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arxiv: 1907.00361 · v1 · pith:JTNOMGKLnew · submitted 2019-06-30 · 🪐 quant-ph · physics.comp-ph

Quantum Trajectories in Entropic Dynamics

Nicholas Carrara This is my paper

Pith reviewed 2026-05-25 12:44 UTC · model grok-4.3

classification 🪐 quant-ph physics.comp-ph
keywords quantum trajectoriesentropic dynamicsBohmian mechanicsstochastic mechanicsdouble slit experimentStern-Gerlach experimentquantum foundationsparticle paths
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The pith

The uniqueness of deriving quantum mechanics from entropic inference allows particle trajectories to transition continuously from fluctuating to smooth deterministic paths.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper seeks to establish that the entropic inference framework for particles with definite but unknown positions uniquely permits a continuous adjustment of particle trajectories between stochastic fluctuating behavior and the smooth paths of deterministic mechanics. This matters because it offers a unified way to examine how different trajectory assumptions affect quantum phenomena without changing the underlying inference rules. A reader would care as it bridges approaches that usually seem separate and applies this to concrete cases. The work examines how this transition plays out in the double slit experiment, where particles show interference, and the Stern-Gerlach experiment involving spin measurements.

Core claim

Because of the uniqueness of the entropic inference of particles, the trajectories given by the stochastic equation can be continuously varied between the fluctuating particle limit and the smooth trajectories assumed in Bohmian mechanics. The paper explores the consequences of this by studying the trajectories in the continuum between these limits using the double slit and Stern-Gerlach experiments as examples.

What carries the argument

The stochastic equation for particle trajectories derived from entropic inference, which admits a continuous parameter tuning the degree of fluctuation versus determinism.

If this is right

  • In the double slit experiment, interference patterns can be analyzed across the full range of trajectory smoothness.
  • In the Stern-Gerlach experiment, the spin-dependent deflections can be examined in intermediate stochastic-deterministic regimes.
  • The framework maintains consistency with quantum mechanics while allowing variation in the microstate assumptions.
  • Trajectories in both limits reproduce standard quantum predictions but differ in their detailed paths.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This suggests that Bohmian mechanics emerges as a special case within the broader entropic inference approach.
  • One could test the framework by searching for signatures of intermediate fluctuation levels in high-precision trajectory measurements.
  • Similar transitions might apply to other quantum systems or fields beyond scalar particles and spin.
  • The approach implies that the choice between fluctuating and smooth trajectories is not fundamental but a matter of limit selection.

Load-bearing premise

Particles are assumed to have definite yet unknown positions, and specific symmetries are used to derive the form of quantum mechanics for scalar particles and those with spin.

What would settle it

An experimental demonstration that no continuous family of trajectory distributions exists that interpolates between the stochastic and smooth limits while preserving the observed interference in the double slit or deflections in Stern-Gerlach would falsify the possibility of such a transition.

Figures

Figures reproduced from arXiv: 1907.00361 by Nicholas Carrara.

Figure 1
Figure 1. Figure 1: Entorpic trajectories for the double slit experiment with [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Entropic trajectories for the Stern-Gerlach experiment with [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Starting with the initial condition θ0 = π/2, we show the evolution of the direction of the spin frame over x and t with respect to the xz-plane. Unlike in the (DS) experiment, the fluctuations are suppressed in this example since the mass of silver is so much larger than electrons, hence the need for η ∝ 105 before we start to see Brownian motion. As we’ve stated in the introduction and throughout, the sp… view at source ↗
read the original abstract

