This episode features physicist Jacob Barandes of Harvard University, who proposes a radical reformulation of quantum mechanics: there is no fundamental wave function, Hilbert space is not fundamental reality, and quantum weirdness like superposition and interference arises from describing deeper, classically probabilistic systems with a particular kind of memory-like dynamics he calls indivisible stochastic processes.
Background and Motivation
Barandes came to physics through early interests in philosophy of mind and consciousness, later shifting to the philosophy of physics and foundations of quantum theory.
He explains that textbook quantum mechanics, based on the Dirac–von Neumann axioms, works empirically but contains unresolved ambiguities: it relies on an undefined notion of “measurement,” requires a collapse postulate, and treats wave functions as central objects even though their physical meaning is unclear.
He argues that wave functions are better understood as mathematical tools—comparable to Hamilton’s principle function in classical mechanics—useful for generating predictions but not describing physical objects in the world.
Why the Wave Function Might Not Be Real
In standard quantum mechanics, the wave function assigns complex numbers to points in a high-dimensional configuration space, not ordinary 3D physical space. For many particles, this space has many more dimensions, and in quantum field theory the number of particles is not even well-defined.
This makes it misleading to think of the wave function as a physical wave in space. Instead, it is a convenient mathematical device for encoding probabilities.
Alternative formulations such as C-algebraic quantum mechanics* show that Hilbert space can be derived from more basic algebraic structures of observables, suggesting Hilbert space may not be fundamental.
Wigner’s Friend and the Measurement Problem
The Wigner’s friend thought experiment highlights the measurement problem: inside a sealed box, Wigner’s friend measures a quantum system and gets a definite outcome, while outside, Wigner has not observed anything.
This raises several options:
Keep collapse as a real process, but then one must define what counts as a measurement.
Make collapse perspectival or deny that the wave function is complete.
Introduce dynamical collapse mechanisms.
Adopt a no-collapse view such as Everett’s many-worlds interpretation, where all outcomes occur and the universal wave function branches.
Barandes argues these options either leave the measurement problem unresolved or introduce other conceptual difficulties.
Indivisible Stochastic Processes
Barandes describes how, while trying to teach quantum mechanics in a simpler way, he discovered a bridge between classical stochastic processes and quantum theory.
Standard stochastic models are usually Markovian: the future depends only on the present state, with no memory of the past.
He found that by using a more general class of probabilistic laws—indivisible stochastic processes—he could reproduce quantum behavior without Hilbert spaces or wave functions.
An indivisible process is one where the dynamical law cannot be broken into smaller time intervals: you can evolve from an initial time to a final time, but the theory does not provide laws for intermediate steps in a way that can be iterated.
These processes are more general than Markov processes and even than typical non-Markovian processes. They first appeared in the quantum literature around 2006–2008 and were later explored for classical systems around 2021.
How Quantum Weirdness Emerges
In this picture, physical systems have classical-like configurations—positions, field intensities, or other ordinary states—and evolve according to indivisible stochastic laws using ordinary probabilities, not complex amplitudes.
When you translate such a system into a more convenient mathematical representation, you obtain a Hilbert space description with a Schrödinger-like equation, complex amplitudes, and interference effects.
Superposition, interference, and coherence are then understood as mathematical artifacts of trying to describe an indivisible, memory-like process using a divisible, continuous-time formalism.
In this sense, the “quantumness” is the price paid for using a mathematically smoother representation.
Rethinking Measurement and Decoherence
In textbook quantum theory, measurement devices and observers are treated as outside the formalism, and collapse is postulated but not explained.
In Barandes’s approach, one can explicitly model the measured system, the measuring device, and the environment as physical systems with their own configurations and indivisible stochastic dynamics.
When these systems interact, the combined evolution naturally leads to outcomes with the correct Born-rule probabilities and generates division events—moments where the evolution can be restarted.
These division events correspond to what standard quantum theory would call measurement or decoherence, but they arise from the dynamics themselves rather than from an external collapse axiom.
There is no need for a special role for conscious observers; any sufficiently large system interacting with a large environment will behave this way.
Classical Probabilities vs Quantum Amplitudes
At the fundamental level, the theory uses classical probabilities: real numbers between 0 and 1 that sum to 1.
Complex amplitudes and mod-squaring appear only in the Hilbert space representation, as a convenient mathematical encoding.
The claim is that quantum mechanics can be understood as a reformulation of a deeper classical-like probabilistic theory, with Hilbert space and amplitudes emerging as useful tools rather than fundamental ontology.
Implications for Quantum Foundations and Interpretations
Because there is no fundamental wave function, there is nothing that branches or splinters into many worlds. Many-worlds interpretations do not arise in this framework.
The approach is deflationary: it removes the metaphysical exoticness of quantum mechanics—no fundamental superposition of cats, no special role for observers—while preserving the empirical predictions of standard quantum theory in all realistic scenarios.
It also resolves the measurement problem by providing a physical account of how definite outcomes and effective collapse-like behavior emerge from ordinary probabilistic dynamics.
Connections to Other Approaches and Practical Prospects
Barandes contrasts his framework with Bohmian pilot-wave theory, which works well for simple particle systems but is hard to generalize to fields and more complex settings.
He notes that in principle there could be tiny deviations from textbook quantum theory in scenarios like Wigner’s friend, but these are extraordinarily small and currently far beyond experimental reach.
He suggests that the correspondence between indivisible stochastic processes and Hilbert space representations might open new applications, such as:
Simulating non-Markovian classical stochastic systems using quantum computers.
Generalizing quantum mechanics in new ways that do not start from Hilbert spaces, potentially aiding work in quantum gravity.
He emphasizes that this is early-stage work and much remains to be understood, especially in fully handling quantum fields and more complex systems.
What Is a Particle in This Picture?
In standard quantum theory, particles are defined abstractly through irreducible representations of spacetime symmetry groups, characterized by mass, spin, and charges.
In Barandes’s framework, a particle is understood more classically: a point-like entity in physical space with properties and dispositions to behave in certain ways when measured.
He does not claim particles are the ultimate fundamental ontology; rather, one chooses whatever ontology—particles, fields, or other configurations—is appropriate for the system being modeled.
He argues it is premature to declare any one such ontology fundamental, and that Hilbert spaces should not be taken as the final grounding of reality.
Advice and Outlook
For students and researchers, Barandes emphasizes that people have unique profiles of strengths and weaknesses, and meaningful contributions come from finding how to bring those strengths to bear on work that matters to them.
He highlights the value of interdisciplinary research, noting that some of the most exciting progress happens at the boundaries between physics, mathematics, philosophy, and other fields.
He sees the opening up of new foundational and mathematical directions as especially exciting, even if practical applications are still developing.
