The Schrödinger-Bell Model of AGI

Image by Dmitry Buterin

In order to take a measurement, the subject pretends to become a physical object and entangles herself with the object of measurement. Of course, such entanglement can only be imaginary. In this sense and only in this can we call the observer a physical system. Furthermore, “the boundary between the observed system and the observer can be displaced arbitrarily”. [1]

I had to re-read the chapter The Measuring Process in John von Neumann’s book The Mathematical Foundations of Quantum Mechanics” several times to understand this.

The problem arises when we believe that quantum entanglement occurs in the individual mind of the scientist who makes the measurement, because the process taking place in her mind has very specific consequences in the physical world — in objective reality that, by definition, should not depend on the subject. That is why Eugene Wigner wrote that quantum mechanics refutes monism in the form of materialism and corresponds to solipsism. A subject, of course, can influence even objective reality, if the latter exists only in her mind alone. This is quite logical. [2]

The problem arises again if we allow the existence of many other consciousnesses that all have the same version of objective reality. How do the changes that one consciousness makes to its objective reality appear in other consciousnesses?

I would really like to say that individual consciousnesses interact with each other using matter and energy as mediums, but each consciousness has its own matter and energy in its individual version of objective reality.

What did Gottfried Leibniz write in his Monadology in 1714? “The monads have no windows through which something can enter or leave.” [3] Exchange of information between individual consciousnesses is impossible. Leibniz’s monads synchronized their objective realities according to some Divine emanation.

Erwin Schrödinger considered the theory of monads absurd and proposed taking the concept of a single consciousness from the Upanishads. [4]

Wigner did not accept Schrödinger’s proposal and became interested in the concept of decoherence of Hans-Dieter Zech, who, following Hugh Everett, decided to improve the theory of Leibniz’s monads, adding to each monad a whole set of copies-monads, for which the objective reality is different. Then Divine emanation is not needed because all possible variants of objective reality are each present in their own copy of the monad. Copies of monads, like the monads themselves, also cannot exchange information with each other, naturally. [5,6,7,8]

It turned out to be an extremely clumsy design. Along the way, Newton’s principle that the laws of nature do not depend on the initial conditions had to be demolished.

John Bell, following Einstein, approached the solution of the problem from a clearly materialistic position. He decided to prove that it was possible to create a completely materialistic scientific theory that describes a process independent of the subject’s consciousness, which will completely duplicate the measurement process in quantum mechanics.

As a result, he proved the opposite. There cannot be a materialistic theory that could replace quantum mechanics. [9] Bell’s conclusion was confirmed experimentally three times by three teams of scientists with a step of ten years. In 2022, those of them who survived received the Nobel Prize for their achievements.

Along with the inequality that made him famous, Bell incidentally solved the problem of measurement theory in the Copenhagen interpretation of quantum mechanics (which is exactly what von Neumann described in his book mentioned above). Let’s “imagine, in the context of the orthodox approach, a sort of ultimate observer, outside the world and from time to time observing its macroscopic aspects. He will see in particular other, internal observers at work, will see what their instruments read, what their computers print out, and so on. In so far as ordinary quantum mechanics yields at the appropriate level a classical world, in which the boundary between system and observer can be rather freely moved, it will be sufficient to account for what such an ultimate observer would see.” The measurement results are registered in the mind of such an observer. This is the unitary subject that acts as an imaginary physical observer in all measurements. Therefore, changes in the unitary consciousness of such the ultimate observer render objective reality that is the same for all local (‘internal’ according to Bell) observers.

Bell also wrote done a formula for what the world would look like in the mind of this ultimate observer. He did not try to change his views to idealism. He did not study philosophy, but physics, and simply imagined what quantum mechanics should look like in order to become complete and remain consistent. [10]

I think Everett pushed him to this idea by replacing the past with memory in his monads.

Bell rejected the idea of splitting worlds, but considered the idea of replacing the past with memory logical, although he did not like it, as a materialist. The past is the memory of the ultimate observer, it turns out. [11]

As a result, we get a single consciousness that is present in all local observers and pretends to be physical objects in order to make measurements. In the process of measurement, it gets entangled with the measurement object in order to obtain all possible values of its parameters, and then selects a particular value — a branch for restoring the wave function of the separate measurement object. In the same way it restores the pure wave function itself and of the entire world because the measurement object before got entangled to the entire world through the entanglement with the measuring instrument. At the moment of choosing a branch, they all unravel, and then become entangled again only in a slightly different configuration than before the measurement.

Click! And the frame of objective reality changed. Click! Changed again. But it is impossible to measure continuously because then the frames will not change. Therefore, only discrete measurements work frame by frame. Alan Turing already saw this and formulated into his quantum Zeno paradox. [12]

This way the movie goes on. I wonder what the frame rate of the Universe is?

Conclusion:

Observable reality in quantum mechanics is a series of discrete observations — discontinued frames which are connected by the state vector — a mental process that establishes continuously a deterministic maximal catalog of expectations containing all possible outcomes of future observations (process 2 according to von Neumann) and discontinuously — delivering a probabilistic matrix of expectations of frequencies with which all that outcomes can be observed in the future (process 1 according to von Neumann).

Therefore, the world of quantum mechanics consists of two realities: (1) observable reality and (2) unobservable reality. Continuous unobservable reality transforms in discontinuous portions into discrete observable reality.

Objective reality in classical physics is continuous regardless of observations. Unobserved reality in classical physics is exactly the same as observed.

Given the above the two theories (quantum mechanics and objective reality) aren’t fully compatible. For this reason, from the point of view of classical physics quantum mechanics seems to be incomplete and vice versa.

