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.