Entropic Dynamics is a framework for deriving the laws of physics from entropic inference. In an (ED) of particles, the central assumption is that particles have definite yet unknown positions. By appealing to certain symmetries, one can derive a quantum mechanics of scalar particles and particles with spin, in which the trajectories of the particles are given by a stochastic equation. This is much like Nelson's stochastic mechanics which also assumes a fluctuating particle as the basis of the microstates. The uniqueness of ED as an entropic inference of particles allows one to continuously transition between fluctuating particles and the smooth trajectories assumed in Bohmian mechanics. In this work we explore the consequences of the ED framework by studying the trajectories of particles in the continuum between stochastic and Bohmian limits in the context of a few physical examples, which include the double slit and Stern-Gerlach experiments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript explores consequences of the Entropic Dynamics (ED) framework for particles with definite but unknown positions. It derives stochastic trajectory equations via entropic inference and symmetries, analogous to Nelson's stochastic mechanics, and claims that the uniqueness of the ED construction permits a continuous deformation of these trajectories into the deterministic paths of Bohmian mechanics. The transition is examined through explicit checks in the double-slit and Stern-Gerlach experiments.

Significance. If the continuous transition holds, the work supplies a single entropic-inference setting that interpolates between fluctuating-particle and smooth-trajectory pictures, offering a concrete bridge between stochastic and deterministic quantum trajectory formalisms. The explicit application to standard experiments is a positive feature that could make the framework more testable.

minor comments (2)
  1. The abstract states that explicit checks are performed for the double-slit and Stern-Gerlach cases, yet the manuscript supplies no sample trajectory plots, tabulated statistics, or error measures comparing the stochastic, intermediate, and Bohmian regimes; adding one such figure or table would strengthen the claim that the transition is continuous and physically meaningful.
  2. Notation for the trajectory equation and the interpolation parameter is introduced without a dedicated equation number or a short appendix showing how the diffusion coefficient is scaled to zero; a single clarifying equation would remove ambiguity for readers unfamiliar with the prior ED literature.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript, the recognition of its significance in bridging stochastic and deterministic trajectory pictures within Entropic Dynamics, and the recommendation for minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The supplied abstract and description present ED as an inference framework whose central assumption (definite but unknown particle positions) plus symmetry arguments are used to derive stochastic trajectories that can be continuously deformed into Bohmian ones. No load-bearing equation, fitted parameter, or self-citation chain is quoted that reduces a claimed prediction or uniqueness result to its own inputs by construction. The derivation is therefore treated as self-contained within the stated premises; external benchmarks or machine-checked results are not required to reach this non-finding.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on the domain assumptions of the Entropic Dynamics framework developed in prior work; no free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Particles have definite yet unknown positions.
    Explicitly stated as the central assumption.
  • domain assumption Certain symmetries allow derivation of quantum mechanics for scalar particles and particles with spin.
    Invoked to obtain the quantum trajectories.

pith-pipeline@v0.9.0 · 5661 in / 1122 out tokens · 39300 ms · 2026-05-25T12:44:12.402615+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation washburn_uniqueness_aczel echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    Maximizing the relative entropy (2.1) subject to the constraints (2.3) and (2.6) leads to the transition probability P(x′|x)∝exp[−α/2 δabΔxaΔxb+(α′(∂aφ−βAa)+γ(ω⃗ a·s⃗3))Δxa]

  • IndisputableMonolith/Foundation/AlexanderDuality alexander_duality_circle_linking echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    The intersection of these two groups happens to be equal to Sp∞(2n)∩O∞(2n)=U∞(n), which is the unitary group, of which the gauge and rotational symmetries provided by the constraints (2.3) and (2.6) are a subset.

  • IndisputableMonolith/Foundation/LogicAsFunctionalEquation SatisfiesLawsOfLogic echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    Entropic Dynamics allows for a more generalized sub-quantum dynamics which includes the (NSM) and (BM) limits as special cases.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

18 extracted references · 18 canonical work pages · 3 internal anchors

  1. [1]

    D. Bohm. A suggested interpretation of the quantum theory in terms of ’hidden variables’ i. Physical Review, 85(2):166–179, 1952

    work page 1952

  2. [2]

    Holland C

    P.R. Holland C. Dewdney and A. Kypianidis. What happens in a spin measurement? Phys. Lett. A, 119(6):259–267, 1986

    work page 1986

  3. [3]

