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A grand idea about the universal universe
07 August 2009
The University of Stavanger
Sigbjørn Hervik at the University of Stavanger in Norway first got he idea of the new method which the international team is now working on. It is indeed a daunting task that one of Norway's youngest professors of mathematics has taken up, together with professors A.A. Coley at Dalhousie University in Halifax, G.W. Gibbons at the University of Cambridge and C.N. Pope at Texas A&M University.
This is the theory that could give us all the answers, also called the Theory of Everything. So far nobody has managed to develop the theory, not even Albert Einstein, the father of the Theory of Relativity.
The "Theory of Everything" is based on the theories of relativity and quantum mechanics and is meant to connect the two. Quantum mechanics describes elementary particles and the structure of atoms and nuclei. The theory was conceived in the 1920s and developed, among others, by Erwin Schrödinger and Werner Heisenberg. The General Theory of Relativity was further developed in 1915 by Albert Einstein. As many will know, it deals with gravity and describes how mass and space are related. It also predicts the structure of the universe and its dynamics.
"The problem is that quantum mechanics does not include gravity and the theory of relativity does not include quantum mechanics", Hervik says.
Many attempts have been made to find a unifying theory of both. String theory is the best candidate so far, according to Hervik.
"String theory is based on vibrating objects called strings. The different fundamental vibrations give rise to different basic particles in the same way a guitar string vibrates to give the different tones. String theory operates with eleven dimensions, but we only know three of them in addition to time. The others are still unknown. String theory is therefore unverified and a lot is still missing before we can declare it the Theory of Everything. What we can do, however, is to consider the problem from another angle as if we did not know what the theory could be. We can describe phenomena, for example the universe, as a consequence of the unknown theory, in spite of the fact that we do not know what the exact theory is", Hervik explains.
An object situated between the Earth and the Sun will cast a shadow, which would be a projection of itself.
"What we need are many so-called projection operators to describe the totality, and we have a systematic way of doing this. We are looking for projection operators. By performing projections we can determine the curvature independently of how you look at the universe, the mathematician elaborates."
The surface of a ball is curved because the ball is round and not flat. The universe will also be curved because the universe is not flat.
"The idea is to construct curvature or projection operators that split geometry into small entities. It is a tool or a method based on mathematical formulas designed to find such operators."
"Our method is built on linear algebra. The quantum leap is that we relate the curvature of space to linear algebra in a special way. This is the great challenge we are facing and nobody has thought of this method before."
According to Hervik certain cases yield few projection operators. For example a red sheet is red regardless of the angle from which one observes it. We call it an invariant quality because it does not change. The projection operator in this case is like a color filter which only sees red. Other colors have corresponding projection operators, but some qualities are "colorless" which means that they are not caught by the color filter.
"These qualities are very special, and this is precisely what makes them interesting in our search for the universal universe", Hervik says.
"This is obviously a long term project, but we can see the end of some parts of it in a few years time. We have the theory. But we need to discover its consequences and find areas of application", Sigbjørn Hervik says.