Last time we have defined coordinate systems. We also made the statement that for two people to agree about something measured with the coordinate system, they had to agree where to position the origin, and how to orient the coordinate system. The latter could e.g. be done by making one of its axis point north and the other point east and the third perpendicular in the heavens. An interesting question is now why we had to agree about orientation and origin. Obviously, a player on the field will not care about how we locate him and how we discuss about his location (I neglect here the possibility of markers on the field for the purpose of playing a game. Just assume that they are not necessary and the rules of the game do not need them). She will just keep on playing, no matter how often we change our agreement or how extreme our conventions are.
With this, we have a first example of a feature which is very central to our understanding of how we can describe physics. This is the concept of invariance. It means essentially that nature is not caring about how we describe it, and whatever we do, we have to respect this. In particular, nothing can depend on us. We are just observers. That seems to be an innocent enough statement, and moreover a pretty obvious one. It is actually not.
First, nothing dictates nature to be that way. There is no reason that nature should not depend on who it observes how. Though this would quite ruin our current understanding of how nature works, it is just an empirical fact, and one which we can not (yet) explain. It is a law of nature, so far.
The second is that as innocent as the statement looks, it has become one of our most powerful tools to devise a description of nature. Lets get back to the players on the field. Given the just said, the numbers which with we describe the position of a player on the field are not of importance. The player is not even aware of them. Things start to change when we add a second player. Also she is not aware of which numbers we assign to her to keep track of her position. What both players are very much aware of, however, is where the other one is, and how far she is away. That is something we can also quantify with our coordinate systems. If the first player is at the origin, say, and the second player is at the next grid point at the first tick in the direction of one axis, their distance is the distance of the tick marks, say one meter. Hence, their distance is one meter.
What happens now if we change our coordinate system? Well, lets flip it somehow, and move the origin to the sun. But this does not change the distance of the two players, it is still one meter. Hence, their distance is (so-called) invariant under a change of the coordinate system! That is a first example of how actually an invariance pops up. Hence, if we try to describe how the two players behave, the numbers of the coordinate system will not matter, but their distance will. So, we know now that a theory describing the players (e.g. to determine the rules of the game) will not make use of the coordinate system, but only of the distance of the two players. Thus, invariance has given us a first tool how to describe the behavior of the players.
This could also be formulated differently (and very popular). The players do not care about the coordinate system we put on the field, despite this having a universe-wide particular point of reference, its origin. They only care about the distance with respect to each other. That is, the absolute frame given by the coordinate system does not matter. Only the relative position of the two players matters. Thus, it is only relative quantities which do matter. The popular phrase made from this fact is that "everything is relative". Here, we have seen that this phrase embodies the principle of invariance under a change of description.
Is the coordinate system now of complete uselessness after we have introduced and bargained about it so much? No, it is still very useful. We can still use it to describe the two players on the field. This makes life much simpler. However, we know now that of the numbers associated with each player only the ones giving their distance will enter the rules of the game, the description of nature, and the remaining ones only serve us to provide a clear picture. It is this possibility to have a clear picture to the human mind, which lets us keep the additional coordinate system when we describe something in most cases.
Tuesday, April 27, 2010
Thursday, March 18, 2010
Coordinate Systems
With the players now on the field, it is about time to say something about the field itself.
One thing quite necessary when one wants to talk about the field in a reproducible way, a central requirement for scientific investigations, is to be able to denote a point on the field. If it would indeed be a field, one could just lay a grid with regular squares of length, say, one meter each, over the field. A position on the field is then just given by denoting a certain square. Or? Well, there are two points which have to be added.
The first is that a square of one meter extension in both directions is rather vague when it comes to an object the size of a cherry, though it may be sufficient to locate a player rather well. So, it is necessary to make the grid finer for a cherry. That can be done by taking each square and subdivide it further in squares of, e.g., one centimeter extension. That should be sufficient for a cherry, but would not be for a bacteria. Then, we would have to subdivide it further into micrometer. And for an atom or a nuclei or a quark even much further. Therefore, such a grid should have a resolution of the field in useful units, such that everything can be located as good as necessary.
The second thing is that it is still very hard to agree on where a player is. The reason is that we have not yet fixed our grid, and two different observers could slide it differently over the field. We therefore need a reference point. For example that a certain square has its lower-left corner in the middle of the field. But this is not enough. Besides sliding the grid, there is also the possibility to rotate the grid. Therefore, we have to have a reference orientation. For example, if the lower left corner of a given square is at the center of the field, we could agree that then the edge which connects it to its upper left corner should point in the direction of the magnetic north-pole. Now, we have a well-defined grid.
Actually, we have already made another choice. We decided to have a grid of squares. We could also have chosen, say, a rectangular grid. Or a circular. Or something more twisted. We just have to specify it.
So, altogether, to be able to locate something on the field requires us to fix a grid with a certain geometry of elementary grid patches, like the squares, having a certain resolution, associate a particular patch with a particular point - this is called the origin of the grid - and its orientation. All these information together define a coordinate system for the field.
We could now go on, and add also a further direction, say, up in the sky, so we can not only talk about where on the field, but also in which height above the field. By this additional direction, we have added a further coordinate axis to the coordinate system. We have tacitly assumed that it has the same patch geometry and resolution, and given it an orientation. Again, we need to fix the point where it touches the field, which is usually then the origin of the grid on the field. With this step, we have promoted our flat coordinate system on the field to one with height and volume: We have added another dimension to it. Originally, we had two directions on the field - depth and width. These are two dimensions. By adding one, we gained another dimension, a third one, the height. We could go on, and add another one measuring (invisibly) the time, so we can specify where and when and how far above the field something happened. These four information are then the coordinates of this something, of this event. It is such a four-dimensional grid, which is usually used to describe things happening in our world in physics.
An important insight is that what we did to set the origin, orientation, and resolution has been arbitrary. If somebody would want to have the origin a bit more to the left, and it direction pointing towards the south-pole, it could have done so as well, and would also be able to specify an event on the field. The important thing is that if we know how he has chosen his coordinate system relative to ours - a bit more to the left and the direction towards south - we are able to translate his coordinates into ours. Hence, though we need the coordinate system to make a definite statement where and when something happens, it is not unique. We could chose any coordinate system, as long, as we know how to relate it to all others.
This is an important idea in the description of physics in general and in elementary particle physics in particular. We can chose an adequate coordinate system for a problem to make things simple, as long, as we keep in mind how to translate it to other coordinate systems.
