The Speed of an Explanation

A reply changes the question

Following my inquiry about The Gate, Nicolas Gisin replied with three papers investigating faster-than-light, finite-speed hidden influences. They move this inquiry beyond the general statement that Bell-local explanations fail. They ask whether quantum correlations could instead be coordinated by an influence that travels extraordinarily fast through space and time.

His response supplies relevant research. The conclusions below are my reading of that research and my proposed direction for The Gate.

A lower bound is a conditional result

In the 2008 experiment by Salart and colleagues, entangled photons were measured at stations separated by 18 kilometres, approximately along an east–west axis. The measurements covered different times of day as Earth’s rotation changed the apparatus’s orientation relative to hypothetical preferred frames. The observed interference remained above the Bell-violation threshold. [1]

Suppose a hidden influence coordinates those results at a finite speed in a preferred universal frame. It must arrive soon enough. Under the example assumption that Earth’s speed relative to that frame is no greater than one thousandth of the speed of light, the paper places the influence’s speed at least four orders of magnitude above light speed: roughly 10,000 times c. [1]

This bounds a hypothetical explanation. The experiment does not detect a controllable signal traveling at that speed. Better timing and larger separations can raise such conditional bounds; they cannot establish an infinite speed by measuring a finite one.

Making the influence faster creates another problem

Bancal and colleagues’ 2012 paper addresses a deeper constraint. Their v-causal models allow hidden influences at any finite speed greater than c, defined in a preferred frame. They require the models to reproduce quantum correlations when the relevant measurements can be connected by those influences. Independent measurement choices remain an assumption. [2][3]

The argument uses four parties. Arrange their measurements so that two parties, B and C, cannot receive each other’s hidden influence in time, although the other relevant causal connections exist. In this model, B and C must then have local correlations conditional on the earlier results. Together with no-signaling, that requirement gives a hidden-influence inequality, S ≤ 7. Suitable quantum states and measurements yield about 7.2. [2]

The inequality uses marginal correlations that omit either B or C. It therefore exposes a conflict without requiring the model to reproduce the complete quantum distribution in the disconnected arrangement. A model that supplies the required quantum marginals must violate no-signaling there. The authors show how collective measurement statistics could then make that signaling available faster than light. [2]

This is a theoretical result about a specified class of explanations. It is not a report of an operating superluminal transmitter.

Continuity is an assumption too

Gisin’s longer paper makes the premise explicit: explanations built from local common causes and direct influences that propagate continuously, at finite speed, through space and time. Even granting a Newtonian preferred frame does not remove the conflict between reproducing the relevant quantum correlations and retaining no-signaling. [3]

Within those assumptions, we face a choice: accept signaling from the proposed finite-speed mechanism, or abandon that mechanism as the explanation of quantum nonlocality. Infinite-speed accounts, retrocausal accounts, and models that relax measurement independence require separate analysis; this theorem does not dispose of every possible interpretation.

For The Gate, the lesson is precise. Part IV gave up Bell-local explanations. Part V also gives up the easy image of a hidden messenger whose only unusual property is moving very quickly while remaining inaccessible to communication. Standard quantum theory’s nonlocal correlations and its no-signaling predictions remain the reference against which a new claim must be tested.