© Matt Strassler [May 7, 2014]
An important concept that plays a big role in modern conceptions of the universe is that of “vacua”, a Latin word meaning the plural of “vacuum”.
Now I hope you’re not thinking of “vacuum” as a verb meaning “to remove dust using an appropriate machine”; if so, switch that idea off, and let the dust settle. But even if you think of “vacuum” as a noun, the way a physicist does — as empty space with nothing in it, certainly no air, and not even stray elementary particles — then there’s something odd about the notion that “vacuum” could have a plural. Clearly, there’s something additional that has been added on to the notion! That’s what I intend now to explain.
A Theory May Offer a Description of Empty Space
First, let me remind you what a theory is, in physics. It’s not a speculation, or an idea; it’s something much more concrete. A theory is a set of equations, and accompanying concepts, that allows scientists to make predictions for how physical objects will behave. Some theories are meant to describe the real world; most of them describe imaginary worlds; but any reasonable theory makes consistent predictions, and describes aspects of a possible world.
For example, Newton’s theory of gravity is one in which the force of gravity between two objects that are a distance r apart is proportional to 1/r²; this (approximately) describes what happens in the real world. A different theory of gravity might be one in which the force is proportional to 1/r³; this is still a physics theory because it does indeed make clear predictions for how objects will pull on each other via gravity, but it describes an imaginary world, not the real world we live in. It’s a perfectly good physics theory, but it doesn’t describe nature… our world’s nature.
Now, some theories (not all of them, by any means) are intended to describe not only things but the absence of things, in the form of empty space — also known as “the vacuum”. In Newton’s day, empty space was simple — it was just that: empty space. But over the years, empty space has gotten more and more complicated. One thing that was learned in the 1800s is that empty space actually has fields in it — and today we think of fields as the most elementary aspects of the universe, so they’re pretty important!
Fields are things that can take a value at any point in space and at any moment in time. In the daily world around us, the temperature of the air is a field — at any time and in any location, you can measure the temperature, and if you knew the temperature everywhere in space, you’d know the temperature field at that time. But this isn’t a proper example for us here, because the temperature of the air is only meaningful where there is air, and there’s no meaning to a temperature field in empty space.
A better example is the electric field (the field that is responsible for lightning, for “static cling”, and for the flow of electrical currents in wires). The electric field is an elementary field of nature, and exists even in empty space. The same is true for all the elementary fields of nature, including the W field, the electron field, the muon field, etc. … including also the now-famous “Higgs field.”
The Vacuum Versus A Vacuum
So when we talk about empty space, we really mean space that is as empty as possible. In some sense it is empty, because it has no particles in it, not even particles of light (photons). (Particles are long-lived and simply-behaved ripples in fields.) But in some sense it is not empty, because the electric field, W field, Higgs field etc. are always in it! The vacuum, or rather, “a” vacuum, isn’t specified just by saying “it’s empty space”, because not only do we have to say that there are no particles in it, we also have to specify what the fields in that empty space are actually doing… Terminology: we say that we have to specify “the configuration of the fields” in that vacuum.
In a specific vacuum, the fields may be configured in such a way that most of the fields have an average value equal to zero. (I say “on average” because quantum “fluctuations”, or quantum jitter, assures they’re always fluttering a bit; but this is a side issue for us today.) But some of them may not be zero on average. Such is the case in our own vacuum; all fields are zero on average except for the Higgs field, whose average value is non-zero and is constant across the visible part of the universe (apart from its quantum jitter.) This is very important! The world we know would not be at all recognizable if instead the average value of the Higgs field were zero; indeed, we would not exist at all.
It is possible for a universe to have more than one vacuum. That is, it is possible for there to be more than one way for space to be as empty as possible — more than one way to configure the fields of the universe even when all particles are absent. Similarly, a theory which describes a universe may predict that it has more than one vacuum. An example of such a theory is the Standard Model, the equations used to describe and predict the behavior of the known elementary particles and forces of nature (but not including more mysterious elements: gravity, dark matter and dark energy). We now know, having measured the Higgs particle’s mass, that the Standard Model predicts there are two different vacua — one in which the Higgs field has the value that we observe in nature, and one in which it has a much larger value. In short, the theory predicts the possible existence of two very different ways that empty space can behave.
But let’s be very, very clear. The theory called the Standard Model predicts that this is the case, for the imaginary universe that the Standard Model describes. We do not yet know, experimentally, whether the Standard Model describes the real universe… i.e. whether the imaginary universe of the Standard Model and the real universe we live in are sufficiently similar that predictions of the Standard Model (theory) match all results from all experiments (data). And therefore, we do not know if the real world has the two vacua that the Standard Model predicts.
