Essay Abstract

One obstacle for further progress on quantum gravity and issues like the discrete vs. continuous debate is the lack of experimental data. To a certain extent, this problem can be overcome by the simulation of models for fundamental physics by other physical systems. Here I focus on graphene as a particularly fascinating example of such a simulator and try to explain how continuous three-dimensional relativistic spacetime emerges from the discrete hexagonal crystal lattice of graphene. The potential of graphene to simulate aspects of fundamental physics is discussed.

Author Bio

As a postdoctoral researcher at the Institute of Photonic Sciences in Barcelona, I mainly work on mathematical methods for quantum foundations and quantum information. I find it enjoyable and challenging to keep a broad scope and to venture into new fields.

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  • Post #2

Hello Tobias!

I guess that good opponent for your essay

would be Mikhail.Katsnelson@fysik.uu.se

You can ask him.

Hi,

I think I've seen something about this at PhysicsWorld.com, but I can't find it right now. Are you from that group?

How would you compare the simulation of fundamental models for physics by other physical systems (as you do) vs. by computer?

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    • Post #4

    Hello dear Tobias Fritz ,

    Interesting essay.Congratulations.

    you say "It seems plausible that the resulting curvature of the graphene sheet

    results in a curvature of the Lorentzian metric determining the Dirac equation .If this is indeed the case, then a crumpled graphene sheet naturally models Dirac particles on a crumpled background spacetime, i.e.

    a background spacetime with gravity!"

    Could you develop please?

    PS THE GRAPHENE IS COMPOSED BY 3D SPHERES and they turn ....

    The aromatics, the benzens,....are relevant in their stability gravitational.I love the biology and all days I Class or link animals, vegetals , minerals...in fact I class all and I search the links of mass and the links of evolution.fetr all we are evolved cells.

    If we take our stabilities, evolved in time as H2O and its pôle + and- ....or tyrosin and its friends CHON......in fact the interactions are relevant considering the ionic link, the atomic link , the hydrogen link and the interactions of London, do you know these interactions between H and C London interactions are very very relevant,....or an other beautiful example is the centriol and its tori.Or the adn and its tori of sortings or synchro......do you know the chlorophyl and the caroten.....HCNO ..they build these spheres dear thinkers....see the cellulose or the pectin or the chitin.... the tetrahedre of spheres indeed( but all rests in 3D and the rotations spinals and orbitals make the rest.

    Still an other with biology,Have you already seen the prophase, meta-, ana-, and telophase, Fascinating these entangled spheres implying complementarity of evolution.

    What do you think?

    Regards

    Steve

    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".

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      • Post #7

      Thanks for your posts, it's interesting.Well

      I am sorry but you are false! No dear it's a real 3D , only the application is in 2D, for a kind of plan;that's all.And yes it's composed by 3D spheres.It's like that everywhere in the micro meso and macro.

      Thus the graphene is composed by points and they do not turn? ok ok

      Good luck in this contest,say hello to Han Gueurdes and Joy Christian, no but frankly we are on rational platform of what???

      ARE YOU SURE YOU UNDERSTAND THE POLARITY BETWEEN MASS AND LIGHT IN TIME SPACE EVOLUTION ???it is well to insert this graphene due to this nobel prize but please make it correctly and not with point and without rotation....If it's that which is learned at universities, I suggest a new library simply.But it's well.

      Regards

      Steve

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      • Post #8

      Dear Tobias, thanks for this very tantalising idea for studying discrete quantum gravity using graphene. I hope someone will be able to put it into practice.

      Your explanation of how massless Dirac fermions emerge on the graphene sheet is very clearly written. I wonder if some structure with the properties of a blackhole could be created. It might then be possible to study the effects of quantum gravity around a black hole in discrete space.

      Good luck in the contest

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        • Post #9

        I have a simple ask, do you think a BH can be created in a lab via the quantyum world, if yes, it's serious, because a BH is a sphere , central of galaxies and others universal rotations.Never we can create a micro BH.That has no sense at my humble and arrogant opinion.