One thing quite necessary when one wants to talk about the field in a reproducible way, a central requirement for scientific investigations, is to be able to denote a point on the field. If it would indeed be a field, one could just lay a grid with regular squares of length, say, one meter each, over the field. A position on the field is then just given by denoting a certain square. Or? Well, there are two points which have to be added.
The first is that a square of one meter extension in both directions is rather vague when it comes to an object the size of a cherry, though it may be sufficient to locate a player rather well. So, it is necessary to make the grid finer for a cherry. That can be done by taking each square and subdivide it further in squares of, e.g., one centimeter extension. That should be sufficient for a cherry, but would not be for a bacteria. Then, we would have to subdivide it further into micrometer. And for an atom or a nuclei or a quark even much further. Therefore, such a grid should have a resolution of the field in useful units, such that everything can be located as good as necessary.
The second thing is that it is still very hard to agree on where a player is. The reason is that we have not yet fixed our grid, and two different observers could slide it differently over the field. We therefore need a reference point. For example that a certain square has its lower-left corner in the middle of the field. But this is not enough. Besides sliding the grid, there is also the possibility to rotate the grid. Therefore, we have to have a reference orientation. For example, if the lower left corner of a given square is at the center of the field, we could agree that then the edge which connects it to its upper left corner should point in the direction of the magnetic north-pole. Now, we have a well-defined grid.
Actually, we have already made another choice. We decided to have a grid of squares. We could also have chosen, say, a rectangular grid. Or a circular. Or something more twisted. We just have to specify it.
So, altogether, to be able to locate something on the field requires us to fix a grid with a certain geometry of elementary grid patches, like the squares, having a certain resolution, associate a particular patch with a particular point - this is called the origin of the grid - and its orientation. All these information together define a coordinate system for the field.
We could now go on, and add also a further direction, say, up in the sky, so we can not only talk about where on the field, but also in which height above the field. By this additional direction, we have added a further coordinate axis to the coordinate system. We have tacitly assumed that it has the same patch geometry and resolution, and given it an orientation. Again, we need to fix the point where it touches the field, which is usually then the origin of the grid on the field. With this step, we have promoted our flat coordinate system on the field to one with height and volume: We have added another dimension to it. Originally, we had two directions on the field - depth and width. These are two dimensions. By adding one, we gained another dimension, a third one, the height. We could go on, and add another one measuring (invisibly) the time, so we can specify where and when and how far above the field something happened. These four information are then the coordinates of this something, of this event. It is such a four-dimensional grid, which is usually used to describe things happening in our world in physics.
An important insight is that what we did to set the origin, orientation, and resolution has been arbitrary. If somebody would want to have the origin a bit more to the left, and it direction pointing towards the south-pole, it could have done so as well, and would also be able to specify an event on the field. The important thing is that if we know how he has chosen his coordinate system relative to ours - a bit more to the left and the direction towards south - we are able to translate his coordinates into ours. Hence, though we need the coordinate system to make a definite statement where and when something happens, it is not unique. We could chose any coordinate system, as long, as we know how to relate it to all others.
This is an important idea in the description of physics in general and in elementary particle physics in particular. We can chose an adequate coordinate system for a problem to make things simple, as long, as we keep in mind how to translate it to other coordinate systems.
Friday, March 5, 2010
The Higgs effect
As has been discussed previously, the weak interactions make a difference between left and right. This has very profound consequences for particle physics, since we do not know how to formulate a theory which at the same time is in agreement with this asymmetry, experiments, and has quarks and leptons with an intrinsic mass. So, it seems that everything build up so far is not very stable. Fortunately, there is a way out. And this way is to let the mass of a particle not be a fixed property but to make it an acquired one. Something, which happens dynamically, and is not static.
We know a vivid example of how such a thing could happen from everyday experience. If we move a spoon through honey, it moves much slower than it would if we use the same force to move it through water. It feels, as if we dragging a much larger mass. So, the environment can give us the illusion of a larger mass than there actually is. It is essentially the same concept, though a bit more sophisticated, which is invoked in particle physics to provide mass to the particles.
Actually, there is not only one concept, but many, which can provide this feature. For the standard model of particle physics, we have settled so far to the most simple one. We are not yet quite sure whether it is the correct one, since we have no experimental confirmation of its main actor. This main actor is the so-called Higgs particle. The search for it is something which many experiments, most notably the Tevatron and the LHC, pursue at the time of writing. Yet without success, and with every passing month it becomes more likely that we need a different concept. But for now, let us remain with the simplest one.
This simplest one foresees this Higgs particle. And the idea now is that this particle condenses, very much like vapor condenses into water. The so-formed condensate fills all of space. Since the Higgs particle interacts with quarks and leptons, they start to stick to this condensate while moving through it. By this, the illusion of their mass is created. The same holds true for the W-bosons and Z-boson of the weak interaction. Only photons and gluons can escape this effect, and remain massless. Even the mass of a single Higgs particle itself is modified by the condensate of all the other Higgs particles, because it can also interact with itself.
And by this mechanism all the particles get their mass. So, all around us the space is filled with the condensate. We can see through it, because the photons do not become slowed down. But the rest is, and so we feel a mass, including our own.
In a sense, the Higgs particle is thus a kind of a fifth force, since it not only forms the condensate, but is also exchanged between the condensate and other particles. At the same time, it is also affected by the other forces, so it is also a bit like the quarks and leptons. Therefore it is commonly not regarded as a force of its own. The theory of the Higgs particle is usually refereed to as the Higgs sector of the standard model. Our quantum theory of it is actually downright ugly, since we need a lot of very special assumptions about the properties of the Higgs to make it compatible with the world around us, and still cannot predict how massive itself is, and if and how we can see it directly with contemporary experiments. That is also one of the reasons for the great popularity of alternative explanations, which nonetheless all boil down to replace this Higgs effect by something else, having essentially the same effect and provide mass for the particles.
With this Higgs particle and its interactions, the last of the players in the standard model have been introduced. The next step is then to think about how describing their physics.
We know a vivid example of how such a thing could happen from everyday experience. If we move a spoon through honey, it moves much slower than it would if we use the same force to move it through water. It feels, as if we dragging a much larger mass. So, the environment can give us the illusion of a larger mass than there actually is. It is essentially the same concept, though a bit more sophisticated, which is invoked in particle physics to provide mass to the particles.
