- Other Apps
One of our researchers, Raymond Aschheim (Ray), here at Quantum Gravity Research (QGR), recently read a book on Finsler geometry to better understand the work of two of our colleagues, Sergiu Vacaru and Carlos Perelman, who are working with Finsler geometry and modified gravity. In this new video Ray talks about finding an easier solution to Einstein equation if you double the space, but with some constraints. So one spacetime will be four dimensions, the ordinary spacetime, and you have another four-dimensional tangent spacetime which is for the velocity of the observer.
In this video 'E8 Shelling By Seven-Spheres', Ray expresses, "by using the two spaces, I was thinking how this is connected to our use of two four-dimensional spaces to build the E8 Elser-Sloane quasicrystal. This Elser-Sloane quasicrystal is built by projecting an eight-dimensional lattice to a four-dimensional space, and selecting some cells which have some property in the perpendicular four-dimensional space. So we have also the two four-dimensional spaces, and one of them on which we project is the final spacetime in our model."
You can check out QGR's many videos on Quantum Gravity Research youtube channel to better understand the theoretical work in development.
Ray continues, " ...recently, I was also interested in the E8 sphere shelling, which is one of the first ways that was used by Jean-Francois Sadoc & Rémy Mosseri around twenty years ago, to build the Elser-Sloane quasicrystal using discrete Hopf fibration. And here we see the circle which has shells of E8, with a beautiful symmetry, we are able to group points together on the lattice, and they will group in shells in the quasicrystal."
"And two weeks ago we had here a meeting with Derek Wise, a scientist who is also working somehow with Garrett Lisi and John Baez, and he was presenting something very very interesting to us, which is Cartan geometry and the observer space. So this is linked to homogeneous space and de Sitter space. The de Sitter space is like the Minkowski spacetime, but with a bonus that it can also integrate dark matter and cosmological curvature. And this notion of expansion of the universe which is naturally in the de Sitter space, is also in the shelling of the quasicrystal."
"We have to go a little bit deeper into mathematics to really see this, but the big picture is that you have spheres around other spheres, and these spheres are seven-dimensional. In the building of the Elser-Sloane quasicrystal, they are S7 spheres, which is also a very specific mathematical object with beautiful properties, but then they are shells, and the observer space proposed by Derek Wise is also seven-dimensional, it’s a quotient space of SO(4,1) which is a de Sitter space, by SO(3). A homogeneous space which was studied before was SO(4,1) divided by SO(3,1) – this is not exactly the same, but you can find a lot of information about this. For example, if you search for SO(4,1) on physicsforums.com there is a very interesting blog where Garrett and John Baez are discussing this mathematical object. And this is new, so this is really where to have the focus, on this. So here we have also the focus on this geometry, but with our view of the quasicrystal."
"And in our quasicrystal, we have also, that one part of the information is the observer. And this is the notion of a viewing vector which was developed by Klee and Fang several years ago, but without being totally precise. And now I really think that we have to link this viewing vector in the quasicrystal to the velocity tangent vector in Finsler geometry and to the observer of the observer space of Derek Wise."
And there ends the short video. Til next time...