However, the important difference is that quantum mechanics can duplicate objective reality but objective reality can’t duplicate quantum mechanics. It leads us to the conclusion that objective reality as a theory is incomplete and secondary compared to quantum mechanics.

Quantum mechanics dramatically expanded our knowledge of objective reality: nuclear fission, nuclear fusion, transistors, quantum entanglement, quantum tunnelling, antimatter and more — could not be discovered but for quantum mechanics.

Objective reality is incomplete because the observer, the subject, is excluded from it for the sake of making it objective.

Quantum mechanics does not only include the observer into its reality but it places both the observer and and the observable reality into the contents of the mind of the observer. That is why the boundary between them can be arbitrarily displaced as von Neumann postulated.

Knowledge is the pure content of mind. Unlike the information processing in objective reality, pure knowledge doesn’t require matter or energy for its manipulations in the mind. Pure thinking exists. Purely manipulating knowledge we can find new ways to manipulate energy and matter, which can’t be derived from manipulating information, energy and matter in objective reality. That is the first of the two most important takeaways that we should get from quantum mechanics.

AGI as a thinking machine should, atop of mimicking information processing with the mathematical apparatus borrowed from thermodynamics, be capable of pure thinking that can currently be modelled only by quantum mechanics.

The second takeaway is even harder to swallow than the first one especially to adherents of all kinds of materialistic and idealistic religions.

In objective reality, ‘the world as it is’ placed outside of the mind of the observer resolves the paradox of many minds experiencing one world. This approach can’t be applied to quantum mechanics without breaking it. Therefore a new resolution of the ‘many minds — one world’ paradox was required. Schrödinger from a philosophical standpoint and Bell as a thought experiment proposed the solution of ‘the unitary subject — the ultimate observer’ postulating that there is only one mind present in all local observers.

The most interesting implication of this hypothesis from the AGI standpoint is that the mind of a human being or of a cell of a human body, or of a bacterium, or of Lord God, Himself, is qualitatively exactly the same. The difference is only quantitative. The capacity of the mind in local observers is determined by the bandwidth of the local access channel as well as by locally stored memories and expectations.

The consequences of such an approach are, on one hand, mind blowing: when we are exploring even the primitive mind of an Escherichia coli bacterium we are actually tinkering with the mind of God. On the other hand, assuming such a hypothesis opens to us so far the most thrilling and promising way to AGI as well as to the new frontiers in science and humanity. It is very important, however, to never forget that here we are talking just physics, not philosophy, theology or information theory.

References:

1. Neumann, John von, and Robert T. Beyer. Mathematical Foundations of Quantum Mechanics: New Edition. Edited by Nicholas A. Wheeler. NED-New edition. Princeton University Press, 2018. https://doi.org/10.2307/j.ctt1wq8zhp
2. Wigner, Eugene (1995) Remarks on the Mind-Body Question. In: Mehra J. (eds) Philosophical Reflections and Syntheses. The Collected Works of Eugene Paul Wigner (Part B Historical, Philosophical, and Socio-Political Papers), vol B / 6. Springer, Berlin, Heidelberg.
3. Leibniz, Gottfried. The Monadology, 1714, English translation by Robert Latta, 1898.
4. Schrödinger,Erwin. Mind and Matter, 1959, Cambridge University Press, Cambridge.
5. Wigner, Eugene P. The Glorious Days of Physics, Quantum Optics, Experimental Gravity, and Measurement Theory, 1983, Plenum Press, New York
6. Zeh, H.-Dieter, The strange (hi)story of particles and waves, 2018, arXiv:1304.1003v23 [physics.hist-ph], https://doi.org/10.48550/arXiv.1304.1003
7. Everett, Hugh, “Relative State” Formulation of Quantum Mechanics, Rev. Mod. Phys. 29, 454 — Published 1 July 1957, DOI: https://doi.org/10.1103/RevModPhys.29.454
8. Everett, Hugh, The Theory Of The Universal Wave Function, The Many-Worlds Interpretation of Quantum Mechanics, Princeton University Press Princeton, New Jersey, 1973
9. Bell, John S. On the Einstein Podolsky Rosen paradox. Physics Physique Fizika 1, 195 — Published 1 November 1964
10. Bell, John S. Quantum mechanics for cosmologists. In: Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. 2nd ed. Cambridge: Cambridge University Press; 2004:117–138. doi:10.1017/CBO9780511815676.017
11. Bell, John S. The measurement theory of Everett and de Broglie’s pilot wave. In: Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. 2nd ed. Cambridge: Cambridge University Press; 2004:93–99. doi:10.1017/CBO9780511815676.013
12. The mathematician Robin Gandy recalled Turing’s formulation of the quantum Zeno effect in a letter to fellow mathematician Max Newman, shortly after Turing’s death:

“[I]t is easy to show using standard theory that if a system starts in an eigenstate of some observable, and measurements are made of that observable N times a second, then, even if the state is not a stationary one, the probability that the system will be in the same state after, say, one second, tends to one as N tends to infinity; that is, that continual observations will prevent motion. Alan and I tackled one or two theoretical physicists with this, and they rather pooh-poohed it by saying that continual observation is not possible. But there is nothing in the standard books (e.g., Dirac’s) to this effect, so that at least the paradox shows up an inadequacy of Quantum Theory as usually presented.”

— Quoted by Andrew Hodges in Mathematical Logic, R. O. Gandy and C. E. M. Yates, eds. (Elsevier, 2001), p. 267.