THE STRINGS RETURN - MATHEMATICS AND THE MODERN VIEW OF THE WORLD - The Remarkable Role of Evolution in the Making of Mathematics - Mathematics and the Real World

Mathematics and the Real World: The Remarkable Role of Evolution in the Making of Mathematics (2014)

CHAPTER IV. MATHEMATICS AND THE MODERN VIEW OF THE WORLD

32. THE STRINGS RETURN

Physicists who deal with elementary particles are engaged in completing the picture of the subatomic world of these particles, but the model on which they are working is not consistent with the order that prevails between the collection of these particles and the theory of gravity. Moreover, to describe different particles, different versions of Schrödinger's equation must be used. In light of past successes in finding mathematical models that brought together different theories, physicists today feel obliged to find one theory, one equation, that will enable them to explain the whole of the subatomic world. The attempt to incorporate all subatomic phenomena within one equation is the development of a mathematical system known as string theory.

From the aspect of the relation between mathematics and nature, string theory presents another stage. Maxwell's revolution presented mathematics that described physics whose components could not be perceived directly but whose effect on other physical quantities could be measured and whose predictions, such as the existence of electromagnetic waves, could be confirmed or disproved. String theory is mathematics that describes physics whose components cannot be perceived and whose effect on other physical elements also cannot be measured at this stage. Moreover, at this time, the theory does not provide predictions that can be confirmed or denied, and it does not seem that it will be able to provide such predictions in the foreseeable future. Is this the picture of the world? Is this physics?

Some of my physicist colleagues deny that this is physics and state that those involved in the theory are just mathematicians. Others are prepared to include that community under the umbrella of physics (also because their work is theoretical and does not compete for expensive research resources). There are also physicists who believe that despite the fact that currently it is difficult to even imagine such a situation, the day may come when the way will be found to examine string theory with experimental methods and to obtain benefit from it.

So what is string theory? The mathematical system of string theory is essentially similar to the systems that define the world of elementary particles, combined with geometric elements. The solutions to these equations are the basic elements that the theory presents. Since the brain cannot analyze mathematics without recognizable metaphors, string theory is described and examined via interpretations of those solutions. We will also relate only to the interpretation of the theory.

The strings are firstly particles of miniature size. They are hundreds of thousands times smaller than the elementary particles (this explains why they cannot be perceived, as the means for perceiving the tiniest particles are based on the elementary particles). These strings are wave solutions, but unlike the electron, for example, which is described as a point particle that revolves around the nucleus of the atom, a string is described as a body that has a length, all of which vibrates and moves like a wave. Hence its name “string.” Once a particle that has a length is permitted, the question immediately arises as to if its ends are joined, like a ring, or are they attached to a plane, or are they free? It turns out that all of these are solutions to the equation, solutions that give strings of various types. The different strings create structures from which, so it is hoped, the subatomic structure can be derived. However, it transpires that for those structures to exist, the physical space must have certain surprising properties. For example, the space must have more than the four dimensions in which we can perceive, that is, three spatial dimensions and time. This means actual physical directions, but the distance along each direction is too small for us to perceive or measure in any way. The number of additional dimensions depends on the specific theory. The latest versions refer to ten or eleven dimensions. Moreover, those equations that describe the strings also have solutions of another type, sorts of membranes that are likely to be huge. Do these solutions have a physical interpretation or perhaps even implementation? If so, those membranes could contain worlds in addition to our own, worlds that we cannot perceive or communicate with, although the distance between us and them might be the smallest. Furthermore, collisions between those worlds are possible and could perhaps cause huge explosions, like the big bang that led to the transformation of energy into mass and, according to the accepted theory, created the world we know today.

To the reader whose reaction at this stage is “I don't understand,” I would say you are not alone. The writer of these lines does not understand much more, if to understand means to be able to translate the metaphors into mathematical language with real implications. This “understanding” means attempting to build a bridge between intuition about the world around us, intuition based on evolutionary development over millions of years and therefore limited by our senses, and the mathematical product that comes to describe situations that are so alien to what our senses teach us. Will this mathematics rise to the challenge of describing a real world? Time, apparently a very long time, will tell.