What's the Matternotes session 2

by Steve Bryson

What's a particle?

The view of what a fundamental particle is and how it acts haschanged radically over the course of this century. A hundredyears ago, the physicist's intuition of what a particle waspretty well matched with the common intuition of today: aparticle is like a very very small, hard, probably roundbaseball. For various reasons, this view has been seen to beuntenable. Among these are:

• Einstein's relativity theory does not permit anythingto be completely hard and solid, as this would allow shock wavesto travel through the particle infinitely fast, exceeding thevelocity of light (an absolute no-no).

• As was predicted by DeBroglie in 1923, electrons (whichare supposed to be particles) were observed (by Davisson andGermer in 1927) to behave in certain experiments just like waves.

• On the other hand, light (which is supposed to be awave) behaves under certain circumstances like particles (butparticles that can pass through each other). This was seen in themid 19th century and then explained by Planck and Einstein around1900-1905.

By 1927 all of these principles were integrated into a theoryof the behavior of matter called quantum mechanics. This theoryassociated to each particle an abstract wave (whose significanceis still somewhat unclear). If you know the wave associated tothe particle, you can figure out certain things about thebehavior of the particle, such as where it is and what is itsstate of motion.

Now the interesting thing about quantum mechanics is that youcannot in general predict from the quantum wave exactly what theparticle's behavior is, rather you can only say that the particleis 'probably here and less probably there', or that the particleis 'probably going this way and less probably going that way'. Inother words, you can give a range of possibilities of how theparticle is behaving but you cannot say that the particle isdefinitely doing any one particular thing. Now as when youobserve the particle it is doing only one particular thing, manypeople view quantum mechanics as an incomplete, unfinishedtheory. It seems, however, that the world behaves exactly asdescribed by quantum mechanics, and the predictions of quantummechanics are the most that we will ever be able to assert inanswer to questions about the behavior of particles.

Admitting that this is still an open question, in this coursewe will assume that the world is exactly as described by quantummechanics, and we will examine the implications of quantummechanics on the idea of a fundamental particle.

An example of the meaning of the quantummechanical wave

There are several significances that can be derived from thequantum mechanical wave, but I will here only talk about one ofthem. Anywhere the quantum mechanical wave is wiggling we have achance of finding a particle. Where this quantum mechanical waveis not wiggling at all, we will find no particles. Now each typeof particle has its own quantum wave associated with it. Anelectron has one quantum wave, a down quark has another quantumwave, a photon has another quantum wave and so on. Where thephoton wave is wiggling we are likely to find a photon. Where theup quark quantum wave is wiggling we are likely to find an upquark.

Thus the answer to the question "what is aparticle?" from a modern physics perspective is thefollowing:

A particle is anything in nature describedby a quantum mechanical wave.

Besides being confusing, this new characterization of particlehas far reaching consequences. First, it is totally unclear fromthis just what kind of thing a particle is. Physicists havelearned to live with this ambiguity, because quantum mechanicsgives very unambiguous predictions about how particles willbehave, and it is only how the predictions match withobservations that the physicist really cares about. This leavesconsiderable 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 somephysicists say that they think of particles as waves. I find inpractice that any physicist I've known has thought of particlesas baseballs when that was most useful, and thought of particlesas waves (often in the next sentence) when that becomes useful.This may all seem like fast double talk to the uninitiated, butit is absolutely clear that using the formal equations of quantummechanics (which are not at all ambiguous) gives the correctpredictions and this is what physics is all about.

The Creation and Destruction ofParticles

This characterization of a particle as something described bya quantum mechanical wave has another rather strikingconsequence: particles can be created and destroyed. This can beunderstood rather handily using the wave point of view. Consideran electron in a box. This particle will be described by theelectron's quantum wave,

which will be wiggling somewhere in the box (corresponding towhere the electron may be). Now as we are viewing the electron asno more than the quantum wave that describes it (as we are takingthe wave point of view), we can ask if we can 'damp out' thewiggling of the wave, so that it is not wiggling anywhere! Thenthat would be a wave which described the state of having noparticle at all! Thus we would have caused our electron to ceaseto exist! Below I will describe two different ways that this isdone in the laboratory: antimatter; and the interaction of thequantum wave of our particle with the quantum waves of othertypes of particles.


There is another striking implication of the wavecharacterization of matter--antimatter. Now a quantum wave is awiggle in some abstract space:

This wiggle is actually moving along with time. This meansthat we could also have the case where the wiggle is moving inthe opposite direction. This would be the quantum mechanical wavethat would describe the anti-matter counterpart of the electron,known as the positron or anti-electron. More metaphorically thantechnically, the waves of the electron and the anti-electronwould look like this if put side by side:

In this static view, you could look at antiparticles as thoseparticles described by an electron quantum mechanical wave withthe opposite phase. Now something interesting happens when youhave two waves which are the opposites of each other movingthrough the same region of space at the same time. Generally whenthis happens, you simply add the motion of the two wavestogether. In this case if you do that, you will find the electronwave going up just as the anti-electron wave is going down andvice versa. Thus the electron wave and the anti-electron wavewould add up to:


In other words, both particles ceased to exist! Now thisdiscussion is necessarily overly simplified, in that to actuallyhave the electron wave and the anti-electron wave interact inthis way we have to use the electromagnectic charge of the twoparticles. This, it turns out, implies that as the electron andanti-electron disappear two rather large wiggles are put into thephoton wave function thus creating two particles of light. Thuswe say that the electron and the anti-electron have annihilatedand two photons were created.

