Imagine a pools coupon with twelve fully hedged games. Without knowing the result you possess the correct answer, or the universal solution, which the UiS scientist and his colleagues aim to find for the universal universe. Together with British and North-American researchers, the mathematician has developed a method that may provide answers to universal problems and characterize and describe the universe.
Sigbjørn Hervik first got he idea of the new method which the team is now working on. A good deal of that work was done in 2008.
"Naturally, it is personally very satisfactory for me to discover something new in the world of mathematics on a par with Columbus' discovery of America", the young scientist says.
"The task now is to develop our method further. In addition to the theory itself, we have to find an application for the universal universe by developing a general idea to help us to better understand the universe, including its state before the Big Bang."
In other words 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. We assume that he became inspired when he received his PhD in theoretical physics at the University of Cambridge in 2004. On the floor above him resided the mathematical and physics genius Stephen Hawking.
Theory of Everything
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 General Theory of Relativity occupies an obvious place in the mystery that Hervik and his colleagues are trying to find answers to. 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.
Splitting geometry
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."
Unique method
"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.
What needs to be done now?
"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.
Would you like to know more?
Sigbjørn Hervik, Department of Mathematics and Science, UiS, phone.: 51 83 21 72
e-mail: sigbjorn.hervik@uis.no
TEXT: Egil Rugland
TRANSLATION: Arne Neset
PHOTO: Elisabeth Tønnessen
