen them. Krauss says the following:

The constants of the universe indeed allow the existence of life as we know it. However, it is much more likely that life is tuned to the universe rather than the other way around. We survive on Earth in part because Earth’s gravity keeps us from floating off. But the strength of gravity selects a planet like Earth, among the variety of planets, to be habitable for life forms like us.

Here Krauss commits the logical fallacy known as presenting a false dilemma. A false dilemma is when a reasoner speaks as if we must choose between two different things, even though the two things are not mutually exclusive. It's the type of reasoning error committed when someone says something like, “You can either be a true patriot or a Democrat – make up your mind,” without explaining why one can't be both. The false dilemma Krauss presents is the idea that we need to make a choice between the idea that the universe is fine-tuned for life and the idea that life is fine-tuned to the universe’s laws. There is not the slightest reason to make such a choice, as the two ideas are not in any way mutually exclusive. Since it is perfectly possible that we have both a universe that is fine-tuned for life, as well as biological life that is fine-tuned to the laws and realities of the universe, the second of these ideas does nothing at all to undermine the credibility of the first idea.

Krauss then discusses the issue of the fine-tuning of the cosmological constant, something I discuss in this blog post. Scientists say that because of the strange facts of quantum mechanics, the vacuum between stars should be teeming with energy, as what are called virtual particles constantly pop in and out of existence. Quantum field theory allows us to calculate how much energy there should be in the vacuum of space because of these virtual particles. The problem is that when scientists do the calculations, they get a number that is ridiculously wrong. According to this page of a UCLA astronomer, quantum field theory gives a prediction that every cubic centimeter of the vacuum should have an energy density of 10⁹¹ grams. This number is 10 followed by 90 zeroes. That is an amount trillions of times greater than the mass of the entire observable universe, which is estimated to be only about 10⁵⁶ grams.

Another name for this vacuum energy density is the cosmological constant. We know that this cosmological constant is not the ridiculously high number predicted by physicists, but some some very, very low number (although apparently non-zero). Scientists speculate that there may be some “accidental cancellation” of all these strange quantum factors that leaves us with a cosmological constant very close to zero. But in order for you to have that, it would have to be an astonishingly improbable coincidence – kind of like the coincidence you would have if you added up all the purchases of everyone in China, and subtracted from them all of the earnings of every one in the United States, and ended up with a number less than 100 dollars. We would not expect that such a lucky coincidence would occur in even 1 in a billion trillion quadrillion random universes, as it requires fine-tuning to more than one 1 part in 1,000,000,000,000,000,000,000,000,000,000,000,000.000.

Here is how Krauss attempts to explain away this “vacuum miracle” as I have called it. He says this about the cosmological constant:

Is this a clear example of design? Of course not. If it were zero, which would be “natural” from a theoretical perspective, the universe would in fact be more hospitable to life. If the cosmological constant were different, perhaps vastly different kinds of life might have arisen. Moreover, arguing that God exists because many cosmic mysteries remain is intellectually lazy in the extreme.

There are four fallacies or misstatements in this short statement, and let me carefully describe each of them.

First, it is not at all true that a cosmological constant of zero is “ 'natural' from a theoretical perspective.” As many scientists have stated, from the perspective of quantum mechanics, a small or zero cosmological constant is shockingly unnatural and a wildly improbable thing, like the chance of the total salaries of all Americans accidentally exactly or almost exactly equaling the total annual purchases of all Chinese people.

Second, let's look at Krauss' claim that the universe “would be more hospitable to life” if the cosmological constant were zero. There is actually no solid basis for this claim. The only scientific paper I can find advancing such a thesis is a very iffy speculative paper that is meekly entitled, “Preliminary Inconclusive Hint of Evidence Against Optimal Fine Tuning of the Cosmological Constant for Maximizing the Fraction of Baryons Becoming Life.” The paper can be read here. The author of this paper (Don N. Page) argues that you might have a “very small increase” in life in the universe if the cosmological constant was zero. But he seems to have no real confidence in his thesis. Referring to other scientists, he says in his paper, “Email comments by Robert Mann, Michael Salem, and Martin Rees have shown me that it is not at all clear that the very small increase in the fraction of baryons that would condense into galaxies if the cosmological constant were zero instead of its tiny observed positive value would also lead to an increase in the fraction of baryons that would go into life.” Page also points out that another scientist suggests the universe would be less habitable to life if the cosmological constant were lower.