Actually, there is not only one concept, but many, which can provide this feature. For the standard model of particle physics, we have settled so far to the most simple one. We are not yet quite sure whether it is the correct one, since we have no experimental confirmation of its main actor. This main actor is the so-called Higgs particle. The search for it is something which many experiments, most notably the Tevatron and the LHC, pursue at the time of writing. Yet without success, and with every passing month it becomes more likely that we need a different concept. But for now, let us remain with the simplest one.
This simplest one foresees this Higgs particle. And the idea now is that this particle condenses, very much like vapor condenses into water. The so-formed condensate fills all of space. Since the Higgs particle interacts with quarks and leptons, they start to stick to this condensate while moving through it. By this, the illusion of their mass is created. The same holds true for the W-bosons and Z-boson of the weak interaction. Only photons and gluons can escape this effect, and remain massless. Even the mass of a single Higgs particle itself is modified by the condensate of all the other Higgs particles, because it can also interact with itself.
And by this mechanism all the particles get their mass. So, all around us the space is filled with the condensate. We can see through it, because the photons do not become slowed down. But the rest is, and so we feel a mass, including our own.
In a sense, the Higgs particle is thus a kind of a fifth force, since it not only forms the condensate, but is also exchanged between the condensate and other particles. At the same time, it is also affected by the other forces, so it is also a bit like the quarks and leptons. Therefore it is commonly not regarded as a force of its own. The theory of the Higgs particle is usually refereed to as the Higgs sector of the standard model. Our quantum theory of it is actually downright ugly, since we need a lot of very special assumptions about the properties of the Higgs to make it compatible with the world around us, and still cannot predict how massive itself is, and if and how we can see it directly with contemporary experiments. That is also one of the reasons for the great popularity of alternative explanations, which nonetheless all boil down to replace this Higgs effect by something else, having essentially the same effect and provide mass for the particles.
With this Higgs particle and its interactions, the last of the players in the standard model have been introduced. The next step is then to think about how describing their physics.
Tuesday, February 23, 2010
The forces of nature IV - The weak force
The last force of nature is the weak force. Actually, its name is a bit misleading, but this will be explained later. This force is something which is even less accessible to our daily experience, but it is as much of relevance to our very existence as the other forces. The most direct evidence of it is already a nuclear process, the so-called beta decay. In such a decay, a neutron transforms, or decays, into a proton, an electron, and an electron-anti-neutrino. Precisely such decays, or the inverse process of neutron formation, is of quite central importance for suns. In the interior of suns, this process is very much involved in the generation of heat and light, which makes live on earth possible. But it is also of relevance in the formation of heavy elements, like lead, during supernova explosions. So, much of the things we see around us exist only due to the weak force. The details of how this works in suns and novas is very intricate, and complicated to model. These are central questions in the field of nuclear astrophysics. However, this has little connection to the research illustrated in this blog, so I will skip it. Many excellent resources on these questions can be found elsewhere on the web.
For my purposes, let me delve deeper into what happens during beta decays. The proton and neutron are themselves build from quarks, and it is actually not the neutron which transforms, but one of the quarks. The neutron consists out of two down quarks and one up quark, while the proton has two up quarks and one down quark. Thus, to get from a neutron to a proton, one down quark has to be exchanged for an up quark. This is exactly what the weak force is doing. For this to happen one of the agents of the weak force needs to become involved. This agent is called the W boson. There are actually two of these, which differ by their electric charge, one having a positive charge like the proton, the other a negative charge like the electron. What happens is that the down quark emits a negatively charged W boson - the down quark itself has a third of the charge of the electron - and by this transforms into an up quark, which has two thirds of the charge of the proton. This transforms the neutron into a proton. The emitted W boson then decays into the electron, which carries the electric charge, and the electron-anti-neutrino, which are observed.
So that is how the weak force acts. But why are the W bosons not itself detected like the photons. Are they strongly bound like the gluons? The answer is no. The reason is rather different. The W bosons have a large mass, which is actually just about half the one of the top quark. They are therefore some of the heaviest particles found so far. Hence, it is favorable for them to decay into lighter particles after traveling a short distance. That is then also the reason why the force appears so weak: It can only act over a very short distance, before its agents decay, and the resulting particles start to act differently.
When investigating this phenomenon more in detail, it turns out that the there is another agent of it, the so-called Z boson. This is electromagnetically neutral, and about ten percent heavier than the W bosons. It is thus the second-heaviest elementary particle we know so far. Because of its properties, it turns out that it often acts very much like a very heavy copy of the photon. Indeed, upon closer inspection it is found that the photon and Z boson are not two particles apart, but mix quite heavily with each other: At long distances what looks like the photon is more of a Z boson at short distances. This is because of the mass of the Z boson, which is so much heavier than the photon and can therefore not travel far without decaying. But at short distances it looks more like a Z boson.
Therefore, and because of the charges of the W bosons, the description of both interactions - the weak and the electromagnetic ones - rest on a common theory, the so-called electroweak theory. QED, described earlier, is actually only its long-distance face. At short distances, reached in modern particle physics experiment, the unification of both forces into one is very evident.
There are two things odd about the weak part of this interaction. First, it acts actually not directly on the particles described earlier, say the up quark, but only on certain combinations of them. Therfore, saying before that the down quark decays is not quite right. It is more like that a combination of the down quark and a strange quark which appears as a quantum fluctuation inside the neutron act together to produce the W boson, and by this change into the up quark and a quantum fluctuation of a charm quark. These quantum fluctuations inside the neutron and proton are not strange - that is something which is natural in quantum physics that things just pop up and vanish here and there. That will be looked at in detail later. The strange thing is that such combinations are necessary. Why this is so is one of the big questions of the theory.
The other thing strange is that the weak interactions makes a difference between left and right. In fact, it prefers left over right as much as possible. This has directly observable consequences. For example, if a decaying neutron is put into a magnetic field, the emitted electron has a preferred direction with respect to the field. Neither the strong nor the electromagnetic force has such a preference. This may be seen as an oddity of nature, at first sight. However, it has very profound consequences for our understanding of nature, as will be discussed next.
For my purposes, let me delve deeper into what happens during beta decays. The proton and neutron are themselves build from quarks, and it is actually not the neutron which transforms, but one of the quarks. The neutron consists out of two down quarks and one up quark, while the proton has two up quarks and one down quark. Thus, to get from a neutron to a proton, one down quark has to be exchanged for an up quark. This is exactly what the weak force is doing. For this to happen one of the agents of the weak force needs to become involved. This agent is called the W boson. There are actually two of these, which differ by their electric charge, one having a positive charge like the proton, the other a negative charge like the electron. What happens is that the down quark emits a negatively charged W boson - the down quark itself has a third of the charge of the electron - and by this transforms into an up quark, which has two thirds of the charge of the proton. This transforms the neutron into a proton. The emitted W boson then decays into the electron, which carries the electric charge, and the electron-anti-neutrino, which are observed.