        Regards

        Steve

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        • Post #10

        Dear Tobias,

        Graphene is considered as a 2D structure in a macro scale. In a micro scale of course it is in a 3D (3 plus 1) as atoms are physical objects. I suppose you take carbon atom as a point and in this case graphene IS a 2D structure.

        good luck, marsep (ioannis hatzidakis)

        P.S. I will refer to your paper later in a post (for my contribution) that my impressions from this contest will be included.

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        • Post #11

        Dear Tobias,

        I do not resist to respond to one of the excellent essays of this contest. As my essay is straightly related to yours (mine is dealing with 3D (3 plus 1 spacetime)) I think more appropriate leave any extensive detail for a private correspondance. However, it is valuable to emphasize that carbon atom together with oxygen, nitrogen, silicon, phosphorous and sulphur are the ones that consist the more interesting part of nature. The first three plus hydrogen consist the "live" part of nature (vis vitalis) the "spirituality" of which causes the most inexplicable causality in nature. These atoms are able to appear in four discrete forms denoted as hybridization. Carbon atom (C) without any hybridization is in atomic form (no interconnection), at sp3 hybridization C occurs as tetravalent (model of 3D spacetime - see our contribution (uc)), at sp2 hybridization C occurs as trivalent (model of 2D spacetime present contribution and uc), at sp hybridization C occurs as divalent (model of 1D spacetime uc). You say that free electrons "are not participating in any chemical bonding to neighboring atoms" this is not so as these "free electrons" are forming double bonds with neighbors. However, because of hybridization they can move freely in a molecular orbital that is extended to the whole structure of graphene and that is why "they behave AS IF they were free". Your two types of C resemble real and virtual points to our essay. Your sublattice is triangle although the quantum space is a parallelogram. In your fig. 2 each C is connected to three (why you depict only two?) C of the same type. This is not so, because the third one should be in a some short of a different kind and this is not shown in your text. In order to be right the two sublattices should be the ones (two) that form 30 degrees angles with horizontal direction (direction that charge is transferring). The vertical direction is the charge front that is moving from left to right. In chemistry, we call your red ellipses double bonds and the structure that you show in fig. 2 is a conjugation form of graphene that is appropriate for the charge flow from left to right (or the opposite). Please do not take my points as criticism but as minor details that I feel clarify your model.

        Best wishes and good luck, narsep (ioannis hadjidakis)

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          • Post #12

          All scales are in 3D, the micro, the meso and the macro,of course if we insert the evolution, the 4d space time helps and duration of time is implied by rotations of the entangled spheres.When you compute you can't consider a 2D , that has no sense,all must be in 3D. We just need to see more our scales by a kind of spherical topology, and its evolution.Still one thing, their rotations spinals and orbitals of these entangled spheres are proportional with mass.They have a mommentum these particles....

          Regards

          Steve

          @Steve: it seems that we had a misunderstanding, which was possibly cleared by Ioannis. So we should be more precise about the issues at hand. Here is what I mean by saying that graphene is a two-dimensional structure: I do indeed think of the atoms as pure points without extent in any direction. These points are aligned in a two-dimensional hexagonal lattice. In the ideal case which I consider as the simplest theoretical model, this lattice is infinite. So when I was talking about "rings" in the previous posts, I meant the small hexagons which make up the lattice.

          Of course in reality, the atoms are not just points, but have some internal structure and in particular a size. In this sense, they are certainly three-dimensional objects. However for the simple model which I consider in my essay---and which is indeed the standard approximation giving results consistent with experiment---the finite size of the atoms is not relevant and enters the calculation only in a very indirect sense.

          Did this clear up the confusion? If not, please explain in detail what you mean by saying that "it's real 3D".

          And then, no, sorry if I don't understand the "polarity between between mass and light in time space evolution". While I am familiar with polarity as a mathematical term in convex geometry, I have never heard it in this context. Sometimes it is difficult to find the sense in your writing; maybe you can try to explain things more precisely and in less prosaic terms?

          @Ioannis: yes, of course, thanks for pointing out that this may have been the misunderstanding!

          @Phil: thanks for the encouragement! I am happy to see you here, as presumably you are the author of two of my references?

