Dear Tobias,
I enjoyed your essay and couldn't help becoming more curious as it progressed. It does seem very attractive to test quantum theory in a controlled environment as you describe. Massless fermions seem especially interesting for study, especially if graphene allows a certain degree of control of the parameters. From your research, is the test something that can be set up in an average lab?
Kind regards, Russell Jurgensen
Dear Florin,
that's very interesting! Thanks for the pointer, it would indeed have been worth mentioning in the essay.
On the other hand, from what I gather from skimming Hestenes' essay and his paper, his zitter model is a theory of a classical point particle, and therefore clearly cannot be realistic. For example, how would it reproduce the spectrum of the hydrogen atom? Certainly one needs some sort of quantization somewhere.
Evaluating the merits of the experiment seems much more difficult. So I don't dare saying anything about whether this could be an experimental detection of zitterbewegung or not, but only notice that it's not well-known and has not been published in an 'important' journal, which makes me a bit skeptical.
oops, my login had expired, the previous post is mine!
Dear Russell,
I'm happy to hear your comments! First of all, I should emphasize again that almost all of what I explained is not 'my' research, but merely a write-up of what I learned from reading the papers.
About the experimental realizations, yes, it seems that one indeed has good control over some of the parameters. For example, one can add hydrogen atoms to the lattice sites, which means that the affected lattice sites are not available for the electron hopping. Also, the two-dimensionality is a big advantage in that one has direct access to each atom, in contrast to three-dimensional crystals.
However, my understanding is that most things can only be observed indirectly. For example, observing a single massless free Dirac particle may be impossible, since how would one isolate a single electron? What has been observed is the correct dependence of the cyclotron mass on the electron filling, as predicted by the Dirac formalism. Or maybe one can use doping to introduce internal electric potentials, of which one might then try to observe the energy levels...? I don't know...
Hola Tobias
I enjoyed your concept of analyzing graphene as a basis of simulating aspects of physics. In my current fqxi paper and my earlier 2005 Beautiful Universe theory on which it is based I have proposed an entire universe made up solely of one type of node - much as your 2-D graphene 'universe' is made up of one type of node: a carbon atom. In my proposed Face-Centered Cubic (FCC) lattice the nodes are magnetic dipoles whose axes can be aligned in any direction in 3D. (N-S) attraction and (N-N) or (S-S) repulsion play an important role in the interactions of the lattice. I wonder if carbon has such polarity, and whether induction plays a role in the unusual binding strength of graphene's chemical bonds.
A related question that arose in my theory and other discussions here is that in 3D (for example in buckminster fullerine molecules Carbon 60) Brouwer's theorem states that a vector field on a sphere will always have one vortex. This implies a 'weak' spot on a C60 molecule - if that is, magnetic polarity plays a role there. Such phenomena highlight the limitations of 2D simulations in a 3D world, and I hope you can extend your fascinating analysis into 3D lattices, particularly FCC. Good luck to you.
Vladimir
Dear Tobias,
Thank you for the extra detail. It makes it clear it is an involved test. Very interesting.
Kind regards, Russell Jurgensen
Dear Tobias,
Hestenes' idea is only a speculation, but the resonance was experimentally observed and the root cause of zitterbewegung and Klein paradox is the SU(2)xU(1) gauge symmetry of Dirac's equation (combined with the a spin current conservation to be 100% rigurous). This generates a departure from the simple Berry phase of standard nonrelativistic QM and uncovers new physics unavailable from the simpler U(1) symmetry. By the way, in quantum Hall effect experiments, spin current is not conserved and the full SU(2)xU(1) symmetry is experimentally observed and is explained as spin-orbit coupling.
Dear Vladimir,
thank you for the excellent questions! As far as I understand, a carbon atom does not a priori have any magnetic moment. However, one can introduce magnetic moments by adding additional atoms of other elements "above" or "below" the carbon atoms; see for example this paper:
http://www.lnsm-zju.cn/lab/Upload/FCKfile/File/2008/5.pdf
Moreover, it seems that there is something like an emergent ferromagnetism going on, a phenomenon poorly understood. See here:
http://physicsworld.com/cws/article/news/19143
Finally, about extending the analysis to higher dimensions: Yes, I am indeed working on that! The goal is to see whether there are any higher-dimensional lattices which also have the property of the emergence of fermions. This is unlikely to be the case in 3D, since otherwise this would be well-known. I think that one would need a "non-rectangular" symmetry of the lattice. I'm not sure what exactly I mean by that, by the hexagonal graphene lattice certainly satisfies it with its ternary rotational symmetry, whereas an FCC lattice doesn't.
But I'm looking forward to study the 4D case, since this is the one relevant for actual physics in spacetime! (I'm thinking of things like lattice simulations of Euclidean Quantum Field Theory.)
Hello to both of you,
What about the magneton of Borh and the nuclear and atomic magnetic momemts.....it's always proportional in factn with the spinning and orbiting spheres.......partition fuction of a sub systems of entangled spheres ...the number is specific and presice for all gravitational stabilities.The entropy is correlated.
The particles inside the system have a spins thus a magnetism nuclear.We can take several quatum numbers which differenciate the different spins and orbitals.If the volumes are inserted also with the biggest volume for th cneter.....we can also differenciate the velocities of these rotations correlated with mass with the magneton of Borh as system of gauge eh/4pimc....we can subtitute the mass of different volumes. You can use the parallelization of Christian also in a deterministic road showing the rationalities of the magnetic momment, all has a momment,only the space hasn't rotations thus mass thus no momment also.It's relevant if the real serie is inserted for the different quantum numbers......the conservation of the parity seems essential as our proprtionalities.
