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Darius M: on 6/22/14 at 9:48am UTC, wrote I think reality how it is in itself is analog, while appearances are...

William Carine: on 7/29/13 at 20:07pm UTC, wrote Hello Mauro, Does the Dirac equation always deal with electron? Where it...

Sridattadev: on 6/9/11 at 19:15pm UTC, wrote Dear Mauro, Congratulations. Are'nt we the quantum computers our selves...

basudeba: on 3/20/11 at 6:23am UTC, wrote Sub: Possibility of manipulation in judging criteria – suggestions for...

Giacomo D'Ariano: on 3/18/11 at 20:31pm UTC, wrote Dear Tobias, I'm sure that the statement of the theorem is correct. I will...

Anonymous: on 3/18/11 at 17:44pm UTC, wrote OK, this may become a very long post... maybe we should switch to email? Or...

Giacomo D'Ariano: on 3/17/11 at 20:54pm UTC, wrote Dear Peter, thank you for your appreciation. I downloaded your paper. It...

Giacomo D'Ariano: on 3/17/11 at 19:51pm UTC, wrote I made another two drawings which describe your theorem. It seems that for...


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December 1, 2022

CATEGORY: Is Reality Digital or Analog? Essay Contest (2010-2011) [back]
TOPIC: A Quantum-Digital Universe by Giacomo Mauro D'Ariano [refresh]
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Author Giacomo Mauro D'Ariano wrote on Feb. 14, 2011 @ 13:07 GMT
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.

Download Essay PDF File

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nikman wrote on Feb. 14, 2011 @ 19:54 GMT
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.

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Giacomo Mauro D'Ariano replied on Feb. 14, 2011 @ 20:57 GMT
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 ...

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nikman wrote on Feb. 15, 2011 @ 00:19 GMT
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?

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Giacomo Mauro D'Ariano wrote on Feb. 15, 2011 @ 13:25 GMT
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"?

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nikman wrote on Feb. 15, 2011 @ 14:39 GMT
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.

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egal wrote on Feb. 15, 2011 @ 16:27 GMT
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…

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Mauro replied on Feb. 16, 2011 @ 13:53 GMT
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.

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Anton W.M. Biermans wrote on Feb. 18, 2011 @ 04:00 GMT
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

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Giacomo Mauro replied on Feb. 21, 2011 @ 06:30 GMT
Dear Anton,

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

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Thomas J. McFarlane wrote on Feb. 20, 2011 @ 08:45 GMT

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?



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Giacomo Mauro replied on Feb. 21, 2011 @ 09:26 GMT
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...

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Thomas J. McFarlane replied on Feb. 25, 2011 @ 04:10 GMT
Dear Mauro,

Thank you for the helpful and detailed response to my question. I understand you as saying an event is simply defined as information in the spaceless here and timeless now. Space and time then arise as ways to organize events in such a way that they are given a spatio-temporal structure. Is this accurate?

If so, it is still not clear to me how information for an event is measured without any reference to space and time. I can imagine a reference frame where local space and time are defined, and then using that to develop a global spacetime structure as Einstein did. But how are the measurements made in the observer's reference frame without even time and space defined for it?

To illustrate, you used the example of space arising from comparisons of the sizes of an image on the retina. But the measurement of size on the retina seems to presuppose space. And the example of time arising from comparing clock measurement now with clock measurement of a memory also seems to presuppose a temporal distinction between the now and the past memory. It also seems to presuppose space to measure the movement of the clock's dials in space.

Your further clarification would be appreciated.

Best regards,


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Jacek Safuta wrote on Feb. 21, 2011 @ 21:43 GMT
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,


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Mauro replied on Feb. 24, 2011 @ 06:49 GMT
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


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Jacek Safuta replied on Feb. 24, 2011 @ 18:34 GMT
Dear Mauro,

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


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Tobias Fritz wrote on Feb. 22, 2011 @ 17:55 GMT
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.

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Mauro replied on Feb. 24, 2011 @ 06:45 GMT
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!


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Tobias Fritz replied on Feb. 24, 2011 @ 12:10 GMT
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.

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Mauro replied on Feb. 24, 2011 @ 16:55 GMT
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!


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Anonymous wrote on Feb. 27, 2011 @ 16:18 GMT
Very nice presentation (clear and well written), congratulations!

However, I'm having some problems understanding how space-time (time in particular) can emerge from the causal structure of the network: I really don't see how you can define "cause" and "effect" without the notion of "time", because a cause must by definition precede IN TIME an effect. (Of course there are also other further requirements for such definition.)

In other words, it seems that the clock time tau of the computation of the quantum computer is "sneaked in" to constitute the elementary building block of time, which then does not really emerge, but it is "sneaked in". [By "clock" here, I mean the clock in a computer, namely the time it takes for a single elementary operation to complete, which in normal computers gives the processor speed.]

I have similar concerns also for the emergence of space.

Probably I'm missing something! Thanks in advance for the clarifications...

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Mauro replied on Feb. 28, 2011 @ 20:16 GMT
Dear Anonymous Reader,

thank you very much for your kind appreciation!

Here's the point that is needed to understand the emergence of space-time from the causal network.

First, causality must be defined in a way that is independent on the arrow of time: otherwise, you cannot consider even the mere possibility that information could be sent from the future. Or, equivalently: you cannot even imagine the possibility of time-travel!

