Theories and Vacuums
An important concept that plays a large role in the modern understanding of the Universe is vacuum, or vacua in Latin, the plural form of the word “vacuum”.
You, probably, know that physicists call vacuum empty space in which there is nothing - neither air, nor even vigorous elementary particles. But then there is something strange about the idea of a vacuum in the plural. Obviously something else has been added to this concept! That is what I will try to explain.
First let me remind you of what theory is in physics. This is not a reasoning or an idea; it is something more specific. A theory is a set of equations and related concepts that allows scientists to make predictions about the behavior of physical objects. Some theories must describe the real world; most theories describe imaginary worlds; but any reasonable theory makes consistent predictions and describes aspects of a possible world.
For example, Newton's theory of gravity, in which the gravitational force between two objects at a distance r is proportional to 1 / r 2 , roughly describes what happens in the real world. There could be another theory of gravity, in which force is proportional to 1 / r 3 . This would still be a physical theory, since it makes clear predictions of how objects should be attracted to each other due to gravity, but it would describe an imaginary world, not ours, the real one. This is a completely normal physical theory, but it does not describe the nature of our world.
Some theories (not all, of course) should describe not only objects, but also the absence of objects in the form of empty space - also known as a vacuum. In Newton's time, empty space was simple. It was exactly that just empty space. But over the years, empty space has become increasingly difficult. In the XIX century it became known that there are fields in empty space - and today we consider fields to be elementary aspects of the Universe, therefore they are extremely important!
A field is an entity capable of meaning at any point in space at any given time. In everyday life, we encounter a field in the form of air temperature — at any given time, temperature can be measured at any place, and if you know the temperature in all space, you know the temperature field at that moment. But this example is not suitable for us, since the air temperature makes sense in the presence of air, and the temperature field is meaningless in empty space.
A better example would be the electric field (responsible for lightning, static adhesion and electrical currents in the wires). An electric field is an elementary field of nature that exists even in empty space. The same is true for all elementary fields of nature, including the W-field, the electron field, the muon field, etc., including the now famous Higgs field.
So when we talk about empty space, we mean the space that is as empty as possible. In a sense, it is empty, because there are no particles, even particles of light (photons). And the particles are long-lived and simply perturbed field perturbations. But in a sense, it is not empty, due to the electric field, W-field, Higgs field, all the time there is present! You cannot define a vacuum with a simple phrase “empty space”, since we need not only to say that there are no particles in it, we also need to say what exactly they are doing in this empty space of the field. That is, we need to determine the configuration of the fields in this vacuum.
In a particular vacuum, the fields can be configured in such a way that most of them will have a zero mean value. On average, because quantum fluctuations guarantee a slight jitter of values. But some of them may not be on average zero. This is also true for our vacuum - all fields are on average zero, except for the Higgs field, whose mean value is nonzero and constant over the entire visible part of the Universe (except for quantum jitter). It is very important! The world known to us could not be known if the average value of the Higgs field would be zero — we would not exist in it at all.
There may be several different vacuums in the universe. That is, space can be as empty as possible in several ways — there is more than one way to adjust the fields of the universe even in the absence of any particles. Similarly, a theory describing the universe can predict the presence of more than one kind of vacuum. An example of such a theory is the Standard Model, the equations used to describe and predict the behavior of known elementary particles and the interactions of nature (not including more mysterious elements: gravity, dark matter, and dark energy). Now, after we have measured the mass of the Higgs particle, we know that the Standard Model predicts two different vacuums - in one of them the Higgs field has the value we observe, and in the other it is much larger. In general, the theory predicts the possibility of the existence of two very different ways of behavior of empty space.
Fig. one
But let's clarify something. A theory called the Standard Model predicts this for an imaginary universe described by the Standard Model. We do not yet know from experiments whether the Standard Model describes the real universe — that is, whether the imaginary universe of the Standard Model and the real Universe in which we live are sufficiently similar for the predictions of the Standard Model (theory) to coincide with all the results of all experiments. (data). Therefore, we do not know whether there are two predicted by the Standard Model vacuum in the real world.