This process can be reversed, and we can have photons turninginto a particle and an anti-particle. Every time a particle iscreated and anti-particle must also be created.

An anti-particle of a particle behaves like the particleexcept that it has opposite charges for each of the forces (andopposite other properties too technical to mention here) but thesame mass.

Remember that anti-particles are just particles described by aquantum wave of a particle where that wave is in some sense goingin the opposite direction. This means that the existence ofanti-particles is guaranteed by the existence of particles, andso we do not consider anti-particles to be a separate class ofparticles. This also leads to talk (especially by RichardFeynman) like 'anti-particles are just like particles goingbackwards in time'. We will not be adapting this point of view inthis course.

Particle Interactions

The other way in which a quantum wave can be 'damped out' thusmaking the particle disappear is in interaction with the quantumwaves of other type of particles. These interactions aredescribed by a class of theories known as Quantum Field Theory.There are two successful quantum field theories today, called TheElectroweak Theory which describes the electromagnetic and weaknuclear interactions (and contains Quantum Electrodynamics (QED),which describes just the electromagnetic interactions), andQuantum Chromodynamics (QCD) which describes the strong nuclearinteraction. These theories completely specify the possibleinteractions between the 24 different types of quantum waves. Thehandout from last class describes all of these possibleinteractions. To translate what is in that handout to the wavepoint of view, take statements like "the photon acts onanything with electric charge" and read it as "Thephoton wave function interacts with any quantum wave that carrieselectric charge." This means that any quantum wave thatcarries electric charge will effect and be effected by the photonwave function. Thus:

The photon quantum wave interacts with any quantum wave thatcarries electric charge (electron, muon, tau, all quark, W+,and W- quantum waves)

The W+, W-, and Z0 quantumwaves interact with all fermion, W+, W-,and Z0 quantum waves.

The eight gluon quantum waves interact with all quark andgluon quantum waves.

No fermion quantum wave directly interacts with any otherfermion quantum wave.

What is the significance of these interactions? Theelectron-anti-electron interaction described above is actually aspecial case of the photon interactions (this is why two photonswere created in the process described). Thus one form of theinteraction is to damp out quantum waves (thus making particlesdisappear) while creating wiggles in other quantum waves (thusmaking other particle appear). Another example of this is thatthe W+ quantum wave can interact with a down quark quantum wave,thus damping out the down quark quantum wave (making the downquark disappear) and creating a wiggle in both the W+ quantumwave and in the up quark quantum wave (making a W+ and an upquark appear). Thus we say that the weak interactions (carried bythe W+ ) turns down quarks into up quarks. There are many othersuch changes in identity allowed, which will be described laterin the class.

Another less dramatic effect that these interactions may haveis to simply change the state of motion of the particlesassociated with the waves. Thus the photon quantum wave mayinteract with the electron wave in such a way that neither theelectron nor the photon disappear, but the motion of both theelectron and the photon is changed. This is technically called'elastic scattering'. This may happen with all of the forces.

The Quantum Existence of Particles

In the quantum mechanical description of the position of aparticle, a general quantum mechanical wave gives a whole rangeof possible positions for a single particle. In the same way, inquantum field theory the quantum wave of a particle will ingeneral give a whole range of possible numbers of particles. Thusin an interaction one may create one electron, or two electrons,or three electrons and so on. Now the theory of the interactionswill give exactly how often you should get one electron vs. twoelectrons etc. Thus you can only predict the probability of acertain outcome in an interaction out of a range ofpossibilities.

Translating these properties ofparticles into particle language

Most physicists, when faced with the choice of treatingparticles as either waves or little particles, will except whenabsolutely forced think of the particles as little baseballs.This means, however, that these little baseballs act very unlikeintuitive little baseballs. In particular, if one of theseelectron baseballs encounters an anti-electron baseball, thenthese 'baseballs' must simply disappear and you will then findsome little 'baseballs' of light in its place. This is a veryunintuitive notion about particles, but it is what you are forcedto if you wish to think of the particles in this theory as littlebaseballs (and this is why I personally prefer to think of themas waves).

Now when a force carrying quantum wave (such as the photonwave) interacts with, say, an electron's quantum wave in such away as to change that electron's motion and then interacts withanother electron's quantum wave in such a way as to change thatelectron's motion we cannot see the force carrying particle thatwould correspond to that force carrying quantum wave. From thewave point of view that is only natural, and from the particlepoint of view that force carrying particle is called a virtualparticle (as we could never see it).

Finally, it is the nature of quantum waves to be wiggling alittle bit all the time. These wiggles must always average out tozero when there are no particles, but there is always a very tinywiggle nonetheless (this is a purely quantum phenomenon). Thismeans that there are tiny wave interactions going on all the timeon a very tiny scale in such a way that we could never observethem directly (though they have been observed indirectly). Fromthe particle point of view it is said that particle-antiparticlepairs are continually being created and destroyed so quickly thatthey cannot be observed in otherwise empty space. Theseparticle-antiparticle pairs are also called virtual particles.

Session 3Notes

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