Rob Speckins’ research program challenges the standard narrative about what makes quantum mechanics truly “quantum.” Most physicists believe that phenomena like interference, superposition, and entanglement are irreducibly non-classical. Speckins argues that almost all of these can be reproduced by a classical theory with one modest innovation: a fundamental restriction on how much you can know about a physical system. The real quantum innovation, he claims, lies elsewhere—in how causation and inference themselves must be reconceived.
The Leibnizian Methodological Principle
Speckins’ entire approach is organized around a principle he traces to Leibniz: the ontological identity of empirical indiscernibles. If two distinct physical scenarios predict exactly the same empirical observations, a good realist theory should not treat them as ontologically different. Any degree of freedom in your theory that has no empirical consequence should be eliminated.
Leibniz used this against Newton’s absolute space: shifting every particle five feet in absolute space changes nothing observable, so absolute position is not real—only relational positions are.
Einstein wielded this principle twice: in special relativity (eliminating the ether by noting that only relative motion between coil and magnet matters, not absolute motion) and in general relativity (the equivalence principle—no experiment can distinguish a gravitational field from acceleration, so they must be the same physical situation).
Speckins sees this as the most successful methodological principle in physics history and refuses to compromise on it, even when quantum no-go theorems seem to force a choice.
Realism, Empiricism, and Causal Explanation
Speckins is a realist, but of a specific kind. He rejects the empiricist view (associated with Mach and the Copenhagen interpretation) that a theory should only predict experimental outcomes and not attempt to describe reality. He argues that all observation is theory-laden—you cannot even state what an experiment yielded without realist presuppositions.
However, he adopts an operationalist methodology: start from the statistical predictions of quantum theory (what everyone can agree on), then ask what realist story explains them.
His core realist demand is that correlations must have causal explanations. If two variables are correlated, a good theory should tell you whether one causes the other or whether a common cause explains both. This is not mere philosophy—it is the same reasoning used in causal inference in statistics and medicine (e.g., randomized controlled trials to determine whether a drug is causally effective).
He distinguishes causal influence from signaling. A causal influence is a functional dependence where intervening on one variable changes another. Signaling is stronger: it means the influence is not washed out by noise. The Vernam cipher (one-time pad) exemplifies this: the plaintext causally influences the ciphertext (otherwise the recipient could not decode), but an eavesdropper learns nothing because the key adds noise that washes out the signal. This distinction is crucial for understanding how hidden variable models reproduce Bell violations without superluminal signaling.
The Toy Theory (2004)
In 2004, Speckins constructed a toy theory that reproduces much of quantum phenomenology using only classical physics plus one restriction: your knowledge is always incomplete. In this model, pure quantum states are represented not as points in state space but as probability distributions over a classical phase space. Non-orthogonal quantum states correspond to overlapping distributions.
This immediately explains the impossibility of discriminating non-orthogonal states: if two distributions overlap, and the physical state happens to lie in the overlap region, no measurement can tell you which distribution was sampled. This is a fact about classical probability, not a mysterious quantum limitation.
The no-cloning theorem also emerges naturally: copying a probability distribution onto another system while preserving the product structure is impossible when the distributions overlap, because copying the physical state would create correlations not present in a product distribution.
Teleportation, steering, and other quantum information phenomena also have natural classical-probability analogs in the toy theory. Speckins did not put these features in by hand—they emerged from the single assumption of incomplete knowledge.
What the Toy Theory Cannot Reproduce
The toy theory reproduces interference, no-cloning, teleportation, state discrimination limits, and more—but it cannot reproduce Bell inequality violations. This is not a failure of ingenuity; it is a proven no-go theorem.
Bell’s theorem shows that any theory satisfying the “ontological models framework” (hidden variables + Bayesian probability) plus local causality (no superluminal influences) must obey certain inequalities. Quantum mechanics violates these inequalities.
The toy theory satisfies both conditions, so it must obey Bell inequalities. This makes it a useful foil: it tells you exactly which quantum phenomena resist classical explanation even when you allow incomplete knowledge.
Speckins’ conclusion is not that nature is non-local, but that the ontological models framework itself must be abandoned. The real innovation of quantum theory is not non-locality or contextuality per se, but a new framework for causation and inference—just as relativity introduced new frameworks for space and time while preserving recognizable versions of those concepts.
