by Steve Bryson
The view of what a fundamental particle is and how it acts has changed radically over the course of this century. A hundred years ago, the physicist's intuition of what a particle was pretty well matched with the common intuition of today: a particle is like a very very small, hard, probably round baseball. For various reasons, this view has been seen to be untenable. Among these are:
• Einstein's relativity theory does not permit anything to be completely hard and solid, as this would allow shock waves to travel through the particle infinitely fast, exceeding the velocity of light (an absolute no-no).
• As was predicted by DeBroglie in 1923, electrons (which are supposed to be particles) were observed (by Davisson and Germer in 1927) to behave in certain experiments just like waves.
• On the other hand, light (which is supposed to be a wave) behaves under certain circumstances like particles (but particles that can pass through each other). This was seen in the mid 19th century and then explained by Planck and Einstein around 1900-1905.
By 1927 all of these principles were integrated into a theory of the behavior of matter called quantum mechanics. This theory associated to each particle an abstract wave (whose significance is still somewhat unclear). If you know the wave associated to the particle, you can figure out certain things about the behavior of the particle, such as where it is and what is its state of motion.
Now the interesting thing about quantum mechanics is that you cannot in general predict from the quantum wave exactly what the particle's behavior is, rather you can only say that the particle is 'probably here and less probably there', or that the particle is 'probably going this way and less probably going that way'. In other words, you can give a range of possibilities of how the particle is behaving but you cannot say that the particle is definitely doing any one particular thing. Now as when you observe the particle it is doing only one particular thing, many people view quantum mechanics as an incomplete, unfinished theory. It seems, however, that the world behaves exactly as described by quantum mechanics, and the predictions of quantum mechanics are the most that we will ever be able to assert in answer to questions about the behavior of particles.
Admitting that this is still an open question, in this course we will assume that the world is exactly as described by quantum mechanics, and we will examine the implications of quantum mechanics on the idea of a fundamental particle.
There are several significances that can be derived from the quantum mechanical wave, but I will here only talk about one of them. Anywhere the quantum mechanical wave is wiggling we have a chance of finding a particle. Where this quantum mechanical wave is not wiggling at all, we will find no particles. Now each type of particle has its own quantum wave associated with it. An electron has one quantum wave, a down quark has another quantum wave, a photon has another quantum wave and so on. Where the photon wave is wiggling we are likely to find a photon. Where the up quark quantum wave is wiggling we are likely to find an up quark.
Thus the answer to the question "what is a particle?" from a modern physics perspective is the following:
A particle is anything in nature described by a quantum mechanical wave.
Besides being confusing, this new characterization of particle has far reaching consequences. First, it is totally unclear from this just what kind of thing a particle is. Physicists have learned to live with this ambiguity, because quantum mechanics gives very unambiguous predictions about how particles will behave, and it is only how the predictions match with observations that the physicist really cares about. This leaves considerable freedom in how the physicist thinks of particles. Most physicists say they think of particles as tiny baseballs (with some complications that I will mention below), and some physicists say that they think of particles as waves. I find in practice that any physicist I've known has thought of particles as baseballs when that was most useful, and thought of particles as waves (often in the next sentence) when that becomes useful. This may all seem like fast double talk to the uninitiated, but it is absolutely clear that using the formal equations of quantum mechanics (which are not at all ambiguous) gives the correct predictions and this is what physics is all about.
This characterization of a particle as something described by a quantum mechanical wave has another rather striking consequence: particles can be created and destroyed. This can be understood rather handily using the wave point of view. Consider an electron in a box. This particle will be described by the electron's quantum wave,
which will be wiggling somewhere in the box (corresponding to where the electron may be). Now as we are viewing the electron as no more than the quantum wave that describes it (as we are taking the wave point of view), we can ask if we can 'damp out' the wiggling of the wave, so that it is not wiggling anywhere! Then that would be a wave which described the state of having no particle at all! Thus we would have caused our electron to cease to exist! Below I will describe two different ways that this is done in the laboratory: antimatter; and the interaction of the quantum wave of our particle with the quantum waves of other types of particles.
There is another striking implication of the wave characterization of matter--antimatter. Now a quantum wave is a wiggle in some abstract space:
This wiggle is actually moving along with time. This means that we could also have the case where the wiggle is moving in the opposite direction. This would be the quantum mechanical wave that would describe the anti-matter counterpart of the electron, known as the positron or anti-electron. More metaphorically than technically, the waves of the electron and the anti-electron would look like this if put side by side:
In this static view, you could look at antiparticles as those particles described by an electron quantum mechanical wave with the opposite phase. Now something interesting happens when you have two waves which are the opposites of each other moving through the same region of space at the same time. Generally when this happens, you simply add the motion of the two waves together. In this case if you do that, you will find the electron wave going up just as the anti-electron wave is going down and vice versa. Thus the electron wave and the anti-electron wave would add up to:
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In other words, both particles ceased to exist! Now this discussion is necessarily overly simplified, in that to actually have the electron wave and the anti-electron wave interact in this way we have to use the electromagnectic charge of the two particles. This, it turns out, implies that as the electron and anti-electron disappear two rather large wiggles are put into the photon wave function thus creating two particles of light. Thus we say that the electron and the anti-electron have annihilated and two photons were created.
