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The conventional wisdom is that general relativity and quantum mechanics
are presently incompatible. Of the "four fundamental forces" gravity is said
to be different because a quantum version of the theory does not exist. We feel
less satisfied with the theory of gravity and exclude it from being recognized
as a full member of the Standard Model. Part of the trouble is that we
have tried to unnaturally force gravity into the mold of renormalizable field
theories. In the old way of thinking, only the class of renormalizable field
theories were considered workable quantum theories. For this reason, general
relativity was considered a failure as a quantum field theory. However we
now think differently about renormalizability. So-called non-renormalizable
theories can be renormalized if treated in a general enough framework, and
they are not inconsistent with quantum mechanics[12]. In the framework of
effective field theories[13], the effects of quantum physics can be analyzed
and reliable predictions can be made. We will see that in this regard the
conventional wisdom about gravity is not correct; quantum predictions can
be made.
The key point of effective field theory is the separation of known physics
at the scale that we are working from unknown physics at much higher energies.
Experience has shown that as we go to higher energies, new degrees
of freedom and new interactions come into play. We have no reason to suspect
that the effects of our present theory are the whole story at the highest
energies. Effective field theory allows us to make predictions at present energies
without making unwarranted assumptions about what is going on at
high energies. In addition, whatever the physics of high energy really is,
it will leave residual effects at low energy in the form of highly suppressed
non-renormalizable interactions. These can be treated without disrupting
the low energy theory. The use of effective field theory is not limited to
non-renormalizable theories. Even renormalizable theories benefit from this
paradigm. For example, there are the well-known divergences in all field theories.
If these divergences were really and truly infinite, the manipulations
that we do with them would be nonsense. However we do not believe that our
calculations of these divergences are really correct, and if our theory is only
a low energy effective field theory of the ultimate finite theory of everything,
the manipulations are perfectly reasonable with the end predictions being
independent of the physics at very high scales. Our feeling of the reality of
the radiative corrections has also convinced many that it is most natural if
the present Standard Model is an effective theory which breaks down at the
TeV scale, where Higgs self-interactions would otherwise become unnaturally
large. We have even found it useful in Heavy Quark Effective Theory to convert
a renormalizable theory into a non-renormalizable one in order to more
efficiently display the relevant degrees of freedom and interactions.
In the case of gravity, we feel that the low energy degrees of freedom and
interactions are those of general relativity. It would be a surprise if these
could not be treated quantum mechanically. To be sure, radiative corrections
appear to involve all energies, but this is a problem that the effective
field theory formalism handles automatically. We will see that gravity very
naturally fits into the framework of effective field theory[14]. In fact it is
potentially even a better effective theory than the Standard Model as the
quantum corrections are very small and the theory shows no hint of a breakdown
before the Planck scale. If we insist on treating general relativity as
the isolated fundamental theory even at very high energies, there will be the
usual problems at high energy. However, the main point is that we can use
the degrees of freedom that we have at ordinary energies to make quantum
calculations relevant for those scales.
Future Directions
The gravitational effective field theory provides a new technology for quantum
gravity. Most discussions of the topic of gravity and quantum mechanics
do not keep track of the high vs. low scales. This "effective" way of thinking
can be very useful in deciding which aspects are trustworthy and which are
speculative.
Within the effective theory, there are several possible directions for future
work. It may be possible to compare the quantum predictions with the results
of computer simulations of lattice gravity. It is too early to entirely give up on
all hopes for real phenomenology. Perhaps quantum effects can build up and
be visible as deviations from various null effects of the classical theory[15].
Perhaps these ideas may be useful in describing the very early universe. There
are also potential theoretical applications, such as the effects of anomalies or
the quantum influence on the development of singularities. Finally there exist
in the literature various suggestions for unusual gravitational effects such as
phase transitions, running G at low energy, solutions to the dark matter
problem etc. Effective field theory should be able to support or refute these
suggestions. At the least, we will put our standard expectations on a stronger
footing.
Nature has apparently given us the fields and interactions of the electroweak
gauge theory, quantum chromodynamics and general relativity at
present energies. All are treatable at those energies by the techniques of
quantum mechanics. It remains a formidable challenge to construct the ultimate
high energy structure of Nature. We expect it to be quite different
from what we presently have. Because physics is an experimental science, it
is possible that we will not be able to truly know the ultimate theory, but
impressive attempts are underway. However we do have a right to expect
that our theories are consistent at the energies that we use them. In this
regard, the effective field theory framework is the appropriate description of
quantum gravity at ordinary energies.
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