It from Qubit by Giacomo Mauro D\'Ariano

Dear Cristi

Thank you for your encouragement. You share my opinion that Quantum Theory is too rigid to be changeable just a little, whereas General Relativity is more flexible to changes, e.g. depending on the physical scale. Let me distinguish between Quantum Theory and Quantum Mechanics, the former being the theory of abstract systems (states, observables, transformations, in terms of Hilbert spaces and operator algebra), the latter containing the "mechanics" (i. e. the explicit operator form of the momentum, the particle Hamiltonian, quantization rules, etc.). The "mechanics" is also more flexible to changes, as for GR. In a sense this flexibility is almost a tautology, since Quantum Theory is an abstract theory of systems, hence more general and fundamental, holding for any kind of physics, a sort of "logic" (von Neuman, Mackey and Varadarajan were the first ones to think of it in this way). The "mechanics" and the GR, instead, may have a more restricted validity, e.g. to a physical scale ranging from Fermi (or probably larger) to the galactic one. And I believe that they are both emergent from a more fundamental theory at a tiny Planck scale. What I showed in my joint paper with Paolo Perinotti is that for SR and for the "mechanics" such emergence can be indeed achieved, and, astonishingly, from very basic principles. This is the way of combining the theories that you are mentioning. And SR must have a limited validity, for small momenta (small here means still huge, much larger of those of UHECR's). At a scale approaching the Planck one one start having a space-time that is really quantum, with coarse-grained events, events that delocalize depending on the boost (the relative locality of Giovanni Amelino Camelia and Smolin), and deformed Lorentz transformations, or dispersive-Lorentz (i.e. that depend on the wave-vector).

Thank you again for stimulating this discussion.

My best regards

Mauro

Dear Matthew,

Thank you very much for your interesting and seriously provoking comments. It is always exciting to discuss with you, since you are always touching interesting points at the basis of the full framework and of the way of looking at things.

Why the quantum automata theory is a continuation of my work on QT with Giulio Chiribella and Paolo Perinotti? Simply because the starting point is exactly QT, to which I add simple principles of unitariety, locality, homogeneity, and isotropy. Therefore, to the original six informational axioms I'm just adding these new simple ones (unitariety is reversibility).

The philosophical schizophrenia is indeed only apparent. You can understand how complete consistence is recovered based on the following main three points:

* My operationalism differs from that of Bridgman. Let me call it "informationalism", the basis of the Pavia axiomatization of QT. Beware that my operationalism may currently differ slightly from that of my young coauthors--though I was the one responsible of corrupting them.

* I am not against onthologies, but only against naïve ones;

* SR is operational. But, operationally, the relativity principle is not logically mandatory. On the top of this, GR is no longer operational.

Let's now analyze point by point.

*My operationalism differs from that of Bridgman*

Bridgman was indeed largely influenced by Einstein's SR, and when he started operationalism he was too ahed of his times, and because of this he burnt too fast the whole philosophy, becoming himself responsible of a sudden decline of his own ideas. As his conceptualization gained acceptance at the beginning, and became shaped into a general philosophical doctrine (becoming very influential outside physicists, e.g. in psychology) operationalism started to be regarded as an old-fashioned extreme position, well before it could express its full potential. The method went so far as to become a new extreme "theory of meaning", stating that every concept has to be identified with a set of operations-a protocol. Surely this was not Bridgman's intent, who was primarily interested at articulating the scientific method from a first-person physicist point of view. However, the operationalist approach weakened, and some scientists and philosophers of science came to dislike it. Another strong case against operationalism was that of another of its advocates, Ernst Mach, who got the extreme position of refusing anything else was not just a description of the same observations, denying any value of a description in terms of new ontologies. This led him to his stubborn refusal of the idea of atom and his consequent opposition to the new atomic theory of Ludwig Boltzmann. With the atom soon becoming the greatest paradigm-shift in science, the Mach's obstinate opinion casted a dark shadow on operationalism, putting many physicists on the side of the realist Einstein in his long debate with the operationalist Bohr. We should remember that Einstein himself started as an admirer of Mach, and was operationalist at the beginning of the theory of relativity (the relativity of simultaneity is indeed based on a notion of time corresponding to a precise synchronization protocol of clocks), but years later, when he laid down his equations of general relativity, he betrayed his original operationalism.

