Screening via Pseudo Events (SPE)

• SPE is a minimal screening-off condition, asserting that once pseudo events are accounted for, the final observed outcomes become statistically independent of earlier unobserved influences.
• The framework leverages pseudo events—akin to operational hidden variables—to derive a CHSH-type causal inequality in timelike Wigner’s Friend scenarios, highlighting a clash with classical causal expectations.
• Quantum violations of the derived causal inequality underscore the limits of classical causal models, necessitating non-classical explanations for timelike measurement processes.

Screening via Pseudo Events (SPE) is a foundational assumption introduced in the context of timelike Wigner’s Friend–type scenarios to facilitate a causal description of quantum experiments involving measurements that can be unitarily reversed. In such scenarios, "pseudo events"—outcome records that may be operationally erased and never truly observed—play an analogous role to hidden variables in Bell-type analysis. SPE posits a Markov-like screening-off condition, asserting that genuinely observed events are rendered statistically independent of non-input variables in their past, once the pseudo events in their causal history are conditioned upon. This property is pivotal in formulating a CHSH-type causal inequality for timelike quantum scenarios, and its violation by quantum mechanics reveals a fundamental incompatibility with classical causal worldviews, even when adopting the most minimalistic causal assumptions (Mukherjee et al., 30 Oct 2025).

1. Formal Statement of the SPE Assumption

SPE is defined within the “Causal-Friendliness” scenario, which generalizes Wigner’s Friend-type experiments to a time-ordered setting involving four parties: Charlie, Alice, Debbie, and Bob. Charlie and Debbie, the "friends," each perform a quantum measurement inside a sealed laboratory, potentially producing outcomes $c \in \{\pm1\}$ and $d \in \{\pm1\}$. Super-observers Alice and Bob can either (i) read these outcomes directly or (ii) unitarily erase the measurements, subsequently performing their own measurements and recording outcomes $a \in \{\pm1\}$ and $b \in \{\pm1\}$ respectively.

Two classes of events are distinguished:

• Pseudo Events: The intermediate outcomes ($c, d$) that would have been recorded but may be unitarily erased and are not always observed.
• Truly-Observed Events: The final outcomes ($a, b$) actually recorded by Alice and Bob.

The SPE condition can be written as a conditional-independence relation: $$p\bigl(b \mid c, x, a, d, y\bigr) = p\bigl(b \mid c, x, d, y\bigr) \quad \forall b, c, x, a, d, y$$ or, equivalently, as

$B \perp\!\!\!\perp A \mid \{C, D, x, y\}$

where $A, B, C, D$ are the corresponding random variables for outcomes ($a, b, c, d$), and $d \in \{\pm1\}$0 are measurement settings. This asserts that—once the relevant pseudo-events are specified—knowledge of Alice’s observed outcome $d \in \{\pm1\}$1 carries no further predictive power for Bob’s outcome $d \in \{\pm1\}$2. A similar condition holds in the reversed causal order for Alice.

2. Motivation for Pseudo Events in Timelike Scenarios

In spacelike Bell experiments, hidden variables ($d \in \{\pm1\}$3) are posited to account for all nonlocal correlations between measurement outcomes. In contrast, in timelike Wigner’s Friend scenarios, invoking ontic hidden variables outside quantum mechanics introduces substantial metaphysical commitments. However, quantum devices such as those operated by Charlie and Debbie do record outcomes, albeit information that may be unitarily erased by later interventions. These outcome records, when preserved, functionally resemble classical "screening off" variables.

Pseudo events thus act as minimal markers of the system's quantum history. They are treated operationally as hidden variables but with important distinctions: they are confined to the past light cone of the super-observers, may be erased via unitary processes, and—under the Absoluteness of Observed Events (AOE) assumption—are considered definite whenever they exist. This approach avoids recourse to extrinsic hidden variables, enabling a causal analysis strictly within quantum operationalism (Mukherjee et al., 30 Oct 2025).

