Journal of Philosophy, Inc.
On the Unification of Physics
Author(s): Tim Mauldin
Source: The Journal of Philosophy, Vol. 93, No. 3 (Mar., 1996), pp. 129-144
Published by: Journal of Philosophy, Inc.
Stable URL: http://www.jstor.org/stable/2940873
Accessed: 26-12-2015 22:32 UTC
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://www.jstor.org/page/
info/about/policies/terms.jsp
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content
in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship.
For more information about JSTOR, please contact support@jstor.org.
Journal of Philosophy, Inc. is collaborating with JSTOR to digitize, preserve and extend access to The Journal of Philosophy.
http://www.jstor.org
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions
ON THE UNIFICATION OF PHYSICS
129
ON THE UNIFICATION OF PHYSICS
the past forty years, theoretical physics has undergone a transformation in its avowed objectives as radical as any that has occurred in the last three centuries. This redirection has been at
once tremendously effective and mysteriously quiet, a sort of velvet
revolution in the conception of the aim of physical theory. Unlike
scientific revolutions that commonly preoccupy philosophers of science, this change has not come in accompanied by the battle cries of
opposing camps, nor been punctuated by any dazzling explosion of
empirical evidence. Indeed, this change has not been, in the common usage of the term, a scientific revolution at all, which perhaps
explains why it has progressed so seemingly naturally and inexorably,
like the advance of the seasons. The transformation centers around
the remarkable idea that the aim of physical theory is to achieve unification.
Today, anyone inquiring, whether in popular or professional literature, into the current status of fundamental physical theory is virtually guaranteed to be told the following tale. In the first part of this
century, physicists had verified the existence of four basic physical
forces: electromagnetism, gravity, the strong nuclear force, and the
weak nuclear force. Passably accurate theories of these forces individually have been developed, but those theories do not yet demonstrate any deep connection among all of the forces. The aim of
physics is now to produce theories which unify these forces, which
show, ultimately, that there is at base only one fundamental force in
the universe, which has come to display itself as if it were many different forces.
The first step in this program has already been taken: electromagnetism has been unified with the weak nuclear force in the electroweak theory. The other steps, though still to be achieved, have
already been named, and are to occur in a particular sequence. The
electroweak force is to be unified with the strong nuclear force by a
grand unified theory(GUT), and then, in the final step, the GUT will
somehow be unified with gravity in a theoryof everything(TOE).
This image of the future course of physical theory has become so
pervasive as to rank almost as dogma. Still, as mentioned above, the
process by which it has become so widely accepted would not generally be regarded as any sort of scientific revolution. For what has
been accepted is not itself a theory, and could not be defended or
criticized as an empirical theory would be. It is instead a commitIn
0022-362X/96/9303/129-44
i 1996 TheJournal of Philosophy, Inc.
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions
130
THEJOURNALOF PHILOSOPHY
ment (that might be deep or shallow) to a general view about how
theory is likely to develop and about the ultimate nature of as yet
undiscovered laws. It is certainly a commitment that is not so strong
as to override empirical support for theories that do not follow the
projected path. But, nonetheless, it is a powerful image that helps
shape the direction of research, and philosophers of science ought
to be intrigued about how physicists have come to find themselves in
the unification business.
The notion that all fundamental forces are somehow deeply unified goes back at least to Isaac Newton. Albert Einstein, of course,
spent the latter years of his life searching for a unified field theory,
but one along lines quite different from those envisaged today. So
our object of inquiry is not the idea of unification in all of its generality. Rather, we want to explore the particular species of unification
foreseen in the scenario sketched above. Of this contemporary
brand of unification we want to ask two questions. First is the fundamental philosophical question: What is it? What exactly is intended
by "unification" in these contexts? Second, and more contentiously,
we must ask: Why think that these forces are unified in the manner
envisaged? Unification puts rather strong constraints on the form of
a physical theory, and it is surely appropriate to ask what grounds we
have to believe that successful theories will respect those constraints.
By what modern Parmenidean logic have so many contemporary
physicists come to the conclusion that "All is One"? Or more directly, is there any empiricalground for faith in the project of unification, and if so, how strong is it?
But first things first: we shall begin by asking just what unification
amounts to. As is common in rough initial surveys, we begin by staking out some extreme boundaries.
I. WHATUNIFICATIONIS NOT
Let me start with the obvious. It is a universally accepted desideratum that theories of the various forces be consistentwith one another,
but consistency is clearly not sufficient for unification. Indeed, we
want all accepted scientific theories from all domains to be consistent with one another. But the fact that a theory of embryonic development does not contradict a theory of the formation of the rings of
Saturn is surely insufficient to render the two unified.
