Essay Abstract

Can Reality be simulated by a huge Quantum Computer? Do we believe that Reality is made of something more than interacting quantum systems? The idea that the whole Physics is ultimately a quantum computation---a strong quantum version of the Church-Turing hypothesis well synthesized by the Wheeler's coinage "It from bit"---is very appealing. It is theoretically very parsimonious: an Occam razor's quality-guaranteed description of the world. But, if this is the case, then we need to understand the entire Physics as emergent from the quantum computation. Here I will make a short exploration on how this may come about.

Author Bio

I am professor at the University of Pavia, where I teach "Physical Theory of Information" and "Foundations of Quantum Mechanics", and enjoy research with a marvelous group of much younger collaborators.

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  • [deleted]

I like the Zeilinger-Brukner, or IQOQI Interpretation of Wheeler (out of Bohr). "It from Bit" is about what we can KNOW, not about "what is". One fundamental quantum system yields one classical bit. A qubit is a fundamental quantum system and you know what you get when you measure it. This is fascinating because our minds are binary too. We construct a world from binary propositions.

Brukner suggests in another couple of papers that we're just crap (coarse-grained) measuring devices. This seems more than plausible. Interestingly, neither of those guys lets the concept of universe-as-quantum-computer pass through his fingertips.

    • [deleted]

    Well said. One thing which has not been appreciated yet is the crucial role of the quantumness of Information in a digital universe. A classical computer would not work, not just in obviously reproducing efficiently reality (that's would be a tautology, being the world quantum), but in being efficiently reversible, efficiently addressable in different directions in a network, and more ...

    • [deleted]

    I didn't express myself as well as I should have in reference to the "quantum computer".

    How can we assume the universe is a computer unless we can verify its computations? Why does it need to be a computer? Isn't it possible that the universe isn't even computable in terms of computation as we understand computation?

    Aren't you assuming there's stuff going on inside of qubits that can't be measured?

    • [deleted]

    Dear Nikman,

    there is no stuff hoing inside of the qubits, there are only qubits from which stuff is emerging!

    It is a theoretical description of reality. The reality being perfectly simulated by a quantum computer (David Deutsch physical Church Turing principle), is everything you need for physics. The rest is for metaphysics.

    I understand that is an hard to swallow ontology, but, this is the theme of the context. Otherwise, what else does iit mean a "digital Reality"?

    • [deleted]

    I love ontology! I love "It from Bit" (at least as interpreted by Brukner, Zeilinger et alia). What I have a problem with is the computer analogy, which B & Z do not adduce. You mention Deutsch, which brings up another issue: many worlds. That seems to go hand-in-hand with the universe-as-computer approach, and which Zeilinger is on record as having no use for.

    Anyway, it needs to be noted that any such quantum computer universe would NOT be a quantum computer of the type that may someday be realized here in the human realm. They're not, as Scott Aaronson regularly notes, "known to be able to solve NP-complete problems in polynomial time." People get really confused about this and expect almost supernatural stuff to begin happening once qcomputers get on line, if they do. It's a public service to disabuse them.

    • [deleted]

    How is your view any different from Seth Lloyd's view? I think Lloyd as you may be giving the quantum a too prominent place when in fact is not needed at all. Of course one can think that quantum mechanics is at the basis of everything else, but you are then already making a choice assuming such a prior statement and then jumping to say that the universe is a quantum computer. In that case it is not longer what a computer means. The standard quantum computer is Turing computable, but quantum mechanics actually allows infinite number of states, so whether the universe is a computer in one or another way is actually as open as the original digital vs. analog question...

      • [deleted]

      Dear Egal,

      there are two different problems related to your point.

      First: if you believe in quantum field theory, then the problem is to see if a discrete field theory (= quantum computation) has some strengths compared to the continuum. And, as I wrote in my essay, it has many, e.g. covariance is a free bonus, all problem of the continuum disappear (especially localization), no need of quantization rules, emergence of Hamiltonian, Dirac as free flow without covariance, and more ...

      The second problem is if a classical computer would do the same job. Answer: It will doit only at the expense of a very complicate computational network! And there are things that will never work, in a classical computer, e.g. simply directing the information by state-preparation (you need a kind of telephone system in the network!). There is more than that. Quantum Mechanicsis the only possibility to have a digital nature: the quantumness is part of the fabric of space-time.

