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On Matters Cosmic & Atomic

Posted by acdtest on September 2, 2003

On Matters Cosmic, Atomic, and Everything In-between

ince childhood I’ve been something of a mathophobe, a non-word I coined to signify a psychoneurotic condition wherein one 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 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 symbolic and abstract language of mathematics, indulging that fascination makes life for all such as myself a tough proposition. We must either stoically and painfully thread our way through expert accounts of physical theory, gleaning what 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 first experience of such a treatment was Lincoln Barnett’s 1948 (rev., 1957) The Universe and Dr. Einstein, a slender volume that substantively lays out the principles, derivation, and implications of special and general relativity in nonmathematical language so lucid, and even at times poetic, that even a mathophobe such as myself emerges with a genuine (if non-functional) understanding of Einstein’s revolutionary and world-transforming contributions to our knowledge of the universe and The Way Things Really Work.

In its scant 118 pages, The Universe and Dr. Einstein skillfully takes the reader from Einstein’s first thought experiments leading to the mind-bending principles and implications of special relativity (and the world-famous E=mc^2), through the equally mind-bending principles and implications of general relativity, all the while sparing the reader no fundamental or important details, but setting everything up and spelling it out in clear nonmathematical language completely understandable to any educated and interested layman.

An authentic tour de force, unhappily now out of print, but sometimes available through the secondhand market (see link above).

But relativity is old-hat theory today. Today the Big Thing is something called string theory.

And just what is string theory all about? Everything — quite literally. It’s an attempt at solving a problem Einstein spent the last quarter century of his life trying to solve: The Theory Of Everything, called by Einstein a Unified Field Theory; a series of mutually consistent equations that seamlessly integrate, first, the forces of gravity and electromagnetism, and ultimately the theories of the very large (general relativity), and the very small (quantum mechanics). Einstein failed in his attempt, and half a century later string theory took up the challenge, and ran with it.

Crudely and briefly (very crudely and very briefly), the problem is that while general relativity explains with astonishing accuracy and surpassing elegance the physical dynamics of things macrocosmic, it runs into problems when applied to the microcosm. More precisely, general relativity seems fundamentally at a loss to explain the dynamics of phenomena operating at the most ultramicroscopic subatomic scale where nothing but the most untoward weirdness prevails. Quantum mechanics, however, works splendidly at providing such explanations, if not quite as neatly and unequivocally as general relativity works at explaining phenomena at the scale of the macrocosm.

So what’s the problem? When one needs explanations of things macrocosmic one uses the equations of general relativity, and for explanations of things at a very tiny subatomic scale, the equations of quantum mechanics. No problem at all, really. Except that it’s intellectually, and even intuitively offensive to imagine the universe operating in two fundamentally different and incompatible ways depending only on the scale of the thing in question. If theory says it does, 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, the results are absurd. More specifically, the marriage of the equations of the two theories 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 having the ability to alter the equations of relativity in just the right way so that a marriage with the equations of quantum mechanics becomes possible, and it begins by replacing the ultimate-lower-size, zero-dimension point particles of classical theory (i.e., relativity and quantum mechanics) 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).

Talk about mind-bending! String theory is all mind-bending stuff — way more so than general relativity — and horrendously complicated (as opposed to horrendously complex, which it also is), and seems to a mathophobic layman such as myself incredibly messy, something which, with the help of the guiding hand of Lincoln Barnett, relativity most emphatically does not.

But help for laymen such as myself 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 quite as successful as Barnett, but he’s successful enough, and for laymen wanting to understand the basic principles of string theory I can’t recommend this book highly enough. It was in fact by virtue of Greene’s guiding hand that I was able to write with confidence what I’ve here written concerning string theory.

(Actually, it’s not quite fair of me to suggest that Greene is less successful than was Barnett. String theory — all five of them — is a theory still in the throes of building, its equations so complex that none has ever successfully been put in precise form, physicists having to make due with approximations, while relativity was a fully worked out, many-times tested, and fairly mature theory by the time Barnett set to tackling an explanation of its complexities for laymen. All things considered, Greene does a more than admirable job of explaining what he sets out to explain.)

I confess I’ve a secret wish that string theory turns out to be the wrong way to go. I intuitively don’t like its messy, complicated feel, in the same way I intuitively dislike the probabilistic basis of quantum mechanics. (I’m in good company vis-ŕ-vis the latter. Einstein was unhappy with quantum mechanics for the same reason. It was what provoked his famous, “I cannot believe God plays dice with the universe.”) But perhaps when the precise equations of string theory (all five of them) are finally derived, solved, and unified under the construct called M-theory (don’t even think of asking!), those equations and what they describe will prove string theory as elegant and, more importantly, as inevitable as relativity. If that day ever comes — and the smart money 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, and a consummation devoutly to be wished.

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