Dear Ben

your essay and your ideas go far beyond what one could expect from a purely mathematical training. My best compliments! Getting some things wrong is part of the process at the beginning: better making some starting mistakes, than working unmistakably on a useless program. It is part of the adventure!

Thank you also very much for your appreciation, which I know as sincere, out of academic competitions and twisted routes. Personally I have a strong believe in the value of my quantum automata program: after now 2.5 years that I started this program, it is really keeping all its promises, and you will soon next papers on Physical Review D. It was the same with my previous axiomatization program: it took eight years to develop completely, but now it is closed with the Physical Review A published with Giulio Chiribella Paolo Perinotti, which got a Viewpoint and quite a recognition around. If I now have decided to involve full-time three collaborators of mine, it means that I'm working seriously to it (and we are doing it currently with no funding, using some remaining overheads).

Now, coming to your questions, which also help me clarifying my ideas when talking to others.

The quantum automaton that I mean is a unitary evolution that is translationally invariant and local in the sense of Werner and Schumacher. To be more mathematically precise the evolution is an isomorphism of a von Neumann algebra, but here we really don't need such precise definition, since in the spirit of Deutsch-Church-Turing thesis we consider only states that have finite support over a locally invariant vacuum, whence we need to evaluate only evolutions in the causal cone, which for finite number of steps is finite (many people call these evolutions "quantum random walks", corresponding to finite numbers of particles in quantum field theory). Thus the lattice is obviously infinite, due to translation invariance. Translation invariance must not be regarded in a metric space, but more precisely as topological homogeneity. Locality means that a finite-dimensional algebra of a single system goes to the linear combination of the algebras of a finite number of next neighbor systems. This is a causal structure of topological nature only, no metric: there is just a simple rule that connects one system to other two (or few) system and so on, making a network. For a mathematician: an Alexandrov topology. The causality of Quantum Theory (first axiom!) gives the order relation. But there is something more than pure abstract causality: the quantum nature of the causal relation. So, in terms of cells, edges, and nodes: the cells are finite sets of finite-dimensional quantum systems, e.g. two qubits in the case of Dirac automaton. The edges are the causal connections and the nodes are unitary interactions between two (or few) quantum systems. Causal connections and quantum systems are the same thing: the cell is just a finite set of them. As an example, take just a simple homogeneous quantum network, i.e. a quantum computer, where infinitely many qubits are connected only through bipartite gates in a brick-wall way. See e.g. figures in my previous FQXi essay. In my case the systems are described by a complex operator in an infinite dimensional Hilbert space (but the algebra locally is finite dimensional!), corresponding to the field labelled by lattice points. The most synthetic and elementary mathematical definition of the automaton is now just a finite matrix (4x4 in the Dirac case) where elements can be just multiplication of the field in a cell by a scalar and operators shifting to next neighbor cells. All coefficients are constant, corresponding to homogeneity of the automaton. The matrix is "unitary", in the sense that it preserves the scalar product between any two states with finite support. That's all!

Regarding your last question, I'm not sure I understand it, but I think that the answer is positive in the sense that if I take an abstract causal network (call this "classical"), namely an (unbounded) graph with no loop, describing a partial ordering, I can associate a unitary interaction to each node and a quantum system to each edge.

Thank you again for your questions. It is very helpful for me to answer questions they are genuinely motivated by the understanding, as yours. It helps me a lot in making my ideas clearer, and affects next scientific writings.

With my best wishes for a career as a natural scientist, not a technician of any technique ...

Mauro

Dear Hai

in my approach inertial mass gets naturally a cinematical definition, solving the loophole definition of mechanics (if you are not considering Machian theories): it is just the slowing-down of information. It is a parameter of the automaton, and coincides with the rest-mass of the particle. Gravitation is still a work in embryo, and the idea is that it is a thermodynamical effect of purely quantum nature. The Higg mechanism is not quantum, and is far from the current status of the theory (just Dirac). In few years, if I get sufficient funding, I will be able to tell you if the Higg's mechanism will emerge as a semiclassical one from the quantum automaton in interaction, not the free one.

