Observational Deferral Logic

Observational Deferral Logic Hyeongmin Kim Department of History, Myongji University Seoul, Korea [email protected] October 18, 2025 1 Contents 1 Introduction: When Does Information “Exist”?) 4 1.1 Motivation: Tension between Quantum Mechanics and Thermodynamics . . . . . . . . . . 4 1.2 Limitations of Existing Interpretations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Proposal of This Paper: Observational Deferral Logic . . . . . . . . . . . . . . . . . . . . 5 1.4 ODLasaTheoreticalTool ................................... 6 1.5 StructureofthePaper...................................... 6 2 Formalization of ODL 6 2.1 Definition of Perfect Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Mathematical Expression of Entropy Deferral . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Ontological Modes of Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 AssumptionsofODL....................................... 7 2.5 Relation of ODL to Existing Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Thought Experiment: “The Near-Infinite Battery” 8 3.1 Motivation for the Experiment Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 SystemSpecifications....................................... 8 3.3 SystemEvolution......................................... 8 3.4 Observation Moment: Entropy Explosion . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.5 Meaning of the “Near-Infinite Battery” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.6 EducationalValue ........................................ 10 4 Structural Similarity with Black Hole Information Paradox 10 4.1 Brief History of the Information Paradox . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.2 Reinterpretation from the ODL Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.3 ODL Interpretation of the Page Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5 ODL Reinterpretation of “Soft Hair” Hypothesis 13 5.1 Soft Hair Hypothesis: A New Proposal for Information Storage . . . . . . . . . . . . . . . 13 5.2 Core Proposal of ODL: Not a Repository but a Delay Mechanism . . . . . . . . . . . . . . 13 5.3 The Journey of Information: A Three-Stage Process . . . . . . . . . . . . . . . . . . . . . 13 5.4 Reinterpreting“Softness” .................................... 14 5.5 FirewallParadoxandODL ................................... 14 5.6 Holographic Principle and ODL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 6 Information Ontology and Philosophical Implications 15 6.1 Three Modes of Information Existence: Potential, Leakage, Actual . . . . . . . . . . . . . 15 6.2 The Role of the Observer: Catalyst of Information Actualization . . . . . . . . . . . . . . 15 6.3 Relativity of Reality: Reality for Whom? . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 6.4 The Arrow of Time: Directionality of Information Actualization . . . . . . . . . . . . . . . 16 7 Physical Limitations and Future Directions 16 7.1 Physical Limitations of ODL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 7.2 Partial Realization: Possibility of Weak ODL . . . . . . . . . . . . . . . . . . . . . . . . . 17 7.3 Four Directions of Theoretical Extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 7.4 Experimental Verification Proposals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 8 Conclusion: Insight Through the Impossible 18 8.1 ODLasaTheoreticalTool ................................... 18 8.2 FiveContributionsofODL ................................... 19 8.3 The Legacy of the “Near-Infinite Battery” . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 8.4 The Black Hole Information Paradox: Contributions and Limits of ODL . . . . . . . . . . 20 8.5 Testability: A Realistic Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 8.6 Final Reflection: The Value of the Impossible . . . . . . . . . . . . . . . . . . . . . . . . . 21 3 Abstract This paper proposes a new theoretical framework, “Observational Deferral Logic (ODL),” to explore the fundamental relationship between quantum information and thermodynamic entropy. The central proposition of this logic is as follows: in a perfectly isolated quantum system, the actualization of information and entropy can be deferred until the moment of observation. To concretize this logic, we introduce an idealized optical cavity thought experiment. Under extreme conditions of 100% reflective mirrors and perfect quantum coherence preservation, the system maintains an entropy state of S= 0 for one year, after which a single measurement instantaneously produces a discontinuous entropy emergence of ∆S∼1034kB. This “entropy explosion” is accompanied by a sudden release of energy on the order of 1015 J (the “almost infinite battery”), vividly illustrating the dramatic consequence of deferred information actualization. This study suggests that Observational Deferral Logic exhibits a structural isomorphism with the black hole information paradox, particularly with the Hawking-Perry-Strominger “soft hair” hypothesis. In both cases, the boundary (mirror/horizon) induces information isolation, and the act of observation actualizes information. Through this analogy, we propose a new interpretation of the information paradox: information is not annihilated; rather, its actualization is merely deferred. Although ODL is experimentally unattainable, it provides value as a theoretical tool in the following respects: (1) offering a new perspective on the connection between quantum measurement and entropy increase, (2) enabling philosophical discussion on the ontological status of information, and (3) serving as a conceptual bridge between quantum information theory and gravitational theory. Situated within the tradition of thought experiments that explore “the limits of the possible” through “the impossible,” this paper aims to provide an alternative perspective on the fundamental problems of modern physics. 