      Dear Giacomo,

      You write

      ---"The big question is now where gravity comes from."---

      The answer is surprisingly straightforward. If a universe is to create itself, then its particles must create themselves, each other. If (the properties of) particles then are as much the product as the source of their interactions, of their energy exchange, then their mass also must be as much the product of their exchange, of gravity between them as its source. As the force between particles then also is a much the product as the source of their interactions, a force obviously cannot be either attractive or repulsive (that is, at least at quantum level). A universe which discovers how to create itself, can hardly stop doing so. It is this continuing creation process which powers, or is powered by gravity, the force we associate with the contraction of masses and the expansion of spacetime between the mass concentrations. For details see my essay.

      Best regards, Anton

        Giacomo,

        Thank you for the engaging essay. I have a question about this passage:

        "The real entities are the events, facts of the world describable by the basic language obeying the rules of predicate logic (the 'facts' of Wittgenstein's Tractatus). ...The notion of 'event' must be regarded as truly primordial: events do not happen in space- time, they build-up space-time. Stated in other words: space-time is our way of organizing events."

        If events are fundamental and space-time derivative, as you propose, then to avoid circularity events can not be specified or described in any way that makes reference to space or to time. Yet you define events as "facts of the world". Could you give an example of such 'facts of the world' that can be specified without reference to time or space?

        Thanks,

        Tom

          • [deleted]

          Dear Anton,

          thank you for your comment. I will look at your essay.

          • [deleted]

          Dear Thomas,

          please, call me Mauro: it is my middle name, but this is the one that everybody uses.

          Thank you very much indeed for your comment, which brings up a relevant and often raised point. Due to length limitations, I didn't have the space to write about this in the essay, and this is a good occasion for doing it. This is also why I like the idea of this Forum: it gives a unique opportunity for receiving genuine feedback, the one that you don't usually get from colleagues e.g. at conferences.

          Essentially your question is: how can you state an "event" in the basic language without reference to space? The answer looks hard, but it is indeed surprisingly simple. And this is the case for every event, if you ask yourself "where" the information about space-time comes from. Whenever you specify the location in space and time of an event you use local information At Your Place and Time (AYPT). In a everyday description of an event you get a rough idea of the distance from your place from the size of the image on your retina compared to your previous experience, and/or from your previous knowledge about measurements that you did in the past. The specification of time is a NOW, or it is the recollection-memory of a reading of a clock made AYPT in the past. In a very accurate specification of space-time using the best state-of-the-art technology you use a very precise clock under your control AYPT, send an em beam toward the place of the event (using previous information AYPT: you have "seen" the place toward which you direct the beam), use signals AYPT from satellites to locate the event with precision in space-time relative to YPT. Every complete and precise description of the event ultimately is given in terms of observations made AYPT, and/or based on previous knowledge and observations made AYPT, including the calibration of the apparatuses, the sending of the satellites, the made of the clock, etc. Therefore, ultimately, the event is specified in terms of events happening AYPT (i.e. at the observer), using information AYPT and relations with previous events.

          In short, the whole space-time is made of events connected to the AYPT word-line.

          Now, it doesn't matter if is you or another observer, it is again a relation with your AYPT storing of information AYPT.

          Another of way of saying: ultimately space-time is made of positions and times of events, it is made of events, each of which is specified with information AYPT. Ultimately space-time is reduced to a single point: AYPT.

          And, this is not my idea: it is the lesson of Albert Einstein, who thought us to synchronize clocks, and to use clocks and the speed of light to measure distances. The building up of space-time that I gave you above gives the equation "reference-frame" = "observer". Einstein did "believe" in an objective reality, but he needed the observer to define his relativity operationally.

          It will be nice to hear from you again, Thomas

          Thank you.

          Dear Mauro,

          Thank you for the beautiful essay. It seems to have something in common with Computational LQG? And maybe I do not get it. But this is not my point.

          You write: what else is out there more than interacting quantum systems? Is it space? No, space is a "nothingness".

          In my essay I propose a very simple "thought experiment": we observe a small region in spacetime (the size of an elementary particle radius) deformed in the way that the wave we actually detect is not emitted or reflected by the observed object but it comes back to us along the geodesic (as the notion of a "straight line" in general relativity). In fact we observe only a strongly deformed spacetime region, "empty" inside and redirecting our wave but apparently... we perceive a particle. Our measuring instruments and our language out of the force of habit say so.

          You also write: gravity must be a quantum effect.

          In general I fully agree. But I propose to look at the gravitation not as a fundamental but emergent interaction. Details in my essay if you are interested. However it is highly speculative.

          Best regards,

          Jacek

            Dear Mauro,

            there is a lot I would like to comment on, mostly very positive things, but there is one point which seems important enough to merit its own post. My question is about Figure 4, where you state that "In a computational network made with tetrahedra [...] the maximal information speed is the same in all directions". Can you provide a proof or a reference for this?

