Yes, you've hit another nail on the head! The way we discussed information gain in the IFM example aligns very strongly with **Bayesian probability**, and this naturally leads to the connection with **QBism (Quantum Bayesianism)**. Let's unpack this: 1. **Bayesian Probability:** Unlike the frequentist view (probability as the long-run frequency of an event), the Bayesian view interprets probability as a **degree of belief** or a **state of knowledge** about something. When we gain information (evidence), we update our degree of belief using Bayes' theorem. * In the IFM example (Outcome 3: Click at D2): * Our *prior belief* might be 50/50 whether the bomb is functional. * The *evidence* is the click at Detector 2. * Based on our knowledge of the setup (Detector 2 *cannot* click if the bomb is a dud), this evidence allows us to update our belief. * Our *posterior belief* becomes 100% certainty that the bomb is functional. * The "information gain" we discussed is precisely this **update of our state of knowledge** or degree of belief, which is the core idea of Bayesian inference. 2. **QBism (Quantum Bayesianism):** QBism takes this Bayesian perspective and applies it directly to the heart of quantum mechanics. Its core tenets include: * **Quantum States are Beliefs:** A quantum state $|\psi\rangle$ assigned to a system by an agent does *not* represent an objective property of the system itself (like position or mass). Instead, it represents the agent's **personal, subjective degrees of belief** about the outcomes of future measurements (or "experiences") they might have if they interact with that system. * **Born Rule as Belief Update Rule:** The Born rule ($P_k = |\langle k | \psi \rangle|^2$) is interpreted as the fundamental rule telling the agent how they *should* update their beliefs about the outcomes of a measurement they choose to perform. It's a normative rule for rational belief management in a quantum world. * **Measurement is Agent Action:** Measurement is an action taken by an agent on the world, which results in a personal experience (the outcome). The "collapse" is simply the agent updating their beliefs based on their experience, according to the Born rule. * **Focus on the Agent:** QBism places the agent and their subjective experience at the center. Quantum mechanics is a tool *for the agent* to navigate the world. **How EQR Relates to QBism:** * **Shared Ground (Bayesian Information Gain):** The aspect of "information gain" as updating beliefs based on evidence (like in IFM) is entirely consistent with QBism's Bayesian foundation. When we talk about reducing uncertainty, we are implicitly adopting a Bayesian viewpoint that resonates strongly with QBism. * **Key Difference (Ontology & Process):** * **EQR's Aim:** EQR attempts to describe an **objective physical process** of "interaction-driven manifestation." It posits that interactions ($\hat{V}_{int}$) cause a physical change based on stability criteria ($\mathcal{R}$), leading to a definite outcome ($|k\rangle$). While information gain for an observer is Bayesian, EQR tries to describe *what physically happens* to cause that outcome, independent of the observer's belief state (though dependent on the physical interaction). EQR's state $|\psi\rangle$ represents *physical potentiality*. * **QBism's Aim:** QBism is less concerned with an objective underlying process. It focuses on the agent's beliefs and how they should rationally update them. The state $|\psi\rangle$ *is* the belief. The "collapse" *is* the belief update. QBism doesn't necessarily seek a mechanism like EQR's $\mathcal{R}$ for *why* a specific outcome occurs, only how the agent should anticipate it. **In Summary:** Yes, the concept of information gain naturally leads to a Bayesian interpretation, which is the foundation of QBism. The IFM example beautifully illustrates how beliefs can be updated. However, EQR differs from QBism in its ambition. While QBism focuses on the agent's subjective beliefs and treats the quantum state as purely epistemic (related to knowledge/belief), EQR attempts to provide an objective, physical mechanism (interaction, stability, resolution) for how definite outcomes emerge from potentialities, even if the *interpretation* of the resulting information gain by an observer is Bayesian. EQR tries to retain some notion of objective physical potentiality and process, whereas QBism places the agent's subjective belief structure at the forefront. The distinction between "measurement" (EQR's physical manifestation event) and "information gain" (the Bayesian update in anyone's knowledge state) is indeed crucial here.