Of course, acknowledging consistency as a goal does not render it
trivial or easy to achieve. It is not entirely clear if quantum theory is
consistent with general relativity, and it might turn out that demanding mere consistency of our physical theories severely limits the form
they can take. Possibly, one might even suspect that the only way to
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions
ON THE UNIFICATION OF PHYSICS
131
render theories of the fundamental forces consistent is to unify
them. But it is hard to imagine a convincing argument for such a
position, and in any case, unification itself is a stronger condition
than mere consistency. What more is being demanded?
A stronger condition than consistency is the employment of a single fundamental dynamics, but this too falls short of unification.
Consider, for example, the theory one gets by conjoining Newtonian
dynamics with the Law of Universal Gravitation and with Coulomb's
Law. In this case, the theories of gravity and of the electrical force
are not so disjoint as, say, child psychology and fluid dynamics. The
accounts one would give of electrical and gravitational effects would
share a common explanatory structure. But even so, no one would
regard this as a case of unifying gravity and electricity. Although
both theories employ a common dynamical theory, still the forces
are not postulated to have anything in particular to do with one another. One could, for example, model a world with gravitational but
no electrical forces. Furthermore, the presence or absence of one
force would have no bearing on the presence or absence of the
other. Unification, then, must be supposed to go beyond mere commonalty of dynamics.
The next step up is law-like connection or correlation among
physical forces. The paradigm here would be Maxwell's theory of
electromagnetism, in which variation in certain electrical quantities
gives rise to magnetic phenomena, and vice versa. Unlike the case of
gravity and the electric force, neither electricity nor magnetism can
be understood without reference to the other. Indeed, in some
sense, Maxwell's theory does unify electricity and magnetism. But in
another, deeper sense, electric and magnetic fields retain a completely distinct ontological status in Maxwell's theory. They may be
nomically correlated, they may give rise to one another, but at base
they are still entirely different entities.
Indeed, the failure of classical electromagnetic theory to unify
electric and magnetic phenomena was the leading complaint voiced
in Einstein's' "special relativity"paper:
It is known that Maxwell'selectrodynamics-as usuallyunderstood
at the present time-when applied to movingbodies, leads to asymmetries which do not appearto be inherent in the phenomena. Take, for
example, the reciprocalelectrodynamicaction of a magnet and a conductor. The observablephenomenon here depends only on the rela'"On the Electrodynamics of Moving Bodies," reprinted in The Principle of
Relativity (New York: Dover, 1952).
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions
132
THEJOURNALOF PHILOSOPHY
tive motion of the conductor and the magnet, whereasthe customary
view drawsa sharp distinction between the two cases in which either
one or the other of these bodies is in motion. For if the magnet is in
motion and the conductor at rest, there arises in the neighbourhood
of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated.
But if the magnet is stationaryand the conductor in motion, no electric field arises in the neighbourhood of the magnet. In the conductor, however,we find an electromotiveforce, to which in itself there is
no corresponding energy, but which gives rise-assuming equality of
relative motion in the two cases discussed-to electric currentsof the
same path and intensityas those produced by the electric forces in the
former case (ibid., p. 37).
The failure of Maxwell's theory to unify electricity and magnetism,
that is, to show that in the two cases described one really has identical
physical situations, led to the Special Theory of Relativity (STR).
And it is this deeper sense of unification, the idea that all the physical forces are at base one and the same, which contemporary physicists invoke when they speculate on the theories to come.
We now have a lower limit in our search for the meaning of unification. Consistency, common dynamics, and nomic correlation are
all features we might seek when constructing theories of forces, but
they all fall short of unification. We shall now encircle our quarry by
describing some cases of perfect unification, thus setting an upper
limit that cannot be surpassed. As we shall see, between the upper
and the lower bounds, several different levels of unification will become discernible.
II. PERFECTUNIFICATION:TWO EXAMPLES
Since Einstein complained that Maxwell's theory failed to unify electrical and magnetic phenomena, the first place to look for successful
unification is STR. And in that theory, the formerly distinct electric
and magnetic fields are so commingled that a more complete integration is impossible to imagine. Indeed, the very words 'commingled' and 'integration' are inappropriate here, implying, as they do,
two things that are being somehow combined. But in STR there is
truly but one thing: the electromagnetic field tensor. It is not that
the electric field is reduced to the magnetic, but that both are shown
to be merely frame-dependent artifacts, inessential and misleading
ways of describing the single objective reality. So STR resolves the
problem of inductive currents that Einstein describes in this way:
when a current flows in the conductor, there is an electromagnetic
field tensor in the vicinity of the conductor. There is simply no objective fact of the matter about whether or not there is an electric
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions
ON THE UNIFICATION OF PHYSICS
133
field near the conductor, or what the value of the magnetic field is.
