Toward a Unified Theory of Quantum Gravity
Most theoretical physicists believe that beneath the complex variety of natural phenomena that we observe there lies a deep and elegant mathematical unity. The history of physics has been a story of the discovery of more and more links between hitherto separate areas of inquiry. Thus Maxwell linked electricity, magnetism, and optics. Einstein linked space and time, mass and energy, and so on. John Wheeler has been at the forefront of attempts to link the two great pillars of 20th century physics: Einstein’s general theory of relativityâ€”a theory of space and timeâ€”with quantum mechanicsâ€”a theory of matter. This subject became known as quantum gravity. The difficulties associated with quantum gravity are legendary. In a nutshell, straightforward attempts at a shotgun marriage of general relativity and quantum mechanics fail spectacularly because almost all quantities of interest are predicted to be infinite!
About 20 years ago it became clear that a successful theory of quantum gravity would have to form part of a bigger amalgamation, one that incorporated the other forces of nature too. The misleading term theories of everything was coined. The idea is that there exists a mathematical scheme, maybe even a formula simple enough to wear on your T shirt, from which space, time, gravitation, electromagnetism, the weak and strong nuclear forces plus descriptions of all the varieties of subatomic particles would emerge, in more or less their familiar form, at low energies. A nearly candidate for such a unified theory went by the name of superstrings. In simple terms the idea here is that the world isn’t made up of tiny particles, in the tradition of Greek atomism. Instead, the ultimate building blocks of the physical universe are little loops of string that wiggle about, mimicking particles when viewed on a larger scale. Since then, string theory has been incorporated into a more ambitious scheme known cryptically as M theory.
One property of many of these theories is the inclusion of additional unseen dimensions of space. It is too soon to proclaim that M theory has produced a final unification of physics, though some proponents are extremely upbeat about this prospect. Part of the problem is that M theory is characterized by processes that occur at ultra-high energies or ultra-small scales of size (the so-called Planck scale). Testing the consequences of the theory in the relatively low-energy, large-scale world of conventional particle physics isn’t easy. Another problem is the plethora of abstract mathematical descriptions swirling around the program. Not only does this make the subject impenetrable for all but a select few workers, it also threatens to smother the entire enterprise itself. There seem to be so many ways of formulating unified theories, that without any hope of experimental constraint, there is a danger that the subject will degenerate into a battle of obscure mathematical fashions, in which progress is judged more on grounds of philosophical appeal than conformity with reality.
But perhaps that is too cynical a view. There is a hope that there will appear a sort of meta-unification, in which the welter of unified theories are themselves unified, and shown to be merely alternate languages for the same underlying structure. The ultimate hope is that this meta-unification will stem from a deep physical principle akin to Einstein’s principle of general covariance, so we find that all the fundamental properties of the physical universe flow from a single simple reality statement.
This vision matches John Wheeler’s closely. Over the years he has provided many striking metaphors for this ultimate principle; I recall in particular the great chain-mail making machine and the rope that looks to beself-interwoven into a complex knot, but when pulled will unravel tonothing. Wheeler’s hope is that underlying all of physics will be a principle as simple as 0 = 0. So simple, in fact, that we will wonder why we have been so stupid as not to have seen it before.