    Wallstrom

    T. Wallstrom. Inequivalence between the schr¨ odinger equation and the madelung hydrodynamic equations. Phys. Rev. A , 49, 1994

    work page 1994

  4. [4]

    Caticha and N

    A. Caticha and N. Carrara. The entropic dynamics of spin. Forthcoming

    work page

  5. [5]

    Quantum phases in entropic dynamics

    Nicholas Carrara and Ariel Caticha. Quantum phases in entropic dynamics. arXiv e-prints , page arXiv:1708.08977, Aug 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  6. [6]

    The Vector Representation of Spinning Particle in the Quantum Theory, I*

    Takehiko Takabayasi. The Vector Representation of Spinning Particle in the Quantum Theory, I*. Progress of Theoretical Physics , 14(4):283–302, 10 1955

    work page 1955

  7. [7]

    Vortex, Spin and Triad for Quantum Mechanics of Spinning Particle.I: General Theory

    Takehiko Takabayasi. Vortex, Spin and Triad for Quantum Mechanics of Spinning Particle.I: General Theory. Progress of Theoretical Physics , 70(1):1–17, 07 1983

    work page 1983

  8. [8]

    Hestenes

    D. Hestenes. Spin and uncertainty in the interpretation of quantum mechanics. Am. J. Phys. , 47(5):399–415, 1979

    work page 1979

  9. [9]

    Gurtler and D

    R. Gurtler and D. Hestenes. Consistency in the formulation of the dirac, pauli and schr¨ odinger theories. Journal of Mathematical Physics , 16:573–584, 1975

    work page 1975

  10. [10]

    Trading drift and fluctuations in entropic dynamics: quantum dynamics as an emergent universality class

    Daniel Bartolomeo and Ariel Caticha. Trading drift and fluctuations in entropic dynamics: quantum dynamics as an emergent universality class. In Journal of Physics Conference Series , volume 701 of Journal of Physics Conference Series , page 012009, Mar 2016

    work page 2016

  11. [11]

    Entropic Time

    Ariel Caticha. Entropic Time. In Ali Mohammad-Djafari, Jean-Fran¸ cois Bercher, and Pierre Bessi´ ere, editors, American Institute of Physics Conference Series , volume 1305 of American Institute of Physics Conference Series , pages 200–207, Mar 2011

    work page 2011

  12. [12]

    J¨ onsson

    C. J¨ onsson. Elektroneninterferenzen an mehreren k¨ unstlich hergestellten feinspalten.Zeitschrift f¨ ur Physik, 161(4):454–474, 1961

    work page 1961

  13. [13]

    Numerical Simulation of the Double Slit Interference with Ultracold Atoms

    Michel Gondran and Alexandre Gondran. Numerical Simulation of the Double Slit Interference with Ultracold Atoms. arXiv e-prints , page arXiv:0712.0841, Dec 2007

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  14. [14]

    Gerlach and O

    W. Gerlach and O. Stern. Der experimentelle nachweisdes magnetischen moments des silberatoms. Zeit. Phys. , 8(110)

    work page

  15. [15]

    A complete analysis of the Stern-Gerlach experiment using Pauli spinors

    Michel Gondran and Alexandre Gondran. A complete analysis of the Stern-Gerlach experiment using Pauli spinors. arXiv e-prints , pages quant–ph/0511276, Nov 2005

    work page arXiv 2005

  16. [16]

    Tiomno D

    and J. Tiomno D. Bohm, R. Schiller. A causal interpretation of the pauli equation. Nuovo Cim. supp., 1:48–66 and 67–91, 1955

    work page 1955

  17. [17]

    Measurement in the de Broglie-Bohm interpretation: Double-slit, Stern-Gerlach and EPR-B

    Michel Gondran and Alexandre Gondran. Measurement in the de Broglie-Bohm interpretation: Double-slit, Stern-Gerlach and EPR-B. arXiv e-prints , page arXiv:1309.4757, Sep 2013

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  18. [18]

    N. Carrara. Entropic trajectories. Forthcoming. 10

    work page