Superstring theory resolves the most enigmatic problem of twentieth century theoretical physics: the mathematical incompatibility of the foundational pillars of quantum mechanics and the General Theory of Relativity. In doing so, string theory modifies our understanding of spacetime and the gravitational force. One recently discovered consequence of this modification is that spacetime can undergo remarkable rearrangements of its basic structure requiring the fabric of spacetime to tear apart and subsequently reconnect. Such processes are at best unlikely and probably impossible in pre-string theories as they would be accompanied by violent physical effects. In string theory, on the contrary, these processes are physically sensible and thoroughly common.

The usual domains of general relativity and quantum mechanics are quite different. General relativity describes the force of gravity and hence is usually applied to the largest and most massive structures including stars, galaxies, black holes and even, in cosmology, the universe itself. Quantum mechanics is most relevant in describing the smallest structures in the universe such as electrons and quarks. In most ordinary physical situations, therefore, either general relativity or quantum mechanics is required for a theoretical understanding, but not both. There are, however, extreme physical circumstances which require both of these fundamental theories for a proper theoretical treatment.

Prime examples of such situations are spacetime singularities such as the central point of a black hole or the state of the universe just before the big bang. These exotic physical structures involve enormous mass scales (thus requiring general relativity) and extremely small distance scales (thus requiring quantum mechanics). Unfortunately, general relativity and quantum mechanics are mutually incompatible: any calculation that simultaneously uses both of these tools yields nonsensical answers. The origin of this problem can be traced to equations that become badly behaved when particles interact with each other across minute distances.

String theory solves the deep problem of the incompatibility of these two fundamental theories by modifying the properties of general relativity when it is applied to scales on the order of the Planck length. String theory is based on the premise that the elementary constituents of matter are not described correctly when we model them as point-like objects. Rather, according to this theory, the elementary ``particles'' are actually tiny closed loops of string with radii approximately given by the Planck length. Modern accelerators can only probe down to distance scales around 10^-16 cm and hence these loops of string appear to be point objects. However, the string theoretic hypothesis that they are actually tiny loops, changes drastically the way in which these objects interact on the shortest of distance scales. This modification is what allows gravity and quantum mechanics to form a harmonious union. There is a price to be paid for this solution, however. It turns out that the equations of string theory are self consistent only if the universe contains, in addition to time, nine spatial dimensions. As this is in gross conflict with the perception of three spatial dimensions, it might seem that string theory must be discarded. This is not true.

The idea that our universe might have more than the three familiar spatial dimensions is one which was introduced more than half a century before the advent of string theory by T. Kaluza and by O. Klein. The basic premise of such Kaluza-Klein theories is that a dimension can be either large and directly observable or small and essentially invisible. An analogy with a garden hose can be helpful. From a distance, a garden hose looks like a long one dimensional object. From a closer vantage point (or from a long distance using a visual aid) an additional dimension --- the circular dimension winding around the hose --- becomes evident. Thus, depending on the scale of sensitivity of the observer, the hose will either appear as one or two dimensional. Kaluza-Klein theories state that the same thing can be true of the universe. No experiment rules out the possible existence of additional spatial dimensions curled up (like the circular dimension of the hose) on scales smaller than 10 cm ( 10 in), the limit of present day accessibility. Although originally introduced in the context of point particle theories, this notion can be applied to strings. String theory, therefore, is physically sensible if the six extra dimensions which it requires curl up in this fashion.

-Yash[D9]

A New Computing Paradigm: Chaos-Based System That "Evolves" Answers May Be Alternative To Current Computers

A revolutionary new computing technique that uses a network of chaotic elements to "evolve" its answers could provide an alternative to the digital computing systems widely used today. Described for the first time in the issue of Physical Review Letters this "dynamics-based computation" may be well suited for optical computing using ultra-fast chaotic lasers and computing with silicon/neural tissue hybrid circuitry.

The system has so far demonstrated an ability to handle a wide range of common operations, including addition and multiplication, as well as Boolean logic and more sophisticated operations such as finding the least common multiplier in a sequence of integers. Because it depends on interaction among its coupled elements, the system is naturally parallel.

"We have shown that this can be done, but we've only seen the tip of the iceberg," said Dr. William L. Ditto, professor of physics at the Georgia Institute of Technology. "This is a glimpse of how we can make common dynamic systems work for us in a way that's more like how we think the brain does computation. It's an entirely new computing paradigm."

For many years, scientists have observed the rich variety of behavioral patterns created by chaotic systems, including those found in living organisms. Ditto and collaborator Sudeshna Sinha of the Institute of Mathematical Sciences in Madras, India, reasoned that these natural chaotic systems should have been eliminated through evolution unless they served a purpose.

"We have the elements interconnected so that they respond to their neighbors like the avalanching that occurs when you pile grains of sand onto a sandpile," Ditto explained. "You allow the elements to avalanche and the system to evolve chaotically, then do the avalanching again until the system settles down to the right answer. It takes a couple of iterations for it to settle down."

Chaotic elements are useful to this system because they can assume an infinite number of behaviors that can be used to represent different values or different systems such as logic gates. "We are not really setting up rules in the same sense that digital computers are programmed," Ditto explained. "The system develops its own rules that we are simply manipulating. It is using pattern formation and self-organized criticality to organize toward an answer. We don't micromanage the computing, but let the dynamics do the hard work of finding a pattern that performs the desired operation."

Just as the numbers can be encoded in a variety of ways, the answer also comes out in a variety of ways: a rate of change, an amplitude, or a specific chaotic behavior. Because this new system differs dramatically from existing digital computers, it is likely to have different strengths and weaknesses. "It might be better than digital computing for those activities that digital computing doesn't do very well -- such as pattern recognition or detecting the difference between two pieces of music," Ditto said.

He compared dynamics-based computation to DNA computing and quantum computing, both of which are new computing paradigms still in their early stages of development.

Ditto believes the new system would work particularly well in optical systems. He has done theoretical work applying dynamics-based computing to an ammonia laser system and hopes to see the system implemented experimentally.

"Potentially, we could stimulate a very fast system of coupled lasers to perform a highly complicated operation like very fast arithmetic operations, pattern detection and Fourier transforms" he said. "We have something that very naturally performs an operation in an optical system. This would provide an alternative to existing efforts, which try to make optical systems do operations more like transistors."

Beyond the systems they have tried, Ditto believes virtually any coupled dynamic system could be used to perform computation. "We hope that you can take any dynamical system, stimulate it in the correct way, and then get it to perform an operation for you," he said. "This would provide an alternative to engineering a system from the ground up." — Yash[D9]