So that is how the weak force acts. But why are the W bosons not itself detected like the photons. Are they strongly bound like the gluons? The answer is no. The reason is rather different. The W bosons have a large mass, which is actually just about half the one of the top quark. They are therefore some of the heaviest particles found so far. Hence, it is favorable for them to decay into lighter particles after traveling a short distance. That is then also the reason why the force appears so weak: It can only act over a very short distance, before its agents decay, and the resulting particles start to act differently.
When investigating this phenomenon more in detail, it turns out that the there is another agent of it, the so-called Z boson. This is electromagnetically neutral, and about ten percent heavier than the W bosons. It is thus the second-heaviest elementary particle we know so far. Because of its properties, it turns out that it often acts very much like a very heavy copy of the photon. Indeed, upon closer inspection it is found that the photon and Z boson are not two particles apart, but mix quite heavily with each other: At long distances what looks like the photon is more of a Z boson at short distances. This is because of the mass of the Z boson, which is so much heavier than the photon and can therefore not travel far without decaying. But at short distances it looks more like a Z boson.
Therefore, and because of the charges of the W bosons, the description of both interactions - the weak and the electromagnetic ones - rest on a common theory, the so-called electroweak theory. QED, described earlier, is actually only its long-distance face. At short distances, reached in modern particle physics experiment, the unification of both forces into one is very evident.
There are two things odd about the weak part of this interaction. First, it acts actually not directly on the particles described earlier, say the up quark, but only on certain combinations of them. Therfore, saying before that the down quark decays is not quite right. It is more like that a combination of the down quark and a strange quark which appears as a quantum fluctuation inside the neutron act together to produce the W boson, and by this change into the up quark and a quantum fluctuation of a charm quark. These quantum fluctuations inside the neutron and proton are not strange - that is something which is natural in quantum physics that things just pop up and vanish here and there. That will be looked at in detail later. The strange thing is that such combinations are necessary. Why this is so is one of the big questions of the theory.
The other thing strange is that the weak interactions makes a difference between left and right. In fact, it prefers left over right as much as possible. This has directly observable consequences. For example, if a decaying neutron is put into a magnetic field, the emitted electron has a preferred direction with respect to the field. Neither the strong nor the electromagnetic force has such a preference. This may be seen as an oddity of nature, at first sight. However, it has very profound consequences for our understanding of nature, as will be discussed next.
Friday, January 29, 2010
The forces of nature III - The strong force (Part II)
As has been told, the hadrons are made up out of quarks. But there is something peculiar about this. When one looks at the constituents of, say, an atom - the nuclei and the electrons - then one can observe all of these also as individual particles. However, this is not applying to quarks. It has not been possible to isolate a quark experimentally. The only thing which can be seen are the hadrons.
When analyzing the structure of the hadrons in search for the reason, it turns out that one can assign to a quark a new charge, the so-called color charge. The name is just fancy and the charge has nothing to do with color. This color charge comes in six types. There are three 'positive' charges, called red, green, and blue (some people occasionally exchange one of the names for yellow), thus carrying the metaphor further. They are like the positive electric charge. Then there are three 'negative' charges, anti-red, anti-green, and anti-blue. They are like negative electric charge. As for electric charges, a negative and a positive color (say anti-green and green) neutralize each other. The amazing difference compared to electric charges is that also three different colors of either type neutralize each other. For example, a red, a green, and a blue quark together are neutral with respect to the color charge.
It is then found that all hadrons are always color-neutral. The mesons are made from one quark with color and one with anti-color, and the baryons are made from three quarks, each carrying one of the colors. In fact, the ones we observe around us are all made of three quarks carrying color. Those which carry anti-color are actually anti-matter, which will be discussed later.
Now, this gives an idea why quarks and hadrons are different. But it does not explain why quarks are not observed. This is now du to the force acting between two color charges. In contrast to all other forces, this force is not getting weaker with distance, but stronger instead. And it gets so quickly stronger that it is not possible to tear a hadron apart into quarks. At least that is what it looks like at the surface. The truth is somewhat more subtle, and not fully understood, and part of my research. Therefore, I will come back to this question many times in the future.
Irrespective of this, the force between colored objects is mediated by gluons. In contrast to photons gluons carry themselves color charges, though they are of a different type than those of quarks, and there are eight different ones, not usually given a name. As a consequence, the enormous strength of the force also binds gluons, and they cannot be observed as freely roaming particles either. In fact, at least in principle it is possible that gluons alone form bound states, much like hadrons. These are called glueballs, but are up to now only hypothetical constructs which have not been observed in nature, though some observations may hint at them. It is an ongoing experimental endeavor to find them.
The justified question is, if the force is so strong, why do we know about quarks and gluons? And why can it still bind the nucleons to nuclei if the nucleons are color-neutral?
Well, the force is not strong at all distances. Indeed, it grows quickly with distance, but on the other hand it diminishes as quickly with shorter and shorter distances. To the best of our knowledge it even ceases completely if one would be able to reduce the distance to zero. That is called asymptotic freedom. Therefore, if one can send a probe close to a quark, then one can identify its existence. For this purpose it helps very much that a quark is not only carrying color charge, but also electric charge. Therefore, it can be registered more easily by hitting it with a photon or an electron. That is somewhat indirect, but that is one of the main sources of experimental information on the quarks. The gluons are even more complicated, since they only carry color charge. Therefore, our evidence for them is rather indirect.
This is then also how nucleons feel each other by the strong force. When they come close to each other, they start to see each others quarks, which then can interact by the strong force. This is a comparatively weak effect, since it is, vastly simplifying spoken, just a bit of penetration what makes them feel each other. Nonetheless, this remainder of the force is so much stronger than the electric force that it makes the nuclei about 100000-times smaller than an atom. This should give an idea of how very strong this force must be that even such a small glimpse of it has such far-reaching consequences.
It is this strong force to which I will return repeatedly, as it is and has been for a long time my major focus of research. The one reason is that our understanding of this force is not very good is because many approaches just have to give up when faced with such an enormous strong force. Only at very short distances we have reliable control over it. Hence, the theory of this force, which is called quantum chromo dynamics (for the Greek word chromos for color and short QCD), is very hard to tackle. There is a simpler version of it, which only deals with the gluons and neglects the quarks (and is therefore not a picture of nature). It is called Yang-Mills theory. Because it contains already many essential features of QCD, it often, and also for me, serves as a prototype theory for the strong force.