Regards
Steve
Hello Tobias
I am glad my comments made some sense to you. There is so much in physics and mathematics I do not know - for example Euclidean Quantum Field Theory or what is ternary rotational symmetry and why it is important in fermion structure. In my (BU) theory the FCC arrangement was suggested almost ad-hoc and because other researchers such as Norman Cook (Models of the Atomic Nucleus (Springer)) was able to simulate nucleon structure using it. The magnetic lattice nodes I proposed self-assemble into some sort of configuration. I wonder if this process can easily be simulated and with what software.- it is outside my proficiency (all I know is the old BASIC !).
Hello Steve I hope you fine. Good luck to us all.
Vladimir
Hi Vladimir,
That goes thanks it's nice.Hope you also. Yes indeed ,you are right.good luck to all, this year, the essays are numerous ,it's well for the 3ème year.And furthermore there are many many relevances in several essays.
Best Regards
Steve
Dear Tobias and others,
have you a look to my essay (concerning 3+1 D)? This model is based on C(sp3 hybridization.
Ioannis Hadjidakis
Dear Tobias,
compliments for your very interesting paper! I'm especially interested in the simulation of Dirac equation by graphene, since this is connected to my work. Can you really consider the carbon atom as a gate in a quantum-computational simulation of Dirac in 2+1 dimensions? In such case I'm indeed very curious about the unitary transformation of the gate!
In the meanwhile I discovered that I didn't see your reply to my answer in my thread, and I answered to it. It seems that you are right. In order to recover an isotropic velocity of light in the analog coordinate system, one needs another way, maybe the thickness of events?
Cheers
Dear Tobias,
Wisdom is more important than imagination is more important than knowledge for all the we know is just an imagination chosen wisely.
Please read Theory of everything at your convenience posted by me in this contest.
Who am I? I am virtual reality, I is absolute truth.
Love,
Sridattadev.
Dear Tobias
Your essay is very interesting, I think the idea of emergence have not been study very seriously until now but models like the one you expose or others based on a discrete computational basis, show that this is the central point. On my essay, I try to explain this emergence from a different perspective but I think there is a very closed connection with your ideas. I will like to hear what do you think about it.
Regards,
J .Benavides
Dear Mauro,
excellent question! I think something like this is indeed possible. In a second quantized formalism, the electrons in the tight-binding approximation to graphene would be modeled as follows: take one qubit for each lattice site, i.e. at each carbon atom. The Hamiltonian is given by
[math]\sum_{\langle i,j\rangle}a_i^\dagger a_j[/math]
where the sum runs over all pairs of adjacent atoms and the a_i are fermionic annihilation operators. Intuitively, this says that the particles hop from one atom to a neighboring one. So for small timesteps, this interaction funtions like a partial SWAP gate with a small swapping angle. If we approximate the continuous time by discrete steps, we therefore obtain a three-dimensional network of partial SWAP gates, and these simulate the massless Dirac equation.
Concerning the other issue, see my reply in your essay's forum.
Tobias,
Your essay is one of the better essays in the lot here. It was an enjoyable reading.
Cheers LC
Dear Tobias,
I really love your idea of the graphene Dirac simulator. The second quantization in the tight-binding approximation to graphene that you give is really juicy! I will iimmediately explore this.
We are currently communicating in parallel on our two blogs, and some of the ideas that I'm posting here are also reported in my reply to your last post on my blog.
My problem is to prove that it is possible to simulate the Dirac equation by a quantum computer with a periodic topology of gate connections. This is also your problem, if your Graphene can be regarded as such a kind of a quantum computer (as you seem to assert in your answer). As you saw in my essay, I showed that this is possible in 1 plus 1 dimensions (with a mass-dependent renormalization of the speed of light). I'm trying now to prove it in 3 plus 1 dimensions (here it seems that a 5-simplex geometry is needed for each gate). Now, the problem is the following. In my blog you are mentioning a simple proof that a regular lattice will never give an isotropic propagation speed. How can you reconcile this with the covariance of the Dirac equation that you are simulating by the regular-lattice quantum-simulator graphene? I'm very intrigued and very curious.
Let me compliment again on your work!
Cheers,
Mauro
He is skilling indeed Tobias.A little of 3D harmonized with 4D and a little of rationality about the entanglement and it's very relevant.
Now of course for a quantum computer , the realism is deterministic in the pure road of real numbers.The graphene is a step, a weak step.but it's well , they try to converge with the reality, it's the most important.
Tobias....... operators hamiltonians and Laplacians more green and stokes more the rotational operators ....and if you insert the real number.....but perhaps an irrotational vectorial field is prefered U=-1/4INTdivVdv/r....poisson helping and the serie respected...and of course the harmonious function...a real puzzle all that ....fourier always is interesting.....now of course the volumes of entangled spheres is essential.....and what about the theory of big number and the probabilities and the errors also...Laplace where are you and Bernouilli....and the law of repartition of maxwell ...and pi always which smiles.....errors...moy. simple,moy. quadratic ,probable and precise...n=1/rac(pih)....DETERMINISM AND FINITE SERIE .....Pierce helping and Wolfram hihihi
Spherically yours.
steve
Hi Tobias,
Thanks for the introduction to graphene.
Question, do you think graphene will show interference patterns similar to C60.
I like your essay and think it is one of the best, but would encourage you to venture a little more into speculation. I think physics is at a local peak and it is going to be hard to get off it into something more productive without some leaps of faith.
Don Limuti