This process can be reversed, and we can have photons turning into a particle and an anti-particle. Every time a particle is created and anti-particle must also be created.
An anti-particle of a particle behaves like the particle except that it has opposite charges for each of the forces (and opposite other properties too technical to mention here) but the same mass.
Remember that anti-particles are just particles described by a quantum wave of a particle where that wave is in some sense going in the opposite direction. This means that the existence of anti-particles is guaranteed by the existence of particles, and so we do not consider anti-particles to be a separate class of particles. This also leads to talk (especially by Richard Feynman) like 'anti-particles are just like particles going backwards in time'. We will not be adapting this point of view in this course.
The other way in which a quantum wave can be 'damped out' thus making the particle disappear is in interaction with the quantum waves of other type of particles. These interactions are described by a class of theories known as Quantum Field Theory. There are two successful quantum field theories today, called The Electroweak Theory which describes the electromagnetic and weak nuclear interactions (and contains Quantum Electrodynamics (QED), which describes just the electromagnetic interactions), and Quantum Chromodynamics (QCD) which describes the strong nuclear interaction. These theories completely specify the possible interactions between the 24 different types of quantum waves. The handout from last class describes all of these possible interactions. To translate what is in that handout to the wave point of view, take statements like "the photon acts on anything with electric charge" and read it as "The photon wave function interacts with any quantum wave that carries electric charge." This means that any quantum wave that carries electric charge will effect and be effected by the photon wave function. Thus:
The photon quantum wave interacts with any quantum wave that carries electric charge (electron, muon, tau, all quark, W+, and W- quantum waves)
The W+, W-, and Z0 quantum waves interact with all fermion, W+, W-, and Z0 quantum waves.
The eight gluon quantum waves interact with all quark and gluon quantum waves.
No fermion quantum wave directly interacts with any other fermion quantum wave.
What is the significance of these interactions? The electron-anti-electron interaction described above is actually a special case of the photon interactions (this is why two photons were created in the process described). Thus one form of the interaction is to damp out quantum waves (thus making particles disappear) while creating wiggles in other quantum waves (thus making other particle appear). Another example of this is that the W+ quantum wave can interact with a down quark quantum wave, thus damping out the down quark quantum wave (making the down quark disappear) and creating a wiggle in both the W+ quantum wave and in the up quark quantum wave (making a W+ and an up quark appear). Thus we say that the weak interactions (carried by the W+ ) turns down quarks into up quarks. There are many other such changes in identity allowed, which will be described later in the class.
Another less dramatic effect that these interactions may have is to simply change the state of motion of the particles associated with the waves. Thus the photon quantum wave may interact with the electron wave in such a way that neither the electron nor the photon disappear, but the motion of both the electron and the photon is changed. This is technically called 'elastic scattering'. This may happen with all of the forces.
In the quantum mechanical description of the position of a particle, a general quantum mechanical wave gives a whole range of possible positions for a single particle. In the same way, in quantum field theory the quantum wave of a particle will in general give a whole range of possible numbers of particles. Thus in an interaction one may create one electron, or two electrons, or three electrons and so on. Now the theory of the interactions will give exactly how often you should get one electron vs. two electrons etc. Thus you can only predict the probability of a certain outcome in an interaction out of a range of possibilities.
Most physicists, when faced with the choice of treating particles as either waves or little particles, will except when absolutely forced think of the particles as little baseballs. This means, however, that these little baseballs act very unlike intuitive little baseballs. In particular, if one of these electron baseballs encounters an anti-electron baseball, then these 'baseballs' must simply disappear and you will then find some little 'baseballs' of light in its place. This is a very unintuitive notion about particles, but it is what you are forced to if you wish to think of the particles in this theory as little baseballs (and this is why I personally prefer to think of them as waves).
Now when a force carrying quantum wave (such as the photon wave) interacts with, say, an electron's quantum wave in such a way as to change that electron's motion and then interacts with another electron's quantum wave in such a way as to change that electron's motion we cannot see the force carrying particle that would correspond to that force carrying quantum wave. From the wave point of view that is only natural, and from the particle point of view that force carrying particle is called a virtual particle (as we could never see it).
Finally, it is the nature of quantum waves to be wiggling a little bit all the time. These wiggles must always average out to zero when there are no particles, but there is always a very tiny wiggle nonetheless (this is a purely quantum phenomenon). This means that there are tiny wave interactions going on all the time on a very tiny scale in such a way that we could never observe them directly (though they have been observed indirectly). From the particle point of view it is said that particle-antiparticle pairs are continually being created and destroyed so quickly that they cannot be observed in otherwise empty space. These particle-antiparticle pairs are also called virtual particles.