When analyzing the structure of the hadrons in search for the reason, it turns out that one can assign to a quark a new charge, the so-called color charge. The name is just fancy and the charge has nothing to do with color. This color charge comes in six types. There are three 'positive' charges, called red, green, and blue (some people occasionally exchange one of the names for yellow), thus carrying the metaphor further. They are like the positive electric charge. Then there are three 'negative' charges, anti-red, anti-green, and anti-blue. They are like negative electric charge. As for electric charges, a negative and a positive color (say anti-green and green) neutralize each other. The amazing difference compared to electric charges is that also three different colors of either type neutralize each other. For example, a red, a green, and a blue quark together are neutral with respect to the color charge.
It is then found that all hadrons are always color-neutral. The mesons are made from one quark with color and one with anti-color, and the baryons are made from three quarks, each carrying one of the colors. In fact, the ones we observe around us are all made of three quarks carrying color. Those which carry anti-color are actually anti-matter, which will be discussed later.
Now, this gives an idea why quarks and hadrons are different. But it does not explain why quarks are not observed. This is now du to the force acting between two color charges. In contrast to all other forces, this force is not getting weaker with distance, but stronger instead. And it gets so quickly stronger that it is not possible to tear a hadron apart into quarks. At least that is what it looks like at the surface. The truth is somewhat more subtle, and not fully understood, and part of my research. Therefore, I will come back to this question many times in the future.
Irrespective of this, the force between colored objects is mediated by gluons. In contrast to photons gluons carry themselves color charges, though they are of a different type than those of quarks, and there are eight different ones, not usually given a name. As a consequence, the enormous strength of the force also binds gluons, and they cannot be observed as freely roaming particles either. In fact, at least in principle it is possible that gluons alone form bound states, much like hadrons. These are called glueballs, but are up to now only hypothetical constructs which have not been observed in nature, though some observations may hint at them. It is an ongoing experimental endeavor to find them.
The justified question is, if the force is so strong, why do we know about quarks and gluons? And why can it still bind the nucleons to nuclei if the nucleons are color-neutral?
Well, the force is not strong at all distances. Indeed, it grows quickly with distance, but on the other hand it diminishes as quickly with shorter and shorter distances. To the best of our knowledge it even ceases completely if one would be able to reduce the distance to zero. That is called asymptotic freedom. Therefore, if one can send a probe close to a quark, then one can identify its existence. For this purpose it helps very much that a quark is not only carrying color charge, but also electric charge. Therefore, it can be registered more easily by hitting it with a photon or an electron. That is somewhat indirect, but that is one of the main sources of experimental information on the quarks. The gluons are even more complicated, since they only carry color charge. Therefore, our evidence for them is rather indirect.
This is then also how nucleons feel each other by the strong force. When they come close to each other, they start to see each others quarks, which then can interact by the strong force. This is a comparatively weak effect, since it is, vastly simplifying spoken, just a bit of penetration what makes them feel each other. Nonetheless, this remainder of the force is so much stronger than the electric force that it makes the nuclei about 100000-times smaller than an atom. This should give an idea of how very strong this force must be that even such a small glimpse of it has such far-reaching consequences.
It is this strong force to which I will return repeatedly, as it is and has been for a long time my major focus of research. The one reason is that our understanding of this force is not very good is because many approaches just have to give up when faced with such an enormous strong force. Only at very short distances we have reliable control over it. Hence, the theory of this force, which is called quantum chromo dynamics (for the Greek word chromos for color and short QCD), is very hard to tackle. There is a simpler version of it, which only deals with the gluons and neglects the quarks (and is therefore not a picture of nature). It is called Yang-Mills theory. Because it contains already many essential features of QCD, it often, and also for me, serves as a prototype theory for the strong force.
Monday, January 18, 2010
The forces of nature III - The strong force (Part I)
If one descends to smaller and smaller scales one always finds that larger things are built up from smaller things. When one looks to a human, she is made from cells. Each cell in turn is built from molecules, small and large.
Each of the molecules, in turn, is made from atoms. These atoms are rather small, like 0,0000000001 m each. There is one thing special about atoms which has not been encountered with molecules and cells: There is only a finite number of different ones of them observed in nature, while there appears to be an infinite number of different molecules and cells. In fact, atoms can be organized into a scheme (ok, this also applies to molecules and to some extent to cells also), the so-called periodic system of atoms. There are roughly hundred of them to be found in nature, and we managed to make a number artificially of them more over the years. Each of the atoms differs by its chemical properties.
So, it seems that atoms can be built, much like molecules. However, it is found that there are some atoms which behave in every respect essentially identical when it comes to chemistry, but they have a different mass. Both facts (and a number of others) suggest that atoms themselves are built from other things.
Indeed, it is found that atoms are made from two parts: Electrons and nuclei. The electrons orbit the nuclei, which is about 100000-times smaller than the atom (the electrons are even smaller as discussed previously). The are different electromagnetically charge with respect to each other, and there is always exactly one nuclei, but so many electrons that the total electric charge is zero.
It turns out that the charge is responsible for the chemistry, so the charge of the nuclei characterizes the atom. The mass of the atom is made essentially by the nuclei, which is about 2000 times heavier than the electrons. So different mass nuclei provide the same chemistry. Why?
Well, it turns out that the nuclei are composed from different objects themselves, the nucleons. That is the reason why new ones can be made and there are chemical identical ones with different mass. They nucleons come in two types, the neutrons and the protons. The latter carry the charge, making the atom chemical active, while the neutrons are chemically essentially inactive. On the other hand both have essentially the same mass. So chemically different atoms differ by their number of protons, but chemically identical atoms having different mass differ by the number of neutrons.
It is found that the nucleons have about the same size as the nuclei, so they are fairly densely packed inside the nuclei (in a typical atom there are a few dozen nucleons). What is keeping them together? It cannot be gravity alone, as it is too weak. If gravity alone should provide this, the nuclei would be much, much larger. It cannot be electromagnetism, as the neutron has no charge. So it must be something different. Indeed it is a new force, the so-called strong (or, since it was discovered in the context of the nuclei, nuclear) force. This force is binding the nucleons together to form the nuclei, and thus shapes the very word we live in as much as electromagnetism does.