Thank you for you interest.

I'll take a look at your essay

Cheers

Mauro

5 days later

Dear Giacomo,

Good essay. If I am not mistaken I think you Simplifying principle is actually Ockam's razor. There are some serious researchers that work in the direction of providing alternatives to Bayesian approaches, such as Kevin Kelly from Carnegie Mellon that you may find interesting. I completely agree that there are untouchable dogmas not only in physics.

Your informational principles are appealing, I am tempted to try to understand them in further detail. Your informational view quite challenges my own ideas on an algorithmic world in ways I didn't expect, because you seem to suggest that some of this informational principles are not mechanical, which it is not completely clear from your essay, certainly in part because of the lack of space to further explain it. I am also delighted by your tidy illustrations, apparently using Mathematica =)

It looks to me that your proposal is related to, if not, a theory of quantum gravity, I would have liked this to be made explicit in either direction.

Dear Hai

Honestly I have difficulties understanding your essay: you have a completely different methodology and language. Sorry! My understanding is not sufficient to express an honest judgement.

Best wishes

Mauro

Dear Hector,

Thank you very much for your appreciation. Personally I have a strong personal belief in the future of the quantum automata extension of quantum field theory proposed in the essay.

Yes, my simplifying principle is the Ockam's razor, since I reduce the whole theory to just quantum theory of interacting systems, plus the Deutsch-Church-Turing principle (information density is bounded from above) and homogeneity. The Dirac equation is then just the free flow of quantum information, with inertial mass defined cinematically as the slowing down of the flow via the coupling between the two chiralities of propagation of information at the maximal speed-i.e. the causal speed (see my essay of last year for d=1). If you want to understand more, I will be happy to explain: what about a Skype meeting?

I would be also very happy if you can provide me a good reference to the work of Kevin Kelly, alternative to my approach, which indeed has a natural Bayesian interpretation, but not necessarily. In a way, also my universe is algorithmic, but of a quantum kind: the algorithm is very small, it is just the automaton, namely a small number of quantum cells (made of few low-dimensional quantum systems) causally connected by a small set of unitary interactions, representing the physical law, or equivalently, the field theory. Can you provide me with a reference to your work on the algorithmic universe?

Yes, the plots are made with Mathematica, with a quite sophisticate parallel graphics! I now will have soon the d=3 automaton: the graphics is astonishingly beautiful, with 3d pixels in space, whose size and transparency represent the quantum amplitude of the superposition, whereas the colors encode some phase and relative weights of the Dirac double spinor!

The proposal is indeed related to the idea of deriving an alternative theory of quantum gravity, essentially via the Jacobson thermodynamic approach. I this point I have some idea in mind, which I will write on a forthcoming manuscript, when it will be clear that it goes to the right direction. For the moment I cannot say more, and you have to wait up to December, when I will have finished teaching my semester course of Quantum Mechanics. At that time I will also post on the arxiv two long technical manuscripts, one with my postdocs Alessandro Tosini and Alessandro Bisio on a powerful asymptotic analytical evaluation of the automaton dynamics in the thermodynamic limit for smooth states (what I call the field limit), and one with Paolo Perinotti on the d=2 and d=3 Dirac automaton from first principles. After that we'll move to QED, but I think we will not need this for gravity. We are four people currently working on this project, with no funding! I hope that we will get some funding soon!

Thank you again,

Mauro

    Dear Hector

    here a beautiful image of a digital 3D version of two particles ...

    My best

    Mauro

    Dear Mauro,

    I couldn't see the 3D version of the two particles.

    Best,

    Hector

    Dear Mauro,

    Re Kevin Kelly: http://www.hss.cmu.edu/philosophy/faculty-kelly.php

    Re my own algorithmic nature research: http://www.algorithmicnature.org

    Best wishes,

    -- Hector

    I uploaded the file, but I need to put some instruction in the text, but the link on howto doit is broken!

