Dear Yuri, Tommaso, Steve,
thank you for your feedback. I am happy to see that there is some interest in my essay. I am also looking forward to read your entries and will do so next week.
@Yuri: yes, I am indeed going to contact some experts.
@Tommaso: without knowing which group exactly you mean, I can definitely say that I'm not a member of it ;) I am not an expert on graphene and have merely studied its simulation capabilities.
About you to compare the simulation by physical systems with the simulation by computer: great question. For the sake of concreteness, let's consider the Dirac equation, although the ideas are general. Then if we use the charge carrier (quasi-)particles graphene as the simulator, we have a system whose dynamics is precisely given by the Dirac equation. There are actual Dirac particles around. However if we do the simulation on a digital computer, there are no (quasi-)particles actually obeying the Dirac equation. There are only bit strings which let us calculate things about the Dirac equation. So in a certain sense, this is not even a simulation, it is only numerics.
@Steve: you asked first why the crumpled graphene sheets may model Dirac particles on a curved spacetime. I should say about this that I am not absolutely sure that this is correct, since I am not an expert on the subject; I should contact the authors of my reference [CV] to see whether this is true. My idea about it is the following: we know that the dynamics of charge carriers in a flat graphene sheet is governed by the Dirac equation. In this sense, the flat graphene sheet simulates a Minkowski spacetime. Now in the presence of ripples, we may imagine the graphene sheet like a landscape which is not flat, but contains valleys and hills. Geometrically, this landscape is curved: it is impossible to map it to a flat surface while preserving all the distances, similarly as to how it is impossible to fabricate a map of the earth in which all the distances are to scale. What about the wave equation governing the charge carriers in this case? They are going to obey a Dirac equation on a curved 3-dimensional spacetime! But according to Einstein's general relativity, "curvature of spacetime" and "gravity" are two words for the same thing. Hence, the rippled graphene sheet should simulate Dirac particles with a background gravitational field.
About your other comments, I'm not sure what to say. I agree that the subject of studying molecular forces and chemical bondings is fascinating. About graphene: no, it is *not* composed by 3D spheres! Rather, the point of graphene is that is a 2-dimensional structure. If you want to say so, it's composed out of 2D rings. But I don't see what one could possibly mean by saying that "they turn".