The force between the nucleons is created by the exchange of mesons. These particles are usually not observable in nature as they decay too fast by the weak interactions to be discussed later. They can be observed in cosmic rays. The most important meson is the pion, having about an eighth of the mass of the nucleon. So, in contrast to the photon, it is massive. It also can carry charge, there is a positive one, a negative one, and a neutral one. There are also other mesons, the kaon, the rho, and the omega, playing a role in the nuclear force. In fact, as it was started to investigate this, more and more of these mesons have been found. Also, it was found that the nucleons are not the only of their kind. There are other, quite similar objects, like the delta or the cascade particles. Those nucleon-like particles have been termed the baryons, in distinction to the mesons. Both together are called hadrons, to distinguish them from the leptons. These mesons and baryons can again be put into a kind of periodic table, and we can produce new ones of them.
As the experience with atoms already told, this indicates that the baryons and mesons are themselves composites from other particles. Indeed, they are built up from quarks. Mesons consists of two, baryons of three quarks. If there are objects which are constructed from four or five or more quarks is not really known. If so, they are rathe short-lived and decay into mesons and baryons. During the recent years, conflicting experimental results made this a hot debate, and the judge is still out. These objects would be called tetraquarks (four quarks) or pentaquarks (five quarks).
In any case, there has to be a force holding the quarks together inside mesons and baryons. It turns out that this is again the strong force, but in another disguise.
Each of the molecules, in turn, is made from atoms. These atoms are rather small, like 0,0000000001 m each. There is one thing special about atoms which has not been encountered with molecules and cells: There is only a finite number of different ones of them observed in nature, while there appears to be an infinite number of different molecules and cells. In fact, atoms can be organized into a scheme (ok, this also applies to molecules and to some extent to cells also), the so-called periodic system of atoms. There are roughly hundred of them to be found in nature, and we managed to make a number artificially of them more over the years. Each of the atoms differs by its chemical properties.
So, it seems that atoms can be built, much like molecules. However, it is found that there are some atoms which behave in every respect essentially identical when it comes to chemistry, but they have a different mass. Both facts (and a number of others) suggest that atoms themselves are built from other things.
Indeed, it is found that atoms are made from two parts: Electrons and nuclei. The electrons orbit the nuclei, which is about 100000-times smaller than the atom (the electrons are even smaller as discussed previously). The are different electromagnetically charge with respect to each other, and there is always exactly one nuclei, but so many electrons that the total electric charge is zero.
It turns out that the charge is responsible for the chemistry, so the charge of the nuclei characterizes the atom. The mass of the atom is made essentially by the nuclei, which is about 2000 times heavier than the electrons. So different mass nuclei provide the same chemistry. Why?
Well, it turns out that the nuclei are composed from different objects themselves, the nucleons. That is the reason why new ones can be made and there are chemical identical ones with different mass. They nucleons come in two types, the neutrons and the protons. The latter carry the charge, making the atom chemical active, while the neutrons are chemically essentially inactive. On the other hand both have essentially the same mass. So chemically different atoms differ by their number of protons, but chemically identical atoms having different mass differ by the number of neutrons.
It is found that the nucleons have about the same size as the nuclei, so they are fairly densely packed inside the nuclei (in a typical atom there are a few dozen nucleons). What is keeping them together? It cannot be gravity alone, as it is too weak. If gravity alone should provide this, the nuclei would be much, much larger. It cannot be electromagnetism, as the neutron has no charge. So it must be something different. Indeed it is a new force, the so-called strong (or, since it was discovered in the context of the nuclei, nuclear) force. This force is binding the nucleons together to form the nuclei, and thus shapes the very word we live in as much as electromagnetism does.
The force between the nucleons is created by the exchange of mesons. These particles are usually not observable in nature as they decay too fast by the weak interactions to be discussed later. They can be observed in cosmic rays. The most important meson is the pion, having about an eighth of the mass of the nucleon. So, in contrast to the photon, it is massive. It also can carry charge, there is a positive one, a negative one, and a neutral one. There are also other mesons, the kaon, the rho, and the omega, playing a role in the nuclear force. In fact, as it was started to investigate this, more and more of these mesons have been found. Also, it was found that the nucleons are not the only of their kind. There are other, quite similar objects, like the delta or the cascade particles. Those nucleon-like particles have been termed the baryons, in distinction to the mesons. Both together are called hadrons, to distinguish them from the leptons. These mesons and baryons can again be put into a kind of periodic table, and we can produce new ones of them.
As the experience with atoms already told, this indicates that the baryons and mesons are themselves composites from other particles. Indeed, they are built up from quarks. Mesons consists of two, baryons of three quarks. If there are objects which are constructed from four or five or more quarks is not really known. If so, they are rathe short-lived and decay into mesons and baryons. During the recent years, conflicting experimental results made this a hot debate, and the judge is still out. These objects would be called tetraquarks (four quarks) or pentaquarks (five quarks).
In any case, there has to be a force holding the quarks together inside mesons and baryons. It turns out that this is again the strong force, but in another disguise.
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.
Friday, November 13, 2009
The forces of nature I - Gravity
After illustrating last time how a force can be created by the exchange of particle, it is about time to make a list of which forces there are in nature, and which of them are included in the standard model.
Actually, there is only one force in nature which we currently know and which is not included in the standard model of particle physics. This is gravity. That is the force which pulls one inevitably to the ground, as long as one is not actively working against it. And the one which makes it so hard to get up in the morning. Or so.
It is actually not only the ground, and thus the earth, that is pulling at you, but actually also the earth is pulled by you. However, since the earth is much heavier than you are, it is rather ignorant of your presence. However, it cannot ignore the pull of the moon, to which it reacts with the tides. Nor can it ignore the sun, and this makes earth orbiting around it. On a larger scale, the solar system feels the pull of the milky way, making the solar system orbiting the center of it. And our galaxy the center of the local cluster of galaxies.
In fact, any object which has mass pulls any other object towards it, which has also mass. Actually, this is not entirely correct: Mass is not necessary, it suffices if there is energy in the game. This will lead a bit too far astray now, as it is necessary to delve into the theory of relativity for why this is the case, and I will leave this to later.
However, the generic concept that some objects act a force on each other because they both have a certain property is far more general. It is the simplest example of a charge. Gravity is simple in that everything pulls everything else to itself. In other cases, which will be encountered next time, this is not always the case: Some charges pushes away other charges.
So, why is gravity not included in the standard model (yet)? The simple answer is that we do not yet know how to really do it. There are quite a number of ideas, going by the fancy names of string theory, quantum loop gravity, and many others. However, none of these ideas could have been yet made so precise that it would actually explain how gravity quantitatively fits into the standard model.