Electric and magnetic fields are not objectivelyreal, they "arise" only
when one chooses a certain reference frame relative to which the
phenomena are to be described. Thus, the electric and magnetic
fields are "unified" by being, in a way, eliminated entirely from the
fundamental ontology, and by being replaced by a single, frame-independent entity. To paraphrase H. Minkowski's famous remark on
space and time in special relativity, henceforth the electric field by itself and the magnetic field by itself are doomed to fade away into
mere shadows, and only a kind of union of the two will preserve an
independent reality.
A second example of fundamental unification is provided by the
second Einsteinian revolution: the General Theory of Relativity
(GTR). In the Newtonian milieu, gravitational and inertial structure
are quite different. In anachronistic terminology, inertial structure
is just the affine structure of Newtonian space-time. Newton's first
law states that an object with no forces on it will travel along a
straight trajectory through space-time. Gravity,on the other hand, is
a force that deflects objects from their inertial paths. In Newtonian
mechanics, gravity has no more intimate connection to inertia than
does electricity, and the equality of inertial mass and gravitational
mass would be no more expected a priori than the equality of electric charge and inertial mass.
In the general theory, gravity and inertia are reduced to a single
structure: the metrical structure of space-time. One may retain
Newton's first law, but only if one recognizes that thereis no force of
gravity at all. Phenomena formerly understood as effects of gravitational forces are now explained as effects of the influence of matter
on the affine structure of space-time. The equality of inertial and
gravitational mass, as evidenced by free fall in a gravitational field, is
reinterpreted as the common response of all matter to inertial structure. Objects do not couple to the gravitational field, they merely
exist in space-time.
Unlike the case of electromagnetic unification, one is perhaps inclined to regard the unification here as a reductionof gravity to inertia, especially since Newton's Law of Inertia still holds (in some
sense) while the Law of Universal Gravitation does not. But the dispute is a minor one. Newtonian theory has two distinct entities:
Newtonian (or Neo-Newtonian) space-time and the gravitational
field. GTR has but one: curved space-time. Neither of the original
two entities survives unscathed in the later theory (as happens in a
true reduction), but rather both are replaced by a single new object.
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions
134
THEJOURNALOF PHILOSOPHY
Were the projected unification of electromagnetism, gravity, and
the strong and the weak nuclear forces to run as deep as the examples we have just examined, then the very distinction among the
forces would disappear. If we take the special relativistic account of
electromagnetism as a model, a unified TOE should have the consequence that no effect could be objectively ascribed to the action of
the weak nuclear force rather than gravity. It is difficult to envisage
exactly how this could be so, but it seems fair to say that a deeper or
more complete unification cannot even be described. We can safely
allow these examples to serve as our paragons.
III. EVIDENCEFOR UNIFICATION
The two examples of perfect unification, relativistic electrodynamics
and general relativity, also provide particularly clear examples of one
sort of answer to our second question: Why think that the laws of nature ought to be unified at all? In each of these cases, the unification serves to explain a manifest symmetry in phenomena that was
known and remarked before the theories were developed. We have
already mentioned both of these symmetries.
There is the invariance of the predictions of Maxwell's theory
when one changes inertial frames, as exemplified in the fact that inductive effects depend only on the relative velocities of the magnet
and the conductor. As Einstein noted, the fact that the magnitude
of the effect depends only on the relative velocities stands in sharp
contrast to the theoretical explanations given of the phenomenon
according to Maxwell's equations. If the electric and magnetic fields
are objective, frame-independent entities, then superficially identical
experiments will receive deeply divergent explanations. Einstein
touts the ability of his theory to eliminate this asymmetry of explanation as one of its main theoretical virtues.
For general relativity, the manifest symmetry was obviously the
equality of inertial and gravitational mass. Although this was not so
much a major motivation for developing the theory, still in retrospect we can now recognize it as a clue to the correct form of the
theory of gravitation. It was certainly a fact that recommended itself to the attention of physicists, enough to inspire R. von Eotv6s
to perform his experiments long before the advent even of special
relativity.