My operationalism differs substantially from that of Bridgman, in the sense that what really matters to me is the distinction between the notions that have the "objectivity status" (these are the experimental data, the preparation of the experimental set-ups, the data-reading protocols) and those that, instead, are only part of our theoretical description, and, as such, are not required to have an operational definition in terms of a protocol. This is the case e. g. of the notion of "atom", or that of "particle": their are useful and precisely defined physical objects, but they are not truly operational in all respects. They are useful onthologies, practically quite concrete in the domain of energies and momenta of contemporary physics, however, they are only temporary. As such, ultimately they may emerge from more fundamental theoretical notions, e.g. Gaussian wave-packets of qubit-states at a tiny Planck scale.

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(CONTINUATION FROM ABOVE POST)

Let's analyze my personal "operational" philosophy when applied to the framework of the Pavia derivation of QT. The fundamental notion of the entire framework is that of "test", which is a collection of outcomes, and is represented by a box with wires--"the systems". The outcomes have the objectivity status: a deterministic outcome can be the simple fact that the box is a mirror, or a laser on the optical table. However, the wires--"the systems"--are only partially operational, they are mostly theoretical notions. For example, we put a laser in front of a detector, and the wire here represents the laser beam. It is true that the laser beam can be "seen" in a smoky air, and we can definitely "align" the two boxes by a suitable protocol. But, at the very end, when we represent the wire connecting the "preparation" (laser) with the "observation" (detector), we say that it represents the traveling "photon", and, as such, we cannot "see" it. Such a system is defined operationally only in part, and, indeed, it is mostly a theoretical notion. It is our way of causally connecting the two objective events "laser-on" and "detector-click". The same can be said of the "field mode". Both kinds of systems are the support of the "information", the register where information is written and read. Informationalism coincides with operationalism as long as information means classical data, "outcomes". "States" are preparation protocols (probabilistic equivalence class of them, to be precise), and, as such, they are operational notions. The same applies to "effects" and " transformations". But it is not the same for the "systems". Systems are theoretical notions, and, as such, their specific instance is theory-dependent, e.g. they can be classical bits, particles, field-modes. When we interpret them as causal connections between objective events, they become theoretical notions, since, at least, we need to restrict to causal theories. And, when interpreted as causal connections, they are "subjective", and this subjectivity reconciles my notion of causality with the Humean one.

Thus, in conclusion, "informationalism" is not equivalent to "operationalism" a la Bridgman.

*I am not against onthologies, but only against naïve ones*

As I wrote in my essay, I consider onthologies as powerful ways of thinking, tools for analyzing mechanisms visually and efficiently. But they are only tools, temporary tools subjected to the evolution of theory. They do not "actually exist" as such out there. They are not the real objects casting the "shadows" that we see.

Is it the Planck scale a new ontology? It will become a full ontology when we will clearly understand the whole physics at that scale. Consider for example the existence of mechanisms, as the "relative locality" of Amelino-Camelia and Smolin, where events delocalize depending on the reference frame. The more closely you look at "reality" the more it becomes "blurred". It is not a veiled reality. It is space-time that emerges in this way from quantum systems in interaction. There is no "empty space" filling the gaps between the denumerable entities. Space as we imagine in the current physics is an ontology that must be changed. Space is more as a blurred quantum-digital screen, which gets a huge resolution when you'll look at it from far apart.

