Mathematical Model Of Medieval Cosmology Produces The Same Conundrums Modern Cosmologists Face

The first attempt to model the 13th century ‘Big Bang’ cosmology of Robert Grosseteste leads to the same fine-tuning problems that plague modern theories, say physicists

Robert Grosseteste was an English philosopher, theologian and statesman during the early 13th century. He is also thought of by some scholars as the first truly scientific thinker and an important contributor to the development of the scientific method.

The reason for this high praise is Grosseteste’s treatise on light, De Luce, which he probably wrote around 1225. In it, he describes a cosmological model in which the universe begins with an explosion of light from which matter condenses. The entire universe then forms in nine nested spheres as a result of the coupling between matter and light.

The similarities between Grosseteste’s model and today’s ideas about cosmology are one reason he is so admired. Some have even claimed that he predicted the Big Bang theory of cosmological expansion eight centuries ahead of modern cosmologists.

It certainly true that modern cosmologies aren’t so different in some ways from Grosseteste’s. Today’s theorists look at the observational evidence and then dream up any number of weird and wonderful models to explain it.

But they also have a powerful additional tool at their disposal: mathematics. An important, even defining, component of the work of modern cosmology is the development of a mathematical model of the universe that can be tested against the observational data.

So an interesting question is how would Grosseteste have modelled the universe had he had access to the same mathematical tools that modern cosmologists possess.

Today, we get an answer thanks to the fascinating work of Richard Bower at Durham University in the UK and a few pals—a team with expertise ranging from modern cosmology and mathematics to medieval philosophy. These guys have created a comprehensive mathematical model of Grosseteste’s cosmology and say it has remarkable similarities to modern ones.

They begin their work by describing Grosseteste’s ideas in modern English, since De Luce was originally written in latin. He says the Universe begins with a Big Bang-like explosion in which light expands in all directions giving matter its three-dimensional nature. Light then draws matter with it as it expands in a sphere. This coupling between light and matter is crucial.

The expansion eventually stops when matter reaches a minimum density. “As a vacuum is impossible within the Aristotelian framework, there must be a minimum density beyond which matter cannot be rarefied and this sets the boundary of the Universe,” say Bower and co.

The result is what modern physicists call a phase change but which Grosseteste calls “perfection”. At this minimum density, the perfect state of light-plus-matter cannot undergo any further change and so forms the first celestial sphere of the universe.

This sphere itself emits light or lumen towards the centre of the universe which also interacts with matter, compressing and rarefying it in the process. This interaction goes on to form other spheres corresponding to the fixed stars, the elements of earth, fire, water and so on.

This continues until the formation of the ninth sphere corresponding to the Moon, which is not perfect enough to continue to process. The end result is a universe consisting of ten nested spheres.

The next stage for Bower and co was to formulate this cosmology mathematically. That required them to make some assumptions based on Grosseteste’s description. They assumed, for example, spherical symmetry, that the rarefaction of matter increases with the radius of the universe and that there is no special length scale which implies that the distribution of matter distribution must follow a power law.

That allows them to write a mathematical equation describing the initial state of the density of matter within the universe. They go on to derive field equations describing the propagation of matter and lumen, which depends on the coupling between them.

Grosseteste also sets boundary conditions, such as the conditions at which the perfect spheres form and so on.

Finally, they put these equations and the boundary conditions into a computer to see how they evolve with time. In other words, they simulate the Big Bang and the evolution of the universe as Grosseteste described it.

The results are fascinating. The simulations reveal that the structure of the universe is hugely sensitive to the initial conditions, such as the strength of the coupling between lumen and matter.

Or as Bower and co put it: “When we solve numerically the mathematical formulation of the problem, we find that there is a complex interaction between the initial density profile, the intensity of the lumen (and the coupling of lumen to matter) and the opacity.”

This produces all kinds of different universes with various numbers of spheres. “For example, there are regions of the parameter space where our models generate fragments of the third sphere interspersed among the inner parts of the second,” say Bower and co.

They could prevent that by introducing a new mathematical condition but this isn’t how Grosseteste described it.

And therein in lies the problem. Only a tiny part of the parameter space leads to universes with ten spheres that are anything like Grosseteste’s vision. “Stable universes with a finite number of spheres are very much the exception,” they say.

What’s interesting about this is that the problem of how to fine tune a cosmological model is something that modern cosmologists are all too familiar with. The currently fashionable way to solve this problem is to imagine a multiverse of all possible outcomes and suppose that the one we live in is somehow special.

And in Grosseteste’s cosmology , it is indeed possible to choose a special combination of fundamental parameters that produces his imagined universe, with nine perfected spheres and a tenth sphere of partially separated elements.

“Following the same logic as modern cosmologists, we are forced to conclude that some additional physical law is at work that singles out points in the parameter space corresponding to the universe we inhabit,” say Bower and co.

That’s the uncomfortable truth that Grossetestes’ cosmology shares with modern ones. Although it is certainly one he could not have suspected.

“The sensitivity to initial conditions resonates with contemporary cosmological discussion and reveals a subtlety of the medieval model which historians of science could never have deduced from the text alone,” say Bower and co

And they conclude with this: “We cannot know Grosseteste’s view, but the computer simulations have revealed a fascinating depth to his model of which he was certainly unaware.”

Fascinating stuff!

Ref: arxiv.org/abs/1403.0769 : A Medieval Multiverse: Mathematical Modelling of the 13th Century Universe of Robert Grosseteste

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