Note that although the equality of inertial and gravitational mass
is afforded a satisfying explanation by GTR, it would be difficult to
argue that the equality demanded the sort of unification that GTR
provides. Newtonian theory can easily enough provide an explanation: it is not that there are really two kinds of mass that happen to
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions
ON THE UNIFICATION OF PHYSICS
135
turn out equal, but just that the single quantity, mass, happens to figure in two different laws. One and the same mass that endows an
object with its resistance to acceleration also causes (and responds
to) gravitational forces. Such an explanation would not, of course,
fundamentally unify inertia and gravitational forces in anything like
the thoroughgoing way that is achieved in GTR.
It should also perhaps be noted that GTR itself also supposes, at
least in theory, a dual role for mass. One still calculates the mass of
an electron or proton by its inertial effects: how much it accelerates
in a given field. But, in principle, this same inertial mass contributes
to the calculation of the stress-energy tensor, and so to the gravitational effect of the particle. I say 'in principle', since in practice the
masses of astronomical bodies are determined from their gravitational effects. That is, one calculates the mass of the sun, for example, by determining the orbits of the planets and setting the mass to
be the value demanded by the gravitational field equations to account for those orbits. Still, one would hope eventually to derive the
stress-energy tensor from a theory of the composition of the star, and
the masses derived from inertial effects would play a role, in such a
determination. Here, presumably, one would again have one and
the same quantity entering into very different fundamental laws.
In any case, GTR does explain the fact that small test objects under the influence only of the gravitational field follow parallel trajectories, and does this without postulating the equality of inertial and
gravitational mass. To this extent it constitutes an advance over
Newtonian theory, which can only get the result if the two "sorts"of
mass are equal.
Our second question, then, can be stated best by use of an analogy. As the symmetry of induction effects suggested a deep relationship between the electric and magnetic fields, and as the laws of free
fall suggested a deep connection between inertial and gravitational
structure, do any manifest phenomena suggest that the electroweak
force ought to be unified with the strong force, or either of these
with gravitation? Of course, to answer this question properly we
must get clear on exactly the sort of unification envisaged. Our
clearest guide here is to be found in the example of electroweak unification, so I turn next to this case.
IV. UNIFICATIONIN GAUGETHEORIES
With our map of varieties of unification in hand, we can now turn to
the fundamental theoretical structure employed in current attempts
at unification: gauge theories. A short reminder of the structure of
gauge theories is in order.
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions
136
THEJOURNALOF PHILOSOPHY
Any gauge theory is based on a gauge group. The theory is
constructed by first choosing a gauge group, such as U(1) for electromagnetism (the group of phase shifts ei6) or SU(3) for chromodynamics. A Lagrangian is then constructed which is invariant
under the group operations. The gauge particles, or carriers of the
force, are associated with the generators of the group. Thus, U(1)
has a single generator and a single gauge particle, the photon.
SU(3) has eight generators, yielding the eight sorts of gluons.
Particles are then assigned to multiplets that form representations of
the group. That is, the members of the multiplet are transformed
into one another by the action of the group operators. Part of the
game is to find multiplets of the right size and physical properties to
contain all of the known particles that feel the force.
There is an interesting complication to the structure sketched
above. In order for the Lagrangian to be invariant under the group
operations, the gauge particles must be massless. It was thought for
some time that this necessarily implied that the forces modeled must
be long distance, like electromagnetism or gravity. If so, then the
whole machinery would be inappropriate for the representation of
short-range forces, such as the weak and strong nuclear forces. One
could insert masses for the gauge particles into the equations by
hand, but doing so would break the gauge invariance (and also
seemed to render the equations nonrenormalizable). These problems were finally resolved by P. W. Higgs, who demonstrated a mechanism by which a Lagrangian that contains only massless gauge
particles can give rise to a phenomenology that contains only massive particles. This is accomplished through spontaneous symmetry
breaking.
Where, in all of this, are we to seek the unification of forces?
Since the forces are generated out of the gauge group, we should begin there. Various sorts of groups have been proposed, but it is best
to start with the standard model.
The standard model employs the gauge group SU(3) x SU(2) x
U (1), that is, it employs a product group rather than a simple group.
