Harvard Scientist Rewrites the Rules of Quantum Mechanics | Scott Aaronson Λ Jacob Barandes

• This episode features a debate between Harvard physicist Jacob Barandes and computer scientist Scott Aaronson about the foundations of quantum mechanics, the source of quantum computing’s power, and whether a new formulation of quantum theory can resolve long-standing interpretive puzzles.
  • Jacob Barandes has developed a reformulation of quantum mechanics called indivisible stochastic processes, which claims to reproduce all the predictions of standard quantum mechanics without wave functions, Hilbert spaces, or complex amplitudes as fundamental ingredients.
  • Scott Aaronson is a leading quantum computing theorist who is sympathetic to the many worlds interpretation in some contexts but remains uncommitted, using whichever interpretive “car” suits the problem at hand.
  • The central question is whether quantum computing’s speedup comes from “parallel universes” (many worlds), from interference in a Hilbert space, or from something else entirely — and whether Barandes’ new framework offers genuine advantages over existing formulations.

The Power of Quantum Computing and the Many Worlds Debate

• David Deutsch’s argument for many worlds from quantum computing: Deutsch argued that if a quantum computer can factor a 2,000-digit number exponentially faster than any classical computer, the computation must have “somewhere” to happen — suggesting a vast, exponentially large reality. He believed even the double-slit experiment already proves many worlds, and quantum computers merely make it psychologically undeniable.

  • Aaronson agrees that quantum computation is dramatic evidence that the state of the universe is vastly larger than classical physics posits, but he resists the language of “parallel universes” because the branches in a quantum computation are not truly independent — they interfere with each other, which is precisely what gives quantum computing its power.
  • Barandes points out a tension: modern Everettians rely on decoherence to define distinct macroscopic worlds, but in a good quantum computation, decoherence is precisely what does not happen — the branches remain coherent and interfere. So the many worlds picture doesn’t actually help explain quantum speedup.

• What actually gives quantum computers their power?

  • Aaronson explains that quantum speedup is fundamentally a negative statement: it means that every possible way of efficiently simulating the quantum computation classically fails. The key ingredients are:
    • Exponentially large Hilbert space
    • Entanglement between qubits
    • Interference — the ability of complex-valued amplitudes to cancel (destructive interference for wrong answers) and reinforce (constructive interference for right answers)
  • He emphasizes that quantum computing is “a weirder resource than any science fiction writer would have imagined” — it is not simply classical exponential parallelism (trying all answers at once), because measurement is destructive and only reveals a tiny amount of information.
  • Barandes adds that if quantum computers really exploited parallel universes, you would expect speedups for all problems, not just a narrow special class. The fact that speedups are rare and hard to find is itself evidence against the “parallel universes” explanation.

• Barandes’ alternative explanation: The power of quantum computing comes from indivisibility — the class of indivisible stochastic processes is simply larger than the class of processes available to classical computers. This gives quantum systems access to a broader space of possible dynamics.

Jacob Barandes’ Indivisible Stochastic Processes

• The core idea: Barandes proposes reformulating quantum mechanics from scratch using only two types of ingredients:

  1. Configurations: A system has a definite configuration at any given time (e.g., positions of particles in 3D space, or discrete states of a computer). This is the “kinematical” part and is similar to classical mechanics.
  2. Indivisible stochastic dynamics: Instead of a differential equation governing smooth evolution (like the Schrödinger equation), the dynamics are given by a sparse set of conditional probabilities — the probability that the system will be in a certain target configuration at a target time, given that it was in a certain conditioning configuration at a conditioning time.
  • These processes are called “indivisible” because they fail a property called iterativeness: you cannot break the evolution into steps and chain transition probabilities together. In general, you cannot ask: “Given the system is here now, what is the probability it will be there next?” You can only ask about probabilities from special “division times” to target times.
  • This is not because the trajectories don’t exist — Barandes insists they do — but because the theory does not supply us with the tools to calculate them. The trajectories are real but unknowable in principle (what he calls “Knightian uncertainty” about the dynamics).