*SR is operational. But, operationally, the relativity principle is not logically mandatory. On the top of this, GR is no longer operational*

As was shown by Ignatowski in 1910, Lorentz transformations can be derived from the simple requirements of linearity, symmetry between any two observers, and the Galileo's principle, the latter including homogeneity and isotropy of space and time. Einstein in his more mature derivation of SR used the Galileo principle, applying it also to electromagnetism. The impression that we got from this derivation is that such a fundamental principle is essentially indispensable to do science, that we cannot even state a physical law if it cannot express it in a way that is frame independent. This is not logically necessary. The physical law can be stated in a preferred frame if we know how to change it when changing the frame. Indeed this is what happens in practice, since we cannot avoid using the frame of fixed stars as a reference inertial frame. So, operationalism has not much to do with the relativity principle as such: SR is mostly based on the no-preferred-frame credo. What is truly operational are the Einstein's clock-synchronization protocol and the use of synchronized clocks to establish a full coordinate system by sending light back and forth between events. But such a protocol is strictly classical. In a Planck world you need quantum clocks, you need to send signals of quantum nature, which spread and have intrinsic imprecision.

Just a final comment on GR. The bending of space due to mass is a purely theoretical ingredient needed to mimic gravity: it is no longer just the equivalence principle. As such, GR has no longer an operational basis. Einstein admitted that, and stated that for a formal system to qualify as a physical theory it was "not necessary to demand that all of its assertions can be independently interpreted and 'tested' "operationally" [See "Operationalism on Stanford Encyclopedia of Philosophy"]. Then, allow me to say that the "bendable" space of Einstein is not more ontic than the emerging space of the Planck scale: it is just classical.

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(CONTINUATION FROM THE ABOVE POST)

I am aware that a thorough discussion will need much more space, and I'll be happy to respond to your next feedback. We have here a full conceptual framework in evolution, and this can give rise to apparent schizophrenias. To conclude: I'm an "informationalist": what exactly this means can be roughly inferred from what I said above, but it would need a much longer piece of writing to state it in a way that can confront most of the many possible questions.

It is always a pleasure to discuss with you

My best regards

Mauro

Dear Manuel

Thank you for your interest and form kindly rating my essay.

I'm curious about Bell's superdeterminism, and I will read and rate your essay. I imagine that, however, it would be not possible to experiment it. If I understand what it is, it is a kind of metaphysical assumption. But I need to read your essay before jumping to conclusions.

My best regards

Mauro

Dear Joe,

It seems to me that you are not a realist, and I'm not sure if your are making jokes about the realist point of view, or about Durr.

My best regards

Mauro

Dear Gordon,

Clearly if the Bell theorem would be refuted, it would not be a theorem anymore. Here we are discussing about its interpretation. However, about this, let's judge people from outside.

My best regards

Mauro

Dear Satyavarapu

Compliments for the positive feedback that you got.

I will take a look at your essay.

My best regards

Mauro

Dear Hoang

Thank you for your post, though I have some difficulties in following your line of thought.

My best regards

Mauro

Dear Anton

Thank you for your compliments. There is no problem with teleporting entanglement, since teleportation is entanglement-swapping, you can swap entanglement of the first system and than that of the second system, ending with the two particles entangled. Regarding SR I had already answered to your comment.

Now, regarding your previous post in Matthew thread about SR,

This is similar to what I did: special relativity emerging from a more fundamental theory--the quantum automaton. Dirac is emergent, and Maxwell as well!

Best regards

Mauro

My best regards

Mauro

Dear Anton,

regarding your post in Matthew thread above,

This is similar to what I did: special relativity emerging from a more fundamental theory--the quantum automaton. Dirac is emergent, and Maxwell as well!

Best regards

Mauro

Dear Tom

Thank you very much for your beautiful compliments, and thanks for the citation of the metaphysical realism of Popper espoused from Tarski's correspondence theory of truth. I will come soon to it, since it is a major point for serious science. I also appreciate your last sentence about QT: indeed, I think that it has been rehabilitated to a new mature kind of realism.