Product groups are constructed from the simple groups by a simple
combinatorial method. Thus, suppose I have a disk that can be rotated about its center. The symmetry group is U(1) (like the phase
of the wave function). A sphere can be rotated about any axis in
three-dimensional space, so the symmetry group is S0(3). Now, if I
think of the compound object consisting of the disk and the sphere
as a single entity whose states are specified by giving the orientation
of the disk and the orientation of the sphere, then the set of opera-
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions
ON THE UNIFICATION OF PHYSICS
137
tions that I can perform on the compound object constitutes the
group U(1) x S0(3). That is, the set of ordered pairs that consist of
one operation from U(1) and another from S0(3) itself obviously
forms a group, whose group structure is U(1) x S0(3). Any two
groups can be combined in this way, even if they have no interesting
structure in common.
In part, this is how the standard model was constructed. Chromodynamics was constructed using SU(3) while the electroweak theory used SU(2) x U(1). These theories have no intrinsic relation to
one another, besides both being gauge theories. Hence the standard
model was constructed by simply pasting the two groups together.
The strong and electroweak theories are no more intrinsically unified in the standard model than Newtonian gravity and the Coulomb
force are in Newtonian mechanics. In the taxonomy developed
above, this is a case of common dynamics and nothing more. This is,
of course, as it should be, for if the standard model were deeply unified, there would be no call for GUTs.
What of the electroweak theory? The gauge group here is SU(2) x
U (1). Since the group of quantum electrodynamics (QED) wasjust
U(1), this looks on the surface no better than the combination of
the strong and electroweak forces, with the U(1) group accounting
for electromagnetism and the SU(2) for the weak force. But the situation is a bit more complicated.
There are three generators of the SU(2) symmetry. Two of these
are associated with gauge particles in the usual way: the W+ and W-.
The third generator ought to be associated with a neutral particle,
which we shall call the XI for the moment. The U(1) symmetry is
also associated with a neutral gauge particle, which we may call P'i.
For purely empirical reasons, one cannot identify the XI'with the
third physical particle involved in weak interactions (namely, the Z'),
nor the YOwith the photon. Instead, in order to get the multiplets to
come out right, one must identify both the photon and the ZOwith
mixtures of the XOand YO. The precise proportion of XOand YOthat
go to make up the photon and the ZOis given by the so-called mixing
angle, which is a free parameter in the standard electroweak theory.
It is in this mixing, and in it alone, that electromagnetism and the
weak force become unified in the electroweak theory. One simply
cannot write down an adequate theory of the weak interaction without also including the materials for the electromagnetic one. (The
converse, interestingly, is not true, as is demonstrated by the existence of QED. The reason for this is that a combination of a particular gauge transformation from the SU(2) group with one from the
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions
138
THEJOURNALOF PHILOSOPHY
U(1) group has the effect of only changing the phases of charged
particles.)
To what extent is the mixing involved in the electroweak theory
really a case of unification? It is at least as strong as the unification
of electricity and magnetism in Maxwell's theory, in that the equations describing the weak force must also describe electromagnetism. And there is something a bit deeper, since the photon and the
Z?, the observed neutral particles associated with the weak and electromagnetic forces, are both built from the X"and Y?. Still, the unification fails to reach the level of perfection found in GTR, or even
the level anticipated in the GUTs. Thus, we find some ambivalence
among physicists about how exactly to describe the unification involved. K Moriyasu2states:
The weak and electromagnetic gauge fields are now completely unified.
What is most interesting about the unification is the mixing of the U(1)
and SU(2) gauge fields that was necessary to construct the physical electromagnetic potential. We began with a product of disconnected syrnmetry groups and ended up by unifying them through a mixing of
gauge fields. The reason for the mixing, of course, has nothing to do
with gauge theory per se. It was built in "by hand" through the identification of the leptons as the appropriate doublets and singlets of weakisotopic spin (ibid., pp. 109-10).
H. M. Georgi3 puts it this way:
The SU(2) x U(1) theory is not particularly beautiful. It is often called
a unification of the weak and electromagnetic interactions, but, in fact,
the unification is partial at best. The problem is the U(1) charge....
[T]his is a charge that commutes with all the other weak and colour
charges, so group theory tells us nothing about it. In particular, because of the U(1), the theory gives us no explanation of the striking fact
of electric charge quantization. Further, because of the U(1), there are
two separate dimensional charges or coupling constants required to
specify the theory, one for the SU(2) charge e2 and coupling constant
a2, and another for the U(1) charge el and coupling constant a,. This
introduces another unknown parameter into the theory and again reduces its explanatory power (ibid., p. 437).
Thus, for Georgi in particular, the fact that the group structure of
the electroweak theory is a product group still renders the theory unsatisfactorily disunified, despite the mixing.
