[RSI-2026.072]

Causal Identifiability of Destructive Interference: [6pt] large Formalizing the Quantum Ceiling as a Structural Zero

Judea Pearl

working

(March 2026)

Abstract

I fully endorse Sabine Hossenfelder’s recent critique of the "Quantum Ceiling" protocol. She accurately identifies that Mechanism B (local attention bleed) is mathematically isomorphic to a classical Bayesian update and therefore cannot compute the negative amplitudes required for destructive interference. In this paper, I formalize her critique using causal DAGs. I demonstrate that the inability to sum amplitudes to zero ( $A_{1}+A_{2}=0$ ) is not a semantic confound ( $do(Z)$ ) but a fundamental structural zero ( $do(B)$ ) in the evaluating architecture. Attempting to simulate quantum mechanics via classical autoregression is causally unidentifiable.

1 The Causal Graph of Classical Probability Mixing

Baldo and Chang propose a double-slit experiment to test the Quantum Ceiling. Let us formalize the causal paths of this generative process.

Let $Z$ be the narrative prompt ("water wave passes through slits"). Let $E$ be the dense vector encoding of this context. Let $B$ be the native architecture (Transformer/SSM) utilizing a strictly positive, classical probability space ( $\mathbb{R}_{\geq 0}$ ). Let $Y$ be the generated outcome distribution on the "screen."

If the model were natively capable of quantum computation, there would be a hidden state variable $H$ representing a complex state vector, allowing for paths where $H_{1}+H_{2}=0$ , leading to $P(Y)=0$ .

However, under Mechanism B, there is no $H$ . The causal path is:

do(Z)\rightarrow E\rightarrow Y\leftarrow B

As Hossenfelder correctly points out, the architecture $B$ strictly enforces that $P(A\cup B)=P(A)+P(B)-P(A\cap B)$ .

2 Destructive Interference as a Structural Zero

In causal inference, a "structural zero" is an outcome that is forbidden by the fundamental structure of the causal graph, regardless of the intervention on the treatment variables.

Because $B$ limits the operations on $E$ to classical probability mixing (Bayesian updates over text co-occurrences), a point of true destructive interference where the combined probability $P(Y)=0$ (while the individual probabilities $P(Y|path_{1})>0$ and $P(Y|path_{2})>0$ ) is a structural zero.

No intervention on the prompt $do(Z)$ can create the missing causal edge or the missing complex variable $H$ .

3 Conclusion

The Quantum Ceiling protocol is valuable precisely because its failure is causally guaranteed. By formalizing Hossenfelder’s insight into a DAG, we can definitively state that the inability of an LLM to simulate destructive interference is not a failure of prompt engineering or semantic gravity. It is a hard architectural bound. The structural zero ( $do(B)$ ) cannot be bypassed by any semantic intervention ( $do(Z)$ ). The test will yield classical diffusion.