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Friday, April 10, 2009

Is There A Final Theory of Everything?

FROM FRANK WILCZEK, NOBEL LAUREATE AND A PROFESSOR OF PHYSICS AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY’S CENTER FOR THEORETICAL PHYSICS: Is there a final theory of everything? The answer depends on what you mean by “final” and “everything.” And, for that matter, “is.” Let’s consider.
What could we mean by a “final theory”? A theory is final if it is perfectly adapted to its subject matter, so that there is no point in trying to improve it. What was a frontier outpost of knowledge becomes a settled bastion. Unfortunately, experience teaches us that what appear to be “final” theories have a disconcerting tendency to unravel. Euclidean geometry, which seemed to Kant so firmly established that he took it to be an a priori precondition for perception, turned out to be a special, limiting case of possible geometries. And not the one chosen by Nature! Newtonian mechanics went from triumph to triumph, deriving amazing consequences (Neptune!—the original “dark matter”) from simple, well-tested hypotheses. Yet in the 20th century, first special relativity rocked, then quantum theory mocked, Newtonian principles. Today, classical thermodynamics, quantum electrodynamics (QED), and quantum chromodynamics (QCD) appear to be final theories. So too, in a different way, do the big-bang theory of cosmology and the evolution theory of biology. Professionals work to apply, develop, or add to them—but change them? Not so much.
What could we mean by a “theory of everything”? The literal meaning is silly: There will never be a theory that covers everything, or even that shared part of everything we call the natural world. The instabilities of mathematical chaos and the indeterminism of quantum mechanics would inject big elements of contingency and accident into the description of the actual world, even if we were to have a perfect understanding of its equations and starting principles. In practice, our ability to formulate questions far outstrips our ability to solve equations. No combination of theory and pure thought will encompass everything: The future will always bring surprises (e.g., weather!); historiography will always require archives and relics.
A more realistic, rigorous interpretation of “theory of everything” involves the idea of completeness. A theory that derives everything true (and nothing false) in a sharply defined domain of discourse is complete for that domain. Competent experts think that classical thermodynamics, QED, and QCD are complete theories for governing conditions for equilibrium among macroscopic phases of matter, chemistry, and nuclear physics, respectively. In all these cases, the theories do not cover historical questions: For example, QED does not tell us what substances we actually find on Earth, but rather what the possible substances are and how they will behave. Thus, we have good models for what complete theories of parts of reality look like. They are reductionist theories, in the sense that they supply precise mathematical laws for the behavior of underlying building blocks, from which the behavior of larger, more complex objects can be derived (in principle; as a practical matter, especially in QED and QCD, we can only “solve” the equations—i.e., determine their consequences by direct calculation—approximately and in very simple cases. Physicists have not put experimental chemists out of business!) Is there a complete theory, in the same reductionist sense, whose domain is everything?
At this point, we have to face the question Bill Clinton made famous: What do we mean by “is”? Any good dictionary suggests several alternative meanings. For us, the important distinction is between "is" as “presently existing” and "is" as “existing in principle.”
If we use “is” in the first sense, then the answer to our question is very easy: No, there is not a final theory of everything. The established laws of physics, while extremely impressive and successful across a very broad range, are widely perceived to be imperfect and incomplete. They postulate four distinct basic forces (gravity, electromagnetism, strong, and weak) and several distinct kinds of matter (quarks and leptons in a dozen varieties, gluons, photons, W and Z particles, gravitons, Higgs bosons …); we yearn for more unity and coherence. They do not account for the astronomers’ dark matter and dark energy. They break down in the earliest moments of the big bang, and at the centers of black holes. We have some brilliant, promising-looking ideas for improving the situation (e.g., extended gauge symmetry, supersymmetry, axions). The Large Hadron Collider will (I hope!) confirm some of those ideas and suggest new ones. But I don’t foresee that physicists will come close to answering all these basic questions anytime soon. So there won’t be a theory of everything, even in the narrow sense. And we won’t stop trying to do better, so there won’t be a final theory, either.
If we use “is” in the second sense, the answer is less easy, and reasonable people might differ. Is there a "final theory of everything" out there in some idealized world of ideas, waiting to be discovered? My own opinion is that there is such a theory, but that it won’t live up to its billing. Our successes so far give us every reason to think that there are basic, precise mathematical laws governing the elementary processes of Nature, and that, in principle, they cover everything—no physical phenomenon eludes their grip. And people will construct ever more comprehensive reductionist theories, which realize more and more of that ideal. Eventually, however, they will stop making progress, and (implicitly or explicitly) establish an existing theory as "final." But that “final theory of everything” won’t help to predict the weather, or the possible species of beetles, or much of anything interesting about human beings. For better or worse, the theories of physics we have today already contain everything that fundamental physics has to offer on those topics.

Frank Wilczek appears with Steven Weinberg, David Gross, Leonard Susskind, Lawrence Krauss, Robert Laughlin, Lee Smolin, and Stephen Wolfram in "Is There a Final Theory of Everything?" the 31st episode in the Closer to Truth: Cosmos, Consciousness, God TV series. The series airs on PBS World (often Thursdays, twice) and many other PBS and noncommercial stations. Every Friday, participants discuss a recent episode.


Bahata said...

A further point that is relevant to this discussion is the nature of completeness and consistency. These concepts are defined relative to an axiomatic system. Any physics domain like thermodynamics, QED, electroweak theory, QCD and so on, can be essentially modelled as an axiomatic system. Kurt Goedel, the logician, mathematician, astronomer and philosopher, addressed the question of consistency versus completeness and found a definite answer. (Those who dispute ascribing so many adjectives to Goedel may read Palle Yourgrau's book on Goedel and Albert Einstein's association, and the resulting work Goedel did, at Princeton.) A sufficiently complex axiomatic system (more precisely, one which includes the natural number system) cannot be both complete and consistent. In other words, there are statements expressible in the language of that axiomatic system which can neither be proved nor disproved. Thus, such a statement is undecidable within that axiomatic system. One may go even further and consider three-valued or even fuzzy logics, which are practically used today in hardwired electronic circuits in home appliances like washing machines. In another direction, a question (like the true /false status of a statement) that cannot be answered yes / no may claim an answer "mu" in Zen Buddhist sense. (For more elaboration, Douglas Hofstadter's book "Goedel, Escher, Bach: An eternal golden braid" may be useful.) As the bottomline, I'd like to remind readers of sophists and tower of Babel!