            I have thought about exactly this issue of information speed in a lattice, albeit in the two-dimensional case, and come to the conclusion that isotropic information speed is impossible. You can see this by marking all the vertices which can be reached by traversing 2 edges, then all those which can be reached by traversing 4 edges, 6 edges, and so on. If you interpret, in each case, these points as vertices of a polytope, you will notice that these polytopes are identical (up to scaling): the shape of the wave fronts does not change! This is easy to understand in terms of Minkowski sums: the 4-edge polytope is the Minkoswki sum of the 2-edge polytope with itself, and similarly for all the other ones.

            Now it seems to me that the same reasoning applies in the 3-dimensional case to show that the wave fronts are polytopes of a fixed shape. In particular, if this is correct, then the speed of information is not isotropic.

            In any case, can you explain in a little more detail how the tetrahedra in figure 4 are arranged? It's not quite obvious to extract this information from the picture.

              • [deleted]

              Dear Tobias,

              thank you for raising your point. The problem of digitalization of field theory in 3D is much more interesting of what I imagined at the beginning. Its is really fascinating. But it is also not easy to formalize mathematically.

              I don't have an analytic proof of the isotropy of information speed in the Regge-like causal network. For the moment, the proof is just the visual one of Fig. 4. Let me try to explain the figure. The figure is a representation of the lattice seen from the top in the direction of time axis. Unfortunately, all planes are merged in the same 2D figure. I think it is very important to understand the way in which the tetrahedra are arranged, and that's probably the reason of the disagreement with your results. I tried to make a 3D, but it comes out not easy to understand either (I need to write a code for Mathematica...)

              Build the lattice in this way. Put 6 tetrahedra with a face on a common horizontal plane to make an hexagon. Take a plane passing through the top vertices of the tetrahedra, and use it to mirror another 6 tetrahedra on the top, having each the verities in common on the mirroring plane. You have now an hexagonal cylinder. Use the cylinder as a tile to span an infinite slab. Stack slabs one over the other, sharing vertexes on the planes. Done!

              On Fig. 4 you see paths that belongs to different planes: each path is raising at each step!

              You can cheek yourself that for increasingly large circle, the number of paths reaching the border are increasing, with increasing number of directions, and the shortest paths all have the same length also in terms of steps!

              I hope that it is now clear.

              I'll try to make a 3D figure as soon as I'll have the time, and try to post it.

              Or else, please, send me an email, and I'll send to you when available!

              Cheers

              • [deleted]

              Dear Jacek,

              thank you for your post! I'm not sure that I have something in common with COmputational LQG, of which, however, I'd like to know more. I think that both we agree that gravity is emergent as a quantum effect. The point on which apparently we don't agree is that also space-time is emergent.

              I'll read your essay.

              Best regards

              Mauro

              Dear Mauro,

              thank you for the vivid explanation, it is very clear now what you mean!

              I may be wrong, but I still think your claim is incorrect. If I connect all the points reachable in 2 steps, I get a hexagon. If I connect all those reachable in 4 steps, I get a hexagon. Likewise for 6 steps, 8 steps, ... My (maybe not so clear) argument above in terms of Minkowski sums shows my these are all hexagons of the same shape.

              • [deleted]

              Dear Tobias,

              with 6 steps in my Fig 4. on the red circle, for 6 steps you get a 12-side polygon, whereas for 2 steps you get an hexagon! However, I like the way in which you are addressing the issue. Thank you for your feedback!

              Mauro

              Dear Mauro,

              I hope that you will read my essay and you will find that in my view the space-time is not emergent.

              Jacek

              Dear Mauro,

              I feel embarrassed for still not being able to agree, but at least we have pinned the issue down to the question of which points can be reached in 6 steps.

              Basically, your figure consists of a big hexagon, with a little triangle attached at each side. Right? Then which points can be reached in 6 'zig-zag' steps from the center? Well, all the vertices on the big hexagon--without the little triangles--can be reached in 6 steps: for some of these vertices, you have drawn the 6-step paths into the figure. For some of the blue paths, in particular for the ones heading to the lower left, one can simply change the direction of the very last step and one ends up at a corner of the big hexagon, outside of the red circle, in 6 steps just the like. This demonstrates how all vertices of the big hexagon can be reached in 6 steps.

              However, none of these outer vertices can be reached in less than 6 steps; this one can see by simple examination. Hence, the farthest one can go in 6 steps is precisely this hexagon.