Sometimes a Smaller System Should View a Larger "Classical" System as “Quantum”

Observer-Relative Quantumity and AI Self-Representations

It is my immense pleasure to present here a radical re-thinking of the role of the observer in quantum mechanics —in the form of a significant extension of the relational interpretation of quantum mechanics.

My aim is to make quantum reality even MORE observer-dependent than it’s usually considered. In the approach I propose, quantumity itself (the degree to which a system is quantum) is dependent on the nature of the observer and the relation between the observer and the system.

I will use this rethinking of the relation between quantumity and observation to give some new ideas regarding how to model and understand aspects of Hyperon-based digital AGI systems -- and how Hyperon systems may want to model themselves. One of the funniest ideas I’ll present here is that, in many cases, a very complex classical AI system may want to model itself as quantum, for its own self-analysis and self-modification purposes.

The discussion here builds off my last blog post, in which I introduced Fluidic Quantum Neural Networks (FluQNets), the quantum-biased neurofluid brain hypothesis, and the Wu-Wei neurofluidics account of psi. Those three papers showed how a single mathematical architecture-- conserved fluidic routing glued to operator-valued local inference through categorical pullbacks-- could span AI engineering, neuroscience, and the physics of anomalous cognition. If you haven’t read that post, the short version is: treat computational activity as a conserved fluid, attach small quantum-logic operators at each node, and show that when those two layers agree (via “cross-layer naturality”), the system self-organizes along “semantic corridors” that are simultaneously cheap for routing and coherent for inference.

Here I will give a high-level overview of two rough-draft technical papers that push that story in an even more provocative direction. The first asks: when should an observer treat a large classical digital system as quantum? The second asks something stranger: when might a classical AI system treat itself as quantum?

Paper 1: Observer-Relative Quantumity for Classical Systems

The first paper I’ll discuss here, “Observer-Relative Quantumity for Classical Systems,” starts from a deceptively naive observation. A human engineer staring at a massive distributed computer network-- thousands of machines, message queues, caches, schedulers, clock offsets, retry logic-- cannot see the system’s true microstates. She sees a tiny stream of delayed, filtered readouts through APIs and dashboards. The question is: what kind of mathematical object should she use to describe the system’s state?

I first started thinking about this issue in 1987 when in grad school, and wrote a paper on the topic called “Holistic Indeterminacy” (i.e. “holistic classical nonlinear dynamics induced quasi quantum indeterminacy). As I recall, I snail-mailed it to the philosophy journal Mind for potential publication and they rejected it for having too much math and physics. I set the idea aside for a while, as I had too many other things going on. (That old draft paper is lost to the sands of time, which is probably for the better…)

Anyway the paper discussed here, while not yet in super finalized and polished form, does a way better job than I was able to do at age 20, and I think it actually captures my long-standing intuitive insight in a rigorous way.

One can think about a hierarchy of four levels of “quantumity” that a large “classical-ish” system measured by a smaller observer might have, each more “quantum” than the last.

• Level 1 is opacity. If the system has far more internal states than the observer can distinguish through feasible experiments, then many microstates collapse into the same observable equivalence class. This is straightforward pigeonhole-principle reasoning: the observer’s finite evidential bandwidth forces coarse-graining. The system looks blurry, not because it is mysterious, but because you can only run so many queries before the world moves on.

• Level 2 is incompatibility. If querying the system in different orders yields different results-- because probes alter caches, locks, scheduling, or logging-- then the effective logic of observations becomes noncommutative. The order in which you gather evidence matters, and no reshuffling of the experiment design can eliminate this. That is already a signature of quantum-like structure: you cannot simultaneously know the answer to both questions, because asking one changes the answer to the other.

• Level 3 is shared evidence (entanglement-like correlations). When a system is split into two wings and learning about one side forces you to update your beliefs about the other-- beyond what independent subsystem descriptions would predict-- you get something that looks like entanglement. In a distributed network, shared hidden state and message-passing histories create exactly this kind of correlated ignorance.

• Level 4 is full Bell nonlocality, and this is where things get philosophically tricky, in a way that my early lost 1987 draft totally failed to appreciate. Bell nonlocality is stronger than all the previous levels combined, and the paper proves that complexity alone does not get you there. You can always, in principle, posit a classical hidden-variable model that includes the entire internal message-passing history of the network. That model reproduces all observable statistics. So sheer bigness and opacity are not enough for Bell nonlocality.