• The stochastic quantum correspondence: There is a mathematical map between this stochastic picture and the standard Hilbert space picture, analogous to the map between Newtonian mechanics and Hamiltonian phase space. Through this correspondence:

  • The complex numbers of quantum theory emerge as a consequence of the formalism, not a starting assumption. The stochastic picture uses only ordinary real-valued probabilities; complex numbers appear when you translate to the Hilbert space description.
  • Interference gets a physical interpretation: it is the mathematical artifact that appears when you try to force an indivisible process into a divisible (step-by-step) framework. If you artificially slice an indivisible process at an intermediate time and try to compute transition probabilities, you get the wrong answer; the difference between the wrong answer and the correct answer is exactly the interference formula.
  • The Schrödinger equation and all the Dirac-von Neumann axioms can be systematically reconstructed from this starting point.

• How this differs from Bohmian mechanics:

  • Bohmian mechanics keeps the wave function as a real physical object (a “pilot wave”) and adds definite particle positions that are guided by the wave function along specific trajectories.
  • Barandes eliminates the wave function entirely from the ontology. He keeps definite configurations (like Bohmian positions) but does not specify trajectories or a guiding equation. The dynamics are given by the indivisible stochastic process, which in general does not provide transition probabilities between arbitrary times.
  • Barandes describes his view as similar to a “nomological” version of Bohmian mechanics (where the wave function is a law rather than a physical object), but without the preferred foliation of spacetime, without a specific guiding equation, and without commitment to what the trajectories are.

• Predictions and the Wigner’s friend thought experiment:

  • Barandes claims his approach makes different predictions from the standard Dirac-von Neumann axioms in situations involving macroscopic quantum systems like the Wigner’s friend experiment.
  • In the Wigner’s friend setup, Wigner’s friend inside a sealed box measures a quantum system and gets a definite result. The question is: has the wave function collapsed (from the friend’s perspective) or is the entire box still in superposition (from Wigner’s outside perspective)?
  • The standard axioms are ambiguous about when to apply the collapse postulate. Barandes resolves this by saying: the overall indivisible stochastic process continues uncollapsed for the whole system, AND the friend genuinely had a definite result. This is a hidden-variables-like option, except the “variables” (the configurations) are not hidden from the friend and are the only things that exist — the wave function is not a physical object.
  • Aaronson notes that any empirical difference would only appear in what the friend experiences during the experiment, not in what they report afterward (since once the experiment is over and records are made, standard quantum mechanics gives the correct answer). This makes the prediction effectively untestable.

Scott Aaronson’s Objections

• The core objection: ontological commitment without explanatory payoff: Aaronson’s main criticism is that Barandes adds ontology (real configurations with real trajectories) without providing the tools to calculate or observe those trajectories. He calls this “ontological commitment that is not paying rent.”

  • In standard quantum mechanics, the wave function encodes everything that is in principle observable. Aaronson’s preference is to keep ontology tightly fitted to what is observable.
  • He acknowledges that many worlds has its own ontological extravagance (infinitely many parallel universes), but at least it attempts to derive everything from a single simple entity (the wave function evolving unitarily). Barandes adds configurations and keeps the stochastic dynamics but refuses to specify the trajectories — which feels like having the disadvantages of both approaches.

• The demand for new applications: Aaronson sets a clear test for any reformulation: it should either (a) make some quantum mechanical phenomena simpler to explain, (b) enable new quantum algorithms or insights about which problems admit speedups, or (c) help with quantum gravity. He acknowledges that Dirac’s path integral and Bohmian mechanics both took decades to find their applications, but he wants to see at least a plausible case for what Barandes’ formulation can do that the standard picture cannot.

  • Barandes responds that the formulation is very new (indivisible processes only entered the literature in 2020) and that its value may lie in opening up generalizations of quantum theory that are hard to see from the Hilbert space starting point. For example, one could imagine conditioning on two or more times instead of one, leading to theories that might not map onto standard quantum mechanics.

• Pedagogical value: Barandes argues that his approach is more intuitive for newcomers because it starts with configurations and ordinary probabilities rather than Hilbert spaces, linear algebra, and complex amplitudes. Aaronson is sympathetic to the goal of better pedagogy but notes that students will still need to learn Hilbert spaces and unitary transformations to do actual calculations, so the reformulation would be an addition to, not a replacement for, the standard curriculum.

