A Quantum-Digital Universe by Giacomo Mauro D\'Ariano

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"?

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.

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...

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

Dear Anton,

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

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.

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.

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.

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,

Tom

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...

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!

Cheers

Mauro

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...