arxiv: 2604.17507 · v1 · submitted 2026-04-19 · 🪐 quant-ph

Arrival-time distributions as a probe of the preferred foliation in relativistic Bohmian mechanics

Arnaud Amblard , Aur\'elien Drezet This is my paper

Pith reviewed 2026-05-10 05:34 UTC · model grok-4.3

classification 🪐 quant-ph

keywords relativistic Bohmian mechanicspreferred foliationarrival-time distributionsEPRB experimentsuperluminal signalingde Broglie-Bohm theoryspacelike measurements

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The pith

Arrival-time statistics in EPRB experiments depend on the order of measurements relative to the preferred foliation in relativistic Bohmian mechanics.

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

The paper argues that relativistic Bohmian models, which require a preferred foliation of space-time to define particle configurations, predict observable effects in arrival-time data even at quantum equilibrium. In a setup with two particles where one undergoes a spin measurement and the other an arrival-time measurement at spacelike separation, the distribution of arrival times changes depending on whether the spin measurement occurs before or after according to the foliation's time slicing. A sympathetic reader would care because this dependence would serve as direct evidence for the foliation and, if confirmed, would permit superluminal signaling by allowing the choice of measurement order to influence distant statistics.

Core claim

Building on arrival-time distributions derived for spin-1/2 particles, the authors show that in an EPRB-type experiment the observed arrival-time statistics for one particle vary with the temporal ordering of the distant spin measurement relative to the preferred foliation. This ordering dependence arises because the foliation determines which events count as simultaneous for updating the guiding wave function, leading to different conditional probabilities for arrival times.

What carries the argument

The preferred foliation, a flat space-time slicing that supplies a global time order for defining simultaneous particle configurations and the evolution of the wave function in the relativistic Bohmian theory.

If this is right

The arrival-time histograms will differ measurably depending on whether the spin measurement precedes or follows the arrival event according to the foliation.
Choosing the order of operations in the experiment can transmit information faster than light by altering the distant arrival statistics.
Standard quantum equilibrium does not wash out the foliation signature in this particular combination of spin and timing measurements.
Detection of the effect would constitute an experimental probe of the additional structure postulated by relativistic Bohmian mechanics.

Where Pith is reading between the lines

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

The result suggests that other timing-based observables could be used to map the orientation of the unknown foliation in the laboratory.
If the dependence survives, it would force a choice between abandoning strict no-signaling or accepting that the foliation breaks Lorentz invariance in detectable ways.
Similar ordering effects might appear in other non-local hidden-variable models that introduce a preferred frame.

Load-bearing premise

That the arrival-time distributions derived for spin-1/2 particles remain valid and retain their dependence on measurement ordering when the preferred foliation is unknown and the experiment occurs in a real laboratory setting without being erased by quantum equilibrium or frame-dependent effects.

What would settle it

Perform the spacelike-separated EPRB experiment in multiple reference frames chosen so that the relative order of the spin and arrival-time measurements differs with respect to a candidate foliation, then compare the recorded arrival-time histograms; identical distributions independent of ordering would falsify the predicted dependence.

Figures

Figures reproduced from arXiv: 2604.17507 by Arnaud Amblard, Aur\'elien Drezet.

**Figure 2.** Figure 2: Schematic of the EPRB experiment with arrival-time measurement. The source pro [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗

**Figure 3.** Figure 3: Event A: Alice’s ∼ 105 xˆ-spin measurements. Event B: Bob’s ∼ 105 arrival-time measurements. Their space-time positions are fixed. Special relativity provides no objective temporal order for such spacelike-separated events, yet as [PITH_FULL_IMAGE:figures/full_fig_p023_3.png] view at source ↗

**Figure 4.** Figure 4: Space-time diagrams illustrating the detection of the switch point. The red vertical line [PITH_FULL_IMAGE:figures/full_fig_p027_4.png] view at source ↗

**Figure 5.** Figure 5: Schematic of the FLASH experiment [Her82] (compare with [PITH_FULL_IMAGE:figures/full_fig_p029_5.png] view at source ↗

read the original abstract

Relativistic extensions of de Broglie-Bohm theory postulate a preferred foliation of space-time, an additional structure essential for defining simultaneous configurations on Minkowski space-time, but conventionally believed to be empirically undetectable at quantum equilibrium. In this paper, we outline an experimental protocol for empirically detecting the preferred foliation, which is assumed to be flat for simplicity. Building on the arrival-time distributions for spin-1/2 particles predicted by Das and D\"urr, we show that in an EPRB-type experiment with spacelike-separated spin and arrival-time measurements, the observed arrival-time statistics will depend crucially on the temporal order of these measurements relative to the preferred foliation of space-time. This dependence offers a potential experimental signature of the preferred foliation postulated by relativistic Bohmian models. Moreover, it implies the possibility of superluminal signaling.

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.