          Anyway, relating graphene to quantum gravity is, at least for my understanding, still a little shady at the present time; not that I have mostly been writing about simulating Dirac fermions in (2+1)-dimensional spacetime, with some ideas about how to extend this to curved spacetime. But while obtaining a quantized form of this spacetime may be possible with graphene, to me it seems extremely speculative at the present time. I bet, however, that some people have thought about this, so the speculation is mostly due to my ignorance. In any case, I have to admit that my choice of title was mainly for effect...

          @Steve: as I have mentioned in my essay, there have been successful *simulations* of black holes by other physical systems. But note that these are only simulations and not actual black holes with a gravitational singularity. For example, while from behind the horizon of an actual black hole no particle can escape, this holds in the simulation only for certain kinds of quasi-particles. About the creation of actual microscopic black holes, I suppose we will have to wait a few years for the LHC to produce more data before we can decide either way.

          Well, while I noticed what happened, I don't know who you're talking about... But it doesn't really matter ;)

          Dear Ioannis,

          my knowledge of chemistry is very superficial, while you're apparently an expert. So, do you think that the phenomenon of hybridization is responsible for the important role they play in biological systems?

          Sorry if I cannot follow your explanation of the lattice structure and the different 'types' of carbon atoms. What I can say is that the red ellipses are *not* supposed to depict double bonds; pairing the atoms up into pairs and defining each atom to be of a certain 'type' is just a mathematical trick. In principle, each atom can be paired up with any of its neighbors. There is no physical/chemical significance to the red ellipses, and neither to the blue lines. Also, basically there exists no physical/chemical connection at all between different atoms of the same type.

          It is very much like in benzene, which is sometimes depicted as having three double bonds and three single bonds, although all of the six bonds are identical, which makes benzene a nicely symmetric molecule.

          Maybe we have been saying the same thing in different words. Feel free to email me if you don't deem the discussion appropriate for this forum; I'll be happy to learn more chemistry!

          I haven't yet looked at your essay in detail yet (will do so tomorrow) in order to be able to comment on the relation.

          Tobias,

          Isn't graphene difficult to work with? What is the effect of a graphene flake lying atop an iridium crystal causing new iridium atoms?

          Not my area of understanding.

          Jim Hoover

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            • Post #18

            Hi Tobias,

            Nice essay and a good idea! I completely agree about the importance of graphene in this context and I am continually amazed by the mapping between a 2D flake of graphite and the Dirac equation. In particular if Zitterbewegung can be seen that would extraordinary.

            Thanks again for the essay, you've given me some things to think about.

            -Cheers,

            Mike Bradley

            PS How do you like ICFO ? I have been there once (more or less by accident) while on holiday in Barcelona; it seems like a nice place.

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              • Post #19

              Dear Tobias,

              Hybridization is (one of) the most important factor(s) that atoms and molecules' properties are depented of. Chemical orbitals are in a sense the application of quantum theory in chemistry. So, double bond is also a mathematical "trick" - model. A figure is attached in order to help understand what I mean by lattices staff (lattices in green). Regards narsep (ioannis)Attachment #1: fig.jpg

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              • Post #20

              thanks I see clearer.You know I am tired to repeat always the same thing, the best is to read my post since 2 years on FQXi, you know I write all days.It was my only solution to show my model of spherization.Thus Of course I must repeat and it's tiring sometimes.What I say is simple, all is in a 3D even our quantum scale and even our cosmological scale, it's essential for the duration implied by rotating spheres and proportional with mass.Now considering an entanglmement and a finite serie, you shall see a fractal of the main central sphere and thus a serie with volumes, with the center as the biggest volume of course.All our universal entropy is with the rotating spheres, the mass is this rotating spheres and the light also and even the space, it's just their rotatioons spinals and orbitals which are different and thus imply the specificity of evolution.THUS OF COURSE THE GRAPHENE IS AN APPLICATION OF THIS SIMPLE UNIVERSAL REALITY....OUR uNIVERSAL SPHERE IS IN THE SAME RELATIVISTIC LOGIC OF RATIONALITY.A center and its spheres inside a sphere.ps eureka.Hope that helps.

              Regards

              Steve