Ambitious attempts to obtain a unified description of all the interactions of nature have so far been more notable for their ingenuity, beauty and chutzpah than for any help they have afforded toward understanding concrete facts about the physical world. In this article we wish to describe one shining exception: how ideas about the unification of the strong, weak and electromagnetic interactions lead to concrete, quantitative predictions about the relative strengths of these interactions.

1.
Other good semipopular introductions to many of the main ideas of gauge theories include S. Weinberg, Sci. Am., July 1974, p. 50; and G. 't Hooft, Sci. Am., June 1980, p. 104. Standard textbooks on gauge theories include I. Aitchison, A. Hey, Gauge Theories in Particle Physics, Adam Hilger, Bristol, UK (1982);
K. Gottfried, V. Weisskopf, Concepts for Particle Physics I and II, Clarendon, Oxford (1984);
C. Quigg, Gauge Theories for the Strong, Weak, and Electromagnetic Interactions, Benjamin/Cummings, Reading, Mass. (1987);
and T. P. Cheng, L.‐F. Li, Gauge Theories of Elementary Particle Physics, Clarendon, Oxford (1984).
See also the excellent annotated reprint collection Gauge Inuariance, T. P. Cheng, L.‐F. Li, eds., Am. Assoc. Phys. Teachers, College Park, Md. (1990).
2.
An early attempt at unification of couplings is
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Pati
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A.
Salam
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Phys. Rev. D
8
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1240
(
1973
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Color unification along the lines discussed here was introduced in
H.
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Phys. Rev. Lett.
32
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438
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Y.
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Phys. Rev.
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P. W.
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Phys. Rev. Lett.
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P. W.
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F.
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G. S.
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C. R.
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T. W. B.
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Phys. Rev. Lett.
13
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585
(
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F.
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H.
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Proc. R. Soc. London, Ser. A
149
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V. L.
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L. D.
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20
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P. W.
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Phys. Rev.
110
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Phys. Rev.
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112
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D. J.
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F.
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Phys. Rev. Lett.
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H. D.
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Phys. Rev. Lett.
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D. J.
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F.
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Phys. Rev. D
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(
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S.
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Phys. Rev. Lett.
31
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M.
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Phys. Lett. B
47
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(
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7.
G.
Miller
et al.,
Phys. Rev. D
5
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(
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A.
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Phys. Rev. D
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9.
For a recent review, see
G.
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Ann. Rev. Nucl. Part. Phys.
39
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49
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H.
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H.
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S.
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Phys. Rev. Lett.
33
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(
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Yu.
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E.
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13
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323
(
1971
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V.
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B.
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See also the very useful reprint collection Supersymmetry (2 vols.), S. Ferrara, ed., North‐Holland/World Scientific, Singapore (1987).
13.
Y.
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,
Phys. Rev. Lett.
4
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(
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G.
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18
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14.
Early papers mentioning the hierarchy problem include
E.
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Phys. Rev. D
14
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1667
(
1976
);
E.
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S.
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,
Phys. Rev. D
15
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(
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);
L.
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,
Phys. Rev. D
20
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2619
(
1979
).
Early papers applying supersymmetry in atempts to ameliorate the hierarchy problem include
M.
Veltman
,
Acta Phys. Pol. B
12
,
437
(
1981
);
S.
Dimopoulos
,
S.
Raby
,
Nucl. Phys. B
192
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353
(
1981
);
M.
Dine
,
W.
Fischler
,
M.
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,
Nucl. Phys. B
189
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575
(
1981
);
E.
Witten
,
Nucl. Phys. B
188
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(
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);
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15.
S.
Dimopoulos
,
S.
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,
F.
Wilczek
,
Phys. Rev. D
24
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(
1981
).
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D.
Freedman
,
P.
van Nieuwenhuizen
,
S.
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Phys. Rev. D
13
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(
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).
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B.
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62
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P.
Fayet
,
Phys. Lett. B
69
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(
1977
);
P.
Fayet
,
84
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(
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S.
Ferrara
,
L.
Ghirardello
,
F.
Palumbo
,
Phys. Rev. D
20
,
403
(
1979
).
18.
S.
Dimopoulos
,
H.
Georgi
,
Nucl. Phys. B
193
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(
1981
).
19.
N.
Sakai
,
Z. Phys. C
11
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153
(
1981
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L. E.
Ibanez
,
G. G.
Ross
,
Phys. Lett. B
105
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(
1981
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M. B.
Einhorn
,
D. R. T.
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196
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(
1982
).
W. J.
Marciano
,
G.
Senjanovic
,
Phys. Rev. D
25
,
3092
(
1982
).
20.
These results from the DELPHI, ALEPH, L3 and OPAL collaborations are in a series of papers too numerous to list here; they mostly have appeared (and continue to appear) in Phy. Lett. B.
21.
U.
Amaldi
,
W.
de Boer
,
H.
Fürstenau
,
Phys. Lett. B
260
,
447
(
1991
).
The possibility of such analysis was demonstrated earlier by
J.
Ellis
,
S.
Kelly
,
D.
Nanopoulos
,
Phys. Lett. B
249
,
441
(
1990
).
A similar analysis was carried out independently by P. Langacker, M. Luo, U. Pennsylvania preprint (1991).
22.
See, for example,
H.
Georgi
,
D.
Nanopoulos
,
Nucl. Phys. B
155
,
52
(
1979
);
L. E.
Ibanez
,
Nucl. Phys. B
181
, (
1981
);
P.
Frampton
,
S. L.
Glashow
,
Phys. Lett. B
135
,
340
(
1983
);
P.
Frampton
,
B.‐H.
Lee
,
Phys. Rev. Lett.
64
,
619
(
1990
);
A. Giveon, L. Hall, U. Sarid, U. Calif., Berkeley preprint (July 1991).
23.
S.
Weinberg
,
Phys. Rev. D
26
,
257
(
1982
).
N.
Sakai
,
T.
Yanagida
,
Nucl. Phys. B
197
,
533
(
1982
).
24.
S.
Dimopoulos
,
S.
Raby
,
F.
Wilczek
,
Phys. Lett. B
112
,
133
(
1982
).
J.
Ellis
,
D. V.
Nanopoulos
,
S.
Rudaz
,
Nucl. Phys. B
202
,
43
(
1982
).
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