Branching Susceptibility Produces a Nonconstant Collapse Bias in State-Chaining Interference Tests

Authors: Sterling Geisel, QBist Lab

Abstract

Roman V. Li proposes an objective collapse model in which irreversible events occur when quantum degrees of freedom are forced into a shared chained state. The model is sparse. Each chaining step carries a universal collapse probability \(1/\Sigma\), and the reported interference data give lower bounds near \(\Sigma \sim 1.5\). This working paper applies Chaos Susceptibility to Li's model. The fit is natural but incomplete. Chaining identifies where a superposition becomes vulnerable. Pudding Theory predicts that vulnerability is not fixed by a universal constant alone. It should scale with the dynamical susceptibility of the receiver that amplifies the chain. Two devices with the same formal number of chaining steps but different measured branching instability should show different residual noninterfering bias after ordinary decoherence is removed. This converts Li's diagrammatic criterion into a laboratory observable: a tunable slope in \(B/I\) against branching susceptibility.

Source Synopsis

Li's paper addresses the measurement problem by proposing a new objective collapse mechanism rather than a reinterpretation of standard quantum mechanics. The central object is the qil, or quantum illustration. A qil records a system through its external degrees of freedom and the cardinality of state sets associated with them. It does not track full amplitudes. It is designed to display when degrees of freedom are entangled, when they remain undefined, and when several subsystems are forced to share one parameter.

The key new relation is chaining. A chaining bracket identifies the corresponding degrees of freedom of several qils, making them one shared degree of freedom. Li then states three theses. All qils are equivalent as external carriers of degrees of freedom. Interactions occur through those degrees of freedom. Chainings trigger events. The operational rule, called Chinese Whispers, assigns a fixed probability \(1/\Sigma\) that the appearance of one or more new chainings along one degree of freedom creates an event. An event is a transition from an undefined degree of freedom to a defined one, with Born-rule weights.

This model separates measurement devices from passive macroscopic objects. A photomultiplier tube or Geiger counter produces many chained subsystems. The probability of collapse approaches unity across many chaining steps. A mirror, by contrast, mainly produces momentum entanglement and need not trigger collapse. A Schrodinger cat setup collapses because detector, poison, tissue, and physiology produce many successive chainings.

Li also applies the model to atomic relaxation and delayed-choice quantum eraser data. For matter-wave interference, he treats a noninterfering bias fraction \(B/I\) as evidence for chaining-induced collapse and estimates lower bounds on \(\Sigma\). Reported examples include neutron beam splitter data, neutron double-slit data, helium atom double-slit data, neon atom double-slit data, and delayed-choice quantum eraser data. The paper concludes that \(\Sigma\) may be near 1.5, while stressing that ordinary decoherence can inflate the apparent bias and therefore make the inferred \(\Sigma\) only a lower bound.

Postulate Lens

The applicable Postulate is Chaos Susceptibility: highly chaotic systems are most susceptible to small coherent inputs.

Li's chaining mechanism is not described as chaos theory. Yet its experimental content is an instability claim. A superposition propagates into a receiver. If the receiver forces many subsystems to share one external degree of freedom, microscopic alternatives cease to remain private. The later state depends on a small early branch choice. That is the same operational structure that makes a high-Lyapunov system susceptible to small inputs.

The Postulate does not replace Li's qils. It supplies a missing weight. In Li's model, every new chaining carries the same intrinsic probability \(1/\Sigma\). A photomultiplier becomes classical because it contains many chainings. Pudding Theory agrees that chainings identify vulnerable places, but denies that all vulnerable places have equal dynamical gain. A cold, weakly coupled chain and a high-gain avalanche may have the same diagrammatic count and different susceptibility.

The practical lens is therefore narrow. Chaining marks the collapse channel. The susceptibility of the channel sets how strongly a microscopic bias is amplified into an event. A detector is not classical because it is large. It is classical because its chain has a large branching gain. A mirror remains coherent because its interaction does not produce a high-gain chain. Li's distinction survives. The universal constant becomes an intercept, not the full mechanism.

Pudding Theory Prediction

Pudding Theory predicts that Li's estimated \(\Sigma\) will not remain constant when the branching susceptibility of the amplification channel is tuned while the formal qil diagram is held fixed.

