Dear Roger

if I understand your position, you want to figure out how can make sense the notion of "space" in the presence of just few events. The answer is: it will make no sense. Think about: what is space for you? You can move in space, you can rotate something, you can walk, look at a distance ... the whole scenario makes sense only in the presence of infinitely many events, or, what we simply call "objects" that are macroscopical and made of a huge number of tiny parts, atoms, molecules, ... Whatever is "extension" needs parts, and not just a few of them.

Therefore, to figure out what does it mean to live with few "entities" and without space, try to imagine that you are an amoeba or any single-cell organism, that has no sight, no hearing, no other sense but e.g. three different kinds of different inputs--call them "a", "b", "c"--that are binary (on/off). Suppose also that the amoeba has brain that is a small subroutine, which is able to discover relations and causal connections. Such a mini-brain would figure out a space which would look similar to a finite group.

For a space like ours, we need to figure out infinitely many potential relations, corresponding to an infinite group. Such a group will be, however, finitely generated, by few simple relations, a bunch of translations, whose number of independent ones will define the space dimension.

Have fun

Mauro

Hi Yutaka,

nice to hear from you.

Yes, I'm implicitly assuming the dimension in the quasi-isometric embedding in R^3. My purpose is not to understand why 3+1. Let me add here that no theory ever, even remotely, had seriously addressed such an issue.

What we may have in the future (in the evolution of this theory) is discovering new unexpected physical features that are connected to the space dimension.

My best

mauru

Dear Mr Alessiani

you wrote your essay in form of a poem. You regard the bit as a metastable object. For me this is an irrelevant feature, since the bit, as a "system", doesn't carry its own dynamics. The dynamics is determined by the interaction.

My best

mauro

Graceful Mr. D'Ariano,

my fear was about a completely wrong argument. i mean the core of my essay.

Really I appreciate Your soft reply.

What about the joint with the Uncertainty Principle in my essay ?

My Best Regards.

    Dear Mauro,

    Thank you for your comments and your perspective.

    Perhaps we are on different planets. Though I suspect that some of the similarities may be due to the robustness or stability of our respective theories, which Gian-Carlo Rota described in lesson #6 of his famous essay "Ten Lessons I wish I had been Taught".

    I also should mention that I am very aware that Bialnycki-Birula's cellular automaton, as impressive as it is, was reverse-engineered. And I should reiterate that I very much appreciate that you are working to directly engineer the theory.

    Cheers

    Kevin

    Mauro,

    Hi. Thanks for the reply. I wasn't trying to make sense of the notion of "space" but was just using a very small subset of a few points in space as an example to try and make sense of the notion of quantum superpositioning. Separate from this, though, I agree completely, of course, that space is much bigger than just a few points. I disagree, however, that whatever has extension needs many component parts. At the most fundamental level, I think our physical reality must be composed of some type of fundamental existent entity no matter whether that entity is called a qubit, a bit, an it, a mathematical construct, whatever. As the most fundamental of all existent entities, this entity would have no component parts. Yet, in order to physically exist and to serve as the foundation of our physical existence which has extension, this entity must itself have extension. It seems possible to me to have a single unit entity that has extension but has no component parts. Given such an entity, space would then be built out of huge, or possibly infinite, numbers of these fundamental entities with each one defining a position in space. There would, of course, be relationships between all these entities as you point out in your essay. But, to have relationships, one has to first have entities to have the relationships be between. In your game example, I think these would be the players Alice, Bob, etc. in group G.

    Thanks!

    Roger

    Dear Giacomo,

    Thank you for your insightful essay.

    I agree with you that the It is from the Qubit, based on quantum information theory. The conditional entropy of the local observer and global quantum potential reciprocally weave the web of interactions that generates relativistic spacetime. (See my essay "A Complex Conjugate Bit and It".)

    Of particular interest is how continuous symmetries can be recovered from desecrate ones due to quantum interference between paths.

    Best wishes,

    Richard Shand

      Dear Mauro

      Physics is hard, I know, and that's why I adopted the ANALOGICAL method as an alternative mode of entry into it.

      Analogies are ramps for people with math deficiencies to see and feel what's going on in in physics and elsewhere. If we don't use the analogical methods, we would be blind as a bat to all the interesting stuffs that is going on in the world of scholarsip and research.

      I also think Feynman's all-paths formulation of quantum mechanics is a confirmation (indirectly of course) of the importance of analogies in our thoughts and thinking. If I remember it correctly, Feynman himself attributed his PI formulation to an analogy he made from Dirac's transformation equation.

      It was analogy as a paradigm of duality that allows me -- a non-physics major -- to see easily and quickly that there are TWO fundamental ways of approaching quantum theory: the Hamiltonian way and the Lagrangian way. Nor was I surprised to know that elsewhere in physics, there are background-dependent and background-independent physical theories. Everything seems to be a replay of what wave is to particle from that famous double-slit experiment.

      Call it what you will "It from Bit", "It from Qubit", "Particle from Wave", "Classical from Quantum", "Logic/Reason from Analogy", we are in this Circle of Twoness.

