11throughout his history man has at describing phenomena that take place over theory, which gives a unified description of wanted to know the dimensions distance intervals of order 10–16 centimeter quantum electrodynamics (QED) and the of his world and his place in it. or larger. These theories may be valid to weak interactions, and quantum chromo- A Before the advent of scientific in- much shorter distances, but that remains to dynamics (QCD), which is an attractive can- struments the universe did not seem very be tested experimentally. A fully unified the- didate theory for the strong interactions. We large or complicated. Anything too small to ory will have to include gravity and therefore will argue that, although Einstein’s theory of detect with the naked eye was not known, will probably have to describe spatial struc- gravity (also called general relativity) has a and the few visible stars might almost be tures as small as 10–33centimeter, the funda- somewhat different status among physical touched if only there were a higher hill mental length (determined by Newton’s theories, it should also be included in the nearby. gravitational constant) in the theory of grav- standard model. If it is, then the standard Today, with high-energy particle ac- ity. History suggests cause for further model incorporates all observed physical celerators the frontier has been pushed down caution: the record shows many failures re- phenomena—from the shortest distance in- to distance intervals as small as 10-]6 cen- sulting from attempts to unify the wrong, too tervals probed at the highest energy ac- timeter and with super telescopes to cos- few, or too many physical phenomena. The celerators to the longest distances seen by mological distances. These explorations end of the 19th century saw a huge but modern telescopes. However, despite its ex- have revealed a multifaceted universe; at unsuccessful effort to unify the description of perimental successes, the standard model re- first glance its diversity appears too com- all Nature with thermodynamics. Since the mains unsatisfying, among its shortcomings plicated to be described in any unified man- second law of thermodynamics cannot be is the presence of a large number of arbitrary ner. Nevertheless, it has been possible to derived from Newtonian mechanics, some constants that require explanations. It re- incorporate the immense variety of ex- physicists felt it must have the most funda- mains to be seen whether the next level of perimental data into a small number of mental significance and sought to derive the unification will provide just a few insights quantum field theories that describe four rest of physics from it. Then came a period of into the standard model or will unify all basic interactions—weak, strong, electro- belief in the combined use of Maxwell’s elec- natural phenomena. magnetic, and gravitational. Their mathe- trodynamics and Newton’s mechanics to ex- The second question examined in this es- matical formulations are similar in that each plain all natural phenomena. This effort was say is twofold: What are the possible strate- one can be derived from a local symmetry. also doomed to failure: not only did these gies for generalizing and extending the stan- This similarity has inspired hope for even theories lack consistency (Newton’s equa- dard model, and how nearly do models based greater progress: perhaps an extension of the tions are consistent with particles traveling on these strategies describe Nature? A central present theoretical framework will provide a faster than the speed of light, whereas the problem of theoretical physics is to identify single unified description of all natural Lorentz invariant equations of Maxwell are the features of a theory that should be ab- phenomena. not), but also new experimental results were stracted, extended, modified, or generalized. This dream of unification has recurred emerging that implied the quantum structure From among the bewildering array of the- again and again, and there have been many of matter. Further into this century came the ories, speculations, and ideas that have successes: Maxwell’s unification of elec- celebrated effort by Einstein to formulate a grown from the standard model, we will tricity and magnetism; Einstein’s unification unified field theory of gravity and elec- describe several that are currently attracting of gravitational phenomena with the tromagnetism. His failure notwithstanding, much attention. geomeh-y of space-time; the quantum-me- the mathematical form of his classical theory We focus on two extensions of established chanical unification of Newtonian mechan- has many remarkable similarities to the concepts. The first is called supersymmetry; ics with the wave-like behavior of matteL the modern efforts to unify all known fundamen- it enlarges the usual space-time symmetries quantum-mechanical generalization of elec- tal interactions. We must be wary that our of field theory, namely, Poincar6 invariance, trodynamics; and finally the recent unifica- reliance on quantum field theory and local to include a