Everything you ever wanted to know about nothing

What physics says about the vacuum: A visit to the seashore.


Imagine you are at the seashore, watching the waves. Somewhere in the distance you see a sailboat — wait, don’t fall asleep yet. The waves and I want to tell you a story about nothing.

Before quantum mechanics, “vacuum” meant the absence of particles, and that was it. But with the advent of quantum mechanics, the vacuum became much more interesting. The sea we’re watching is much like this quantum vacuum. The boats on the sea’s surface are what physicists call “real” particles; they are the things you put in colliders and shoot at each other. But there are also waves on the surface of the sea. The waves are like “virtual” particles; they are fluctuations around sea level that come out of the sea and fade back into it.

We have learned a thing or two about quantum mechanics since 1900. Public domain image.

Virtual particles have to obey more rules than sea waves, though. Because electric charge must be conserved, virtual particles can only be created together with their anti-particles that carry the opposite charge. Energy too must be conserved, but due to Heisenberg’s uncertainty principle, we are allowed to temporarily borrow some energy from the vacuum, as long as we give it back quickly enough. This means that the virtual particle pairs can only exist for a short time, and the more energy they carry, the shorter the duration of their existence.

You cannot directly measure virtual particles in a detector, but their presence has indirect observable consequences that have been tested to great accuracy. Atomic nuclei, for example, carry around them a cloud of virtual particles, and this cloud shifts the energy levels of electrons orbiting around the nucleus.

Virtual particles can do more. Photons, the quanta of light, are electrically neutral and do not interact with each other. This is why light of different colors adds without distortion. But a photon can decay into a virtual pair of an electron and its anti-particle, the positron. If this happens for two photons at the same time, then their virtual electron-positron pairs can interact with each other. In this way, light can scatter with itself. This is so unlikely to happen that we do not normally see it, but it can and has been observed with high intensity lasers.

This diagram shows how photons (wavy lines) can interact via electrons and positrons (straight lines). Image: Discovering Particles

So we know, not just theoretically but experimentally, that the vacuum is not empty. It’s full with virtual particles that constantly bubble in and out of existence.

Vizualization of a quantum field theory calculation showing virtual particles in the quantum vacuum. Credits: Derek Leinweber

Let us go back to the seashore; I quite liked it there. We measure elevation relative to the average sea level, which we call elevation zero. But this number is just a convention. All we really ever measure are differences between heights, so the absolute number does not matter. For the quantum vacuum, physicists similarly normalize the total energy and momentum to zero because all we ever measure are energies relative to it. Do not attempt to think of the vacuum’s energy and momentum as if it was that of a particle; it is not. In contrast to the energy-momentum of particles, that of the vacuum is invariant under a change of reference frame, as Einstein’s theory of Special Relativity requires. The vacuum looks the same for the guy in the train and for the one on the station.

But what if we take into account gravity, you ask? Well, there is the rub. According to General Relativity, all forms of energy have a gravitational pull. More energy, more pull. With gravity, we are no longer free to just define the sea level as zero. It’s like we had suddenly discovered that the Earth is round and there is an absolute zero of elevation, which is at the center of the Earth.

In best manner of a physicist, I have left out a small detail, which is that the calculated energy of the quantum vacuum is actually infinite. Yeah, I know, doesn’t sound good. If you don’t care what the total vacuum energy is anyway, this doesn’t matter. But if you take into account gravity, the vacuum energy becomes measurable, and therefore it does matter.

The vacuum energy one obtains from quantum field theory is of the same form as Einstein’s Cosmological Constant because this is the only form which (in an uncurved space-time) does not depend on the observer. We measured the Cosmological Constant to have a small, positive, nonzero value which is responsible for the accelerated expansion of the universe. But why it has just this value, and why not infinity (or at least something huge), nobody knows. This “Cosmological Constant Problem” is one of the big open problems in theoretical physics today and its origin lies in our lacking understanding of the quantum vacuum.

But this isn’t the only mystery surrounding the sea of virtual particles. Quantum theory tells you how particles belong together with fields. The quantum vacuum by definition doesn’t have real particles in it, and normally this means that the field that it belongs to also vanishes. For these fields, the average sea level is at zero, regardless of whether there are boats on the water or aren’t. But for some fields the real particles are more like stones. They’ll not stay on the surface, they will sink and make the sea level rise. We say the field “has a non-zero vacuum expectation value.”

Image credit: TheGingerBeardedBiologist of Imgur, via http://imgur.com/user/Kisrah/favorites/DRt2Z.

On the seashore, you now have to wade through the water, which will slow you down. This is what the Higgs-field does: It drags down particles and thereby effectively gives them mass. If you dive and kick the stones that sunk to the bottom hard enough, you can sometimes make one jump out of the surface. This is essentially what the LHC does, just call the stones “Higgs bosons.”

I’m really getting into this seashore thing ;)

Next, let us imagine we could shove the Earth closer to the Sun. Oceans would evaporate and you could walk again without having to drag through the water.

Image credit: Mark Garlick / HELAS.

You’d also be dead, sorry about this, but what about the vacuum? Amazingly, you can do the same. Physicists say the “vacuum melts” rather than evaporates, but it’s very similar: If you pump enough energy into the vacuum, the level sinks to zero and all particles are massless again.

You may complain now that if you pump energy into the vacuum, it’s no longer vacuum. True. But the point is that you change the previously non-zero vacuum expectation value. To our best knowledge, it was zero in the very early universe and theoretical physicists would love to have a glimpse at this state of matter. For this however they’d have to achieve a temperature of 10^15 Kelvin! Even the core of the sun “only” makes it to 10^7 Kelvin.

One way to get to such high temperature, if only in a very small region of space, is with strong electromagnetic fields.

Image credit: Lawrence Livermore National Laboratory / National Ignition Facility.

In a recent paper, Hegelich, Mourou, and Rafelski estimated that with the presently most advanced technology high intensity lasers could get close to the necessary temperature. This is still far off reality, but it will probably one day become possible!

Back to the sea: Fluids can exist in a “superheated” state. In such a state, the medium is liquid even though its temperature is above the boiling point. Superheated liquids are “metastable,” this means if you give them any opportunity they will very suddenly evaporate into the preferred stable gaseous state. This can happen if you boil water in the microwave, so always be very careful taking it out.

The vacuum that we live in might be a metastable state: a “false vacuum.” In this case it will evaporate at some point, and in this process release an enormous amount of energy. Nobody really knows whether this will indeed happen. But even if it does happen best present estimates date this event into the distant future, when life is no longer possible anyway because stars have run out of power. Particle physicist Joseph Lykken estimated something like a Googol years; that’s about 10^90 times the present age of the universe.

According to some theories, our universe came into existence from another metastable vacuum state, and the energy that was released in this process eventually gave rise to all we see around us now. Some physicists, notably Lawrence Krauss, refer to this as creating a universe from “nothing.”

If you take away all particles, you get the quantum vacuum, but you still have space-time. If we had a quantum theory for space-time as well, you could take away space-time too, at least operationally. This might be the best description of a physical “nothing” that we can ever reach, but it still would not be an absolute nothing because even this state is still a mathematical “something”.

Now what exactly it means for mathematics to “exist” I better leave to philosophers. All I have to say about this is, well, nothing.


If you want to know more about the philosophy behind nothing, you might like Jim Holt’s book “Why does the world exist”, which I reviewed here.

And if you have a comment on this, leave it at the Starts With A Bang forum here.

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