32 INTRODUCTORYphoton, and there were two fundamental interactions, electromagnetism and grav-
itation. At present the number of particles runs into the hundreds. A further
reduction to more fundamental units appears inevitable. It is now believed that
there are at least four fundamental interactions. The unification of all four types
of forces—gravitational, electromagnetic, weak, and strong—is an active topic of
current exploration. It has not been achieved as yet.
Relativistic quantum field theories (in the sense of special relativity) are the
principal tools for these explorations. Our confidence in the general field theoret-
ical approach rests first and foremost on the tremendous success of quantum elec-
trodynamics (QED). One number, the g factor of the electron, may illustrate both
the current level of predictability of this theory and the level of experimental pre-
cision which has been reached:
u/ _ ox -f^1 159 652 46 ° (^127 > (^75 ) X 10"^12 predicted by pure QED*(g ' (1 159652200(40) X 10-' (^2) observed
It has nevertheless become evident that this branch of field theory will merge with
the theory of other fields.
'If we could have presented Einstein with a synthesis of his general relativity
and the quantum theory, then the discussion with him would have been consid-
erably easier' [PI]. To date, this synthesis is beset with conceptual and technical
difficulties. The existence of singularities associated with gravitational collapse is
considered by some an indication for the incompleteness of the general relativistic
equations. It is not known whether or not these singularities are smoothed out by
quantum effects.
There is hope that gravitational waves will be observed in this century (15d).
The ultimate unification of weak and electromagnetic interactions has probably
not yet been achieved, but a solid beach-head appears to have been established in
terms of local non-Abelian gauge theories with spontaneous symmetry breakdown.
As a result, it is now widely believed that weak interactions are mediated by mas-
sive vector mesons. Current expectations are that such mesons will be observed
within the decade.
It is widely believed that strong interactions are also mediated by local non-
Abelian gauge fields. Their symmetry is supposed to be unbroken so that the cor-
responding vector mesons are massless. The dynamics of these 'non-Abelian pho-
tons' are supposed to prohibit their creation as single free particles. The technical
exploration of this theory is in its early stages.
Promising steps have been made toward grand unification, the union of weak,
electromagnetic, and strong interactions in one compact, non-Abelian gauge
*In this prediction (which does not include small contributions from muons and hadrons), the best
value of the fine-structure constant a has been used as an input: a"^1 = 137.035 963 (15). The
principal source of uncertainty in the predicted value of (g — 2) stems from the experimental uncer-
tainties of a, leading to the error (127). The error (75) is mainly due to uncertainties in the eighth
order calculation [Kl].