The photon - the particle which makes up light - is probably one of the best known elementary particles. Nonetheless, everything can be made more involved. Thus, we studied a more complicated version of it in our most recent paper.
"Why in the world should we do this?" is a valid question at this point. That proceeded in multiple stages. I have written quite some time ago that for a particle physicist it is baffling that chemistry works. Chemistry works, among other things, because the electric charge of nuclei and electrons are perfectly balanced. Well, as perfect as we can measure, anyhow. In the standard model of particle physics there is no reason why this should be the case. However, the standard model is mathematical consistent only if this is the case. In fact, only if the balance is really perfect. Mathematical consistency is not a sufficient argument why a theory needs to be correct. Experiment is. So people have investigated this baffling fact since decades. In this process, the idea came up that there is a reason for this. And that reason would be that the standard model is only a facet of an underlying theory. This underlying theory enforces the equality of the electric charges by combining the weak, strong, and electromagnetic forces into one force. Such theories are called grand-unified theories, or short GUTs.
Such GUTs use a single gauge theory to combine all these forces. This is only possible with a certain kind, which is fundamentally different from the one we use for electromagnetism alone. It is more similar to the ones of the strong and weak force. We have investigated this type of theories for a long time. And one central insight is that in such theories none of the elementary particles can be observed individually. Only so-called bound states, which are made from two or more elementary particles, can be. That is very different from the ordinary photon of electromagnetism, which is, essentially, elementary.
The central question was therefore whether any such bound state could have the properties of the photon which we know from experiment. Otherwise a GUT would (very likely) not be a possible candidate to explain the balance of electric charges in chemistry. The photon has three important features. It does not carry itself electric charge. It is massless. And it has one unit of so-called spin.
Thus we needed to build a bound state in a GUT with these properties. The spin and absence of charge is actually quite simple, and you get this almost for free in any GUT. It is really the fact that it should not have mass which makes it so complicated. It is even more complicated to verify that it has no mass.
We had some ideas from our previous work, using pen-and-paper calculations, how this could work. There had also been some numerical simulations looking into similar questions in the early 1980ies, though they were, given resources back then, very exploratory. So we set up our own, modern-day numerical simulations. However, it is not yet possible to simulate a full, realistic GUT. For this all computing power on earth would not suffice, if we want to be done in a lifetime. So we used the simplest possible theory which had all the correct features relevant to a true GUT. This is an often employed trick in physics. One reduces a problem to the absolutely essential features, throwing away the rest, which has no or little impact on the particular question at hand. And by this getting a manageable problem.
So we did. And due to some ingenious ideas of my collaborators, especially my PhD student Vincenzo Afferrante, we were able to perform the simulations. There was a lot of frustrating work for the first few months, actually. But we persevered. And we were rewarded. In the end, we got our massless photon in exactly the way we hoped! We thus demonstrated that such a mechanism is possible. We got a massless photon made up out of elementary particles! A huge success for the whole setup. In addition, the things which make up the photon are (partly) very massive. That a bound state can be lighter than its constituents is an amazing consequence of special relativity. For us, this is an added bonus. Because you cannot see the fact that a particle is made up of other particles if you have not enough energy available to create the constituents. Again, this comes from the theory of relativity. In this scenario one of the constituents is indeed so heavy that we would not be able to produce it in experiments yet. Hence, with our current experiments, we would not yet detect that the photon is made up from other particles. And this is indeed what we observe. So everything is consistent. Very reassuring. Unfortunately, it is so heavy that also none of the currently planned experiments would be able to do so. Hence, we will not be able to test this idea directly experimentally. This will need to resort to indirect evidence.
Of course, I gloss over a lot of details and technicalities here, which took most of our time. Describing them would fill multiple entries.
Now, the only thing we need to do is to figure out whether anything we neglected could interfere. None of it will at a qualitative level. But, of course, we have very good experiments. And thus to make the whole idea a suitable GUT to describe nature, we also need to get it quantitatively correct. But this will be a huge step. Therefore we broke it down in small steps. We will do them one by one. Our next step is now to get the electron right. Let's see if this also works out.
