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

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    • 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!

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      • 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

          Dear Giacomo

          A very interesting essay. I find particularly interesting your purification principle: "that irreversibility and mixing can be always regarded as the result of discarding an environment, otherwise everything being describable in terms of pure states and reversible transformations." The question is who or what decides what is included or discarded, and by what mechanism is this implemented? This is some process or choice that takes place at a different level from that of the dynamics itself. So how does this happen?

          I fully agree with your view on infinity: "Richard Feynman himself is reported to like the idea of nite information density, because he felt that there might be something wrong with the old concept of continuous functions. How could there possibly be an in finite amount of information in any finite volume?" Yes indeed.

          George Ellis

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            • Post #32

            Thank you Bob. The quantum nature of the causal network is crucial for getting the isotropy of space for relativistic momenta, and this is because informations flows in a superposition of paths. Otherwise, if you want the causal network to be classical, you need it to be random, as in the Rafael Sorking approach. But then you loose the nice automaton framework for Dirac. In my knowledge, by no way you can get the same physics of Dirac by a classical random walk. The analogy with your Frobenius algebra is exactly the same as with the operational boxes of Giluio me and Paolo in our informational derivation of quantum theory. We should discuss about this at length in person, and Barbados could be a very inspiring place!

            See you soon

            My best

            Mauro

            Thank you Bob. The quantum nature of the causal network is crucial for getting the isotropy of space for relativistic momenta, and this is because informations flows in a superposition of paths. Otherwise, if you want the causal network to be classical, you need it to be random, as in the Rafael Sorking approach. But then you loose the nice automaton framework for Dirac. In my knowledge, by no way you can get the same physics of Dirac by a classical random walk. The analogy with your Frobenius algebra is exactly the same as with the operational boxes of Giluio me and Paolo in our informational derivation of quantum theory. We should discuss about this at length in person, and Barbados could be a very inspiring place!

            See you soon

            My best

            Mauro

            Dear Georgina,

            thank you very much for your compliments, which are exactly what desired most to hear, namely that the essay is easily understandable and every point is made clear. I thought for now many years about the issue of reformulating physics on more solid principles. What I consider amazing about the principles proposed in my essay is the fact that by just pursuing them, and without anything else, one can derive so much physics! I strongly believe in this quantum automata program: we are now four people working on it, temporary with no funds, and I hope that this essay will help the program to take off.

            Dear Sergey

            I understand your point, the rating is just the average, but nobody knows the average, so many essay are overestimated, because in order to get them up then people vote 10. I'm not sure, but maybe you are right in proposing the rating being visible. I saw indeed big fluctuations in mine. Last nigth was at the 5th place, now is at the 15th ... I hope that it will remain before 35th, and will not miss the opportunity of a judgement from Referees!

            Dear George,

            thank you for your interesting post, which gives to me more opportunity of talking about the principles of Quantum Theory (my joint work with Chiribella and Perinotti). Indeed, what we learn at school is that unitariety of Quantum theory is a rule, but this indeed is not true: the theory can survive without the requirement of unitariety keeping perfect thorough logical coherence, and using quantum channels (completely positive trace-preserving maps) instead. Also the motivation for unitariety that "transformations must be reversible for a closed system" is false, since, strictly speaking, for this purpose one needs the evolution to be just isometric. Requiring that the reverse of the reversible transformation is also reversible is a matter of simplicity. I think that unitariety is just for historical reasons, due to the Schroedinger equation, which, however, is needed for the "mechanics" of the theory, quantization rules and so on. If one wants a theory that is autonomous from the classical one (but from which classical mechanics emerges from pure quantum theory of systems, as for the quantum cellular automaton), then unitariety is not strictly needed for the logical coherence and closure of the theory. In the automaton, however, unitariety is dictated by the requirement of having the Dirac field emerging at the Fermi scale.

            Therefore, is up to you to believe that the purification actually exists. We know that Quantum Theory allows for purification of any transformation using an environment (and by the way the purification of the postulate is an isometry, which then we know can be further extended with a unitary). But you are not obliged to have the actual purification: everything works as if the purification exists. If now you ask me for "a mechanism" for such a purification (in case you believe that there is an actual environment), that's an interesting question. Maybe one should try to describe the "informaton" as an incompressible fluid, or something similar. By the way, if one believes that the purification always exists, than also the GRW spontaneous collapse is due to an environment! Which means that GRW is always the same quantum theory, but we just add another hidden quantum field (Bassi would say that it can be done with a classical field, but I'm not sure of this). The true point is to decide what is spontaneous, and what is not-the chicken and the egg again.

            Finally, let me say that I liked your essay very much (it was one of the first I read). I can agree with your idea of your top-down causation, within my definition of causality (axiom 1 of QT), and as a Bayesian, in the sense that since causal relations are established by parametric dependences of probabilities, in a Bayesian interpretation they are themselves "beliefs", and such they are established by us, as any theory is formulated (this also agrees with the Humean point of view of causation). And, as such, you are right when you say, "Understanding the emergence of genuine complexity out of the underlying physics depends on recognising this kind of causation".

            Thanks for that response, appreciated.

            "By the way, if one believes that the purification always exists, than also the GRW spontaneous collapse is due to an environment!" - yes indeed.

            "Which means that GRW is always the same quantum theory, but we just add another hidden quantum field (Bassi would say that it can be done with a classical field, but I'm not sure of this)." - well I think there is a god case that the "hidden variable: is the local context. It is hidden because its variables are located at the level above the one that one has in mind - and this environment is just taken for granted.

            George

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            • Post #39

            You mainstreamsians controle science for over 50 years. You mainstream and Hawking failed. The bad science is because of the Top-Down controle of the people like you. Why do you need money and fame from FQXI where the authors are mostly jobless, are mostly independent researchers, are mostly viXra.org authers? Do you need money and fame by controling jobless???

            I want to rate you 0!

            Dear Ben

            thank you very much for your support. I just discover today your really interesting reply to my post on your thread: I'm going to think about, and try to answer this same evening.

            As regards my position in the list, it is fluctuating, so let me cross fingers.

            My best to you,

            I'm happy that you are at the top.

            Mauro

            Dear George,

            if you like it, the local context can be always considered as the environment that is purifying.

            Mauro

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            • Post #42

            MAX PLANK:

            An important scientific innovation rarely makes its way by gradually winning over and converting its opponents; it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out and that the growing generation is familiarized with the idea from the beginning.