The major problem encountered is that it is very hard to make gravity a quantum theory. That has rather technical reasons, and there are some hot leads how we can possibly circumvent this in the future. But not yet. The basic problem is essentially that we do not yet know how to cope with a pileup of gravitons, the (hypothetical) particles carrying the gravitational force, which inevitable always occurs in a quantum theory. That is actually an involved technical problem. For that reason gravity is not yet part of the standard model of particle physics, but instead described by a classical theory, general relativity.
The question is whether this matters when we want to talk about particle physics. The fortunate answer is that it does not, in most cases. The reason is that gravity is a very weak forces. Compared to those described by the standard model, it is about 10000000000000000000000000000000000000 times weaker than the weakest other force of the standard model. Therefore, only if there is a large charge - thus mass or energy - gravity becomes important. That happens only at energy scales which are more than 10000000000000 times larger than accessible in any experiment so far. In nature, it only occurs very close to a black hole or very, very early in the history of the universe. So, for most purposes, and in particular the ones of this blog, gravity can be neglected.
However, there are a number of open questions related to our limited understanding of gravity which have to do with large scales rather than particles: E.g., why is the universe expanding today? Also these questions will not be discussed for the moment in this blog.
Actually, there is only one force in nature which we currently know and which is not included in the standard model of particle physics. This is gravity. That is the force which pulls one inevitably to the ground, as long as one is not actively working against it. And the one which makes it so hard to get up in the morning. Or so.
It is actually not only the ground, and thus the earth, that is pulling at you, but actually also the earth is pulled by you. However, since the earth is much heavier than you are, it is rather ignorant of your presence. However, it cannot ignore the pull of the moon, to which it reacts with the tides. Nor can it ignore the sun, and this makes earth orbiting around it. On a larger scale, the solar system feels the pull of the milky way, making the solar system orbiting the center of it. And our galaxy the center of the local cluster of galaxies.
In fact, any object which has mass pulls any other object towards it, which has also mass. Actually, this is not entirely correct: Mass is not necessary, it suffices if there is energy in the game. This will lead a bit too far astray now, as it is necessary to delve into the theory of relativity for why this is the case, and I will leave this to later.
However, the generic concept that some objects act a force on each other because they both have a certain property is far more general. It is the simplest example of a charge. Gravity is simple in that everything pulls everything else to itself. In other cases, which will be encountered next time, this is not always the case: Some charges pushes away other charges.
So, why is gravity not included in the standard model (yet)? The simple answer is that we do not yet know how to really do it. There are quite a number of ideas, going by the fancy names of string theory, quantum loop gravity, and many others. However, none of these ideas could have been yet made so precise that it would actually explain how gravity quantitatively fits into the standard model.
The major problem encountered is that it is very hard to make gravity a quantum theory. That has rather technical reasons, and there are some hot leads how we can possibly circumvent this in the future. But not yet. The basic problem is essentially that we do not yet know how to cope with a pileup of gravitons, the (hypothetical) particles carrying the gravitational force, which inevitable always occurs in a quantum theory. That is actually an involved technical problem. For that reason gravity is not yet part of the standard model of particle physics, but instead described by a classical theory, general relativity.
The question is whether this matters when we want to talk about particle physics. The fortunate answer is that it does not, in most cases. The reason is that gravity is a very weak forces. Compared to those described by the standard model, it is about 10000000000000000000000000000000000000 times weaker than the weakest other force of the standard model. Therefore, only if there is a large charge - thus mass or energy - gravity becomes important. That happens only at energy scales which are more than 10000000000000 times larger than accessible in any experiment so far. In nature, it only occurs very close to a black hole or very, very early in the history of the universe. So, for most purposes, and in particular the ones of this blog, gravity can be neglected.
However, there are a number of open questions related to our limited understanding of gravity which have to do with large scales rather than particles: E.g., why is the universe expanding today? Also these questions will not be discussed for the moment in this blog.
Tuesday, November 3, 2009
Particles
In the previous post particles appeared which are said to be exchanged between other particles. These particles are also called 'force' particles, in contrast to those objects exchanging them, the matter fields.
To the matter fields belong the leptons, the neutrinos and the quarks.
The force particles are the photons, the gluons, and the W and Z bosons.
The Higgs takes a role in between. On the one hand it can exchange force particles, on the other it is itself exchanged.
But how can one imagine the 'exchange' of a particle?
It is a little bit like when two boats pass by each other on a quiet sea. If they move, the generate waves which travel from one to the other, and are very much felt by each other. Anyone having traveled in a boat can confirm that it can get quite rocky if another fast boat comes close by.
The situation in particle physics is somewhat similar. The boats are the particles. The water is essentially a medium made up of force particles. If a particle now crosses this medium, it generates disturbances in it, which can travel and can be felt by other boats.
Why are then the force particles are called particles? The waves are indeed very much different from the boats. The reason is that the medium is very much different from water. If the waves in the medium are strong enough, they actually become very narrow, and look very much like a boat (a particle) themselves. Therefore, at strong waves, or if much energy has been invested in creating a wave, the wave looks like another boat (another particle). In fact, some of these can then exchange waves themselves, the force particles become matter particles in their own right.
So there is an interesting duality between the force carriers and those affected by the force, similar to the Higgs particle itself.
As a consequence, it has become common to talk even of the medium as an ensemble of particles, though this is not entirely right: If the waves are shallow, there is no structure which could be recognized as a particle. It is exactly this domain, which is least understood. The reason is that the medium is also in another respect different from water. If the waves are shallow, they affect the remaining medium much stronger than do water waves. In fact, only on the contrary, if the waves are strong, they more or less ignore the remaining medium, but only then.
To understand how this medium behaves is one of the central questions in my own research, but also one of the great unsolved questions in the standard model during its more that thirty year old history.
To the matter fields belong the leptons, the neutrinos and the quarks.
The force particles are the photons, the gluons, and the W and Z bosons.
The Higgs takes a role in between. On the one hand it can exchange force particles, on the other it is itself exchanged.
But how can one imagine the 'exchange' of a particle?
It is a little bit like when two boats pass by each other on a quiet sea. If they move, the generate waves which travel from one to the other, and are very much felt by each other. Anyone having traveled in a boat can confirm that it can get quite rocky if another fast boat comes close by.
The situation in particle physics is somewhat similar. The boats are the particles. The water is essentially a medium made up of force particles. If a particle now crosses this medium, it generates disturbances in it, which can travel and can be felt by other boats.