I’ll discuss these vacua in much more detail in a later article.
A Vacuum is Analogous to the Bottom of a Bowl
Here, I’d like to conclude by describing one of the essential properties that a vacuum has to have. It’s the same type of property that allows a marble to be stationary at the bottom of a bowl, which I talked about in some detail in this article about quantum tunneling. (Tunneling will turn out to be relevant for vacua too, but that’s something I’ll cover in another article.)
The bottom of a bowl is a “stable location” for a marble. That’s because if you move the marble a small distance in any direction, it rolls back to where it started, rattling around for a short while before friction causes it to stop back at the bottom of the bowl. Equivalently, if you move the marble a small distance away from the bottom, its energy (from its interaction with the Earth’s gravity) inevitably increases, and it will tend to try to reduce that energy by returning to its starting point, where its energy from gravity was as small as possible. A stable location is one in which any shift in the location of the marble increases the energy (or at least does not decrease it.) Conversely, if you could move the marble in such a way as to decrease its energy, the marble would start rolling in that direction and wouldn’t necessarily come back… so that would make its starting point an unstable location.
By definition, “a vacuum” is a “stable configuration of the fields of the universe (and of space itself).” In a vacuum, if anyone were to change the values of the fields by a small amount, the values of the fields would tend to return to where they started, bouncing around for a while until they eventually settled down to what they were originally. Equivalently, a vacuum is a configuration of fields for which the energy of the universe is minimized; any small change in the fields leads to an increase (or at least no decrease) in the universe’s energy, and the fields always will tend to return to their values in the vacuum.
Let’s return to our marble. I could imagine a situation where I have two identical bowls, each with a stable location for a marble. Or I could imagine I have a weirdly shaped bowl with two different stable locations at different heights. Or I could imagine a much more complicated bowl, with many stable locations. I can imagine placing the marble in any one of the places marked in Figure 3 by an arrow, and it would stay there indefinitely, because a small shift in the marble’s position wouldn’t be enough to move it from any one stable point to any other. [For objects much smaller than marbles, quantum tunneling complicates this story — see Figure 7 of that article — but let’s leave that aside for the moment.]
Similarly, a universe can have — or a theory of a universe can predict the existence of — more than one stable configuration of its fields, i.e., more than one vacuum. There is no limit to the number of possible vacua, though simple theories tend to have very few. Only theories with many types of fields commonly turn out to have many vacua. The question is therefore, at least indirectly, tied to the issue of how many types of fields does our universe really have? Just the ones we know? Or thousands more?
Does Our Universe Have Multiple Vacua?
How does it happen that the Standard Model predicts that our universe has two vacua? Well, first, it is easy to show (if you know how to do the calculations) that every elementary field in the Standard Model except the Higgs field has to have an average value of zero in any vacuum. But the Higgs field is different; it can and does have a non-zero average value in the vacuum we know, and can do so in any other vacuum that might exist. To figure out what the stable values are for the Higgs field, we calculate the energy of empty space as a function of the average value of the Higgs field. And interestingly, now that physicists have
- measured the top quark mass carefully,
- discovered the Higgs particle (of which there will be only one type, if the Standard Model is right), and
- measured the Higgs particle’s mass,
they can do a rather detailed calculation. And they find something similar to what is shown in Figure 4. [Note Figure 4 is merely a qualitative sketch! the true picture cannot be drawn to scale.] Just like the double bowl in the middle of Figure 3, which has two stable locations where any motion of the ball increases the energy of the ball, the energy of the Higgs field is predicted by the Standard Model to have two minima. That means that there are two vacua, as indicated by the arrows in Figure 4, with the properties indicated in Figure 1: one vacuum is the one we know, with a rather small value for the Higgs field, while the other, “exotic” vacuum has a huge value.
The precise location and depth (i.e., the value of the Higgs field, and the energy of empty space) for the exotic vacuum is in question. They depend quite sensitively on the masses of the top quark and of the Higgs particle, our knowledge of which is still subject to small but crucial changes as more is learned from data at the Large Hadron Collider (where the Higgs was discovered.) Figure 4 shows the current best guess, where our vacuum has somewhat higher energy than the exotic one. The importance of this fact will be addressed in another article.
But again, it must be kept firmly in mind that the Standard Model may not describe our universe well enough for any of this conclusion to hold. We already know the Standard Model leaves out gravity, dark matter and dark energy; it may leave out a whole host of as-yet-unknown particles. There may even be more types of Higgs particles, for all we know. Consequently, we don’t know anything for sure yet. Our universe may actually have just one vacuum, or it may have three, a hundred, or many more. Learning about the vacua of the universe remains a wide-open area of current research, one which quite possibly could continue for centuries.