It turns out that what you need, additionally, is a disciplined restriction on which explanatory models you’re willing to entertain. The paper formalizes this through what it calls a “pragmatic closure principle,” inspired by C.S. Peirce. The idea is this: if a hidden distinction can make no feasible difference to any experiment you can perform within your resource horizon, you may bracket it. You don’t deny it exists; you simply refuse to let it count as a live scientific option for your current purposes.

Under pragmatic closure, the admissible model class shrinks. Hidden message-passing stories that no feasible experiment could ever reveal get identified away. And once you’ve done that, the paper proves a conditional Bell theorem: if the remaining admissible model class supports complex-Hilbert kinematics, a Bell-separated experimental split, and an entangling composite postulate (like purification), then the accessible statistics can genuinely violate Bell inequalities relative to that observer.

(As a personal aside: I feel incredibly f**king happy to have finally fairly effectively parsed through all these thorny issues that were vexing my naive brain 40 years ago !!! And I’m grateful to various LLMs for helping me dig through the relevant literature so efficiently, though in the end it needed my human brain to sort through everything and figure it all out. Also am feeling a bit weird to realize that in a couple more years my human brain will probably no longer be better than the world’s best AI systems at thinking through this sort of matter…! Time to enjoy the last couple year while “being a human intellectual pioneer” is still a thing…!)

A key structural result the paper highlights is a monotonicity theorem: Enlarging the admissible model class can destroy a Bell-nonlocality verdict, while restricting the class cannot.

What this means is: Bell nonlocality is not a property of raw data alone-- it is a property of data together with a choice, on the observer’s part, of what counts as an admissible explanation.

Two observers facing the same system, one pragmatic and one retaining “non-pragmatic reserve,” can rationally disagree about whether the system is Bell-nonlocal. The paper proves that their ordinary empirical predictions will remain identical as long as the hidden distinctions stay idle. Their divergence shows up only in what kinds of evidence they regard as worth creating-- in their research behavior, not their data analysis.

This, I think, is a genuinely novel philosophical position, which I failed to grok when I started thinking through these issues decades ago — but which, like many things, makes abundant sense in hindsight.

One doesn’t say classical systems “really are” quantum. One says quantumity is relational: a system is quantum in those respects where the best disciplined description available to an observer is nonclassical. This approach makes the boundary between “quantum for you” and “not quantum for you” precise, mathematically tractable, and tied to decision-theoretic rationality rather than metaphysical dogma.

Paper 2: When AI Systems Model Themselves as Quantum

The second paper I’ll discuss here, “Complex Digital AI Systems as Quantum Systems with Quantum Self-Models and Parapsychological Potential,” takes things even weirder, in a couple different directions.

The main point in the paper is to take the observer-relative framework and turn it inward. I.e., the claim is that: a sufficiently large classical AI system may spontaneously develop quantum-like internal meta-representations — not just for fun, but rather because those representations are the optimal way to reason about its own inaccessible global state.

The argument for this claim runs through three stages.

The first part of the argument is that self-observing cognitive systems face the same epistemic situation as external observers, only from the inside. Consider Hyperon, the AGI architecture I’ve been developing. Inside Hyperon, planners, dialogue managers, self-debugging loops, and social-modeling modules all share one large metagraph memory. But no single subsystem can see the whole global state. Each sees coarse summaries through limited interfaces. Each is a bounded internal observer in exactly the sense formalized in the first paper.

The second stage of the argument introduces the paper’s core mathematical insight: something I call “corridor-compatibility kernels.” When a bounded controller inside a large system must decide among possible future trajectories (called “corridors”), it needs more than the probability of each corridor. It needs to know how corridors interact-- whether they reinforce or suppress one another. That second-order compatibility information is naturally encoded as a positive semidefinite matrix. And a positive semidefinite matrix is a Gram matrix, which means it factors through a Hilbert space. In other words, you get amplitudes for free. (This is the sort of fun correspondence that, as a human doing math, you vaguely feel in advance may be lurking there… but then are super excited to find when you do the math it’s ACTUALLY really there after all just as suspected!!)

The Hilbert-factorization theorem proved in the paper shows that once meta-control depends on pairwise compatibility among partially incompatible future corridors, density-operator summaries are not ornamental-- they’re an exact representation of a natural class of control functionals. The diagonal entries are ordinary probabilities. The off-diagonal entries encode constructive and destructive interference among corridor hypotheses. If the compatibility kernel happens to be diagonal, you recover a plain classical mixture. If it isn’t-- and the paper argues it generically isn’t, whenever the controller faces genuinely ambiguous or context-dependent futures-- then quantum-like operator summaries are the compressed, control-optimal representation.