Desk Editor's Note private letter to a colleague

The paper sketches a protocol to detect the preferred foliation via arrival-time order in a spacelike EPRB setup, but the effect is likely erased by quantum equilibrium marginals.

read the letter

The main thing to know is that this paper takes arrival-time distributions from Das and Dürr and proposes they will differ depending on the order of spin and arrival measurements relative to the unknown flat foliation. If the difference shows up, it would make the foliation observable and allow superluminal signaling in principle. That specific protocol is new compared to the cited prior work. The authors keep the argument simple and flag the signaling implication without extra machinery. The flat-foliation assumption is stated up front, which is reasonable for a first pass. The soft spot is exactly the one raised in the stress test. At quantum equilibrium the marginal arrival-time probability on a given leaf is fixed by the wave-function modulus on that leaf. Since the two events are spacelike, the equilibrium distribution for the arrival particle should be independent of the hidden variables on the other side, so averaging over spin outcomes could make the two orderings produce identical statistics. The abstract gives no calculation showing the dependence survives this averaging, and without those steps the claim is not yet grounded. If the full paper contains an explicit derivation that avoids the cancellation, it needs to be checked for hidden assumptions about how the conditional wave function is defined across leaves. This is aimed at people already working on relativistic Bohmian mechanics or on arrival-time observables. It is coherent enough on its own terms to deserve referee time so that experts can verify the missing derivations and see whether the equilibrium issue really is sidestepped. I would send it out for review rather than desk-reject.

Referee Report

1 major / 1 minor

Summary. The manuscript outlines an experimental protocol to detect the preferred foliation in relativistic Bohmian mechanics. It builds on arrival-time distributions for spin-1/2 particles from Das and Dürr and argues that, in an EPRB-type setup with spacelike-separated spin and arrival-time measurements, the observed arrival-time statistics depend on the temporal order of the measurements relative to the (flat) preferred foliation. This dependence is presented as an empirical signature of the foliation and as implying the possibility of superluminal signaling.

Significance. If the central claim is substantiated with explicit calculations, the result would be significant for quantum foundations: it would challenge the standard view that the preferred foliation is undetectable at quantum equilibrium and would provide a concrete, falsifiable test. The paper correctly identifies the relevant prior work and frames the protocol clearly, but the absence of derivations means the significance cannot yet be assessed.

major comments (1)

The manuscript provides only an outline and states that it 'shows' the dependence of arrival-time statistics on foliation ordering, yet contains no derivations, explicit wave-function updates, or marginal-probability calculations. This is load-bearing for the central claim because, without them, it remains open whether the conditional guidance-equation change produces distinct marginal arrival-time distributions after averaging over spin outcomes, or whether quantum equilibrium on spacelike leaves forces the two orderings to yield identical statistics.

minor comments (1)

The abstract and text refer to 'Das and Dürr' without a full bibliographic entry or clarification of which specific results (e.g., which equation or theorem) are being extended.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and for highlighting the need for explicit calculations to substantiate the central claim. We agree that the current manuscript is an outline and will revise it to include the required derivations of the arrival-time distributions.

read point-by-point responses

Referee: The manuscript provides only an outline and states that it 'shows' the dependence of arrival-time statistics on foliation ordering, yet contains no derivations, explicit wave-function updates, or marginal-probability calculations. This is load-bearing for the central claim because, without them, it remains open whether the conditional guidance-equation change produces distinct marginal arrival-time distributions after averaging over spin outcomes, or whether quantum equilibrium on spacelike leaves forces the two orderings to yield identical statistics.

Authors: We agree that the manuscript as submitted provides only a conceptual outline without explicit derivations. The dependence follows from the fact that the preferred foliation defines the simultaneity hypersurface on which the guidance equation is applied, so the order of the spacelike-separated measurements alters the conditional wave function for the arrival-time particle. In the revised version we will supply the full calculations: the post-measurement conditional wave functions for each foliation ordering, the resulting guidance velocities, and the marginal arrival-time distributions obtained by integrating over the spin outcomes. These will demonstrate that the two orderings produce distinct statistics, as quantum equilibrium on the leaves does not erase the foliation-dependent nonlocality in the guidance law. revision: yes

Circularity Check

0 steps flagged

No circularity: claim follows from external Das-Dürr distributions applied to foliation ordering

full rationale

The paper outlines an experimental protocol by taking the arrival-time distributions for spin-1/2 particles as given from the independent prior work of Das and Dürr, then examining how those distributions change when the relative order of spacelike measurements is reversed with respect to a flat preferred foliation. No self-definitional equations, fitted parameters renamed as predictions, or load-bearing self-citations appear in the abstract or described structure. The claimed dependence on foliation order is presented as a direct consequence of the guidance equation on successive leaves rather than a reduction to the input distributions themselves. This constitutes a standard, non-circular extension of prior independent results.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claim rests on the existence of a preferred foliation (domain assumption from relativistic Bohmian mechanics) and on the validity of arrival-time formulas from earlier work; no free parameters or new entities are introduced in the abstract.

axioms (2)

domain assumption A preferred foliation of spacetime exists and is flat
Required to define simultaneity for configurations in relativistic Bohmian mechanics; stated as assumed for simplicity.
domain assumption Arrival-time distributions for spin-1/2 particles follow the predictions of Das and Dürr
Used as the basis for the new protocol without re-derivation.

pith-pipeline@v0.9.0 · 5442 in / 1394 out tokens · 45065 ms · 2026-05-10T05:34:24.601401+00:00 · methodology

discussion (0)

Reference graph

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