I will describe one of the main properties of vacuum. The same property allows the ball to rest at the bottom of the bowl.
Fig. 2
The bottom of the bowl is a stable position for the ball. If you move the ball a short distance in any direction, it will roll back, imitate a little, and then the friction force will stop it at the very bottom. When you move the ball a small distance from the bottom, its energy (interactions with the gravity of the Earth) increases, and it tends to decrease this energy through a return to the starting point, where the gravity energy is the lowest. A stable position is one in which any shift of the ball increases its energy, or at least does not reduce it. Accordingly, if you can move the ball so as to reduce its energy, the ball will roll in that direction and will not necessarily return - in this case, the initial current will not be in a stable position.
By definition, a vacuum is a stable configuration of the fields of the universe and of space itself. "If someone changes the field values in vacuum a little, the field values will tend to return to the initial position, then they will grow around it a little and calm down. Vacuum is a field configuration for the energy of the universe is minimal, any small change in the fields leads to an increase (or at least does not lead to a decrease) the energy of the universe, and the fields will always tend to return to their values in a vacuum.
Fig. 3: different bowls with different stable positions for the ball
Let's go back to the ball. You can imagine a situation in which I have two identical bowls, each of which has a stable position for the ball. Or you can imagine a strange shaped bowl with two different stable positions at different heights. Or you can imagine a much more complex bowl with many stable positions. You can imagine how we put the ball in one of the various positions marked in fig. 3 arrows, and it remains there indefinitely, because any small shift in the ball position will not be enough to move it from one stable position to another (the effect of quantum tunneling complicates this situation, but we will tell about it next time).
Similarly, the universe may have — or the theory of the universe can predict the existence — of more than one stable configuration of fields, that is, more than one vacuum. Nobody limits the number of possible vacuums, although simple theories usually have quite a few of them. Only theories with many types of fields usually have many vacuums. It turns out that the question, albeit not directly, is related to how many types of fields are there in our Universe? Only known to us? Or thousands of them?
How is it that the Standard Model predicts that there are two vacuums in our Universe? First, simply to show (if you know how to calculate) that every elementary field in the Standard Model, with the exception of the Higgs field, must have a zero average value in any vacuum. But the Higgs field is not like that; it can and does have a non-zero average value in the vacuum we know, and can have it in any other possible vacuum. To find out what the stable values are for the Higgs field, we calculate the empty space energy as a function of the average value of the Higgs field. Interestingly, today physicists can make very detailed calculations, since they already:
• accurately measured the mass of the upper quark,
• discovered the Higgs particle (which, according to the Standard Model, is only one type), and
• measured the mass of the Higgs particle.
As a result, they come to a conclusion similar to that shown in fig. 4. As with the double bowl in the middle of fig. 3, which has two stable positions, where any movement of the ball increases its energy, the Higgs field energy Standard Model predicts two minima. This means that there are two vacua indicated by arrows in fig. 4, with the properties indicated in fig. 1: one vacuum, known to us, with a rather small value of the Higgs field, another, an exotic vacuum, with a large value.
The exact location and depth (the value of the Higgs field and the energy of empty space) of an exotic vacuum is an open question. They are very dependent on the masses of the upper quark and the Higgs particle, our understanding of which can still undergo small but critical changes based on data from the Large Hadron Collider. Fig. 4 shows the current best guess, where our vacuum has more energy than exotic.
Fig. four
But we must always remember that the Standard Model may not describe our Universe well enough so that all these conclusions are correct. We already know that the Standard Model does not take into account gravity, dark matter and dark energy; it may not take into account the whole carriage of unknown particles. There may even be other types of Higgs particles. Accordingly, we do not know anything for certain. In our universe there can be only one vacuum, or three, a hundred, or much more. The study of the vacuum of the universe remains an area of active research, which in principle can continue for centuries.