Showing posts with label QED. Show all posts
Showing posts with label QED. Show all posts
Tuesday, April 21, 2020
Thursday, October 21, 2010
Electromagnetism, photons, and symmetry
After this rather abstract enumeration, it is time to take a closer look at a particular example. The simplest sector embedding a local symmetry in the standard model is electromagnetism. Classically, electromagnetism describes electric and magnetic fields, and thus also light, X-rays, and every other form of electromagnetic waves. As their names already hints, electric and magnetic fields are so-called fields. Fields in physics are something which associate with each point in space and with each instance in time a quantity. In case of electromagnetism this is a quantity describing the electric and magnetic properties at this point. Each of these two properties turn out to have a strength and a direction. Thus the electric and magnetic fields associate with each point in space and time an electric and a magnetic magnitude and a direction. For a magnetic field this is well known from daily experience. Go around with a compass. As you move, the magnetic needle will arrange itself in response to the geomagnetic field. Thus, this demonstrates that there is a direction involved with magnetism. That there is also a strength involved you can see when moving two magnets closer and closer together. How much they pull at each other depends on where they are relative to each other. Thus there is also a magnitude associated with each point. The same actually applies to electric fields, but this is not as directly testable with common elements. Ok, so it is now clear that electric and magnetic fields have a direction and a magnitude. Thus, at each point in space and time six numbers are needed to describe them: two magnitudes and two angles each to determine a direction.
When in the 19th century people tried to understand how electromagnetism works they also figured this out. However, they made also another intriguing discovery. When writing down the laws which govern electromagnetism, it turns out that electric and magnetic fields are intimately linked, and that they are just two sides of the same coin. That is the reason to call it electromagnetism. In the early 20th century it then became clear that both phenomena can be associated with a single particle, the photon. But then it was found that to characterize a photon only two numbers at each point in space and time are necessary. This implies that between the six numbers characterizing electric and magnetic fields relations exist. These are known as Maxwell equations in classical physics, or as quantum Maxwell dynamics in the quantum theory. If you would add, e. g., electrons to this theory, you would end up with quantum electro dynamics - QED.
So, this appeared as a big step forward in describing numerically electromagnetism. However, when looking deeper into the mathematical concepts, it turned out to be technically rather complicated to describe all electric and magnetic phenomena with just these two properties of the photon. It was then that people noticed that including a certain redundancy things became much simpler. An ideal solution was found to describe electromagnetism with four numbers at each space-time point, instead of two. These can then not be independent, of course. And it is here where the symmetry comes into play: It is a symmetry concept which connects these numbers.
First, here is a simple example of how it works. Take someone walking only along the circumference of a circle. Then you can either describe her position by the height and width from the center of the circle. Or you can use the angle around the circle's circumference. Both is equally valid. Hence, the two numbers of the first choice are uniquely connected to the second choice: Changing the angle will change both height and width simultaneously! And because this connection comes from the fact that the circle is rotationally symmetric, it is this symmetry. And the symmetry of a circle is called U(1). Now, the relation between the four convenient numbers and the two important ones is quite in analogy to this case, and is therefore also a U(1) symmetry. That is how the symmetry becomes associated with electromagnetism. This tells us that if we change the four numbers by, so to say, moving them around on the circle, we do not change the two numbers describing the photon (or the six describing the electric and magnetic field). Only when we move away from the circumference, the two (and six) numbers change. In this way the symmetry is only helping us in a mathematical description, but is not influencing what we can measure. It is therefore also called a gauge symmetry. It is actually a local gauge symmetry, because these are fields, and we can do this at every point.
When in the 19th century people tried to understand how electromagnetism works they also figured this out. However, they made also another intriguing discovery. When writing down the laws which govern electromagnetism, it turns out that electric and magnetic fields are intimately linked, and that they are just two sides of the same coin. That is the reason to call it electromagnetism. In the early 20th century it then became clear that both phenomena can be associated with a single particle, the photon. But then it was found that to characterize a photon only two numbers at each point in space and time are necessary. This implies that between the six numbers characterizing electric and magnetic fields relations exist. These are known as Maxwell equations in classical physics, or as quantum Maxwell dynamics in the quantum theory. If you would add, e. g., electrons to this theory, you would end up with quantum electro dynamics - QED.
So, this appeared as a big step forward in describing numerically electromagnetism. However, when looking deeper into the mathematical concepts, it turned out to be technically rather complicated to describe all electric and magnetic phenomena with just these two properties of the photon. It was then that people noticed that including a certain redundancy things became much simpler. An ideal solution was found to describe electromagnetism with four numbers at each space-time point, instead of two. These can then not be independent, of course. And it is here where the symmetry comes into play: It is a symmetry concept which connects these numbers.
