A good scientific theory is one that makes precise and accurate predictions.
We scientists are even happier when multiple theories agree with one another. This gives
us confidence that we know what we’re doing. And, by and large, we do. However,
there is one prediction in modern physics that is really, really, bad- perhaps the worst in all of
science. And I think it’s time that I come clean and share one of physics’ dirty little secrets.
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Modern physics can predict lots of pretty complicated things,
like the aerodynamics involved in flying a supersonic jet and how a star explodes.
And, while videos on both of those topics would be very fascinating, in this video,
I’m not going to focus on the complicated- rather, I want to talk about what seems like
the simplest measurement of all of physics. What is the energy density of empty space?
So, what do I mean about empty space? I mean truly empty space. Nothing in it. No people.
No atoms. No electric fields. No gravity. Nothing.
If I could make a volume that is truly empty, then
it seems pretty obvious that the energy density of this volume would be zero. Stands to reason.
And yet, when we turn our most modern theories to this question,
we find that the energy density of space isn’t zero. Let’s see what the theories predict.
The two theories that underpin all of modern physics are Einstein’s
theory of general relativity and the Standard Model of particle physics.
General relativity explains the behavior of gravity. This explanation also includes the
nature of space and time. Relativity is a theory that describes big things;
cosmic things; the universe as a whole. The Standard Model is the opposite. It
focuses on the world of the small– the quantum and subatomic world
of quarks and leptons and the nature of matter and energy in the microcosm.
So, what happens if we ask each of these theories to predict the energy density of empty space?
Let’s start with general relativity. We learned over a hundred years ago that the
universe was expanding. Just shy of fourteen billion years ago, the expansion began.
We call this process the Big Bang. And, until a quarter century or so ago,
we thought that the expansion was slowing down. That made sense. If you throw a ball upward,
gravity pulls it downward and causes it to slow. The universe is basically the same
and therefore astronomers expected gravity to slow the expansion of the universe.
However, in 1998, we discovered that this wasn’t true. Not only is the universe expanding,
it’s expanding faster and faster. The only way that could be true is if something was
pushing the universe apart harder than gravity is pulling it back together.
The phenomenon that provides this repulsion is called dark energy and it’s basically a repulsive
form of gravity. Dark energy is essentially the energy of empty space and it’s very,
very tiny. Converted to familiar units, dark energy is the energy equivalent of
four individual hydrogen atoms per cubic meter of space. Dark energy is super, super, tiny.
Okay- that’s what general relativity says. What does the Standard Model say?
Well, the Standard Model says that even in empty space- completely devoid of all matter,
electric fields, gravity and whatnot- it still contains fields. These fields don’t do much-
they’re just there. However, if they vibrate in the right way, the vibrations become electrons,
quarks, and all of the fundamental subatomic particles we study here at Fermilab.
On the other hand, if the fields are left alone, not vibrating in ways that make
long-lasting particles, they still vibrate a bit like a subatomic white noise generator.
You might have heard about this sort of thing in a different way. Quantum mechanics says
that things like electrons are both particles and waves, which means that these white-noise
vibrations are equivalent to very short-lived particles that are constantly appearing and
disappearing. These particles are called “virtual particles” and they don’t seem like they’re real,
but we have lots of evidence that they are. The Muon g-2 experiment here at Fermilab actually
probes this persistent quantum hum. I made a video on the idea, and a link is in the description.
The bottom line is that these vibrating fields exist and they contain within them some energy,
which you can calculate. This is the energy of empty space.
Now, when you do that, you have to add up the contribution of all of the frequencies of all
possible vibrations, including shorter and shorter wavelengths. Since shorter
wavelengths means higher energy, that means you add up higher and higher energies.
A mathematician would say that you have to add up all wavelengths all the way down to zero length,
but we know that the Standard Model fails for lengths shorter than the
Planck length. I made a video on that, and the link is in the description.
So what we need to do is to add up the quantum hum for all wavelengths bigger
than the Planck length and this gives us the energy of empty space according to
the Standard Model. And what you find is way more quantum energy density than you
get with the dark energy of the cosmos. The density is a staggering ten to the 120 times
bigger than the dark energy density. To understand just how big that is,
that’s equivalent to taking all the mass of the visible universe, multiplying it
by a hundred quintillion, then packing all of that mass into a cube a meter on a side.
That’s a big disagreement. On the general relativity side, the energy of empty space is
equivalent to four hydrogen atoms per cubic meter of space, while on the Standard Model side, it’s
equivalent to the mass of a hundred quintillion universes in the same volume. And that, as any
precocious toddler would say- that's a lot. So that’s the first message. Cosmic and subatomic
theories give hugely different predictions for the energy density of empty space. Given
that the discrepancy is so enormously different, something must be wrong.
What could be causing the disagreement? Well, it could be that we don’t understand gravity.
It could be that we don’t understand the quantum world. Or it could be that there is some sort of
physical phenomenon that we haven’t discovered that somehow cancels out that huge number from
the quantum calculation. Which one is it? Unfortunately, the simple answer to that
question is that we don’t know. A lot of explanations have been suggested,
but none of them are accepted by the scientific community. Not only are none of them accepted
by the community, there isn’t even a consensus on the broad strokes of what a solution would be.
Some ideas rest on the idea of quantized spacetime- meaning there is a smallest
quantity of space and time, like how a grain of sand makes up a desert.
Other ideas invoke additional dimensions of space – tiny dimensions that can’t be seen,
but mean that the equations of the Standard Model are overlooking some super-important factors.
My own personal guess is that when a proper calculation of the contributions of the various
fields that hum in empty space is done, that the effects of some will be a positive energy
and some will be a negative energy and they will end up pretty much canceling each other out.
By the way, you shouldn’t believe that idea. I certainly don’t. It’s important for a scientist
talking about speculative ideas to remember to not believe what they think. And you should keep in
mind that if I’m right, there is still a problem. It’s one thing for two fields to cancel exactly,
like plus one and minus one add to zero. But with the field idea, the plus and minus quantum fields
almost, but don’t quite, cancel. After all, we’re left with dark energy. This imperfect cancellation
is a problem that remains unsolved. I put a link in the description to an
accessible article on the topic. It explores some of the ideas, but you should be aware that
every single one is a bit on the crazy side. I say crazy, but crazy isn’t always bad. Indeed,
I’m fond of a quote by Niels Bohr when he heard a lecture by Wolfgang Pauli. In the
question-and-answer session of the lecture, he is reported to have said “We all agree
that your theory is crazy. The question which divides us is whether it's crazy enough?”
No matter. The real thing is the mystery. As Sir Arthur Conan Doyle wrote in “The Return of
Sherlock Holmes,” “The game’s afoot!” And if you’re some bright young lad or lass looking
to make a name for yourself by solving a question that has eluded some of the best minds in physics
for nearly a century, this is a good one to work on. I mean- who wouldn’t want to
be the person known as the one who resolved the worst prediction in all of science?
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Okay- this topic is a fascinating one. Two of the most successful theories of all time
disagree very badly. Fascinating and frustrating stuff indeed. If you enjoyed learning about this
dirty little secret of science, be sure to like the video and subscribe to the channel. There’s
lots of stuff to learn about physics. Lots! After all, physics is everything.
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