You, probably, know that physicists call vacuum empty space in which there is nothing - neither air, nor even vigorous elementary particles. But then there is something strange about the idea of a vacuum in the plural. Obviously something else has been added to this concept! That is what I will try to explain.
The theory can offer a description of the empty space.
First let me remind you of what theory is in physics. This is not a reasoning or an idea; it is something more specific. A theory is a set of equations and related concepts that allows scientists to make predictions about the behavior of physical objects. Some theories must describe the real world; most theories describe imaginary worlds; but any reasonable theory makes consistent predictions and describes aspects of a possible world.
For example, Newton's theory of gravity, in which the gravitational force between two objects at a distance r is proportional to 1 / r 2 , roughly describes what happens in the real world. There could be another theory of gravity, in which force is proportional to 1 / r 3 . This would still be a physical theory, since it makes clear predictions of how objects should be attracted to each other due to gravity, but it would describe an imaginary world, not ours, the real one. This is a completely normal physical theory, but it does not describe the nature of our world.
Some theories (not all, of course) should describe not only objects, but also the absence of objects in the form of empty space - also known as a vacuum. In Newton's time, empty space was simple. It was exactly that just empty space. But over the years, empty space has become increasingly difficult. In the XIX century it became known that there are fields in empty space - and today we consider fields to be elementary aspects of the Universe, therefore they are extremely important!
Fields
A field is an entity capable of meaning at any point in space at any given time. In everyday life, we encounter a field in the form of air temperature — at any given time, temperature can be measured at any place, and if you know the temperature in all space, you know the temperature field at that moment. But this example is not suitable for us, since the air temperature makes sense in the presence of air, and the temperature field is meaningless in empty space.
A better example would be the electric field (responsible for lightning, static adhesion and electrical currents in the wires). An electric field is an elementary field of nature that exists even in empty space. The same is true for all elementary fields of nature, including the W-field, the electron field, the muon field, etc., including the now famous Higgs field.
Vacuum against vacuum
So when we talk about empty space, we mean the space that is as empty as possible. In a sense, it is empty, because there are no particles, even particles of light (photons). And the particles are long-lived and simply perturbed field perturbations. But in a sense, it is not empty, due to the electric field, W-field, Higgs field, all the time there is present! You cannot define a vacuum with a simple phrase “empty space”, since we need not only to say that there are no particles in it, we also need to say what exactly they are doing in this empty space of the field. That is, we need to determine the configuration of the fields in this vacuum.
In a particular vacuum, the fields can be configured in such a way that most of them will have a zero mean value. On average, because quantum fluctuations guarantee a slight jitter of values. But some of them may not be on average zero. This is also true for our vacuum - all fields are on average zero, except for the Higgs field, whose mean value is nonzero and constant over the entire visible part of the Universe (except for quantum jitter). It is very important! The world known to us could not be known if the average value of the Higgs field would be zero — we would not exist in it at all.
There may be several different vacuums in the universe. That is, space can be as empty as possible in several ways — there is more than one way to adjust the fields of the universe even in the absence of any particles. Similarly, a theory describing the universe can predict the presence of more than one kind of vacuum. An example of such a theory is the Standard Model, the equations used to describe and predict the behavior of known elementary particles and the interactions of nature (not including more mysterious elements: gravity, dark matter, and dark energy). Now, after we have measured the mass of the Higgs particle, we know that the Standard Model predicts two different vacuums - in one of them the Higgs field has the value we observe, and in the other it is much larger. In general, the theory predicts the possibility of the existence of two very different ways of behavior of empty space.
Fig. one
But let's clarify something. A theory called the Standard Model predicts this for an imaginary universe described by the Standard Model. We do not yet know from experiments whether the Standard Model describes the real universe — that is, whether the imaginary universe of the Standard Model and the real Universe in which we live are sufficiently similar for the predictions of the Standard Model (theory) to coincide with all the results of all experiments. (data). Therefore, we do not know whether there are two predicted by the Standard Model vacuum in the real world.