Why are then the force particles are called particles? The waves are indeed very much different from the boats. The reason is that the medium is very much different from water. If the waves in the medium are strong enough, they actually become very narrow, and look very much like a boat (a particle) themselves. Therefore, at strong waves, or if much energy has been invested in creating a wave, the wave looks like another boat (another particle). In fact, some of these can then exchange waves themselves, the force particles become matter particles in their own right.
So there is an interesting duality between the force carriers and those affected by the force, similar to the Higgs particle itself.
As a consequence, it has become common to talk even of the medium as an ensemble of particles, though this is not entirely right: If the waves are shallow, there is no structure which could be recognized as a particle. It is exactly this domain, which is least understood. The reason is that the medium is also in another respect different from water. If the waves are shallow, they affect the remaining medium much stronger than do water waves. In fact, only on the contrary, if the waves are strong, they more or less ignore the remaining medium, but only then.
To understand how this medium behaves is one of the central questions in my own research, but also one of the great unsolved questions in the standard model during its more that thirty year old history.
Wednesday, October 14, 2009
The standard model
Let me introduce the players in the standard model. These are the so-called elementary particles. These elementary particles are the smallest objects we known in nature. And small means small: We are sure they are smaller than 0.0000000000000000000001 meters. That is really tiny. However, it would not be the first time that when we look closer they are actually consisting out of something even smaller. But let me for the moment assume that this is not so.
So, what are the players then. Well, they can be divided in a number of groups.
First, there are things we call leptons. An example for a lepton is the electron. Electrons are the things that make up electrical current, so we have to deal with them every day. There are two heavier copies of the electron: The muon and the tau, about 400 and 3600 times heavier than the electron. If they would be stable, we could use them also for electrical energy, but they are not: They decay in some other elementary particles after fractions of a second.
There is a second group of leptons, the so-called neutrinos. These are the lightest particles which have a mass. We are not yet sure what their mass exactly is, just that they are at least 500000-times less heavy than an electron. Again, there are three of them, one for the electron (called electron neutrino), one for the muon (muon neutrino) and one for the tau (tau neutrino).
The second group of particles are called quarks. Quarks make up composites of quarks, known as hadrons. The most prominent hadrons are the proton, the nuclei of a hydrogen atom, and the neutron. The latter two are composites of the up and down quarks. Besides these two, which have both approximately ten times the mass of an electron, there are four more. The strange quark, about 200 times heavier than an electron, the charm quark (neat names), 3000 times as heavy as an electron, the bottom quark (9000 times), and the big guy, the top quark (350000 (!) times). Again, the heavier quarks are not stable, they decay.
Then there is light. Yes, ordinary light (and X-rays, and infrared light, and so on) is made up out of particles, the photons. They are exchanged between anything that has an electric charge, e.g., a quark and an electron.
But they are not the only thing, which can connect particles. There are gluons, which connect quarks. Neither photons, nor gluons have a mass. And gluons are a bit strange, but this will be discussed much more in detail latter. Sufficies to say, we do not see gluons as we do see photons.
Then there are the W and Z, both of approximately half the mass of a top quark. They are important for radioactive decays, and they are also a bit strange. They connect both quarks and leptons. Also, because they are so heavy, they are not very stable.
Finally, there is an elusive guy, called the Higgs. We did not yet find it - perhaps we will at the next big particle physics experiment, the Large Hadron Collider LHC at the European Center of Particle and Nuclear Physics CERN. But it is important, because it seems to be connected with all the masses which have been floating around.
So, what are the players then. Well, they can be divided in a number of groups.
First, there are things we call leptons. An example for a lepton is the electron. Electrons are the things that make up electrical current, so we have to deal with them every day. There are two heavier copies of the electron: The muon and the tau, about 400 and 3600 times heavier than the electron. If they would be stable, we could use them also for electrical energy, but they are not: They decay in some other elementary particles after fractions of a second.
There is a second group of leptons, the so-called neutrinos. These are the lightest particles which have a mass. We are not yet sure what their mass exactly is, just that they are at least 500000-times less heavy than an electron. Again, there are three of them, one for the electron (called electron neutrino), one for the muon (muon neutrino) and one for the tau (tau neutrino).
The second group of particles are called quarks. Quarks make up composites of quarks, known as hadrons. The most prominent hadrons are the proton, the nuclei of a hydrogen atom, and the neutron. The latter two are composites of the up and down quarks. Besides these two, which have both approximately ten times the mass of an electron, there are four more. The strange quark, about 200 times heavier than an electron, the charm quark (neat names), 3000 times as heavy as an electron, the bottom quark (9000 times), and the big guy, the top quark (350000 (!) times). Again, the heavier quarks are not stable, they decay.
Then there is light. Yes, ordinary light (and X-rays, and infrared light, and so on) is made up out of particles, the photons. They are exchanged between anything that has an electric charge, e.g., a quark and an electron.
But they are not the only thing, which can connect particles. There are gluons, which connect quarks. Neither photons, nor gluons have a mass. And gluons are a bit strange, but this will be discussed much more in detail latter. Sufficies to say, we do not see gluons as we do see photons.
Then there are the W and Z, both of approximately half the mass of a top quark. They are important for radioactive decays, and they are also a bit strange. They connect both quarks and leptons. Also, because they are so heavy, they are not very stable.
Finally, there is an elusive guy, called the Higgs. We did not yet find it - perhaps we will at the next big particle physics experiment, the Large Hadron Collider LHC at the European Center of Particle and Nuclear Physics CERN. But it is important, because it seems to be connected with all the masses which have been floating around.
Wednesday, October 7, 2009
Introduction
So, this is the blog in which I will discuss my research. I will try to be as general as possible, though at times it might get a bit tricky.
The general scope of my work is the standard model of particle physics - that is our current idea of how the smallest objects, the elementary particles, work. Very nice general introductions to this topic can be found at the large particle physics laboratories in Europe, at CERN or, in German, at DESY. Here I will only discuss what is of direct relevance to my own work.
An additional companion to this blog is my twitter account, on which I push some insights, some news, or some general remarks on my research, and on what is going on in the world of particle physics from my perspective.
Enjoy!
The general scope of my work is the standard model of particle physics - that is our current idea of how the smallest objects, the elementary particles, work. Very nice general introductions to this topic can be found at the large particle physics laboratories in Europe, at CERN or, in German, at DESY. Here I will only discuss what is of direct relevance to my own work.
An additional companion to this blog is my twitter account, on which I push some insights, some news, or some general remarks on my research, and on what is going on in the world of particle physics from my perspective.
Enjoy!
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