What is the Matter?
Published on Jul 25, 2006 at 10:02 pm.
2 Comments.
Filed under physics.
Some time back, I had a post about dark matter. So, I thought that I’d say a bit more about matter. First of all, just what is matter? After all, if we are going to talk about dark matter, we should have some idea what non-dark matter is, right? This is going to be a bit more technical post than most that I have done. Long time readers will note that I once in a while toss in things like this.
Ages ago, in a physical science class in high school, I learned a definition of matter that I still hear bandied about. That definition went something like: Matter is something that has mass and takes up space. Well, that’s cute. So, what is mass, and what is space? After all, if you are going to use a definition, then the terms used in that definition should also be understood. What I find, though, is that my physics students, much less the non majors, don’t understand the terms matter, mass, and space. Heck, a number of physicists seem unclear on the concepts, too.
Already, in a previous post, I talked about space not really being empty. This is a clue that there is something more going on in space than simply dimensional measure. In cosmology, we learn that space can expand. Two galaxies can each be sitting stationary in space, and yet be getting farther away from each other because the space between them is expanding. This is hard to understand if you are stuck with the idea that space is simply a dimensional measure. It may be more appropriate to think of space as an interaction realm. Things can interact with one another, and the realm and range of that interaction is space. This is still not quite right, but I don’t think that anyone really understands space completely, and this way of looking at it is a bit better than most people do. The dimensions (length, width, height) are simply a way of quantifying how much space there is. Space itself is something beyond just the dimensions.
Now, this throws a monkey wrench into our definition of matter. Implicit in the definition is that two separate pieces of matter can not occupy the same space. But, if two objects do not interact, what keeps them from occupying the same space? After all, if they don’t interact at all, they for all practical purposes can’t occupy the same space, since one object’s space is not the same as the other object’s space. That’s a tough concept, I know. Furthermore, it is not at all clear that some particles, such as electrons, actually take up any space at all, at least in terms of dimensions. Electrons, and some other particles, are essentially point particles. Now, we can discuss the interaction range of an electron with a probability distribution described by a wave function, but that isn’t really the same as saying that the electron is occupying space. Now, there does exist a limit to how small a piece of space we can describe in physics, something called the Planck Length, which is about 1.6×10-35 meters. At this distance scale, the normal rules of physics start to break down, and something new is needed. So, we can’t really say if such point particles are really point particles, or just tiny things the size of the Planck Length, but for all practical purposes, the statements are equivalent.
But, no one argues that electrons are not matter. So, we are left with matter being something that has mass. But, don’t be mislead. Matter is not mass. These are separate concepts. However, mass is a property of matter. All matter has mass. But, doesn’t everything have mass? No. Photons, particles of light, don’t have mass, and neither do gravitons, the particles postulated to carry the gravitational force. So, that makes photons and gravitons, and numerous other particles not matter.
So, let’s talk about mass for a moment. What is mass? Actually, this is a deep question. If mass is that makes something matter, then we should understand what we mean by the term mass. There are two basic types of properties of matter that we call mass. This means that there are two separate masses. These are the Inertial Mass and the Gravitational Mass. These are different properties, but interestingly, they have the same value.
The inertial mass is that property at the heart of Newton’s Second Law of Motion:
F = m a.
Or, to put in another way, m = F/a. You apply a force to some object, and it accelerates. The ration of the applied force to the acceleration is the object’s inertial mass. The more mass it has, the harder it is for the force to accelerate it. Once moving, though, it takes force to slow it down or to stop it. Again the ratio of the force to the deceleration is the mass, and this quantity is the very same as the mass that was determined in speeding the object up in the first place. There are various reasons to expect this to be the case, but we don’t want to get even more technical than this is already.Gravitational mass, though, is a different beast altogether. Two pieces of matter interact with one another through the gravitational force. They may also interact via the electromagnetic force, the weak force, or the strong force. These four forces are the only forces in nature that we know about. Everything that you can conceptualize as a force is really one or more of these forces at work (most commonly experienced forces in the macroscopic world other than gravity are electromagnetic in nature). Now, not all pieces of matter interact via all of these forces. Some don’t interact at all through one or more of these forces, but all interact via the gravitational force. The magnitude of the interaction between matter objects depends upon a quantity associated with the objects called their gravitational masses. The magnitude of the interaction is given by Newton’s Universal Law of Gravitation:
F = (G m1 m2) / r2.