So there is no solid basis at all for Krauss' claim that the universe “would be more hospitable to life” if the cosmological constant were zero – merely a super-iffy unsubstantiated speculation that it might be slightly more hospitable to life, a speculation other scientists dispute. Also, even if you were to get somewhat more life in a universe with a zero cosmological constant, it would still appear to be a case of enormous fine-tuning to get a cosmological constant as low as ours, given the vacuum energy density issue discussed above, and the need for all these quantum contributions to the vacuum to miraculously cancel each other out. One does not disprove a case of fine-tuning by showing that a slightly better result could have been achieved. For example, if I buy you a ticket to a hot Broadway show, and get you a seat in the middle of the second row, that is a type of fine-tuning – and you don't show it isn't fine-tuning by arguing that I could have got you a seat in the middle of the first row.

Third, in the statement above Krauss argues, “If the cosmological constant were different, perhaps vastly different kinds of life might have arisen.” No, that doesn't work to explain away this issue. The issue with the cosmological constant is that if you don't have fine-tuning to more than 1 part in 1,000,000,000,000,000,000,000, then you get no galaxies, no stars, and empty space that is a seething super-dense quantum vacuum with much more mass-energy than the density of solid steel. Under such conditions, no life of any type is possible, no matter how weird it may be.

Fourth, Krauss is using a “straw man” argument when he says that this type of reasoning is “arguing that God exists because many cosmic mysteries remain.” That's not what is going on when people use the cosmological constant (and similar cases of cosmic fine-tuning) to suggest that there is a purpose and plan behind the universe. It is instead a case of reasoning from an extreme case of fine tuning to the likelihood of a fine-tuner, not a case of arguing from the mere existence of cosmic mysteries. One would have a case of “arguing that God exists because many cosmic mysteries remain,” if one used silly reasoning such as “blacks holes and quasars are mysterious, so God probably exists.” But I am not aware of anyone using such reasoning.

Krauss then wraps up his comments with that old skeptic's slogan that extraordinary claims require extraordinary evidence, which is kind of an all purpose excuse for not believing in anything you don't want to believe, no matter how much evidence piles up. First, of all it should be noted that “extraordinary claims require extraordinary evidence” is an inappropriate slogan, similar to claims such as “Bald men require bald wives,” and “Stupid people require stupid leaders.” Imagine if I claimed that John Riser had levitated twenty feet into the air in the middle of the street. That would be an extraordinary claim, but I would not necessarily need any extraordinary evidence to show its likelihood. I could show its likelihood through ordinary, common type of evidence such as the sworn testimony of 20 reliable impartial witnesses, or live television camera footage taken by two different network television cameramen. A much better slogan is, “Extraordinary claims require good, convincing evidence, whether it be a common type of evidence or an unusual type of evidence.”

I may also note that the evidence for the fine-tuning of fundamental constants is extraordinary, involving the work of many scientists over a period of decades, regarding the fundamental traits of physical reality. How is this not extraordinary? 

To read more about the topic of cosmic fine-tuning, with many good examples, read my blog posts here and here.  The first of these posts explains the color-coded table below, which summarizes lots of requirements for the existence of civilized creatures such as us.

 

“Vacuum Catastrophe” Should Be Called the Vacuum Miracle

We tend to think of science as something that gives us the right answers. Almost always science does give us the right answer. But there is at least one case when science gives us the wrong answer – a really, really wrong answer. In fact, there is one case in which science gives us an answer wronger than any answer that you ever gave in school, even on those tests when you wrote wild guesses on your exam sheet because you had daydreamed through every class session.

The wrong answer given by science is the answer that it gives to the question: how much energy is in a vacuum?

A person not familiar with quantum mechanics tends to think of a vacuum as being just empty space. But according to quantum mechanics, empty space is not really empty. It is instead a seething froth of very short-lived particles called virtual particles. A virtual particle with mass is a particle that pops into existence and then pops out of existence a tiny fraction of a second later. Scientist think that the vacuum is filled with virtual particles corresponding to every type of actual subatomic particle that has been discovered. For example, they think that the vacuum includes incredibly short-lived virtual electrons, and incredibly short-lived virtual quarks (because both electrons and quarks are known types of subatomic particles).

You can get an idea of the modern concept of the vacuum by looking at the animation below. Each of the fleeting little specks represents one of the virtual particles that pop into existence, disappearing a fraction of a second later.

Imagine if there was a weird rule in your living room that every second 10,000 fireflies had to pop into existence, but that each of them would disappear a fraction of a second later. You might then then see in your living room these weird little streaks of motion and flashes that would be the signs of short-lived fireflies existing for an instant before disappearing. Scientists think that the vacuum of space is a little like that, except that the fireflies are subatomic virtual particles, so we can't see anything like the streaks and flashes.

Quantum field theory allows us to calculate how much energy there should be in the vacuum of space because of these virtual particles. The problem is that when scientists do the calculations, they get a number that is ridiculously wrong. According to this page of a UCLA astronomer, quantum field theory gives a prediction that every cubic centimeter of the vacuum should have an energy density of 10⁹¹ grams.  This number is 10 followed by 90 zeroes. That is an amount trillions of times greater than the mass of the entire observable universe, which is estimated to be only about 10⁵⁶ grams.