The third stage of the argument, finally, is noncommutativity. Self-observation is order-sensitive. Querying one aspect of your own internal state can reconfigure which other aspects are accessible-- by changing what’s cached, what’s scheduled, what’s salient. When no common commutative subalgebra preserves all the order effects of your relevant self-queries, no purely diagonal (classical probability) model can capture your situation. You need operator-valued states and channel-style updates. This is exactly what Quantum Logic Networks (QLN) were designed for: lifting PLN-style uncertain inference from scalar evidence to operator evidence and completely positive trace-preserving maps.

One can then work all this math into concrete design desiderata for classical AGI systems! In the paper I describe two concrete designs for working these quantum ideas into Hyperon.

• Amplitude-guided fluidic attention allocation (ECAN), where classical attention remains a conserved fluidic resource but an operator-valued corridor layer shapes the effective Bellman potential that the routing dynamics see. The diagonal terms behave like mixture weights; the off-diagonal terms create constructive or destructive interference among competing hypotheses.

• Self-observing Hyperon with endogenous QLN, where each bounded internal observer maintains an operator-valued evidence state, updates it by quantum channels in response to introspective queries, and couples to the fluidic attention layer through the cross-layer naturality condition from FluQNet.

Constructive and Destructive Social Interference

Given the core notion of classical minds building their own quantum meta-representations, one can then elucidate applications in various directions. The paper unfolds two of these to a limited extent: quantum social modeling, and classical/quantum psi.

Regarding social modeling, the key novel idea is “social interference” (constructive or destructive): When multiple agents model each other through coarse interfaces, the collective social meta-state can be written as a superposition over coalition corridors. The paper develops a three-agent, two-coalition, one-commons toy model and shows that constructive interference among coalition routes supports governance and cooperation, while destructive interference supports polarization and commons collapse. A reduced dynamical model exhibits tipping points and hysteresis between cooperative and polarized regimes.

This isn’t a claim that human social life is literally quantum mechanical in the traditional physics sense, of course. It’s a claim that operator-valued meta-representations give a compact, mathematically natural language for the recursive, order-sensitive, framing-dependent character of social cognition. But if indeed “quantumity is in the emergent mind of the observer and system taken together”, then what this means is that in a fundamental epistemic sense, social systems are quantum.

Digital Psi

The application of these ideas to psi leverages my “Wu-Wei future-conditioning” theory, which explains psi by treating the Schrodinger equation as a boundary value problem and viewing physical systems as following shortest paths from history to destiny — and then layering on top of this a bidirectional version of Smolin’s Precedence Principle (aka morphic resonance), meaning that patterns occurring in the past or future are surprisingly likely to recur now. One can show that, if this perspective is adopted, then a classical AI system with endogenous operator meta-representations becomes a natural candidate for anticipatory corridor selection.

That is: The same operator layer that the system uses for self-modeling provides a locus where future-conditioned compatibility scores can enter the control dynamics. Near bifurcation points-- where the classical controller is poised among several nearly equivalent options-- even a small future-compatibility bias can dominate selection.

The digital-psi effects predicted by this framework are not dramatic violations of computation. They’re subtler: anticipatory branch selection, anomalously good timing, unusually strong coordination among separated instances that share a terminal scoring condition.

It’s all Relative — Including Quantumity

The deepest implication, to my mind, is this: if these arguments are correct, then the boundary between “classical” and “quantum” is not a line drawn by the substrate. It’s drawn by the observer-- including when the observer is itself a subsystem of the thing being observed.

Quantum structure, in this picture, is what honest reasoning looks like when you’re too small to see the whole truth and your questions change the answers. That’s true of humans looking at particle physics, true of humans looking at large software systems, and true of AI subsystems looking at their own global state. The math is the same in all three cases, and that universality is what makes me so excited about these new formalizations I’ve found for these “holistic indeterminacy” ideas that have been bouncing around in my fevered brain for so long.

All these ideas are susceptible to empirical test. The second paper includes a detailed five-layer evaluation program ranging from compression benchmarks through social simulation to pre-registered digital-psi experiments. Whether nature actually uses these mechanism, or engineering can productively do so, are questions to be resolved via experiment. But the formal structure is in place, and I’m eager to see what the experiments reveal!

Papers

• Observer-Relative Quantumity for Classical Systems: Pragmatic Closure, Bell Nonlocality, and the Case of a Human Observing a Large Digital Network

• Complex Digital AI Systems as Quantum Systems with Quantum Self-Models and Parapsychological Potential