Causality is defined in my Ref. [8] (and also in [10]) without reference to time. There you have events in input-output connection: causality is the assumption that the marginal probability of any event does not depend on the set of events connected at the at its output. We then assume the time-arrow coincide with the causality arrow, i.e. with the in-out direction. In short: cause and effect are defined simply through an asymmetric dependence of marginal probability.

The emergence of time (as well as space) should now be regarded as the emergence of the Minkowsky "metric" from pure "topology" through event-counting. And this can be done via building-up of foliations over the quantum circuit. The time tau and distance a are just the digital-analog conversion from pure dimensional numbers (event counting) to the usual seconds and meters.

I hope that I answered your question!

You can convince yourself that space-time is always referred to events (not that events happen within space-time), by taking the lesson from Einstein literally: time and space must be defined operationally through measurements. Then, ultimately, each measurement is referred to a single observer, the AYPT (at your place and time) through an history of previous observations (please, read my answer to Thomas). Thus whatever happens in the four-dimensional Minkowsky space-time is precisely contained in a zero space-dimensional local memory. It is like the stream of bits of a 3D movie.

Let me know your opinion now!



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Anonymous replied on Mar. 2, 2011 @ 09:51 GMT
Thanks for the clarification! I'm still a little confused though. If events are "facts of the world describable by the basic language obeying the rules of predicate logic", I'm not sure how I can assign a probability to an event (and hence calculate a marginal). The event either happens, or it doesn't happen. Probabilities pertain to our predictions only (namely to our ignorance of some fact). What exactly do you mean by "probability of an event"?

Also, when you speak of the events connected to the input and to the output, you are implying that the input happens before (IN TIME) than the output. I would say that is implicit in the notion of input-output. Can you instead define input and output without resorting to time?

In other words, I'm sorry, but still don't see how you can relate events without assuming time...

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Mauro replied on Mar. 4, 2011 @ 06:07 GMT
Dear Anonymous,

From your answer I infer that for you the impossibility of time-travel is a tautology, still many authors believe that time-travels are possible!

In a time-travel the input is in the future and the output is in the past...


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Guilford Robinson wrote on Mar. 11, 2011 @ 17:51 GMT

I enjoyed reading your article. I have been interested in how the quantum computer would combine the digital and the analog properties.

Relative to the mass-dependent refraction index of the vacuum, what would the effect be if there is a different Planck mass employed? One that is on the order of the mass of the electron and the mass of the proton--at the same time, keeping the Planck length. See my article, and review the connection of the Planck length realm and the election-proton realm.

Guilford Robinson

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Author Giacomo Mauro D'Ariano replied on Mar. 15, 2011 @ 23:48 GMT
Dear Guilford,

thank you for your interest and your compliments! I just downloaded your paper: I'll take a closer look at it (it doesn't look easy to follow at first sight).

The refraction index of vacuum is a function of the ratio between the Compton wavelength and the distance 2l between two next neighbor in-out independent gates, and the same ratio expressed in terms of mass ratio gives the Planck Mass if you take 2l equal to the Planck length. One would need indeed another good reason to chose 2l as the Plank length: the only thing that I can say is that it is the minimum distance in principle between causally independent events. Clearly, if you take 2l larger than the Planck length, you may incur in imaginary refraction indexes (corresponding to absorption?) which is odd. Whence the Planck mass must be the largest possible mass of the field, and information halts at such mass value!

I hope that this is what you were looking for. Please let me know.

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Peter Jackson wrote on Mar. 16, 2011 @ 00:17 GMT
Dear Guacamo

In a last minute 'trawl' of essays I hadn't read I was pleased to come across yours. Your clear and lucid description of a quantum computer was very interesting and refreshing, and a new angle on my own model.

I hope you'll read my rather analogue version of what seems to be QC=SR, entirely equivalent, explaining special relativity logically with a quantum mechanism and deriving Equivalence with a = g.

Probably too late for you to vote now, but I'd like your take on it anyway. The lower string gives some good analogies.

Best wishes


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Author Giacomo Mauro D'Ariano replied on Mar. 17, 2011 @ 20:54 GMT
Dear Peter,

thank you for your appreciation.

I downloaded your paper. It looks very nice, but with a lot of physics that I cannot check myself.

Best regards,


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basudeba wrote on Mar. 20, 2011 @ 06:23 GMT
Sub: Possibility of manipulation in judging criteria – suggestions for improvement.


We had filed a complaint to FQXi and Scienticfic American regarding Possibility of manipulation in judging criteria and giving some suggestions for improvement. Acopy of our letter is enclosed for your kind information.

“We are a non-professional and non-academic entrant to the Essay...

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Sridattadev wrote on Jun. 9, 2011 @ 19:15 GMT
Dear Mauro,

Congratulations. Are'nt we the quantum computers our selves hooked in the network of the universe?

who am I?

I am virtual reality, I is absolute truth.

I am a quantum computer, I is the network.



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William Amos Carine wrote on Jul. 29, 2013 @ 20:07 GMT
Hello Mauro,

Does the Dirac equation always deal with electron? Where it does, is there an upper limit of how much energy or information it can have, a point that to go above or further would be a violation of some principle or mathematical sense?

Thanks for directing me back to your other two essays.



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Darius M wrote on Jun. 22, 2014 @ 09:48 GMT
I think reality how it is in itself is analog, while appearances are digital.

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