This means that according to quantum field theory every cubic centimeter of empty space should have more mass-energy than all the mass-energy in the entire observable universe.

How far off is this calculation? It varies on how you do the calculations. According to one type of calculation, the predictions of quantum field theory is wrong by a factor of 10⁶⁰, which is a factor of a trillion trillion trillion trillion trillion times. According to a different way of estimating it, the predictions of quantum field theory is wrong by a factor of 10¹²⁰, which is a factor of a million billion quadrillion quintillion sextillion septillion octillion times.

This prediction has been repeatedly referred to as the worst prediction in the history of physics. It could just as well be called the most wrong prediction in the history of human thought. No zealous apocalyptic doomer ever made a prediction more wrong, not even the preacher who predicted the end of the world would occur in 1843.

The matter is discussed in this well-written post by physicist Matt Strassler, which includes some nice graphics. Scientists don't talk about this matter very much, as it is something of a skeleton in their closet. But when they do discuss the matter, they refer to it as the vacuum catastrophe or the cosmological constant problem. Scientists think that the vacuum does have a very slight energy density (believed to be the main driver of what is called the cosmological constant, which is causing the universe's expansion to accelerate). But that energy density is less than .00000000000000000000000000000000001 percent of the amount predicted by quantum field theory.

Now it might be easy for us to just dismiss quantum mechanics, because of this ridiculously wrong prediction – we could just say, “This just shows that quantum mechanics is all wrong.” But the problem is that quantum mechanics makes many other specific predictions that turn out to be exactly right. So scientists have to try struggle towards some guess as to how quantum mechanics could be right despite its very wrong prediction about the energy density of the vacuum.

One idea Strassler discusses is that the energy of the virtual particles related to bosons (one class of subatomic particles) is positive, and the energy of the virtual particles related to fermions (another class of subatomic particles) is negative. Could it be that these two somehow nearly cancel out each other, resulting in a vacuum with almost no energy density? But as Strassler points out, this doesn't work out, because there are “way too many fermions.”

Another problem is that for you to have an exact balance of positive and negative contributions to the vacuum energy density would require fine-tuning of about 1 part in 10⁶⁰, which is 1 part in trillion trillion trillion trillion trillion times.

It could conceivably be that there are many additional undiscovered types of subatomic particles. It could also be that when one adds up the positive energy from all of the virtual particles corresponding to these particles, and subtracts from that the negative energy from all of the virtual particles corresponding to these particles, one ends up with a vacuum energy density of zero or almost zero. But that would require an incredibly improbable coincidence, one which randomly would have less than 1 chance in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. It would be like the chance of you adding up all the money earned on planet Earth, comparing it to all the money borrowed, spent or charged on credit cards, and finding that the two sums matched exactly, to the penny – but it would be far more improbable.

As Professor Strassler puts it:

To say this another way: even though it is possible that there is a special cancellation between the boson fields of nature and the fermion fields of nature, it appears that such a cancellation could only occur by accident, and in only a very tiny tiny tiny fraction of quantum field theories, or of quantum theories of any type (including string theory).  Thus, only a tiny tiny tiny fraction of imaginable universes would even vaguely resemble our own (or at least, the part of our own that we can observe with our eyes and telescopes).  In this sense, the cosmological constant is a problem of “naturalness” as particle physicists and their colleagues use the term: because it has so little dark energy in it compared to what we’d expect, the universe we live in appears to be highly non-generic, non-typical one.

If such a coincidence has occurred, then scientists are using the wrong term to discuss this problem. They use the term “the vacuum catastrophe,” but the word catastrophe means something very bad. The fact that the vacuum is not even .000000000000000000000000000001 percent as large as predicted by quantum field theory, is however, something that is very good, because a very low vacuum energy density is necessary for our existence. If the vacuum energy density was even  .000000000000000000000000000001 as large as predicted by quantum field theory, empty space everywhere would be far denser than steel, and intelligent life never could have appeared in the universe. There would be many reasons why suns could never have formed, and if they did exist, the super-dense vacuum would block all sunlight from ever reaching planets.

What is the proper term for an incredibly improbable but fortunate occurrence? The term is miracle. One definition of miracle is simply a very fortunate but very unlikely event, as in “the miracle of the jet landing on the Hudson River,” or “the miracle that no one was killed by the bomb.” 

So rather than referring inappropriately to the “vacuum catastrophe,” as scientists do, we should be talking about the vacuum miracle by which a vacuum that is supposed to be super-dense turns out to be not dense at all.