However, this interpretation, while adequate within classical general relativity, becomes incomplete within the emerging postmodern view of quantum gravity. When even the gravitational field -- geometry incarnate -- becomes a non-commuting (and hence nonlinear) operator, how can the classical interpretation of as a geometric entity be sustained? Now not only the observer, but the very concept of geometry, becomes relational and contextual.

The synthesis of quantum theory and general relativity is thus the central unsolved problem of theoretical physics; no one today can predict with confidence

what will be the language and ontology, much less the content, of this synthesis, when and if it comes. It is, nevertheless, useful to examine historically the metaphors and imagery that theoretical physicists have employed in their attempts to understand quantum gravity.

The earliest attempts -- dating back to the early 1960's -- to visualize geometry on the Planck scale (about centimeters) portrayed it as ``space-time foam'': bubbles of space-time curvature, sharing a complex and ever-changing topology of interconnections. But physicists were unable to carry this approach farther, perhaps due to the inadequate development at that time of topology and manifold theory (see below).

In the 1970's physicists tried an even more conventional approach:
simplify the Einstein equations by pretending that they are
*almost linear*, and then apply the standard methods of
quantum field theory to the thus-oversimplified equations.
But this method, too, failed:
it turned out that Einstein's general relativity is, in technical language,
``perturbatively nonrenormalizable''.
This means that the strong nonlinearities of Einstein's general relativity
are intrinsic to the theory;
any attempt to pretend that the nonlinearities are weak
is simply self-contradictory.
(This is not surprising: the almost-linear approach destroys the most
characteristic features of general relativity, such as black holes.)

In the 1980's a very different approach, known as string theory, became popular: here the fundamental constituents of matter are not point-like particles but rather tiny (Planck-scale) closed and open strings. In this theory, the space-time manifold does not exist as an objective physical reality; rather, space-time is a derived concept, an approximation valid only on large length scales (where ``large'' means ``much larger than centimeters''!). For a while many enthusiasts of string theory thought they were closing in on a Theory of Everything -- modesty is not one of their virtues -- and some still think so. But the mathematical difficulties in string theory are formidable, and it is far from clear that they will be resolved any time soon.

More recently, a small group of physicists has returned
to the full nonlinearities of Einstein's general relativity,
and -- using a new mathematical symbolism invented by Abhay Ashtekar --
they have attempted to visualize the structure of the corresponding
quantum theory.
The picture they obtain is intriguing:
As in string theory, the space-time manifold is only an approximation
valid at large distances, not an objective reality.
At small (Planck-scale) distances, the geometry of space-time is
a *weave*: a complex interconnection of threads.

Finally, an exciting proposal has been taking shape
over the past few years
in the hands of an interdisciplinary collaboration of
mathematicians, astrophysicists and biologists:
this is the theory of the morphogenetic field.
Since the mid-1980's evidence has been accumulating that this field,
first conceptualized by developmental biologists,
is in fact closely linked to the
quantum *gravitational* field:
(a) it pervades all space;
(b) it interacts with all matter and energy, irrespective of whether or not
that matter/energy is magnetically charged;
and, most significantly,
(c) it is what is known mathematically as a ``symmetric second-rank tensor''.
All three properties are characteristic of gravity;
and it was proven some years ago that the only
self-consistent *nonlinear* theory of a symmetric second-rank tensor
field is, at least at low energies,
precisely Einstein's general relativity.
Thus, if the evidence for (a), (b) and (c) holds up,
we can infer that the morphogenetic field
is the quantum counterpart of Einstein's gravitational field.
Until recently this theory has been ignored or even scorned
by the high-energy-physics establishment,
who have traditionally resented the encroachment of biologists
(not to mention humanists) on their ``turf''.
However, some theoretical physicists have recently
begun to give this theory a second look, and there are good prospects for
progress in the near future.

It is still too soon to say whether string theory, the space-time weave or morphogenetic fields will be confirmed in the laboratory: the experiments are not easy to perform. But it is intriguing that all three theories have similar conceptual characteristics: strong nonlinearity, subjective space-time, inexorable flux, and a stress on the topology of interconnectedness.

Thu Jun 6 15:34:37 EDT 1996