    • [deleted]

    • Post #20

    Giacomo wrote:

    "Universal automata constants. The three quantities lP ; tP ;mP are the

    irreducible universal constants of the automata theory, and the adimensional

    mass is the only parameter characterizing the Dirac automaton. The Planck

    constant can be now rewritten in terms of the automata universal constants ..."

    Dear Giacomo

    Be careful with Planck length and read Wilczek doubts about it

    Wilczek:"we must extract roots",

    "can be taken outside the square roots",

    "In the strong system of units no square roots

    at all appear in [M], [L], [T ]."

    Read Wilczek http://arxiv.org/abs/0708.4361

      Dear Yuri,

      I agree with Wilczek: my system of universal constants is strong: they define indeed [M], [L], [T] units, and I don't need any square root, even for defining G!

      Thank you for suggesting this positive aspect of my system!

      My best

      Mauro

      Giacomo

      Thank you for an initial excellent resume, but can't claim to have kept harmonic resonance to the end. None the less I think I saw some astonishing analogies ("evolutions for finite number of steps2) etc. with some more astonishing findings of mine. I still need to comprehend you 'quantum automaton', but I hope you'll read my essay, considering your; "localized states and measurements, for whose description quantum field theory is largely inadequate," in a slight different way.

      I agree it is not "blasphemy to regard the non existence of an absolute reference frame as a dogma," and find a consistent alternative to the illogical 'fixed stars' frame, so problematic to astronomy.

      I expose some wrong assumptions, using epistemological elements in an ontological model, proving to reproduce a logical (TPL) construction of hierarchical compound propositions (read 'frames'). The SR postulates (Local CSL) seem to emerge direct from a Quantum Mechanism, looking like unification via Raman scattering and dynamic logic. Which I think may be very important. It certainly looks wrong and too simple at first, so meeting all requirements of the answer we seek, but is quickly intuitive.

      I do hope you can read it, visualise the kinetic evolution, and comment and advise.

      Very may thanks, and best wishes.

      Peter

      Good job, Mauro! It's great to see you making progress with this.

      You talk about gravity in your essay, but I wonder: what about gauge fields? For simplicity, let's take electrodynamics. Implementing electrodynamics in the quantum digital universe should be easier than implementing gravity, no? It seems like a natural intermediate step between the Dirac equation which describes free fermions -- still a relatively simple thing -- and the case of gravity, where all sorts of problems arise (diffeomorphism invariance, possibly indefinite causal structure, etc).

      Let me ask more concretely: do you have any idea yet about what will happen to gauge symmetries in the quantum digital universe?

      best wishes,

      Tobias

        6 days later

        • [deleted]

        • Post #24

        Dear Mauro:

        I have two general philosophical comments on your paper, which, I hasten to add, do not affect your overall argument, which I found quite promising and exciting.

        First, as concerns the epistemological principle, you say: "This is the principle that I consider the most solid one: a principle that cannot be violated, even in-principle, because its violation will involve contradicting a logical argument. Somebody would argue that claiming principles only of this [epistemological] kind is equivalent to claiming an 'ultimate theory of everything'. True." (p. 3) I would contend that this is not necessarily true. Even assuming that there is only one such epistemological principle (moreover, as an ineluctable principle of this type), it may only imply an ultimate constraint upon any theory we may have, but it does not imply an ultimate theory of everything. Indeed, it is quite possible that such a theory is in fact impossible, even though there is a definitive principle of that kind. In other words, nature may allow us to have such a principle, and yet disallow us to conceive how it ultimately works, including why we must have such a principle. We may, however, have partial theories conforming to such a principle or, since there may be more than one, such principle. In short, you don't need to concede even this point to the opponent of epistemological principles.