First, here is a simple example of how it works. Take someone walking only along the circumference of a circle. Then you can either describe her position by the height and width from the center of the circle. Or you can use the angle around the circle's circumference. Both is equally valid. Hence, the two numbers of the first choice are uniquely connected to the second choice: Changing the angle will change both height and width simultaneously! And because this connection comes from the fact that the circle is rotationally symmetric, it is this symmetry. And the symmetry of a circle is called U(1). Now, the relation between the four convenient numbers and the two important ones is quite in analogy to this case, and is therefore also a U(1) symmetry. That is how the symmetry becomes associated with electromagnetism. This tells us that if we change the four numbers by, so to say, moving them around on the circle, we do not change the two numbers describing the photon (or the six describing the electric and magnetic field). Only when we move away from the circumference, the two (and six) numbers change. In this way the symmetry is only helping us in a mathematical description, but is not influencing what we can measure. It is therefore also called a gauge symmetry. It is actually a local gauge symmetry, because these are fields, and we can do this at every point.
Monday, December 21, 2009
The forces of nature II - Electromagnetism
Electromagnetism is another force that everyone of us experiences in their daily lives. Of course, everything that is electric is based on electromagnetism. But it is not only that. When we knock on the desk, the force we feel is actually also electromagnetism. The force which keeps a crystal together, or the desk, or make water not spontaneously evaporate: All this and much more is electromagnetism. In fact, even light is electromagnetism. Our eye registers electromagnetic radiation and turns it with the brain into visual information.
As the name already suggests - Electro-magnetism - electromagnetism is the unification of the electric force, which make electric things work, and magnetic force, which is the force making magnets act like they do.
Indeed, both forces are not fundamentally different. If one takes special relativity, the theory of movements close to the speed of light, into account, they turn out to be just two sides of the same coin.
If looked at from the quantum perspective, this is even more manifest: Both forces are mediated by the same particle, the photon. The photon itself is not feeling the force itself it mediates. This makes electromagnetism fundamentally different from the weak and strong forces, which will be described next.
In turn, almost all matter feels electromagnetism: All quarks carry an electric charge. A charge, like the mass in case of gravity, is the fundamental docking port for the exchange particles. Also electrons, and their heavier cousins the muon and tau, carry electric charge. On the other hand, the neutrinos and the ever-searched-for Higgs particle are both neutral, and do not interact with the photon (there is a subtlety in this statement which will be discussed much later).
An amazing difference between mass and electromagnetic charge is that it is quantized. There appears to exist an elementary charge of which the charged particles carry a certain number. For historical reason, this is counted in thirds, instead of integer. So, the up quark carry 2/3 of an electric charge, while the electron carries -1, and so on. This is different in two respects from mass, the charge of gravity.
One is that it is quantized. Though we understand how to describe this quantization, the standard model of particle physics actually gives no explanation for it. In particular, the fact that electrons and up quarks have electric charges in a ratio of whole numbers is not understood, though it is required for the standard model in its current form to work. There are many unified theories which try to explain it, but none of them has produced yet observable effects which are different from the standard model and could be accessed in experiments.
The other property is that there is a positive and a negative charge. Mass comes only in positive portions. Electric charge comes in two varieties, + and -, which can compensate each other. As a consequence, the net charge of an array of objects can be zero, which is not possible for gravity. Such an exact zero is only possible because of the quantization. In general, almost all objects have almost zero charge. As a consequence, electromagnetism is screened at long distances: Net zero charge objects can only pull at each other, if for some reasons their internal charge array is such that positive and negative charges are not evenly distributed. Then another such object can pull, say, at the top side and push at the bottom. But this is a weak effect compared to the electromagnetism of charges objects. Only close by this can be important, and yields many of the everyday experiences with electromagnetism. And that is pretty good: As stated before, electromagnetism is very much stronger than gravity, and if it would not be screened, everything would pull or push at each other with enormous strength, creating an immediate collapse.
The only electromagnetic objects not affected by this screening are photons. Therefore, they can travel freely. The most common experience with this is light, but also the cosmic microwave background or radio is based on this. If photons would also be charged, this would not be possible.
Hence, electromagnetism introduces two new concepts: Quantization of charge and different signs of the charge, yielding the possibility of screening. Both will become very important for the strong and weak forces as well.