The clean experiment uses a matter-wave or photon interferometer in which the candidate chaining stage can be coupled to receivers with the same visible degree-of-freedom identification but different avalanche gain. One can vary dynode voltage in a photomultiplier, carrier multiplication in an avalanche photodiode, gas pressure in a Geiger-like detector, or gain in a superconducting threshold sensor. The interferometer should measure two quantities. First, it should measure the ordinary visibility loss expected from environmental decoherence. Second, it should measure the residual noninterfering bias \(B/I\) after that decoherence contribution is subtracted.

Li's model in its simplest form predicts a residual bias controlled by the number of chaining opportunities and by \(1/\Sigma\). For a fixed diagrammatic chain count, \(B/I\) should be stable within experimental error. Pudding Theory predicts a monotonic excess. The corrected bias should rise with independently measured branching susceptibility, such as avalanche multiplication variance, effective Lyapunov exponent of the detector response, or gain-normalized sensitivity to injected calibration pulses.

The effect should be absent in passive beam splitters and mirrors that create entanglement without a chained amplification path. It should be strongest near threshold, where a microscopic branch choice controls a macroscopic detector state and where small coherent perturbations are maximally amplified. It should not depend primarily on atomic mass or internal particle count. That point agrees with Li's treatment of neutrons, helium atoms, and neon atoms. The difference is that Pudding Theory ties collapse strength to the receiving dynamics, not only to formal state identification.

A secondary prediction follows for quantum computing. Elementary-particle qubits should not merely avoid chaining-induced collapse because they lack compound occupation chains. They should also show longer coherence when their readout chain is kept below high branching susceptibility until the final measurement window.

Falsifiable Observable

The distinguishing observable is the fitted slope \(\partial(B/I)_{\mathrm{res}}/\partial\chi_{\mathrm{branch}}\), where \((B/I)_{\mathrm{res}}\) is the residual noninterfering bias after environmental decoherence subtraction and \(\chi_{\mathrm{branch}}\) is an independently calibrated branching susceptibility of the detector chain. If the fitted slope of \((B/I)_{\mathrm{res}}\) against \(\chi_{\mathrm{branch}}\) were measured to be \(0 \pm 0.01\) over at least a tenfold change in \(\chi_{\mathrm{branch}}\), this Postulate would be falsified.

Editorial Dialogue

Tanaka: Li's proposal is attractive because it is austere. One event probability. One constant. One kind of diagrammatic trigger. Your reading adds a susceptibility parameter and makes the theory less sparse.

Sterling: Sparseness is useful only if it survives controlled variation. Li already concedes that the estimate of \(\Sigma\) may be contaminated by decoherence and may be a lower bound. That is the place to test structure, not to hide it.

Tanaka: But his qils ignore internal structure by construction. That is the point of equivalence. A neutron and a neon atom should be treated alike if their external degree of freedom is the same.

Sterling: The Postulate does not attach collapse to internal particle count. It attaches amplification to the receiver. A mirror and a detector can meet the same incoming quantum state and produce different outcomes. Li makes that distinction. I am sharpening it.

Tanaka: Then the experiment must separate receiver gain from ordinary decoherence.

Sterling: Yes. That is why the observable is residual bias after decoherence subtraction. If the residual is flat while the branching susceptibility changes by an order of magnitude, the Postulate fails. If it rises, a universal \(\Sigma\) is incomplete.

Discussion

The main limitation is experimental separation. Detector gain, thermal noise, dark counts, and environmental entanglement can all reduce interference visibility. A false positive is easy. The required test must measure standard decoherence independently, vary only the receiver's branching susceptibility, and keep geometry, flux, wavelength, and postselection rules fixed.

Li's qils are valuable because they avoid a crude mass threshold. Pudding Theory should not reintroduce such a threshold under another name. The proposed correction concerns dynamical amplification, not size. A large passive optical element may be weak. A small threshold detector may be strong.

The open theoretical question is whether \(\Sigma\) is a fundamental constant or an effective parameter extracted after coarse-graining over receiver dynamics. Li allows the possibility that the Chinese Whispers rule approximates a deeper mechanism. The present application takes that possibility seriously. A measured flat residual bias would favor Li's parameter-sparse form. A susceptibility-dependent residual would favor the Pudding Theory reading and would require revising collapse models that treat all chaining steps as equal.

References

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