No, not the opera, but the subject matter of the opera.
Sort of.
Since childhood I've been something of a mathophobe, a coinage of mine to denote a psychoneurotic condition wherein the sufferer virtually breaks into a cold sweat on encountering any mathematical symbol less familiar than those of the four arithmetic operations. That pathetic condition notwithstanding, I've forever had a deep fascination with the principles, derivation, and implications of the fundamental laws that govern the physical processes of the universe. As all such laws are expressed in the abstract symbolic language of mathematics, however, indulging that fascination makes life for such as myself something of a tough proposition. We must either thread our way, stoically and painfully, through expert accounts of physical theory, gleaning what little we can along the way, or content ourselves with reading pop expositions which mostly simplify to the point of almost deception while producing in us a false sense of real comprehension.
Every once in a very rare while, however, there appears in print a treatment of this esoteric domain that meets the impossible challenge of explaining substantively in nonmathematical language the principles of a physical theory in a way that neither overwhelms the nonmathematical intellect, nor simplifies to pap the theory's inherent complexities. My best experience of such a treatment is Lincoln Barnett's 1948 (rev., 1957) The Universe and Dr. Einstein, an amazingly slender volume that substantively lays out the principles, derivation, and implications of special and general relativity in nonmathematical language so straightforward, even though at times poetic, that one emerges with a genuine understanding of Einstein's revolutionary, world-transforming contributions to our knowledge of the universe and The Way Things Really Are. In its scant 118 pages, The Universe and Dr. Einstein, with astonishing lucidity, takes the reader from Einstein's first thought experiments leading to the mind-bending principles and implications of special relativity (and the most famous equation in history: E=mc2), through the even more mind-bending principles and implications of general relativity, all the while sparing the reader no fundamental or important details, but setting everything out in illuminating language comprehensible to any intelligent layman.
An authentic tour de force this slender volume, and happily now again in print thanks to a soon to be available reprint (128pp, release date: January 2006) by that indispensable publisher of beautiful, affordable, large-format reprints of music scores, Dover Publications. This book is one that ought to be in every intelligent person's library, and consulted often if only for the pure pleasure of reading an authentic masterpiece of the genre.
But today, the many-times confirmed theory of relativity is pretty much garden-variety, used-every-day stuff in the worlds of physics and mathematics. In physics and mathematics today, the New Big Thing is something rather unthreateningly called string theory (or, more correctly, superstring theory).
And just what's that all about? Well, everything, actually. It's an attempt at a theory Einstein spent the last quarter century of his life trying to derive: a Theory Of Everything (TOE), called by Einstein a Unified Field Theory; a series of mutually consistent equations that seamlessly describe and unify the forces of gravity and electromagnetism, and the two principal theoretical pillars of modern physics: general relativity and quantum mechanics. Einstein failed in his quest, and at the time, and for some time after, was thought more than just a little eccentric for even embarking on such a quest. But today, half a century after his death, TOE has become the Holy Grail of physics, and string theory is being trumpeted as its incarnation.
But why the need for TOE? I mean, we already have proven-to-work theories; one that explains the workings of gravity and the very large (general relativity), and one (quantum mechanics) that explains the workings of the very small (for all the stuff in-between we have the still valid centuries-old theories of Newton which work spectacularly well for all ordinary-sized, commonly experienced physical phenomena), and so if you've a question that needs answering in the domain of the very large you use the equations of general relativity, and in the domain of the very small, those of quantum mechanics.
So, what's the problem? The problem is that the two theories are mutually incompatible, and seem to be telling us that underlying the workings of the universe are two totally independent, fundamental underlying realities depending only on scale, and that what's true of one is not true of the other.
Intolerable. Impossible. Ridiculous. If theory says that's the way reality really is, then that's the signal — the red-light, alarm-bell signal — that something is amiss with theory, not the universe. What's needed is a theory that accounts for all physical phenomena in a mutually consistent way regardless of scale. The difficulty is that when a marriage of the equations of general relativity and quantum mechanics is attempted it results in absurd offspring. More specifically, any attempt at the marriage of the equations of the two theories invariably gives infinity as an answer when such an answer is pure gibberish (e.g., an infinite probability).
