A Pre-Registered Falsification of Deterministic Measurement-Triggered Relaxation

In the paper's words

The hydrodynamic re-grounding of quantum mechanics proposes that measurement outcomes arise from a deterministic relaxation of a probability fluid into eigenstate basins, rather than from a discontinuous collapse. A prior adjudication of this program found its central weakness to be the absence of any concrete mechanism: no equation of motion was specified for the claimed relaxation. This paper reports a pre-registered computational test of the strongest available form of that proposal.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

No sentence of this paper reports a figure with a unit or a quantity word, so none is shown.

How it is done

1. The test uses a two-level system with Hamiltonian $H = \frac{\omega}{2}\sigma_z$ (in natural units, $\omega = 1$), represented in Bloch coordinates $(x, y, z)$, where the density operator is $\rho = \frac{1}{2}(I + x\sigma_x + y\sigma_y + z\sigma_z)$ and the Born probability of the upper eigenstate is $p = (1+z_0)/2$ for an initial state with Bloch component $z_0$.

   from 2. The Sealed Test Protocol

2. In an experiment that prepares the same state repeatedly, every shot follows that same trajectory, so every shot yields the same outcome.

   from 4. Why Determinism Forces Degeneracy

3. The subquantum H-theorem program proposes that relaxation to quantum equilibrium occurs dynamically within de Broglie–Bohm-type theories; explicit simulations of relaxation to the Born rule were given for such theories, and timescale analyses of the relaxation were provided.

   from 5. Relation to Prior Work

4. The deliverable is a reusable, audit-proof falsification package for claims of the form "a deterministic relaxation reproduces the Born rule": Reproduce the verdict.

   from 7. What a Practitioner Can Do With This Result

What would falsify it

1. Where the premises end: the falsification is scoped to deterministic, fixed-initial-state, threshold-terminated dynamics on two-level systems; it does not adjudicate stochastic, ensemble-based, or contextual alternatives, and it does not claim the hydrodynamic program is false in full — only that this mechanism, as specified, is falsified.

   from Abstract

2. The present result is consistent with that literature: it falsifies a mechanism that the reconstruction literature never supplied.

   from 5. Relation to Prior Work

3. This paper closes that gap in the direction of falsification: for the strongest available deterministic specification, the mechanism cannot work.

   from 6. Implications for the Hydrodynamic Program

Where the claim stops

1. It cannot: the maximum deviation from the Born rule was $0.5$ across all seven configurations and all fifty-nine states, fifty times the pre-registered tolerance, because a deterministic map from a fixed initial state yields a degenerate outcome channel.

   from 8. Conclusion

2. The reader should care because this converts a conceded gap into a demonstrated one: within the tested family, deterministic measurement-triggered relaxation cannot reproduce the Born rule; reproducing it requires an ensemble over initial states, stochasticity in the dynamics, or measurement-contextual variables, each of which corresponds to a distinct existing research program.

   from Abstract

3. Where the premises end: the falsification is scoped to deterministic, fixed-initial-state, threshold-terminated dynamics on two-level systems; it does not adjudicate stochastic, ensemble-based, or contextual alternatives, and it does not claim the hydrodynamic program is false in full — only that this mechanism, as specified, is falsified.

   from Abstract

Where to read

1. Abstract262 words · 1 min
2. 1. Introduction186 words · 1 min
3. 2. The Sealed Test Protocol470 words · 2 min
4. 3. Results252 words · 1 min
5. 4. Why Determinism Forces Degeneracy244 words · 1 min
6. 5. Relation to Prior Work369 words · 2 min
7. 6. Implications for the Hydrodynamic Program150 words · 1 min
8. 7. What a Practitioner Can Do With This Result214 words · 1 min
9. 8. Conclusion105 words · 1 min
10. Declarations241 words · 1 min