My best regards

Mauro

Dear Edwin Eugene,

even though I know that you are a realist opponent of my point of view, I very much appreciate your post, since it allows me to peek more inside the realist's mind, and enrich my arguments. From the fact that I need to tell a tale, made of real objects and persons, in order to help the reader have an intuition of what is "emergent space", you conclude that the world must be really made of objects and matter, since we cannot imagine a world made of pure software without having an intuition made of hardware. You are exactly the incarnation of a "matter-realist" (no offense). You say that, ultimately, my tale represents a process of abstraction, from real things toward mathematical notions. You should just consider that space itself in your view is pure abstraction. And the same is motion. But what is substance then? Quantum theory (QT) thought us a really stunning lesson about reality, and to what extent the lesson is amazing can be realized exactly from your post. A physical theory, QT, is now capable of destroying our most obvious intuition: that of "substance". The matter-realistic substitutes of QT, as the Bohm's theory, are indeed very poor from the materialistic point of view: particles are point-like, their trajectories are indiscernible by definition, and they change instantaneously and non-locally when we locally change the boundary. What is the Bohm's potential made of? Is it what you mean by hardware? Are such abstract point-like particles an hardware? Besides, Bohm's theory is doomed to never be able of achieving quantum field theory. We know that a better interpretation of "substance" is a force field, and that what we feel as substance is indeed empty space (the various kind of "radius" for particles are just heuristic notions). What is then pure energy? What is a field? Is it hardware?

What matter for a theory to be good is to minimize the assumptions to explain everything we see, and in the automata theory, we just assume quantum bits in interaction, and very basic principles, as homogeneity, isotropy, locality, unitariety. My point is that we shouldn't be obsessed by our matter-realism, and we should keep our minds open to simplification of theories, and to a corresponding change of our intuition of how the world is made. We should never forget that our intuition--what somebody calls our "ontology"--is only a powerful tool, and, as such, is temporary. Think in this way: you are wearing powerful glasses that hugely improve your vision, to e.g. a Tera-pixel per microsecond. But your brain is not capable of processing such a large amount of information: it synthesized it, and this is what you actually see. What is your ontology now? What you actually see? Or the full Tera-pixel image?

My ontology is a space-time being a huge 3d digital screen made of quantum pixels. You may not like this new ontology, but my seven-year-old daughter loves it. We must be more open minded, not be crystalized on our old way of looking at things, but look at reality from a new angle, and coherently pursue the new point of view. This always provides new powerful insights.

My best regards

Mauro

Dear Roger,

Thank you for your post. Your compliments and your feedback are very much appreciated. Here my answer, point by point.

1A. About holism, everybody including me will agrees that the whole is not necessarily the sum of the parts. What is not so obvious is that we can still think the whole as composed of parts when properties of the whole are incompatible with any property of each part! What then does it mean to be an object? Does the notion of object make sense without a consistent notion of property?

1B. Allow me to correct your "more fundamental state" into "more fundamental entity", and there are infinitely many entities having all properties still incompatible with some properties of the whole (holism), but that, at least in principle, we can observe locally thanks to local-discriminability of QT.

2. It seems to me that we are on a similar wavelength. I just want to emphasize that I'm using the world "state" the way we use in QT. The state is one (for the whole universe), the systems are many. The specific state is not controlled by the theory: the theory provides only its evolution.

3A. Objects are usually located in space. This doesn't mean that the space location define the object: it is a property of the object. Besides, a moving object is always the same object, it is not a different object at each different time. In this sense a teleported object is the same object moved to another place. The fact that matter is the same everywhere is the indistinguishability of identical particles in QFT.

3B. We agree here that space is made by "relations between things". For me such things are quantum systems, not objects.

Nice to talk with you, Roger

Thank you again

My best regards

Mauro

Dear George,

Thank you very much for the "master as a lector and writer".

I hope my students are not completely spoiled by me.

My best regards

Mauro

Dear Antony

Thank you for your very nice compliments. I really appreciate them.

My best regards

Mauro

Dear Torsen,

Thank you for your very kind appreciation.

Regarding my opinion about geometry, I strongly advise you to take a look of the new geometry coming out from the Geometric-group theory of Gromov. You would love it. Though, it may look as new-age music compared to the classical one of differential manifolds. There are still differential manifolds there. Look at the book of Misha Kapovich https://www.math.ucdavis.edu/~kapovich/EPR/kapovich_drutu.pdf

You would love it!