The quantum theory of electromagnetism, in contrast to the case of gravity, is very well understood. It is called quantum electrodynamics (QED), and it is one of the best and most successful theories today. As such, it is also part of the standard model of elementary particles, and there it is called the electromagnetic sector.
Unfortunately, it is not as good as it could be. If you increase the speed, and thus energy, of the particles, QED starts to get into trouble eventually. It appears that at very high energies the theory collapses, and electromagnetic interactions ceases altogether. However, this is likely stabilized when QED is embedded into the standard model.
Still, QED is more than only a successful theory. In fact, the structure of the theory, a so-called quantum gauge theory, is prototypical, and more complex versions of it are the theories describing the strong and weak forces, and also many attempts for quantum gravity. To our knowledge, it is the most important type of theories. What such a theory is precisely will be described after the introduction of the other two forces of nature: The weak and the strong one.
As the name already suggests - Electro-magnetism - electromagnetism is the unification of the electric force, which make electric things work, and magnetic force, which is the force making magnets act like they do.
Indeed, both forces are not fundamentally different. If one takes special relativity, the theory of movements close to the speed of light, into account, they turn out to be just two sides of the same coin.
If looked at from the quantum perspective, this is even more manifest: Both forces are mediated by the same particle, the photon. The photon itself is not feeling the force itself it mediates. This makes electromagnetism fundamentally different from the weak and strong forces, which will be described next.
In turn, almost all matter feels electromagnetism: All quarks carry an electric charge. A charge, like the mass in case of gravity, is the fundamental docking port for the exchange particles. Also electrons, and their heavier cousins the muon and tau, carry electric charge. On the other hand, the neutrinos and the ever-searched-for Higgs particle are both neutral, and do not interact with the photon (there is a subtlety in this statement which will be discussed much later).
An amazing difference between mass and electromagnetic charge is that it is quantized. There appears to exist an elementary charge of which the charged particles carry a certain number. For historical reason, this is counted in thirds, instead of integer. So, the up quark carry 2/3 of an electric charge, while the electron carries -1, and so on. This is different in two respects from mass, the charge of gravity.
One is that it is quantized. Though we understand how to describe this quantization, the standard model of particle physics actually gives no explanation for it. In particular, the fact that electrons and up quarks have electric charges in a ratio of whole numbers is not understood, though it is required for the standard model in its current form to work. There are many unified theories which try to explain it, but none of them has produced yet observable effects which are different from the standard model and could be accessed in experiments.
The other property is that there is a positive and a negative charge. Mass comes only in positive portions. Electric charge comes in two varieties, + and -, which can compensate each other. As a consequence, the net charge of an array of objects can be zero, which is not possible for gravity. Such an exact zero is only possible because of the quantization. In general, almost all objects have almost zero charge. As a consequence, electromagnetism is screened at long distances: Net zero charge objects can only pull at each other, if for some reasons their internal charge array is such that positive and negative charges are not evenly distributed. Then another such object can pull, say, at the top side and push at the bottom. But this is a weak effect compared to the electromagnetism of charges objects. Only close by this can be important, and yields many of the everyday experiences with electromagnetism. And that is pretty good: As stated before, electromagnetism is very much stronger than gravity, and if it would not be screened, everything would pull or push at each other with enormous strength, creating an immediate collapse.
The only electromagnetic objects not affected by this screening are photons. Therefore, they can travel freely. The most common experience with this is light, but also the cosmic microwave background or radio is based on this. If photons would also be charged, this would not be possible.
Hence, electromagnetism introduces two new concepts: Quantization of charge and different signs of the charge, yielding the possibility of screening. Both will become very important for the strong and weak forces as well.
The quantum theory of electromagnetism, in contrast to the case of gravity, is very well understood. It is called quantum electrodynamics (QED), and it is one of the best and most successful theories today. As such, it is also part of the standard model of elementary particles, and there it is called the electromagnetic sector.
Unfortunately, it is not as good as it could be. If you increase the speed, and thus energy, of the particles, QED starts to get into trouble eventually. It appears that at very high energies the theory collapses, and electromagnetic interactions ceases altogether. However, this is likely stabilized when QED is embedded into the standard model.
Still, QED is more than only a successful theory. In fact, the structure of the theory, a so-called quantum gauge theory, is prototypical, and more complex versions of it are the theories describing the strong and weak forces, and also many attempts for quantum gravity. To our knowledge, it is the most important type of theories. What such a theory is precisely will be described after the introduction of the other two forces of nature: The weak and the strong one.
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