        Secondly, while it may be true that "the non existence of an absolute reference frame" (p. 2) is a dogma (even though some see it as an epistemological principle [p. 3]), I am not sure that "denying the existence of an absolute [reference frame?] is a relic of the repudiation of the anthropocentrism that followed the Keplerian revolution," that is, that it is only a relic of this repudiation. There are physical reasons for this "dogma" (if it is one), especially in Einstein's special relativity, reasons that are not at all anthropocentric. Also, do you mean by "an absolute" here "an absolute reference frame" or any "absolute"?

        Thank you!

        Arkady Plotnitsky

        Purdue University

        email: plotnits@purdue.edu

        Dear Arkady

        thank you for your interesting post, which further clarify my point expressed in a too succint way. I agree with you completely that having epistemological principles is not sufficient to axiomatize a full theory, but we cannot exclude that there is a sufficiently complete set of them, and this seems to me more logically well defined than the not well specified dream of the "final theory" of Weinberg et al. But, in any case, there is no doubt that we cannot dismiss principles of epistemological nature, which are truly meta-theoretical laws. And this was supposedly the case of the principle of relativity-I'm saying the one of Galileo-of which Enstein's principle is just a thorough specification, with the inclusion of Maxwell laws.

        Regarding the relativity principle, I anyway agree with you that it is more than a reaction to anthropocentrism, since we witness the principle at work everyday. However, everyday we also see that Earth is flat, but we know taht this is only an approximation, and actually Earth is round. Similarly, the relativity principle may just be an approximate one (and violations of Lorentz covariance are becoming more and more popular in the community). What I am disputing here is that the relativity principle be a truly epistemological one (a thing that I believed for many years), in the sense that it is not logically necessary in order to formulate the physical law. As I noticed in my essay, one can easily formulate the law in a preferred system (playing the role of the Newtonian "absolute") and then transform it to any reference system. And this is what in practice we do normally when invoking the reference system of fixed stars to define an inertial frame (since, as you know, the definition of inertial frame is circular!). And if you ask a cosmologist, he will agree that e.g. the background radiation is a preferred frame that one can experimentally establish even inside a blind black-box.

        Thank you so much for your erudite and relevant comments, which gave me the opportunity of clarifying more. I'm looking forward to having the pleasure of discussing more with you also in person.

        With my best regards

        Mauro

        Sorry Hector, I've been very busy lately. Here I'm putting the figure that I promised. This is the way in a digital 3D-pixels universe two particles would look. Please let me know if you have seen this figure.

        My best regards,

        Mauro

        Two particles in a 3D quantum-digital universe.

        Dear Tobias

        your question got the target as a sharp arrow! Sorry for not having answered soon.

        Indeed, what I think is that I will not need to implement qed before getting quantum gravity! I believe that gravity should come out from Dirac alone, and the equivalence principle must be a consequence of the fact that gravity is a quantum effect that emerges at the large scale. How and from where? This is still a secret (I have an idea, but don't have a definite answer yet). But I can just tell that it will come out from the automaton diffusion in 3D.

        Believe it or not, this is what it must be if we rely on solid principles, and not in the mere chance that a "theory" may luckily work a posteriori.

        Thank you again for the most interesting question

        Mauro

        Hi Mauro, nice one. Like the idea that quantumness is required for the emergence of space-time at the automaton level. I've always been a believer of classicization of a default quantum theory rather than the other way around. I'd like to see how the automaton formulation relates to the Frobenius algebras which correspond with the dots in our graphical language. They represent classical context of which space is one. We can discuss this in Barbados next year!

          • [deleted]

          • Post #29

          Dear Giacomo Mauro D\'Ariano,

          I have taken a quick look at your essay. I love that it is written very clearly in comprehensible language and that it is set out into easily digestable sections. You examine the way in which ideas are considered in physics, making it very relevant to the essay question. It strikes me as an essay that I must return to, to read thoroughly, as there is a lot I could learn from it. Well done, Good luck in the contest, Georgina : )

            If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

            Sergey Fedosin