The m’s are the masses, the r is the separation of the masses, and G is a quantity known as the universal gravitational constant. Its value is determined by the strength properties of the gravitational force and the particular choice of units that we select. People who work on this sort of thing even talk about two types of gravitation mass: active mass and passive mass. The passive mass is the mass that interacts with a gravitational field, and the active mass is the mass that makes the gravitational field. There are excellent reasons that the two are the same thing, but again we won’t go into that.
Now, the interesting thing about the inertial mass and the gravitational mass is that they seem to be the exact same quantity. It isn’t altogether clear why they should be the same quantity, after all the gravitational mass is related to the gravitational field, and unless you are dealing with a gravitational force, then the mass has nothing to do with the force, so why should acceleration be dependent upon it? There is actually still work being done on this to try to explain why things work this way. But, as I said, it is not clear why this must be the case, so theorists have discussed what might happen if the two were different, even by a very tiny bit. The things that would happen if the gravitational mass and the inertial mass are not the same quantity are called the Nordtvedt Effect, after the theorist who proposed it. So far, every experiment to detect the Nordtvedt effect has failed to yield any measure of it. If the Nordtvedt effect did exist, it would be most apparent in very large masses, such as those of galaxies or galaxy clusters. So, this is the realm of the astrophysicist. Again, we see absolutely no evidence of any Nordtvedt effect. So, the matter goes back to the theorists to explain why the inertial mass and the gravitational mass must be the same. One theory that I have heard is that perhaps a body moving through space interacts with the virtual particles there (see my earlier space post) and that might cause the quantities to be the same. I don’t know. That seems to perhaps be stretching it, but I am not a theorist.
Interestingly, Einstein has shown us that matter and energy are interrelated. His famous equation E = mc2 shows that energy and matter can be interchanged. Photons, which are not matter, can become matter. In fact, high energy physicists sometimes quote the mass of a particle as how much energy it takes to make one. For example, they may way that an electron has a mass of 511 keV, meaning that it takes 511,000 electron volts of energy to make an electron. However, a problem does arise when you create matter from energy. There seems to be a conservation law in effect. Matter has some property other than just mass. Some particles of matter also have electric charge. The conservation laws of charge tell us that with any interaction, you have the same electric charge before the interaction that you did after the interaction. So, if you make a proton, having charge +e, out of a photon, which has no charge, then you have a problem. Likewise, if you made an electron, having charge –e, from an uncharged photon, you have a problem. So, you might suggest that you simply need an energetic enough photon to make both and electron and a proton, thus their charges of –e and +e balance each other out. Well, that is correct, their charges would balance out, and if conservation of charge were the only thing going on, that would be fine. But, there is more that goes on here. As it turns out, you have to conserve all kinds of other properties besides electric charge. Furthermore, it appears that there is some other hidden variable that must be conserved, so you can’t just balance a proton with an electron. The only thing that can balance the equation for these other properties for a proton is something exactly opposite of a proton, or to balance an electron would require something exactly opposite of an electron. As it turns out, such things exist. There are particles exactly opposite protons that we call antiprotons. They have the same mass, the same spin, the same everything else, except that they have charge –e. Likewise, there exist anti-electrons (which we call positrons), which are just like electrons, but with charge +e. These antiparticles, we call antimatter. You can even have a positron encircling an antiproton to make antihydrogen. Having mass, you’d think that we’d just call these antiparticles matter. Well, the sort of are matter, in that they do interact with matter particles and other antiparticles with gravitational forces. However, there is something different about them, because if a particle and its corresponding antiparticle meet, they annihilate each other, and both are converted into pure energy. Likewise, energy, say from photons, for example, always creates a particle and its corresponding antiparticle if you make matter out of that energy. There have been all sorts of interesting ideas about what antiparticles really are, including a suggestion that they might be particles moving backwards in time. So, a creation or annihilation event is simply the particle changing direction in its time path.
