How long is a piece of string?
I’ve always thought that string theory-a theory that unites quantum mechanics and general relativity-was a sort of callous trick played upon us mere mortals by intellectual mathematicians who spoke a language that was arcane and largely impenetrable.
I’ve always thought that string theory-a theory that unites quantum mechanics and general relativity-was a sort of callous trick played upon us mere mortals by intellectual mathematicians who spoke a language that was arcane and largely impenetrable. Some mathematical “tricks” we can see through easily but string theory as we know it so far, is hardly one of those Victorian “parlor” tricks.
For example, try this. Think of a number (any number will do, integer or fraction, but the mental arithmetic is simpler if you choose a whole number between, say one and ten). Double the number and add 10. Now divide by two and then subtract the number you first thought of. Your answer (roll of drums!) is five! You don’t have to be a mathematical genius to spot the “trick.”
Now comes eminent Columbia University professor Brian Greene with a powerful examination of string theory and a few examples of mathematical legerdemain that make the topic accessible to us nonmathematicians. Greene’s book, The Fabric of the Cosmos: Space, Time, and the Texture of Reality, (Knopf, New York, NY, 2004), is a beautifully written and carefully edited volume of some 500 pages. And Greene understands that he is talking to the informed layperson and not to some esoteric university post-doc seminar.
For example, here’s Greene introducing the history and rationale for string theory: “A conflict in the known laws of physics means a failure to grasp a deep truth and that was enough to keep these scientists from resting easy. Those who plunged in, though, found the waters deep and the currents rough. For long stretches of time, research made little progress; things looked bleak. Even so, the tenacity of those who had the determination to stay the course and keep alive the dream of uniting general relativity and quantum mechanics is being rewarded. Scientists are now charging down paths blazed by those explorers and are closing in on a harmonious merger of the laws of the large and the small. The approach that many agree is a leading contender is superstring theory.”
Greene, of course, is something of a leading authority on the subject of superstring theory. And, there is a neat trick that makes superstring theory both possible and plausible. Greene suggests that the proposed fusion of general relativity becomes much more likely if we abandon our usual concept of a four-dimensional universe (three spatial dimensions and one time dimension) for one with ten space dimensions and one time dimension. Just try to picture that on your laptop’s screen.
Naturally, Greene does not quite have the world on a string at this point! He dives unapologetically into the universes of strings and branes (shorthand for M-branes, another component of M-theory). “The grand expanse of the space-time of which we are aware-may itself be nothing but an enormous brane,” claims Greene. So it would seem that ours may be a brane new world. Thank you, Professor Greene.
Well, of course, none of this tells us exactly how long a piece of string is-a question that Werner Heisenberg would, no doubt, have appreciated although with a dose of some well-deserved hesitation. And do we really need to know? As the Rolls-Royce salesman in a posh London dealership when asked how fast the latest model of the legendary car would go, reportedly said to an Arabian potentate’s son, “Fast enough, sir, fast enough.”
So we must conclude that the length of a piece of string is “long enough” to meet the theoretical demands of Professor Green and the much smaller intellectual demands of this “ink-stained wretch.” Or, at least, long enough to secure your holiday gifts aganst the percussive delivery of the United States Post Office.
With that thought, I offer you all my most sincere Season’s Greetings and I trust you will keep all those letters and e-mails coming my way in 2006!