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What Is an Elementary Particle? by STEVEN WEINBERG

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What Is an Elementary Particle? by STEVEN WEINBERG What Is An Elementary Particle? by STEVEN WEINBERG HEN A STRANGER, hearing that I am a physi- W cist, asks me in what area of physics I work, I generally reply that I work on the theory of elementary particles. Giving this answer always makes me nervous. Suppose that the stranger should ask, “What is an elemen- tary particle?” I would have to admit that no one really knows. Let me declare first of all that there is no difficulty in saying what is meant by a particle. A particle is simply a physical system that has no continuous degrees of freedom except for its total mo- mentum. For instance, we can give a complete description of an electron by specifying its momentum, as well as its spin around any given axis, a quantity that in quantum mechanics is discrete rather than continuous. On the other hand, a system consisting of a free electron and a free proton is not a particle, because to describe it one has to specify the momenta of both the electron and the proton— not just their sum. But a bound state of an electron and a proton, such as a hydrogen atom in its state of lowest energy, is a particle. Everyone would agree that a hydrogen atom is not an elementary particle, but it is not always so easy to make this distinction, or even to say what it means. Copyright © 1996 by Steven Weinberg. Research supported in part by the Robert A. Welch Foundation and NSF Grant PHY 9511632. BEAM LINE 17 OR THE FIRST FEW decades electrons.) It was the 1936 discovery of this century there did not of the charge independence of nuclear Fseem to be any trouble in say- forces by Merle Tuve et al. that ing what is meant by an elementary showed clearly that neutrons and particle. J. J. Thomson could use the protons have to be treated in the electric field in a cathode-ray tube to same way; if protons are elementary, pull electrons out of atoms, so atoms then neutrons must be elementary were not elementary. Nothing could too. Today, in speaking of protons be pulled or knocked out of electrons, and neutrons, we often lump them so it seemed that electrons were el- together as nucleons. ementary. When atomic nuclei were This was just the beginning of a discovered in Ernest Rutherford’s lab- great increase in the roster of so- oratory in 1911, it was assumed that called elementary particles. Muons they were not elementary, partly be- were added to the list in 1937 (though cause it was known that some ra- their nature was not understood un- dioactive nuclei emit electrons and til later), and pions and strange par- other particles, and also because nu- ticles in the 1940s. Neutrinos had clear charges and masses could be ex- been proposed by Wolfgang Pauli in plained by assuming that nuclei are 1930, and made part of beta-decay composed of two types of elementary theory by Enrico Fermi in 1933, but James Chadwick who discovered the particles: light, negatively charged were not detected until the Reines- neutron in 1932. (Courtesy AIP Meggers electrons and heavy, positively Cowan experiment of 1955. Then in Gallery of Nobel Laureates) charged protons. the late 1950s the use of particle ac- Even without a definite idea of celerators and bubble chambers re- what is meant by an elementary par- vealed a great number of new parti- ticle, the idea that all matter consists cles, including mesons of spin higher of just two types of elementary par- than 0 and baryons of spin higher ticle was pervasive and resilient in a than 1/2, with various values for way that is difficult to understand to- charge and strangeness. day. For instance, when neutrons On the principle that—even if were discovered by James Chadwick there are more than two types of el- in 1932, it was generally assumed ementary particles—there really that they were bound states of pro- should not be a great number of tons and electrons. In his paper an- types, theorists speculated that most nouncing the discovery, Chadwick of these particles are composites of offered the opinion: “It is, of course, a few types of elementary particles. possible to suppose that the neutron But such bound states would have to is an elementary particle. This view be bound very deeply, quite unlike has little to recommend it at present, atoms or atomic nuclei. For instance, except the possibility of explaining pions are much lighter than nucle- the statistics of such nuclei as N14.” ons and antinucleons, so if the pion (One might have thought this was were a bound state of a nucleon and a pretty good reason: molecular spec- an antinucleon, as proposed by Fer- tra had revealed that the N14 nucle- mi and Chen-Ning Yang, then its us is a boson, which is not possible binding energy would have to be if it is a bound state of protons and large enough to cancel almost all of 18 SPRING 1997 the mass of its constituents. The composite nature of such a particle would be far from obvious. How could one tell which of these particles is elementary and which composite? As soon as this question was asked, it was clear that the old answer—that particles are elemen- tary if you can’t knock anything out of them—was inadequate. Mesons come out when protons collide with each other, and protons and antipro- tons come out when mesons collide with each other, so which is a com- posite of which? Geoffrey Chew and Jr. Ehrenfest, P. others in the 1950s turned this ONG BEFORE Heisenberg Werner Heisenberg, left, talking with dilemma into a point of principle, reached this rather exaggerat- Neils Bohr at the Copenhagen Conference, Bohr Institute, 1934. known as “nuclear democracy,” ed conclusion, a different sort L (Courtesy AIP Emilio Segrè Visual Archives) which held that every particle may of definition of elementary particle be considered to be a bound state of had become widespread. From the any other particles that have the ap- perspective of quantum field theory, propriate quantum numbers. This as developed by Heisenberg, Pauli, view was reflected decades later in a and others in the period 1926–34, the 1975 talk to the German Physical So- basic ingredients of Nature are not ciety by Werner Heisenberg, who particles but fields; particles such as reminisced that: the electron and photon are bundles of energy of the electron and the elec- In the experiments of the fifties and sixties . many new particles tromagnetic fields. It is natural to de- were discovered with long and fine an elementary particle as one short lives, and no unambiguous whose field appears in the funda- answer could be given any longer mental field equations—or, as the- to the question about what these orists usually formulate these the- particles consisted of, since this ories, in the Lagrangian of the theory. question no longer has a rational It doesn’t matter if the particle is meaning. A proton, for example, could be made up of neutron and heavy or light, stable or unstable—if pion, or Lambda-hyperon and kaon, its field appears in the Lagrangian, it or out of two nucleons and an anti- is elementary; if not, not. nucleon; it would be simplest of all This is a fine definition if one to say that a proton just consists of knows the field equations or the La- continuous matter, and all these grangian, but for a long while physi- statements are equally correct or cists didn’t. A fair amount of theo- equally false. The difference be- tween elementary and composite retical work in the 1950s and 1960s particles has thus basically disap- went into trying to find some objec- peared. And that is no doubt the tive way of telling whether a given most important experimental dis- particle type is elementary or com- covery of the last fifty years. posite when the underlying theory is BEAM LINE 19 We will not be able to say which particles are elementary until we have not known. This turned out to be composites of quarks and gluons, not a final theory possible in certain circumstances because we can knock quarks and in nonrelativistic quantum me- of force and matter. gluons out of them, which is believed chanics, where an elementary par- to be impossible, but because that is ticle might be defined as one whose the way they appear in the theory. coordinates appear in the Hamilton- The one uncertain aspect of the ian of the system. For instance, a becomes incorrect, and instead we Standard Model is the mechanism theorem due to the mathematician get a formula for the scattering length that breaks the electroweak gauge Norman Levinson shows how to in terms of the nucleon mass, the symmetry and gives the W and Z par- count the numbers of stable non- deuteron binding energy, and the ticles their masses, thereby adding elementary particles minus the num- fraction of the time that the deuteron an extra helicity state to what would ber of unstable elementary particles spends as an elementary particle (that have been the two helicities of a in terms of changes in phase shifts is, the absolute value squared of the massless W or Z particle of spin 1. as the kinetic energy rises from zero matrix element between the physi- Theories of electroweak symmetry to infinity. The trouble with using cal deuteron state and the elemen- breakdown fall into two categories, this theorem is that it involves the tary free-deuteron state).
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