Research

The Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO)’s joint detection of the GW150914 black hole binary merger consolidated the field of gravitational wave astronomy into normal science after decades of controversy and failed detections. After three observation
runs, we now have a flourishing statistical population of gravitational wave transients. Furthermore, the discovery of gamma-ray burst GRB 170817A as the electromagnetic counterpart to GW170817 has inaugurated a new observational paradigm for multi-messenger astrophysics in which astronomers may timely observe a compact binary inspiral’s aftermath across all bands of the electromagnetic spectrum. Despite these successes, current gravitational wave searches still depend strictly on a template library of numerical relativity simulations to identify candidate signals: without a binary inspiral simulated model, astronomers cannot find a gravitational wave signal in the interferometers’ calibrated strain data. The explicit goal of my thesis research has been to circumvent this obstacle by attempting to answer the following question: Can we reconstruct a confirmed gravitational-wave signal without making any theory-laden assumptions about a source’s inspiral parameters? The tool we chose for the job is Information Field Theory (IFT)—a Bayesian inference framework capable of recovering unknown or partially known signal fields from noisy, incomplete, and otherwise corrupted measurements with proven successes in radio and X ray astronomy, observations of the cosmic microwave background, and even medical imaging. For my project, we have built a generative model to reconstruct the gravitational wave signal GW150914 in interacting IFT by means of its correlated field methodology. Since our work here is IFT’s first application to gravitational wave data, a major challenge has been to translate LIGO’s instrument response and noise modelling pipelines into IFT’s numerical implementation, NIFTy. Thus, reconstructing GW150914 constitutes a paradigmatic proof of concept of IFT’s general applicability. The success of our project would provide a new signal detection methodology potentially capable of identifying gravitational waves from sources not predicted by orthodox general relativity.

Should we commit to only one geometry being the best fit for the objects of nature, including space-time? Or would we be better off allowing for whatever geometrical system best fits the scientific application we have in mind? Since antiquity and up to the mid 19th Century, there was no room for the second option. Scientists and philosophers only had one tool available for their investigations: Euclidean geometry. When mathematicians started to go beyond the constraints of its axioms, they were met with strong resistance from philosophers refusing to accept the possibility that non-Euclidean geometry could help describe nature. The bitter controversy that ensued culminated with General Relativity’s explicit use of Riemannian geometry in Einstein’s theory of gravitation. (Friedman, 2002) This marked a great revolution in thought: physical space is not globally flat as Euclidean geometry would suggest, but rather has a variable curvature. With the development of new geometries, we may be on the verge of another revolution.
Benoit Mandelbrot’s fractal geometry departs both from Euclidean and Riemannian geometry by dropping their shared commitment to the smoothness of space. It deals explicitly with shapes that are inherently rough, like the coast of Britain (Mandelbrot 1967). It also describes shapes whose basic features repeat themselves across multiple scales, such as tree branches and the bronchioles of a lung (Mandelbrot 1982). This success where Euclidean geometry failed inspired Mandelbrot to assert that “there is a fractal face to the geometry of nature.” (Rouvray, 1996) But Mandelbrot’s proposal has also met resistance from philosophers. In 1994, Orly Shenker argued strongly against the effect that fractal geometry could be the geometry of nature, claiming that the mathematical descriptions of naturally occurring objects using the tools of fractal geometry are not, in fact, genuine fractals (Shenker, 1994).
I refute Shenker’s claim that fractal geometry is not the geometry of nature by arguing that her chosen definition of a fractal is wholly unpragmatic to the empirical reality of working scientists. Indeed, the way in which physicists continued to use the terminology of fractals in their models despite Shenker’s criticisms shows a reappropriation of these concepts to fit the phenomena they encountered in the laboratory. (Avnir et al., 1998) As far as many physical and biological systems are concerned, fractal geometry offers the best description possible. Whether fractal geometry may revolutionize our understanding of physical space like what happened with General Relativity is of course a different matter. But this possibility has already been dealt with seriously in proposals to unify this theory with quantum mechanics such as Scale Relativity (Nottale 2011). Thus, the jury is still out on whether the geometry of nature really has a fractal face to it or not. But we may rest assured that, as far as many natural-occurring objects are concerned, fractal geometry really is the right geometry for them.