symmetry among the bosons tion of electromagnetism with the weak symmetry may be similarly misdirected, al- (particles of integer spin) and fermions force. Each of these advances is a crucial though we suppose here that it is not. (particles of half-odd integer spin). One of component of the present efforts to seek a Two questions will be the central themes the intriguing features of supersymmetry is more complete physical theory. of this essay. First, should we believe that the that it can be extended to include internal Befo,re the successes of the past inspire too theories known today are the correct compo- symmetries (see Note 2 in “Lecture Notes— much optimism, it is important to note that a nents of a truly unified theory? The compo- From Simple Field Theories to the Standard unified theory will require an unprecedented nent theories are now so broadly accepted Model). In the standard model internal local extrapolation. The present optimism is gen- that they have become known as the “stan- symmetries play a crucial role, both for erated by the discovery of theories successful dard model.” They include the electroweak classifying elementary particles and for de- 74 Summer/Fall 1984 LOS ALAMOS SCIENCE Newton’s Gravity Classical Orlglns ++ - I Einstein’s Gravity Quantum Development of Mechanics Quantum Theories T Quantum Electrodynamics Yang-Mills 5 Theories Electroweak Model Supergravity SU(2) x u(1) E I Chromodynamics I SU(3) I I J / Kaluza-Klein “Grand” Unification Theories //~u Extended Supergravity Development of Gravitational Theories Including Other Forces Superstrings I Fig. 1. Erolution of fundamental theories of Nature from the direct and well-established extension, or theoretical gen - clajsicaljie!d theories of .Vewton and Maxwell to the grand- erali:ation. The wide arrow s~’mboii:es the goal of presenr tvt theoretical conjectures of toda~. ‘The relationships among research, the unification of quantum fle[d theories n’ith these theories are discussed in the text. Solid lines indicate a gravit~’. 1()$! \] \\ I()$. .>( 11-\( 1 \ll:ll,ll L, 1.,11I(IM .< termining the form of the interactions among ories are encouraging because some of them there exists a gauge field and its correspond- them. The electroweak theory is based on the reduce, in a certain limit, to the only super- ing particle, which is a vector boson (spin-1 internal local symmetry group SU(2) X U(l) gravity theories that are likely to generalize particle) that mediates the interaction be- (see Note 8) and quantum chromodynamics the standard model. Moreover, whereas tween particles. Quantum electrodynamics on the internal local symmetry group SU(3). supergravity fails to give the standard model has just one independent local symmetry Gravity is based on space-time symmetries: exactly, a superstring theory might succeed. transformation, and the photon is the vector general coordinate invariance and local It seems that superstring theories can be boson (or gauge particle) mediating the inter- Poincari symmetry. It is tempting to try to formulated only in ten dimensions. action between electrons or other charged unify all these symmetries with supersym- Figure 1 provides a road map for this particles. Furthermore, tbe local symmetry metry. essay, which journeys from the origins of the dictates the exact form of the interaction. Other important implications of super- standard model in classical theory to the The interaction Lagrangian must be of the symmetry are that it enlarges the scope of the extensions of the standard model in super- form e.P’(.x),4Y(.x),where .P(.x) is the current classification schemes of the basic particles gravity and superstrings. These extensions density of the charged particles and A ~(x) is to include fields of different spins in the same may provide extremely elegant ways to unify the field of the vector bosons. The coupling multiplet, and it helps to solve some tech- the standard model and are therefore attract- constant e is defined as the strength with nical problems concerning large mass ratios ing enormous theoretical interest. It must be which the vector boson interacts with the that plague certain efforts to derive the stan- cautioned, however, that at present no ex- current. The hypothesis that all interactions dard moclel. Most significantly, if supersym- perimental evidence exists for supersym- are mediated by vector bosons or, equi- metry is made to be a local symmetry, then it metry or extra dimensions. valently, that they originate from local sym- automatically implies a theory of gravity, metries has been extended to the weak and called supergravity, that is a generalization of then to the strong interactions. Einstein’s theory. Supergravity theories re- Review of the Standard Model quire the unification of gravity with other Weak Interactions. Before the present under- kinds of interactions, which may be, in some We now review the standard model with standing of weak interactions in terms of future version, the electroweak and strong particular emphasis on its potential for being local symmetry, Fermi’s 1934 phenomeno- interacticms.