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March 10, 2008 | by  | in Opinion |
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Victorian Theses

Céline Cattoën is a French mathematics PhD student, whose thesis covers two separate areas of theoretical physics: cosmology and numerical relativity.

Her work in numerical relativity hopes to build up a model which can be used in future simulations in general relativity, a field which has traditionally been very theoretical, and not easily simulated. However, in the past few years, there has been a significant growth in the number of simulations of binary black holes and neutron stars. Cattoën aims to apply a much more accurate method, known as ‘spectral elements’, to enable more accurate simulations of black holes.

Spectral elements is used primarily in aerodynamics, seismology and photomechanics. The domain to be studied is split into many smaller elements, which are then individually simulated. When these elements are then recombined, the approximation of the whole is much more accurate, and a much more efficient use of processor power. However, before coding of a simulation can begin, an enormous amount of work must first be done in mathematical calculations and analysis. Cattoën will be the first to apply this method to black holes.

The purpose of her research is to aid the detection of black holes. Scientists hope to detect gravitational waves predicted by Einsteinian physics that are released when two black holes collide and merge. However, the sensitivity of the instruments used needs to be of the order of 10-17m – smaller than the diameter of a proton. These waves have not yet been detected, but Cattoën’s more accurate simulations will contribute to the analysis of experimental data that will enable scientists to know exactly what they’re looking for.

Her project in cosmology, with her supervisor Matt Visser, aims to serve as a reminder to other scientists of the systematic assumptions made by various models, and that there is greater uncertainty than simple statistical estimates of error imply.

Conventional wisdom on the nature of the universe is that the universe is not just expanding, but that its expansion is in fact accelerating. By coding the same physics (gained from data on supernovae) into different physical models, Cattoën and Visser have shown that there is some doubt as to whether this is in fact the case.

The models differ in their assumptions about space. The concept of ‘distance’ in space is not fixed. Models measuring distance based on ‘flat space’ (as we perceive it on Earth) confirmed the universe’s acceleration, but models based on ‘curved space’, where time and space are altered by gravity, did not. By taking into account both statistical and systematic errors resulting from imperfect instruments (which are not reflected on the graph), she has raised doubts as to whether the acceleration is in fact occurring. Recent studies overseas have produced similar results.

Cattoën and Visser have visually represented their results in an easy to understand way: if the line slopes upwards (from left to right), the universe is accelerating, if it slopes downwards, it is decelerating. As can be seen from the graphs (to the left), the uncertainty, both statistical and systematic, is sufficient to render the results incomprehensible – it is simply not possible to say whether the universe is accelerating or decelerating when such high uncertainties are present.

The upshot of all this is that physicists, who are not normally statisticians, and may not have studied the biases inherent in their methods, need to make a greater effort to appreciate how it will affect their conclusions. They may appear sound on one model, but other models do not provide support.

Academic reactions have tended to support their conclusions. While some have welcomed their analysis, those who are most in favour of the standard model have challenged their findings, suggesting there must be some flaw with her methodology, instead of reconsidering their own, as Cattoën intended.

Cattoën feels very lucky as a PhD student in the Mathematics Department at Vic. Because her field is so specialised, there is little opportunity for academic debate in this country. However, Vic and Matt Visser’s Marsden funds have provided funding for her to attend conferences overseas and present her findings.

Céline Cattoën holds an MSci from Victoria University and an MSci equivalent in Mathematical modelling from the Institut National des Sciences Appliquée.

Are you or someone you know doing a really interesting thesis? Because if you are, I’d like to talk to you! The awesomer the topic, the better. I can be contacted at matt@Salient.org.nz

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