Jacob Barandes proposes a radical rethinking of quantum mechanics — no wave function, no many worlds, no collapse problem. Just probability, seen clearly for the first time.
B.A. Columbia University · Ph.D. Harvard University (Physics)
Jacob Barandes occupies a rare position: genuinely bilingual in both physics and philosophy, holding appointments in both departments at Harvard. He teaches graduate general relativity, advanced electromagnetism, and philosophy of quantum theory — often to the same cohort of students.
He did not set out to find a new interpretation of quantum mechanics. He was preparing to teach QM to undergraduates without linear algebra or complex numbers — trying to build a bridge between classical probability and the quantum world — and inadvertently stumbled into something far deeper.
"Without some form of realism, science undermines itself. You can't have emergence without a substrate. You can't do experiments without measurement outcomes existing in some sense."
He founded and organizes the Foundations of Physics @ Harvard seminar series and the New England Workshop on the History and Philosophy of Physics — building communities where the two disciplines speak honestly to each other.
Quantum mechanics makes the most precise predictions in the history of science — and yet nobody agrees on what it means. Every proposed interpretation carries a fatal philosophical or physical cost.
Tells you to shut up and calculate. Refuses to say what is real between measurements. Breaks down entirely at the quantum-classical boundary (Wigner's Friend).
Avoids collapse by branching the universe infinitely at every quantum event. Cannot derive the Born rule from a purely deterministic picture. Requires infinitely many unobservable worlds.
Restores particle trajectories with a "pilot wave." Elegant for non-relativistic particles, but cannot handle relativistic quantum field theories — cannot even explain why the sky is blue.
Introduces spontaneous wavefunction collapse as an explicit new physical mechanism. Adds unexplained parameters and has no clear relativistic extension.
Barandes argues that all these approaches share a hidden assumption — and that dropping it dissolves the problems rather than papering over them.
Barandes' central discovery: quantum theory and classical probability are not separated by anything mysterious. They are separated by exactly one assumption — Markovianity — which classical stochastic processes satisfy and quantum systems do not.
A Markovian process is one where the future depends only on the present state — not on how you got there. A coin flip is Markovian: it doesn't care what happened before.
Barandes introduces indivisible stochastic processes: ones where you cannot even define what the system is doing at intermediate times. The law only tells you how things evolve over a whole interval, not moment to moment.
If you allow indivisible stochastic processes, you get all the strange features of quantum mechanics — interference, superposition, entanglement, the Born rule — for free, as mathematical consequences.
The wave function? Not a real physical object — a mathematical bookkeeping device. The particle always has a definite location, evolving under indivisible stochastic laws.
The measurement problem? Dissolved: a measurement is an interaction that creates a new division event. No mysterious collapse, no observer required.
The double-slit experiment? The particle always goes through one slit. The interference pattern arises not because the particle is a wave, but because the indivisibility of its dynamics makes it impossible to split the evolution into "which slit" then "where it lands."
The wave function is demoted to a convenient tool — like the luminiferous aether, useful historically but not fundamental.
Systems always have definite configurations. Schrödinger's cat is always alive or dead. Superposition is classical probability over real states.
No "quantum probability." Just regular probability extended to indivisible processes. Hilbert space is a representation, not fundamental reality.
Measurement is an ordinary physical interaction. No special role for observers, no collapse. It creates a division event in the stochastic process.
The central theorem: every quantum system maps onto an indivisible stochastic process in a classical configuration space, and vice versa.
A stochastic process is described by a transition matrix Γ(t←0), where Γij gives the probability of transitioning from configuration j to i. For a Markovian process, matrices compose step-by-step. An indivisible process is one where this composition fails at intermediate times.
Any indivisible stochastic process can be embedded into a larger unistochastic system — one whose transition probabilities are modulus-squares of a unitary matrix Θ:
Γij(t ← 0) = |Θij(t ← 0)|²
The entries of Θ are complex numbers — and the space they live in is the Hilbert space. It emerges as a mathematical convenience, not fundamental reality. Observables split into be-ables (genuine properties) and emerge-ables (emergent patterns in the dynamics).
Let C = {1,…,N} be a finite configuration space. A generalized stochastic system (GSS) is a family of transition matrices Γ(t←t₀) satisfying non-negativity, column-stochasticity, and Γ(t₀←t₀) = 𝟙. A GSS is Markovian if the Chapman-Kolmogorov equation holds for all intermediate t'. It is indivisible if this factorization generically fails.
The stochastic-quantum correspondence: any GSS can be embedded as a subsystem of a unistochastic system (where Γij = |Θij|² for unitary Θ) by marginalizing over an ancilla C' with |C'| ≤ N². This dilation is the Kraus decomposition of the corresponding quantum channel.
Density matrix evolution: ρ(t) = Θ(t) ρ(0) Θ†(t). The Born rule emerges from the diagonal: pk(t) = Tr(Pk ρ(t)). Bell's theorem is bypassed because Bell's argument implicitly assumes Markovianity — a factorizability condition indivisible processes need not satisfy.
A curated selection of talks, interviews, and debates — from accessible introductions to technical colloquia.
The foundational paper establishing the mathematical equivalence between indivisible stochastic processes and quantum systems. Derives the Born rule, interference, and entanglement from stochastic principles. Start here.
Deepens the framework with gauge invariance, dynamical symmetries, and Hilbert-space dilations. Explores downstream implications for causation, locality, and Bell's theorem.
A detailed critical assessment by one of philosophy of physics' leading figures. That Albert engaged seriously is itself a mark of the theory's significance.
A well-written accessible companion to Barandes' key ideas. Good starting point for non-physicists who want more structure than a podcast conversation.
A careful independent analysis of the theory's mathematical structure, including the quantum reconstruction program and where Barandes' approach fits within it.
Science advances through genuine disagreement. Here are the strongest objections raised by peers — and how Barandes responds. Intellectual honesty matters more than hagiography.
Scott Aaronson's challenge: if the theory makes identical predictions to standard QM, what's the philosophical gain? You assert trajectories exist but can't say what they do moment to moment.
If you're a realist about trajectories, don't you need a measure on the ensemble of paths? But indivisibility forbids asking about intermediate times — creating an apparent tension.
The stochastic-quantum correspondence may not carry full physical content. Quantum interference might need additional structure not captured by simply dropping Markovianity.
Does the framework extend cleanly to relativistic quantum field theories — the actual arena of all known fundamental physics?
The framework provides a coherent realist picture: systems have definite configurations evolving under indivisible laws. The measurement problem dissolves entirely. That's not nothing.
The inability to define intermediate probabilities is precisely what generates quantum behavior. Demanding those probabilities is like asking for the color of a sound — a category error.
He compares it to Hamiltonian vs. Lagrangian mechanics — different mathematical frameworks for the same physics that open entirely different roads for generalization and new applications.
Relativistic extension is active research. Barandes frames this as an open research program, not a finished theory — analogous to early Hamiltonian mechanics before Hamilton himself.