Vacuum is like the bottom of a bowl.
I will describe one of the main properties of vacuum. The same property allows the ball to rest at the bottom of the bowl.
Fig. 2
The bottom of the bowl is a stable position for the ball. If you move the ball a short distance in any direction, it will roll back, imitate a little, and then the friction force will stop it at the very bottom. When you move the ball a small distance from the bottom, its energy (interactions with the gravity of the Earth) increases, and it tends to decrease this energy through a return to the starting point, where the gravity energy is the lowest. A stable position is one in which any shift of the ball increases its energy, or at least does not reduce it. Accordingly, if you can move the ball so as to reduce its energy, the ball will roll in that direction and will not necessarily return - in this case, the initial current will not be in a stable position.
By definition, a vacuum is a stable configuration of the fields of the universe and of space itself. "If someone changes the field values in vacuum a little, the field values will tend to return to the initial position, then they will grow around it a little and calm down. Vacuum is a field configuration for the energy of the universe is minimal, any small change in the fields leads to an increase (or at least does not lead to a decrease) the energy of the universe, and the fields will always tend to return to their values in a vacuum.
Fig. 3: different bowls with different stable positions for the ball
Let's go back to the ball. You can imagine a situation in which I have two identical bowls, each of which has a stable position for the ball. Or you can imagine a strange shaped bowl with two different stable positions at different heights. Or you can imagine a much more complex bowl with many stable positions. You can imagine how we put the ball in one of the various positions marked in fig. 3 arrows, and it remains there indefinitely, because any small shift in the ball position will not be enough to move it from one stable position to another (the effect of quantum tunneling complicates this situation, but we will tell about it next time).
Similarly, the universe may have — or the theory of the universe can predict the existence — of more than one stable configuration of fields, that is, more than one vacuum. Nobody limits the number of possible vacuums, although simple theories usually have quite a few of them. Only theories with many types of fields usually have many vacuums. It turns out that the question, albeit not directly, is related to how many types of fields are there in our Universe? Only known to us? Or thousands of them?
Does our universe have many vacuums?
How is it that the Standard Model predicts that there are two vacuums in our Universe? First, simply to show (if you know how to calculate) that every elementary field in the Standard Model, with the exception of the Higgs field, must have a zero average value in any vacuum. But the Higgs field is not like that; it can and does have a non-zero average value in the vacuum we know, and can have it in any other possible vacuum. To find out what the stable values are for the Higgs field, we calculate the empty space energy as a function of the average value of the Higgs field. Interestingly, today physicists can make very detailed calculations, since they already:
• accurately measured the mass of the upper quark,
• discovered the Higgs particle (which, according to the Standard Model, is only one type), and
• measured the mass of the Higgs particle.
As a result, they come to a conclusion similar to that shown in fig. 4. As with the double bowl in the middle of fig. 3, which has two stable positions, where any movement of the ball increases its energy, the Higgs field energy Standard Model predicts two minima. This means that there are two vacua indicated by arrows in fig. 4, with the properties indicated in fig. 1: one vacuum, known to us, with a rather small value of the Higgs field, another, an exotic vacuum, with a large value.
The exact location and depth (the value of the Higgs field and the energy of empty space) of an exotic vacuum is an open question. They are very dependent on the masses of the upper quark and the Higgs particle, our understanding of which can still undergo small but critical changes based on data from the Large Hadron Collider. Fig. 4 shows the current best guess, where our vacuum has more energy than exotic.
Fig. four
But we must always remember that the Standard Model may not describe our Universe well enough so that all these conclusions are correct. We already know that the Standard Model does not take into account gravity, dark matter and dark energy; it may not take into account the whole carriage of unknown particles. There may even be other types of Higgs particles. Accordingly, we do not know anything for certain. In our universe there can be only one vacuum, or three, a hundred, or much more. The study of the vacuum of the universe remains an area of active research, which in principle can continue for centuries.
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