In an antimatter particle is the same as a particle, except for opposite charge, what about electrically neutral particles? Particles such as neutrinos, actually seem to act as their own antiparticles. That can add a whole layer of weirdness to this. But, neutrons are not the same thing as antineutrons. It turns out that neutrons are actually composed of smaller things, called quarks, and those quarks have electric charge. The quarks composing a neutron simply have charge that adds up to zero. So, antineutrons are composed of antiquarks, with each antiquark being the same as its corresponding quark, but with opposite charge.
It turns out that subatomic particles have a property that we call spin. The name comes from the fact that a number of their behavioral characteristics can be accounted for by pretending that they actually are little spinning things. Really, they aren’t. They just have angular momentum. Don’t ask me how they can do that if they are point particles and don’t really spin, like an electron. It turns out that there are only certain spins that a particle can have, and an exchange of spin always occurs in units of a fundamental unit of angular momentum. Particles can be classified by their spin behavior. Particles that always have angular momentum that is an even multiple of this fundamental angular momentum are called bosons. All the particles that mediate, or transmit, force between things are bosons. However, particles that have spins that are always odd multiples of ½ of the fundamental angular momentum (such as +1/2, or -1/2), are called fermions. Electrons, protons, and neutrons are fermions. Particle physicists generally only consider fermions to be matter, even if some of the bosons have mass. Fermions have an interesting property, one that without which the universe as we know it would not function the way that it does, and we would not be here. That property is that no two fermions that can interact can be quite identical in every way. They must have one property or another (angular momentum, spin, energy, etc) different from one another. This is called the Pauli Exclusion Principle. Without it, chemistry, nuclear physics, and all sorts of other things would not work. You would not have stars, planets, galaxies, or people.
Fermions, themselves, can be grouped into two categories: hadrons and leptons. Hadrons are particles that can experience the strong force, and leptons do not experience the strong force. Neutrons and Protons are hadrons, and electrons and neutrinos are leptons. Hadrons are actually composed of smaller particles called quarks. Hadrons can be classified as two types, baryons (composed of three quarks, and are fermions) and mesons (composed of two quarks, and are bosons). As I indicated, many would not include mesons in matter, though I rather think of them that way. Quarks are the only particles that interact using all four fundamental forces. Interestingly, the current models suggest that hadrons are composed of a sea of quarks of all types, with only two or three of these quarks (called valence quarks) lending their properties to the hadron. That they can be composed of a sea of quarks, allows one hadron to transform into another one by a change of valence quarks. Thus, though neutrons have zero charge, the approximate mass of a neutron and proton combined, and they decay into a proton, electron, and neutrino if left alone for a while, they are most definitely NOT a combination of electron and proton, but are entirely separate particles from each.
Dark matter, whatever it is, is not simply matter that is not lit up. It is composed of something that does not interact via the electromagnetic force, and thus we are unable to detect it except by its gravitational effects (light is electromagnetic in character). This suggests that it is most definitely not made of hadrons, because hadrons are composed of quarks, which do have electric charge and will interact with the electromagnetic force.
Ah, the joys of subatomic physics. I get to confuse my general physics students with this stuff at the end of their second semester class. I hope that I haven’t confused you too much.
-Astroprof
a. m. rowe (rau) on July 13, 2007 at 3:47 pm: 1
I have two questions:
1. what would happpen if two black holes “collided”?
2. is the extreme gravity due to the distances between masses being essentiially zero for black holes? ( Newton’s law of gravitation).
Astroprof on July 13, 2007 at 4:08 pm: 2
Black holes colliding would make a bigger black hole. Now, they’d likely release a bit of gravitational potential energy when they collided, though, in the form of gravity waves. And, if you are far enough from a black hole, it is just like being far from anything else, so you wouldn’t feel the extreme gravity effects.