Jacob Barandes

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Jacob Barandes

(1980?-)

Jacob Barandes has joint faculty appointments in the physics and philosophy departments at Harvard University, and does research in the philosophy of physics.

"Stepping outside the wave function paradigm," Barandes says, he proposes a new formulation of quantum mechanics (not simply an interpretation) in terms of old-fashioned configuration spaces together with what he calls "unistochastic" laws.

Barandes' formulation replaces the abstract wave function of Erwin Schrödinger's wave mechanics formulation and the eigenfunctions, eigenvectors, and eigenstates of Werner Heisenberg's matrix mechanics formulation, and John von Neumann and P.A.M.Dirac's axiomatic formulation on Hilbert vector spaces.

In particular, Barandes replaces their transition probabilities between quantum states with "directed conditional probabilities" in stochastic processes. And he describes their time evolution with linear maps that describe the dynamics of a quantum system. In the realm of quantum information theory these maps are referred to as quantum channels. These linear maps can be interpreted as a Hilbert space.

If the time evolution of a system from t=0 to t=2 can be divided into first t=0 to t=1, then t=1 to t=2, he calls it divisible, otherwise time evolution is indivisible.

In his 2025 paper The Stochastic-Quantum Correspondence, for the Philosophy and Physics Group at the London School of Economics, Barandes shows how his stochastic approach recovers the familiar Schrödinger wave equation, von Neumann's unitary time evolution, and other equations of standard quantum theory.

In his 2024 paper "New Prospects for a Causally Local Formulation of Quantum Theory," Barandes introduces a "new principle of causal locality" that is " intended to improve on [John] Bell's criteria."

Barandes first defines the terms "signal-local" and "signal-nonlocal."

In physical theories like Newtonian mechanics that involve forces, one can ask whether those forces are limited by the speed of light, or instead consist of faster-than-light action at a distance...
In principle, there are no constraints in Newtonian mechanics that would preclude sending superluminal signals—say, by exploiting the action-at-a-distance features of Newtonian gravitational forces. Newtonian mechanics is therefore presumably signal-nonlocal.
By contrast, the aptly named no-communication theorem ensures that appropriately defined quantum systems— such as local quantum fields—cannot be used to send superluminal signals, so these quantum systems are signal-local

"New Prospects," p.1

He then defines a type of locality he calls causal locality

This paper will be concerned with a different type of locality, called causal locality, which will be taken to consist of the following statement:
Causal influences should not be able to propagate faster than light.

"New Prospects," p.1

Finally, Barandes describes Bell as introducing a new principle of local causality.

Bell’s principle of local causality is the assumption that the asserted common causes in question must specifically take the form of variables that can be conditioned on and then summed or integrated over...
Bell’s principle of local causality...implicitly depends on an assumption that goes beyond questions of locality. That implicit assumption is called Reichenbach’s principle of common causes.
Reichenbach’s principle of common causes states that if two variables A and B are correlated, in the sense that their joint probability P(A,B) fails to factorize as the product of their standalone probabilities P(A) and P(B),

P(A,B) ≠ P(A)P(B),

and if A and B do not causally influence each other, then there should exist some other variable C such that conditioning on C leads to the following factorization:

P(A,B|C) = P(A|C)P(B|C).

That is, Reichenbach’s principle positively asserts the existence of a ‘common-cause’ variable C for A and B. In this way, the variable C is said to ‘explain’ or ‘account for’ the correlation between A and B.
Bell’s principle of local causality...clearly invokes Reichenbach’s principle, with the role of the asserted common cause variable C played by the variables λ representing beables localized in the overlap of the past light cones of the measurement results A and B.

"New Prospects," p.5

Barandes "especially thanks" Travis Norsen. Norsen mentions Bell's formulation of local causality and illustrates Barandes' point about overlapping past light cones.

Fig. 8.4 Space-time regions relevant to Bell’s formulation of local causality. Bell writes: “Full specification of what happens in 3 makes events in 2 irrelevant for predictions about 1 in a locally causal theory”
Ref. "La Nouvelle Cuisine," in Speakable and Unspeakable in Quantum Mechanics, Cambridge, p.240

But Norsen then explicitly shows how a common cause from the initial entanglement is still in the past light cone of the "separated" measurements at A and B.

Fig. 8.5 Space-time diagram for the Bell experiment. The particle pair is emitted at the “flash’' at the bottom of the diagram; world-lines for the two individual particles flying apart in opposite directions are represented by the gray dashed lines. The (large!) region 3 encompasses both particles at some intermediate time and shields the two measurement regions, 1 and 2. from their overlapping past light cones in the way that is required in Bell's formulation of locality.

Barandes provides a similar diagram of the diverging paths of particles he calls Q and R leaving an initial entanglement at time t' and traveling to measurement devices at A and B at time t.

He describes the time evolution of the particles.

Suppose that the two subsystems Q and R are not kept at spacelike separation during the physical process in question, but locally interact at some intermediate time t′ between 0 and t. Then, again following standard textbook arguments, the overall system’s unitary time-evolution operator U_QR(t) will fail to tensor-factorize at t′:

Note that the intermediate time t' is precisely the moment the particles Q and R are in contact and causally local entangled. These locally causal influences do not propagate faster than light. Erwin Schrödinger said Ψ_AB cannot be represented as a simple product of two independent single-particle states Ψ_A Ψ_B

U_QR(t′) ≠ U_Q(t′) ⊗ U_R(t′). (59)
Because the corresponding transition matrix Γ_QR(t) encodes cumulative statistical effects starting at the initial time 0, the transition matrix will continue to fail to tensor-factorize for all times t ≥ t′ (at least until the next division event):
Γ_QR(t) ≠ Γ_Q(t) ⊗ Γ_R(t) [for t ≥ t′]. (60)
The breakdown in tensor-factorization for t ≥ t′ is precisely entanglement, as manifested at the level of the underlying indivisible stochastic process... so one can conclude that the two subsystems Q and R exert causal influences on each other, stemming from their local interaction at the time t′.

The initial entanglement at t' is an initial casually local event that puts the particles in a spherically symmetric state with total spin zero.

During the time evolution from t' to t, the conservation of spin angular momentum is a condition or constraint on total spin (a "hidden constant" if not a hidden variable?) that will locally cause? the measurements at A and B to be perfectly correlated as long as Alice and Bob agree ahead of time t to measure at the same angle (maintaining planar symmetry)

If their measurements diverge by angle Θ, correlations will fall off by cos²Θ, as observed in all Bell experiments. (the "law of Malus")

Notice that this local interaction, despite being the ‘common cause’ of the correlations between Q and R, is not the sort of ‘variable’ that can be plugged into the unistochastic theory’s microphysical conditional probabilities. Reichenbach’s principle of common causes therefore does not hold.

"New Prospects," p.12

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