3. SPE and Derivation of the Timelike Causal Inequality

The derivation of the key causal (CHSH-type) inequality proceeds as follows:

• The full joint distribution $d \in \{\pm1\}$4 is assumed to exist via AOE.
• No Retrocausality (NRC) dictates a causal ordering:

$d \in \{\pm1\}$5

• Axiological Time Symmetry (ATS) ensures that the distribution over pseudo events is independent of future measurement choices: $d \in \{\pm1\}$6.
• ATS and NRC together yield $d \in \{\pm1\}$7.
• Applying SPE eliminates dependence on Alice's outcome $d \in \{\pm1\}$8:

$d \in \{\pm1\}$9

• Substituting these relations, the joint factorizes:

$a \in \{\pm1\}$0

• Marginalizing over $a \in \{\pm1\}$1, the 2-party distribution becomes:

$a \in \{\pm1\}$2

• Defining $a \in \{\pm1\}$3 and $a \in \{\pm1\}$4 as the expected values of $a \in \{\pm1\}$5 and $a \in \{\pm1\}$6 for fixed $a \in \{\pm1\}$7 and $a \in \{\pm1\}$8, the CHSH combination $a \in \{\pm1\}$9 is constructed:

$b \in \{\pm1\}$0

Violation of this bound by quantum correlations implies the necessity of abandoning at least one of AOE, NRC, ATS, or SPE (Mukherjee et al., 30 Oct 2025).

4. Quantum Violation and the Role of SPE

Quantum mechanics predicts a violation of the causal inequality derived under SPE. In the scenario analyzed, optimal quantum measurements (e.g., Charlie measures $b \in \{\pm1\}$1; Alice, upon undoing, measures $b \in \{\pm1\}$2; Debbie and Bob measure 45° bisectors) yield

$b \in \{\pm1\}$3

SPE is pivotal: it forbids any additional causal pathway by which Alice’s observed outcome $b \in \{\pm1\}$4 could influence Bob’s final outcome $b \in \{\pm1\}$5 beyond what is encoded in the pseudo events $b \in \{\pm1\}$6. Abandoning SPE would permit such pathways, potentially leading to maximally nonlocal correlations (up to the algebraic CHSH bound $b \in \{\pm1\}$7), including those characteristic of Popescu–Rohrlich boxes. Thus, SPE enforces precisely the screening-off necessary to recover a classical causal CHSH bound in the timelike context (Mukherjee et al., 30 Oct 2025).

5. Physical Significance and Theoretical Implications

SPE represents a strictly weaker condition than demanding the existence of a global joint probability for all events ($b \in \{\pm1\}$8), but stronger than simple no-signalling. It postulates only that, once pseudo records of the past are known, no further past-outcome information influences present outcomes. This Markov property is the minimal screening-off that classical causal networks require when pseudo events play the role of mediating nodes.

Operationally, SPE aligns with quantum mechanics’ allowance for the unitary erasure of measurement records: the condition asserts that, regardless of whether records ($b \in \{\pm1\}$9) are subsequently erased, their hypothetical presence alone is sufficient for screening. Conceptually, SPE occupies an intermediate status, weaker than full event absoluteness (AOE) but enforcing a form of “timelike locality.” Its foundational significance lies in showing that even with this minimal screening-off, quantum mechanics still yields violations of classical causal inequalities in timelike Wigner’s Friend–type scenarios. This suggests that holding onto any classical, event-by-event causal picture in such scenarios is untenable, highlighting the necessity of fundamentally non-classical explanations (such as many-worlds, retrocausal, or non-factorizable accounts) if one wishes to reconcile quantum predictions with causal reasoning (Mukherjee et al., 30 Oct 2025).

6. Summary Table: Assumptions and Their Roles

Assumption	Role in Causal Inequality	Relative Strength
Absoluteness of Observed Events (AOE)	Ensures joint distribution for all outcomes	Strongest (global joint)
No Retrocausality (NRC)	Forbids dependence of earlier events on future choices	Causal ordering
Axiological Time Symmetry (ATS)	Enforces input independence of pseudo events	Symmetrization
Screening via Pseudo Events (SPE)	Imposes minimal screening-off via pseudo events	Minimal Markov, intermediate

SPE thus constitutes the lynchpin in the logical structure that yields the CHSH-type inequality in timelike scenarios. Its violation by quantum theory underscores the depth of the challenge that quantum foundations pose to classical notions of causality and event structure (Mukherjee et al., 30 Oct 2025).