Last week I attended a seminar by Ian Hawthorn of our Maths Department. He talked about some work which he'd done with a couple of students, Matt Ussher and William Crump. The title is a bit of a mouthful "The physics of sp(2,R)" (what does that mean?) and I have to say that I didn't follow most of it. But I did follow some of what Ian said, some of the time, in some places.
Before I comment on what Ian said, first I need to say what dark matter is. Actually, that's quite hard, because we really don't know. It's matter that we think is in the universe, but we can't see. Why do we think it's there? We can observe the structure of galaxies, and how they move and interact, and how they bend light. On a galactic scale, gravity dominates the other forces, and is what is responsible for galaxies. The gravitational force is generated by mass. So by observing galaxies, we can attempt at calculating the amount of mass in they contain. The problem is, when these calculations are made, there appears to be far more mass than we can account for.
This extra, unobserved mass, is labelled 'dark matter'. It's matter - it has a gravitational effect - but it doesn't interact electromagnetically - that means it does not emit visible, infra-red, radio waves etc. We can't "see" it in any electromagnetic sense. There have been various theories put forward to describe dark matter, but researching it is tricky because we can't actually see any.
Back to Ian's talk. He used a ten-dimensional algebra to describe the universe. As well as recovering the electromagnetic interaction from it, he recovered Einstein's description of gravity - except with a 'twist'. In Einstein's description, the gravitational effect is seen as a bending of space-time casued by a mass. It's often illustrated by the mass-on-a-membrane analogy. A regular grid on the membrane is distorted by the presence of the mass. Einstein's field equations describe this in a mathematical sense. The description might be complicated but it boils down to this - mass distorts the space-time in which we live, and we perceive this as gravity.
Now, Ian's result is a bit different. On a 'small' length scale (which actually means something pretty big) everything's the same. But on larger scales the source in Einstein's equation is itself distorted. In other words, what is bending the space-time is not the mass, but something else that is itself caused by the mass. Does this explain dark matter? It looks as if there must be hidden mass in galaxies, but is this down to the fact that the bending of space-time isn't directly caused by the mass we see, but via some intermediate? Maybe there is no dark matter at all - it's just our description of gravity that needs modifying.
Ian used the analogy of a car suspension. With no suspension on the car, the car feels all the bumps on the road. But put in a suspension system, and the effect felt by the car is a distorted image of the bumps. The up-and-down movement of the car is still caused by the bumps, but there's an intermediate step (the suspension). The end result is different. So, using this analogy, mass is 'suspended' - the universe feels a distorted version of it. Ian, Matt and Will conclude their commentary on this (which, for those more mathematically-trained than I, you can tackle here), with:
We have explained dark matter by concluding that there is no dark matter as such. There is only gravity behaving as though matter were present where there is none.
Is this interpretation correct? Is there really no such thing as dark matter? Probably time will tell, but nonetheless it's certainly an interesting possibility.