The PBR Theorem and Speckins’ Response
The PBR theorem (Pusey, Barrett, Rudolph) is widely interpreted as ruling out “psi-epistemic” models—models where the quantum state represents knowledge rather than reality. Speckins argues this interpretation is mistaken.
The theorem’s key assumptions include “ontic separability” (the properties of a composite system are just the properties of its parts—no holistic properties) and “independence preservation” (independent preparations produce uncorrelated ontic states).
Speckins argues these assumptions, if applied consistently, rule out both psi-epistemic AND psi-ontic models. Psi-ontic models (like Bohmian mechanics) violate ontic separability because entangled states are holistic—they cannot be decomposed into properties of individual subsystems. So the PBR assumptions, taken at face value, simply rule out the entire ontological models framework, not just the epistemic variant.
The version of the assumption that actually gets the desired conclusion (ruling out only psi-epistemic models) is what Speckins calls the “entanglement-holism link”: entangled states have holistic properties, but product states do not. He argues this assumption is only plausible if you already believe the quantum state is real—it begs the question against the psi-epistemic view, where entangled states are just correlated probability distributions with no holistic properties whatsoever.
His broader point: many no-go theorems against psi-epistemic models rely on assumptions that are either equivalent to the Leibnizian principle (in which case Bell and Kochen-Specker already rule out all ontological models) or are question-begging. The right lesson is to abandon the ontological models framework, not to conclude that the wave function is ontic.
The Hieroglyph Analogy
Speckins compares the current situation in quantum foundations to the decipherment of Egyptian hieroglyphs. For 1,400 years, scholars assumed hieroglyphs were ideograms (each symbol represents a concept directly). This was a category mistake. The symbols were phonetic—they represented sounds in a spoken language (Coptic).
The analogy: just as the cartouches (proper names) were correctly decoded phonetically long before the rest of the system, certain sub-theories of quantum mechanics (Clifford sub-theories) admit natural psi-epistemic, Leibnizian ontological models. These are the “cartouches”—they provide evidence that the quantum state is epistemic, even before we have the full “Coptic language” (the new formalism for causation and inference) that would let us interpret all of quantum theory this way.
The challenge for psi-ontic proponents: explain why these sub-theories admit such natural epistemic interpretations if the quantum state is truly a state of reality. Before Champollion, scholars had an explanation for why cartouches were special (proper names must be sounded out). Speckins has not heard an equally compelling explanation from the psi-ontic side for why Clifford sub-theories are misleading.
Causation, Inference, and the Path Forward
Speckins’ research program aims to “unscramble the omelet” of causation and inference in quantum theory. Classically, causation can be formalized as functional dependencies (category of sets and functions), and inference as Bayesian updating (category of substochastic matrices). These interact cleanly.
In quantum theory, these notions are entangled in the formalism. Speckins believes the key to a realist interpretation is finding the quantum analogs—new mathematical structures for causation and inference that reduce to the classical ones in the appropriate limit, just as relativistic space-time reduces to Newtonian space and time at low velocities.
He does not yet have this formalism. His research program is at the stage of having secure foundations (the Leibnizian principle, the demand for causal explanations) but not yet the full house. He compares existing interpretations to houses built on shaky foundations (they all violate Leibniz in some way), while he has only the foundation.
His oracle question: if he could ask a truthful oracle one question, it would be “How do you unscramble causation and inference in the quantum formalism?” He believes this is the key clue needed to identify the principle that distinguishes classical from quantum theories.
On the Philosophy of Physics
Speckins defends the value of philosophical training for physicists. He did a joint honors degree in physics and philosophy at McGill. The most valuable skill from philosophy is not any particular doctrine but the discipline of making arguments bulletproof—defining terms carefully, identifying hidden premises, and subjecting your own reasoning to ruthless criticism.
He argues that the great revolutions in physics (Newton, Einstein) were driven by people thinking deeply about philosophical questions—the nature of space, time, simultaneity, and observation. Technical sophistication alone produces incremental progress; revolutionary progress tends to require philosophical savvy.
He is often misunderstood. He spends enormous effort writing papers and giving talks that cannot be misunderstood, yet people consistently attribute to him the view that he endorses the ontological models framework. He does not—he studies it as a foil, the way Picasso mastered classical painting before transcending it. The right lesson of all the no-go theorems is to go beyond ontological models, not to pick sides within that framework.
