Arbiter elegantiae


The great scientist Ludwig Boltzmann has commented that the role of the elegance of mathematical and physical methods are tailor's concerns. If this were true, Demiurgos (the creator of the world in the ancient Greek and Roman tradition) certainly deserves the tribute of "the highest tailor", or if it sounds too profane to you, arbiter elegantiarum, how the Poet Gaius Petronius was named in the age of Nero. The feeling that the fundamental laws of Nature are beautiful and elegant has been expressed by many great physicists and after reading Greene's book you can understand why.

Even in the field of aesthetics it is quite difficult to define what the source of elegance is. One of the sources is a certain austere functionality in the choice of the elementary ingredients, which together make up the total impact. The perfect coherence between these ingredients is another source, and last, but not least, the amazement arising from the use of new ideas. The old Greek philosophers were able to divine the first two features by observing the world of Nature that we perceive in our everyday lives. This led them to the concept of a world composed of one or few basic building blocks in which mathematical and geometrical simplicity plays an important role. Thus, the idea of a "theory of everything" is not an outgrowth of the modern physical reductionist imperialism.

Both in classical and modern physics, the idea of building a diverse world from a small number of elementary building blocks controlled by reasonably simple fundamental laws, is remarkably successful (it is the main theme of the Greene's book). Modern physics also satisfies my last characteristic of elegance, namely the noteworthy and surprising character of answers to many old philosophical questions as well as answers to new problems found by people investigating still deeper layers underlying the realm of everyday experience. Is the universe finite or infinite? Did it always exist or does it have an origin? Even the renowned philosopher Immanuel Kant considered such questions to be clean-cut, but at the same time, both possibilities looked implausible to him (therefore he named them antinomies, i.e. inevitable contradictions). General relativity, however, offers an unexpected possibility to solve the first question, i.e. the possibility of a closed world which has a finite volume but no boundaries. It also suggests a way to make the infinite world sensible and, when combined with quantum mechanics, surprisingly, sheds light on the question about the beginning of the world. Can matter be divided indefinitely or do we have to end up with some indivisible pieces of matter, say, atoms? String theory claims that the basic building blocks are superstrings, but can we call them elementary "pieces of matter"? If we follow our everyday experience, we tend to think that the only thing this can imply is that strings are composed of certain "pre-metal" that somewhat mimics what we call matter or material in everyday life. But the observed properties of particles such as mass and charge are only determined by the state of the string, its vibrations etc. and the question about the composition of strings is meaningless.

It seems clear to us (just like it was to Immanuel Kant) that the geometry of our world must be Euclidean and that space has exactly three dimensions; objects have height, width and length and nothing more (there is no other possibility). After reading Greene's book, we begin to understand that the world has many dimensions, which cannot by observed by the usual means and which can hardly be perceived because of their elegant compactification to small size.

We see that apparently self-evident claims are often not self-evident at all. Why is it that our intuition leads us astray while trying to understand the world of modern physics? At the beginning of his Cathedral and Citadel, Pavel Eisner wrote: "Our native language is the air breathed by the lungs of our soul ... We can learn six or ten foreign languages, study their literature, learn a great deal about other nations, but something deep inside us does not believe that someone in the world could really speak French, English, Spanish etc. (always only in one of those tongues and never Czech). We think that this is just an arranged game, that the people in Paris and London must apparently reel off their French or English pensum, but as soon as they come home, they take their language shoes off and start to speak in Czech."

The language in which we talk about the natural life of our experience is so native to us that we perceive it to be the right and inevitable tool to convey an idea. When we hear that this language is not enough for the description of the deeper layers of reality, something inside us wants to reject it, even though we are physicists and try to convince others about it. We elevate our experience collected in this world of very low energies, not-too-small and not-too-large dimensions, with quite a weak gravity, to an inevitability in our subconscious. When we hear about elementary particles, we imagine a little nugget; when we hear the word "wave", we immediately think of waves on the water, which automatically implies the existence of another matter which oscillates; our conception of reality is naturally Newtonian. Indeed, the conceptual apparatus of classical physics was close to the concepts we learned under the everyday conditions.

At first glance, my linguistic metaphor seems to break down. Anything that can be expressed in English can be said in Czech, too. But imagine that we play charades (your teammate tries to express a certain word by gestures). When he waves his hands and points out of the window, we (Czechs) will understand that the word was výlet (trip). Germans in our group will also understand it: Aus-flug is constructed identically. But Englishmen will miss the point, out-fly means something absolutely different, and the gestures to define the word "trip" would have to be drastically altered. Note that the nations have pretty similar cultural background. In the context of languages with very different culture and history, the problems with translations will be much more severe and many facts of their life simply do not have a faithful counterpart in Czech.

At the deeper levels of investigating the physical world, the concepts are really so different that they force us to use a very different language, which can be adequately formulated only in terms of mathematics. However the author of this book has proven that he is a brilliant translator. It was not an accident that the book became a bestseller and was awarded prestigious awards for the popularization of science. Without the mathematical language, it is of course impossible to explain the mysteries of modern physics faithfully, but by using sophisticated metaphors and analogies, he is able to capture the essence of the basic ideas. The main topic of this book is the latest sensation in theoretical physics, string theory, which has been extensively studied in the last two decades. Greene himself has written a series of important papers on string theory, and so, he can not only describe its ideas as an insider, but can also paint the atmosphere of enthusiasm in which the theory is developed. Although strings emanate throughout the book, you have not read only about them. You have been introduced to modern cosmology, as well as to bizarre objects like black holes. The author has tried to convince you that string theory is the right candidate for the ultimate theory that unifies quantum mechanics with Einstein's general relativity and will be the final word in the development of the fundamentals of theoretical physics. After being a fantastic success in the USA, the book has been translated to about twenty languages. Luboš Motl, who has translated it to Czech, is currently a graduate student in the USA and he has already actively contributed to the field by several excellent papers. The translation has therefore been done in a qualified way. His sometimes unusual, we could say bold formulations match the original style and he has also adapted the refreshing requisites for the Czech reader in a witty way. I am happy to affirm that the translation was prepared with an attention that the original deserves.

I am far from being competent to predict whether the hopes in string theory are justified. Let me however, return to my original considerations. The meaning of the word demiurgos is not only the literal "working for the people" but also a "skillful craftsman". It is enough to glance at the pictures of worldtubes representing the history of interacting strings to see how they resemble the pants or sleeves, and thus, to understand that the craft of string theory is truly very close to tailoring (thus, Boltzmann was correct). Indeed, the universe came from the tailor's workroom. Reading this book is not going to help the reader tailor new universes right afterwards, but the reader can leave the book convinced that the word "elegant" is fully appropriate to products from this workroom.

Poslední úprava: 2007-01-18 13:52 CET
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