Enter string theory. It seems to have the promise of explaining all physical phenomena in a mutually consistent way regardless of scale by its possessing the ability to adjust the equations of general relativity in just the right way (because, unlike quantum mechanics, an accounting for gravity is native to string theory) so that a marriage with the equations of quantum mechanics is a natural result, and it begins this magic by replacing the static, ultimate lower size zero-dimension point particles of classical theory (i.e., relativity and quantum mechanics) that are supposed to constitute the underlying irreducible fundamental stuff of the world with spatially extensible, one-dimensional vibrating filaments or strings whose extensible size is, on average, on the order of what is called the Planck length, an incredibly tiny number (10-33 cm), the vibration patterns of which underlie and determine the properties of the fundamental building blocks of all matter and energy; in short, underlie and determine the properties of all the world stuff.
Talk about mind-bending! String theory is all mind-bending — way more so than general relativity — and horrendously complicated and complex; so complicated and complex that its equations have never been able to be put into finished, precise form, physicists having to make due with approximations to those equations. To a mathophobic layman such as myself it all seems incredibly messy, inelegant, and impossible to understand, something which, with the help of the guiding hand of Lincoln Barnett, relativity most emphatically does not.
But help for all laymen, mathophobic or not, is at hand. Brian Greene, in his 1999 book, The Elegant Universe, attempts to do in 448 pages for string theory what Barnett did in 118 for relativity. Greene's not nearly as successful as Barnett, but that's not because Greene's not as skillful a writer, but because string theory is whole orders of magnitude more complicated and complex than relativity, not to even speak of the fact that even string theorists themselves don't fully understand the theory. But Greene's successful enough notwithstanding his often annoying, almost pitchman-like advocacy of string theory as almost certainly The Way To Go despite the utter lack (and perhaps ultimate utter impossibility) of direct experimental confirmation of the validity of its theoretical constructs, and the (at present) impossibility of even expressing its equations in finished and precise form. (The PBS Nova miniseries, "The Elegant Universe", based on Greene's book, and hosted by Greene himself, suffers, unlike the book, from its clumsy attempts at simplification via common-experience examples with its elaborate, gimmicky, involved, and ultimately silly pop stagings and graphics. I realize I'm probably in the minority in my objection to the handling of these common-experience examples, but I object nevertheless.)
For the layman wanting to understand the basic principles of string theory, however, this book is as good a primer as can be imagined even if, in its later chapters, one has to work one's way through the difficult and gruesome details of the more arcane aspects of string theory, and I can recommend it if not with the unbridled enthusiasm that accompanied my recommendation of Barnett's volume on relativity.
I confess I've a secret wish and suspicion that string theory — with its fundamental requirement of a 10-dimensional space-time universe (as opposed to our 4-dimensional one; and N.B., string theory doesn't merely predict a 10-dimensional space-time universe; it requires it), and its fundamental non-disprovability — will turn out ultimately to be the bust some few physicists think it will turn out to be. I intuitively don't like its messy, complicated, exercise-in-masturbatory-mathematics feel, in the same way I intuitively dislike the probabilistic basis of quantum mechanics. (I'm in good company vis-à-vis the latter. Einstein, one of the founders of quantum theory, was distrustful of quantum mechanics for the same reason which provoked his famous statement that, ultimately, he was convinced God "does not play dice.") In short, from this mathophobic layman's vantage point, string theory seems but a complexly elaborate sandbox in which theoretical physicists can play about for decades without getting bored while seeming to be engaged in something on the verge of revealing the true nature of the reality underlying all the physical phenomena of the universe, and the true nature of the reality underlying the very universe itself from its birth to its ultimate death, if indeed it can be said to have either.
But perhaps when the final equations of string theory — all five(!) string theories — are finally derived, solved, collated, and experimentally confirmed under the construct called M-theory (which requires an 11-dimensional space-time universe — don't even think of asking!), those equations and what they describe will prove string theory as simple, elegant and, more importantly, as inevitable as relativity. I have my mathophobic layman's doubts, but if that day ever comes — and today the smart money in physics is betting that it's a matter of when, not if — man will truly have succeeded, in the words of Stephen Hawking, in reading the very mind of God.
Neat trick, that, although a consummation I'm not entirely convinced is devoutly to be wished.
