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Gravity and continuum, with Christian Böhmer

By James M Heather, on 14 February 2013

Dr Christian Böhmer from UCL Mathematics took to the stage for this instalment of the popular UCL Lunch Hour Lectures to tell us all about gravity.The Earth's gravitational field

The lecture opened on a history of gravity, or rather how humans through the ages have looked at what we call gravity.

It started with the ancient Greeks, who refined what the Babylonians and others had observed before.

Just before the years started counting upwards (BCE to CE), there was Ptolemy, who took what was known and made a model of the solar system which – all things considered – was not too shabby.

Previous ideas had all looked a bit too neat and circular, and didn’t take into account the rather inconvenient fact that the planets don’t just travel one way across the sky.

Instead, they periodically look to travel backwards before continuing on. Ptolemy’s model, while a bit fiddly, managed to make sense of this. Sure, the Sun and the Earth were the wrong way round, but based on the knowledge and tools available to him, it worked pretty well.

To Ptolemy’s credit, no-one thought of a better idea for 1,500 years, until Copernicus thought to put the Sun in the middle, where it should be, and adjust the rest accordingly – which was later backed up by Keppler and Galileo.

After the stars came the apple; Newton arrived on the scene in a physics-spree, inventing laws and whole branches of mathematics all over the place.

Among them was his law of Universal Gravitation, which says that every bit of matter attracts every other bit of matter, with a force depending on how much there is of the original bit of matter.

After Newton there was Einstein, who really shook things up. His take on gravity meant that the concept of force was no longer important.

Instead, thanks to special relativity, space and time are no longer separate and gravity is better described as the bending of that space-time.

At this point, Christian pulled out the great quote from Wheeler: “Space-time tells matter how to move; matter tells space-time how to curve.”

This brings us up to the present. Gravity, in a nutshell.

Or is it?

The talk segued into another branch of physics called continuum mechanics.

Continuum mechanics seeks to model materials with a more encompassing approach. Instead of seeing materials and things as being lots of individual particles stuck together, it aims to think of them more as whole, continuous structures (hence the ‘continuum’).

But that’s nothing to do with gravity, is it? Well, it turns out that it just might be.

Gravity left off with Einstein effectively equating gravity to matter, and leaves it at that. Dr. Böhmer’s work deals with the possibility that perhaps there’s more to it than that.

Drawing on continuum mechanics, his idea is that maybe the structure is not trivial and that maybe the universe does has some internal structure. If it does, then this means that gravity might be observed differently, depending on where within that structure you were.

Christian seems pretty proud of this idea. As a theory, it’s a relatively easy one to pitch; no fields, particles or dimensions need to be invented, just applying an old concept to an old theory.

This makes Gravity 3.0, where matter now equates to geometry (or space-time), multiplied by some form of structure.

Under this theory, general relativity as we know it now is just an instance that we happen to observe where there is no structure. Moreover, this theory could be put to the test, and measured.

Christian really seems to see both the lyrical and mathematical beauty in the science that he studies, and was able to share that with his audience. The pre-print of his paper is available on the Cornell University Library website.

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