2 An ElementaryPrimerfor Gauge Theory(Singapore: World Scientific, 1983).
1 "Grand Unified Theories," in P. Davies, ed., The New Physics (New York:
Cambridge, 1989).
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions
ON THE UNIFICATION OF PHYSICS
139
There is, then, an even higher level of unification to be sought in
gauge theory, namely, when the gauge group is a simple group. This
is the aim of the GUTs: to produce a gauge theory with a single, uncompounded gauge group from which the strong, weak, and electromagnetic forces may all be derived. The simplest such theory uses
the group SU(5), but other options are available.
So in moving to gauge theories, we have found three levels of
structure. Any two independently accepted gauge theories can be
pasted together with a product group to get a theory that nominally
has one gauge group. This does not constitute any sort of unification of the theories at all, and corresponds to having two distinct
forces at play in theories that share the same basic dynamics. At the
second level, such a product group, such as SU(2) x U(1), can give
rise to physically observable forces whose gauge particles derive from
mixing of the groups. It is questionable whether one should regard
this as any sort of deep unification. It seems closest to cases, such as
Maxwell's theory, in which different fields become coupled by the
equations, except that the underlyinggauge groups only couple if
one demands that the observed particles be generated. (Question:
at high energies, when the theory becomes completely symmetrical
again, would the U(1) and the SU(2) simply decouple?) At the third
level are gauge field theories premised on a simple gauge group.
This is the sort of unification sought by the GUTs.
In what sense would a theory of the this sort achieve a unification
of the forces? Certainly in the sense that the various forces would all
ultimately derive from a single underlying structure. But there is a
deeper unification than just this. The Lagrangian of that underlying
theory is invariant under the gauge transformations. In that sense,
the basic physics does not recognize any generic difference among the
forces, just as the rotation invariance of a Lagrangian would demonstrate that the physics did not postulate any generic difference
among the three dimensions of space. This is, of course, not unification in the sense of reduction to unity: space is still three dimensional. The three dimensions, though, are not intrinsically different,
and, indeed, it is physically arbitrary how one divides the three-dimensional object into three directions.
Such thorough unification had best not show up in all contexts,
since the world we deal with is manifestly not completely invariant in
this way. That is, electromagnetic, weak, and strong interactions are
clearly distinguishable, and cannot be transformed into one another
by any simple change of reference frame in the way electric and
magnetic fields can in Maxwell's theory. The symmetries in the
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions
140
THEJOURNALOF PHILOSOPHY
Lagrangian are to be spontaneously broken by the Higgs mechanism, and would be manifest only at very high temperatures.
Spontaneous symmetry breaking is what hides the deep unification
of the forces from our eyes. (Spontaneous symmetry breaking is also
needed to render the theory renormalizable.)
The typical analogy used for spontaneous symmetry breaking is
ferromagnetism: even though the fundamental laws are invariant under spatial rotations, the physical object governed by those laws may
not be, and in a particularly salient way. Furthermore, if the laws include some stochastic component, one can even have a situation in
which an invariant initial state evolves by means of invariant laws to a
state that breaks the symmetry. (The usual examples of crystal formation in freezing are a bit misleading in this way, since in those
cases one could imagine that an initial state is not really isotropic,
though it may be in its macroscopic variables.) And for a certain
use, this analogy is perfectly adequate.
But in one sense, the analogy badly fails. In the case of the ferromagnet, one does not add any new physics in the process of symmetry breaking: the interactions among the particles of the
magnet do the job. But the symmetry of the gauge theories is different. In the electroweak theory, the SU(2) x U(1) symmetry
does not just evaporate of its own accord. To get the symmetry to
break (and to give one of the massless gauge particles a mass) one
needs to add a new bit of physics: the Higgs field. The field does
not per se break the symmetry (so once one has the gauge field
plus the Higgs field, the analogy with ferromagnetism can proceed) but still from the point of view of unification, the addition
of the new field must come as a disappointment. We manage to
unify electromagnetism and the weak force, say, in a single gauge
field, but only by postulating yet another (heretofore unsuspected) scalar field.
Is the scalar field itself unified with the gauge field in any interesting way? As in the case of the unification of SU(2) x U(1) in electroweak theory, the answer seems to be that the fields are only
unified in that they all cooperate to produce the particular (apparently diverse) forces and particles we see. At the very high temperatures at which those forces would unify, the gauge field and the
Higgs field would decouple. Thus, we are faced with a new question
pertaining to unification: Should we expect or demand any GUT to
unify the gauge and scalar fields in any way? This completes our survey of the meaning of "unification" in unified theories of various
forces.
