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 10

^{91}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 10^{56}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 10

^{60}, 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 10^{120}, 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 10

^{60}, 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.