      With respect and regards

      Than Tin

      Dear Professor D'Ariano,

      Thank you for a very enlightening and thoughtfully written essay. I like the fact that your points are clear and insightful, and your thesis sets out to demonstrate exactly what you claim in your abstract: the "It" is emergent from pure information, an information of special kind: quantum. The paradigm then becomes: "It from Qubit". My essay also makes the case for information being more fundamental, and I try to put forward various questions along the way based on experiments and analysis to guide the reader to this viewpoint, but I think you demonstrate it more directly. I really liked your analysis of the qubit, and how you applied your reasoning to so many physical properties and phenomena, even to describe for example a field. And how you derived spacetime using the web game model was very much insightful. Your ideas derive a more fundamental meaning to these concepts, continuing what Einstein/Pauli did for fields originally, which itself was the next level of abstraction after Gauss. My essay also looks at the qubit, and like you I utilize Bell's inequality to support a deeper basis for my discussion of reality. This is a great topic!

      Thanks again for contributing this piece, and I hope you have a chance to review and rate my essay as well - I do really appreciate feedback from people who are directly involved in fundamental physics such as yourself.

      At some point I also will check out your other essays that you submitted on earlier topics.

      Sincerely,

      Steve Sax

        Mauro,

        "electrons are states of the electron field,photons are states of the electromagnetic fields, neutrinos of the neutrino field,and so on. The process of demoting particles to states and introducing the notion of quantum field as the new "object" for such states is known as "second quantization".The field is not an "object".But is now the field an object in the usual sense? Not at all. The field is everywhere. And it is not made of matter: its states are."

        I'm struggling with your densely-packed essay. How are states of qubits pure quantum software, objects, matter, HW completely becoming vaporized (paraphrasing)? States are matter rather than information or particles themselves?

        Jim

        Challenging essay!

          Wlth all due respect, prof. Mauro, but we are trying here to clarify the logical flow of your own position not mine.

          The question is: how may one understand that given a "holism" ("...according to which the properties of the whole CANNOT be understood in terms of the properties of the parts.) but you still have "local discriminability" ("...namely the possibility of discriminating between any two states of the whole by performing only observations on the parts."). Trouble is: how then are these parts apparent enough for one to carry out observations on them?

          You don't seem to allow that what we (the ordinary people) observe or have been observing repeatedly is what actually we get to believe IS OUT THERE and not vice versa. Meaning, we are quantum measurements going on NATURALLY.

          So I say again, the question frames naturally this way.

          All the best,

          Chidi

          Dear prof. Mauro,

          How may one understand that given your "holism" ("according to which the properties of the whole CANNOT be understood in terms of the properties of the parts.) but you still have "local discriminability" which is "the possibility of discriminating between any two states of the whole by performing only observations on the parts.". It seems to me a contradiction.

          Question is: how then are the parts apparent enough for one to carry out observations on them?

          Regards,

          Chidi

            Dear Giacomo

            in a way the uncertainty is contained in the Qubit of "quantum information".

            Information, on the other hand, means generally "uncertain information".

            Cheers

            Mauro

            Dear Richard

            thank you for your beautiful compliments. You got what I think is indeed the most relevant insight, namely that the nature of space-time must be intrinsically quantum if we regard it as something emergent, and not as a stage for something else. Now, my next step will be to understand the holographic principle (that you mention in your essay) within the quantum automata scenario.

            My best regards

            Mauro

            Dear Chidi,

            the fact that "properties of the whole cannot be understood in terms of the properties of the parts" is logically unconnected with the "the possibility of discriminating between any two states of the whole by performing only observations on the parts". Indeed, take a singlet state of two qubits. It is an eigenstate of the Bell observable (four projectors, one over the singlet and three over the triplet states). The marginal single-qubit states are completely mixed. The Bell observable does not commute with any tensor product of single-qubit projectors. Thus the marginal states do not allow us to understand the state of the whole, the Bell measurement is incompatible with all properties of the parts. But you can discriminate the singlet from any other joint state by some local effect, i.e. a projection on single qubit states. For example, the singlet is perfectly discriminated by the |00> state, by simply projecting on |00> (probabilities 0 and 1 for the two states, respectively). So if such an outcome occurs you know for sure that the state is |00>.

            Unfortunately quantum theory is not so intuitive. It is not my fault. You should make your own analysis more carefully.

            Cheers

            Mauro

            Dear Steve

            your compliments are the best I could desire. I am happy that you got exactly my points, and that you share my way of looking at physics. I downloaded your paper, and I found it very attractive. I put it in my collection, since I need to read it more closely. I found your sentence "Do the above experiments suggest information is more fundamental than physical reality,...?" very stimulating. I will definitely rate it after reading it well.

            Thank you again

            Mauro

            Dear James

            yes, in synthesis: quantum fields are pure software, space-time and particles are emerging features, as in a huge 3d quantum-computer graphics. As you see from my essay, this is the only logical way out all the problems of quantum mechanics and of quantum field theory. Up to now I haven't seen any other way that is actually working.

            My best

            Mauro

            Dear prof. Mauro,

            Permit me. We are both in pursuit of clarity. The point I make is that in light of the present question "it from bit or bit from it" once you assume non-locality as first principle (and as defining the "it") next the burden is to show how the "Bit" EMERGES from this non-locality.

            One cannot just jump to PRESUME the existence of "locality" on which to carry out experiments.

            Best regards,

            Chidi