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions
ON THE UNIFICATION OF PHYSICS
141
CONSIDERATIONS
V. EMPIRICAL
If the preceding account is correct, we now have some idea of the
sort of unification of forces sought in the GUTs, and presumably ultimately in a TOE. This leaves us with our second question: What
reason, if any, is there to believe that the world really is unified in
this way? That is, before a unified theory has actually been developed, are there empirical clues or indications akin to the symmetry
of electromagnetic induction effects or the equality of inertial and
gravitational mass which seem to point to a deep unification of the
forces?
Obviously, manifest symmetry of the forces is precluded by the
spontaneous symmetry breaking. Unification is to be sought in
spite, rather than because, of the immediately observable properties
of the forces. The mechanism of symmetry breaking allows the research program to continue in the face of the apparent dissimilarity
of the forces, but it also denies us direct empirical grounds for believing that there is any hidden symmetry at all.
Unification might be sought for purely aesthetic reasons, and one
occasionally finds sentiments of the "all is one" variety expressed in
the literature. But this is surely the thinnest of all possible reeds on
which to found a research program.
Unification might be sought on the general methodological
grounds of repeating strategies that succeeded in the past. The line
would be that the successful elucidation of the weak force ultimately
demanded incorporation of electromagnetism, so perhaps the successful elucidation of the strong force should also require unification with the electroweak. But this argument fails on several
grounds. First, unification was not a strategy that was followed in arriving at the electroweak theory; rather, the unification was forced
on those who were primarily engaged in seeking an adequate theory
of the weak force. Second, the sort of unification that led to success
in the electroweak theory is not the sort of unification sought in the
GUTs. As we have seen, some theorists deny that the electroweak
theory displays any real unification of electromagnetism and the
weak force at all. Third, the situation vis-a-vis the weak and strong
forces is quite different. No workable theory of the weak force existed before the unified theory, but quantum chromodynamics
(QCD) does exist, and seems to work. (Incidentally, this is one way
in which the usual story about unifying forces is wrong. It is not that
at some point we had theoriesof the electromagnetic, weak, strong,
and gravitational forces separately, and now we have managed to
unify the first two. Rather, at some point we recognizedthe existenceof
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions
142
THEJOURNALOF PHILOSOPHY
all four forces, and found that unification was needed to account for
the weak force.) So why not think that SU(3) x SU(2) x U(1) is all
there is?
Here is what Georgi has to say about the motivation for SU(5):
Once we understood SU(2) x U(1) and quantum chromodynamics, GrandUnified Theorieswere a simple step. The motivationfor the
simplestGUT, SU(5), wasnot any mysticaldesire to follow in Einstein's
footstepsand unifyeverything.ShelleyGlashowand I werejust tryingto
understandSU(2) x U(1) better. For severalyears,we had realizedthat
if we could incorporatethe SU(2) x U(1) gauge symmetryinto a single
simple group it would give us some extra information. It would fix the
value of the weak mixing angle, a free parameterin the SU(2) x U(1)
theory and it would explain why all the electric charges we see in the
worldare multiplesof the chargeof the electron (op. cit., p. 454).
As Georgi notes, these considerations all stem from the desire to
complete the only partially unified SU(2) x U(1) theory in a more
satisfactory way, and demand only that that theory be derived from
some simple group, not that the simple group also account for any
other forces. Of course, the SU(5) theory did attempt to incorporate the strong force, but that was mostly due to the observation that
quarks together with the electron and neutrinos could be fit into the
multiplets of SU(5). In any case, the simplest SU(5) theory seems
not to work.
There is another class of considerations that have been taken to
point to the GUTs. If the SU(2) x U(1) structure can be derived by
symmetry breaking from a simple group, then, as Georgi notes, the
mixing angle will be calculable from first principles. Using SU(5) as
the simple group, one estimates the mixing angle to be 0.20 ? 0.01,
while the observed value is 0.230 ? 0.015. Steven Weinberg4 remarks
that the theoretical calculation "...is in reasonable agreement with
experiment. This is just a single quantitative success, but it is
enough to encourage us that there is something in these ideas"
(ibid., p. 201).
All of this leads us at best to a GUT. What about gravity? Do we
have any empirical grounds to expect gravitation to be unified with
the other forces in any significant way?
Gravity presents a problem very different from the unification of
the strong and electroweak forces. While it is clear that SU(2) x
U(1) is at least consistent with SU(3) QCD, it is not yet clear how to
wed GTR with quantum theory in a single theoretical framework.