The Many Worlds Interpretation Under Scrutiny

• The “Stone Soup” problem: Barandes argues that the many worlds interpretation (MWI) advertises itself as simple — “just the Schrödinger equation and unitary evolution” — but to actually work, it requires adding more and more assumptions (decoherence, preferred basis, decision-theoretic arguments for the Born rule, etc.), like the folktale where soldiers claim to make soup from stones but keep asking for more ingredients.

  • The key problem: if branches are fundamental, you can assign them probabilities in the axioms, but then you face the preferred basis problem (what singles out one basis over another?). If branches are emergent (via decoherence), you cannot assign them axiomatic probabilities because they’re not fundamental objects — but then all the decision-theoretic derivations of the Born rule become circular.
  • Aaronson agrees that none of the existing derivations of the Born rule from MWI are convincing, but he notes that every interpretation has some analogous problem.

• The “Library of Babel” problem: Barandes argues that MWI predicts everything — including “super-maverick branches” where totally bizarre things happen. Since it puts no constraints on what kinds of worlds occur (other than the Born rule probabilities, which it can’t derive), it is vacuous in the same way as the Library of Babel, which contains all possible books and therefore conveys no information.

  • Aaronson concedes this is a serious problem and part of why he is not a “hardcore many worlder,” but he notes that the same objection applies to some degree to any interpretation — the question is whether the theory plus reasonable additional assumptions can account for what we observe.

• Aaronson’s pragmatic stance: He describes himself as someone who “takes Ubers” — using whichever interpretive framework is most useful for the problem at hand. For teaching quantum computing, he finds the Everettian picture useful (e.g., explaining decoherence via CNOT gates as “measurement by the environment”). For other problems, he uses Copenhagen or other approaches. He is not an instrumentalist — he wants to know what is really out there — but he insists that ontological commitments should be tightly constrained by what is observable.

The Nature of Laws and Unobservables

• Knightian uncertainty in physics: Barandes embraces the idea that there can be genuine unpredictability in physics that is not even probabilistic — what Frank Knight (and Aaronson in his paper “The Ghost in the Quantum Turing Machine”) called “Knightian uncertainty.” In Barandes’ framework, the theory simply does not supply transition probabilities for certain questions (e.g., given the system is here now, what is the probability it will be there next?). This is not a limitation of our knowledge but a feature of the laws themselves.

  • Aaronson is willing to accept Knightian uncertainty about initial conditions (as in general relativity, where the Einstein equations don’t specify what the initial state is) but is much more hesitant about allowing it in the evolution rules themselves.
  • Barandes counters that even in general relativity, there are Cauchy horizons beyond which the equations make no predictions — so the idea of laws that don’t determine what happens next is not unique to his approach.

• Unobservables in physical theories: Both agree that all physical theories contain unobservables (the moon when no one looks, the global phase of the wave function, spacetime points behind horizons). The question is where to draw the line. Aaronson wants to minimize unobservables; Barandes argues that his configurations are no more unobservable than the parallel universes of MWI, and that having a clear physical picture (even with unobservable elements) is preferable to having no picture at all.

• The value of physical models: Barandes cites John Bell’s rediscovery of the flaw in von Neumann’s no-hidden-variables theorem as an example of how having a concrete physical model (Bohmian mechanics) can lead to new insights that pure formalism misses. He suggests that his formulation might similarly lead to new connections with statistics, new generalizations of quantum theory, and new ways of thinking about causation.

Closing Positions

• Aaronson’s final position: He is “not buying” Barandes’ formulation at this time, not because he thinks it is wrong, but because he has not been shown what it can do that he cannot already do with existing tools. He is open to revisiting if it leads to new quantum algorithms, insights about quantum speedups, or progress on quantum gravity. He encourages Barandes to demonstrate the formulation’s value by explaining specific quantum phenomena (like the double-slit or Stern-Gerlach experiment) entirely within the new framework without translating back to Hilbert space.

• Barandes’ final position: He acknowledges that not everyone will find his approach useful or compelling, and he is not trying to force anyone to adopt it. He sees value in having a formulation that (a) is empirically adequate, (b) is not vague, (c) makes unambiguous predictions even for macroscopic systems, and (d) does not require a long list of speculative metaphysical hypotheses. He believes his approach meets these criteria better than existing interpretations and is excited about the possibility of new generalizations and interdisciplinary connections. He has provided Aaronson and the host with a document explaining the double-slit experiment in his framework, which he hopes will demonstrate its pedagogical value.