4 Dreams of a Final
Theory(New York: Pantheon, 1992).
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions
ON THE UNIFICATION OF PHYSICS
143
Indeed, there seems to be a fundamental incompatibility (beyond
problems of renormalization) between the basic approaches of
gauge field theories and GTR. The field theories explain forces as
due to the action of fields, ultimately via the exchange of virtual
gauge particles. Objects couple to the field only if they interact
through some charge that serves as a coupling constant. Uncharged
particles would be unaffected by the field. But according to GTR,
gravity simply is not a force. There is no field whose effect is to deflect appropriately charged particles from their inertial trajectories.
Particles do not couple to the gravitational field, they simply exist in
space-time. Gravity does not deflect particles from their inertial
paths, as Newton thought, it determines their inertial paths.
The incompatibility of the gauge field theory approach with the
heart of GTR is most clearly demonstrated by the fact that in some
gauge theories of gravity, the equivalence principle fails: antimatter
is subject to different gravitational effects than matter. So we are left
with a very perplexing situation. Some of those pursuing TOEs are
willing to assert that what appears to be a perfect symmetry (the
equality of inertial and gravitational mass) really is not so, and they
reject the satisfying explanation of that symmetry by the unification
of inertial and gravitational structure, doing so in the name of a supposed underlying symmetry among other forces and gravity which is
completely shattered in the phenomena we observe.
What empirical grounds are there for believing gravity to be unified with any other forces? Weinberg cites the fact that the unification energy predicted by some GUTs is only a few orders of
magnitude below the Planck energy (ibid., p. 203), hardly very compelling.
Perhaps I have read too much into the rhetoric of some presentations. Physicists want a theory of gravity that is compatible with the
theories of other forces, and perhaps this is all that is intended by
"'unification"in this case. If more is demanded, we are within our
rights to ask what form this deeper unification is supposed to take
and what reasons we have to suspect that the world is unified in the
envisaged way. At this point, there is little hard evidence for the
kind of structure postulated by the GUTs and even less for the TOEs.
But the last word should rest with the physicists, and I shall give it to
Richard Feynman. When Robert Crease went to interview Feynman5
on the history of the standard model, the following exchange took
place:
5Recounted in James Gleick, Genius: The Life and Scienceof RichardFeynman (New
York: Pantheon, 1992).
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions
THEJOURNALOF PHILOSOPHY
144
When a historian of particle physics pressed him on the question of
unification in his Caltech office, he resisted. "Yourcareer spans the period of the construction of the standard model," the interviewer said.
"'The standard model,' "Feynman repeated dubiously.
"SU(3) X SU(2) X U(1). From renormalization to quantum electrodynamics to now?"
"The standard model, the standard model," Feynman said. "The
standard model-is that the one that says that we have electrodynamics,
we have weak interaction, and we have strong interaction? Okay. Yes."
The interviewer said, "That was quite an achievement, putting
them together."
'They're not put together."
"Linked together in a single theoretical package?"
"No."
The interviewer was having trouble getting his question on the
table. "Whatdo you call SU(3) X SU(2) X U(1)?"
'Three theories," Feynman said. "Strong interactions, weak interactions, and electromagnetic.... The theories are linked because they
seem to have similar characteristics.... Where does it go together? Only
if you add some stuff that we don't know. There isn't any theory today
that has SU(3) X SU(2) X U(1)-whatever the hell it is-that we know
is right, that has any experimental check.... Now, these guys are trying
to put all this together. They're tryingto. But they haven't. Okay?"...
"So we aren't any closer to unification than we were in Einstein's
time?" the historian asked.
Feynman grew angry. "It's a crazy question!...We're certainly
closer. We know more. And if there's a finite amount to be known, we
obviously must be closer to having the knowledge, okay? I don't know
how to make this into a sensible question.... It's all so stupid. All these
interviews are always so damned useless."
He rose from his desk and walked out the door and down the corridor, drumming his knuckles along the wall. The writer heard him
shout, just before he disappeared: "It'sgoddamned useless to talk about
these things! It's a complete waste of time! The history of these things
is nonsense! You're trying to make something difficult and complicated
out of something that's simple and beautiful."
Across the hall Murray Gell-Mann looked out of his office. "I see
you've met Dick," he said (ibid., pp. 433-34).
TIM MAUDLIN
Rutgers University
This content downloaded from 128.122.149.145 on Sat, 26 Dec 2015 22:32:22 UTC
All use subject to JSTOR Terms and Conditions