1 Introduction: When Does Information “Exist”?) 1.1 Motivation: Tension between Quantum Mechanics and Thermodynamics The two pillars of 20th-century physics, quantum mechanics and thermodynamics, treat information differently: Quantum Mechanics [5],[22]: •Information is preserved (unitary evolution) •Entropy of pure states: S= 0 •Time-reversal symmetric Thermodynamics [4], [3]: •Information is lost (irreversible processes) •Entropy increases: dS dt ≥0 •Arrow of time exists This tension is maximized in the measurement problem [18]. Before measurement, unitary evolution preserves information, but at the moment of measurement, entropy increases with wavefunction collapse. Fundamental Question: Where is the information of the system before measurement? Does measurement “create” information, or “reveal” it? 4 1.2 Limitations of Existing Interpretations Existing answers to this question are unsatisfactory: Copenhagen Interpretation [2]: •Physical quantities are “undefined” before measurement •Problem: How can something undefined follow unitary evolution? Many-Worlds Interpretation [11]: •All possibilities are real, and the universe branches •Problem: Why do we experience only a single outcome? (the origin of probability) Objective Collapse Theories [7]: •Spontaneous collapse occurs probabilistically •Problem: Introduction of new parameters, lack of experimental verification Decoherence Theory [24], [13]: •Classicality emerges through entanglement with the environment •Problem: “Which observable is preferred?” (basis problem) 1.3 Proposal of This Paper: Observational Deferral Logic We propose a new theoretical framework: Observational Deferral Logic (ODL) Core Proposition: Information passes through three ontological modes: 1. Potential: Perfectly isolated quantum superposition state •Information “exists” but is inaccessible •Entropy S= 0 •Observer-independent 2. Leakage: Gradual entanglement with the environment •Information diffuses into the environment •Entropy 0< S < Smax •Reversible in principle (quantum error correction) 3. Actual: Classical record through observation •Information is acquired by the observer •Entropy S=Smax •Irreversible The key claim of ODL: If Stage 2 (Leakage) is perfectly suppressed, the actualization of information can be deferred until the moment of observation. 5 1.4 ODL as a Theoretical Tool ODL does not claim that it actually occurs in nature. Rather: •A conceptual tool idealized like the ideal gas •An extreme-case approximation like Fraunhofer diffraction •A limiting concept like reversible processes in thermodynamics Such idealizations are essential in physics. They are unattainable, but they help us understand the limits of actual processes. Therefore, ODL has the following value: •Clarifies the relationship between information and entropy •Explores the nature of the quantum-classical boundary •Provides a new interpretive framework for the information paradox 1.5 Structure of the Paper •Section 3: Physical conditions and mathematical formalization of ODL •Section 4: “Almost Infinite Battery” thought experiment (visualization of ODL) •Section 5: Connection with the black hole information paradox •Section 6: Reinterpretation of the “soft hair” hypothesis •Section 7: Philosophical implications for information ontology •Section 8: Physical limitations and future directions 2 Formalization of ODL 2.1 Definition of Perfect Isolation For ODL to hold, system Smust be perfectly isolated from environment E. Therefore, we present the following assumption. Definition 1. (Perfect Isolation): The coupled state always remains a product state: |Ψ(t)⟩SE =|ψ(t)⟩S⊗ |E0⟩E,∀t < Tobs Here, |E0⟩is the fixed state of the environment, and Tobs is the observation time. Mathematical Condition: TrE(|Ψ⟩SE⟨Ψ|) = |ψ⟩S⟨ψ| The system density matrix remains in a pure state. Physically, this means the environment state does not depend on the system state, and thus measuring the environment cannot provide information about the system. (Information leakage = 0) 6 2.2 Mathematical Expression of Entropy Deferral Definition 2. (Entropy Deferral): The von Neumann entropy remains zero until observation. SS(t)=−Tr ρSln ρS= 0 ∀t < Tobs At observation, it increases discontinuously: SS(T+ obs)=Smax >0 Entropy growth rate: dS dt =Smax ·δ(t−Tobs) (where δis the Dirac delta function) Note that this is an idealization. In reality, measurement requires finite time τmeas >0, so dS dt real ∼Smax τmeas but in the limit τmeas →0, the delta function is recovered. 2.3 Ontological Modes of Information Definition 3. (Potentiality of Information): The Shannon information Iof the system is I(S:E)=SS+SE−SSE Under perfect isolation (SSE = 0, SS= 0, SE= 0), I(S:E)=0[12]. Therefore, although there is no mutual information between the system and the environment, it is assumed that information potentially exists within the system, and the amount of this potential information is defined as: Ipotential = ln dim HS This can be explained with the analogy: “An unread book contains information, but provides you with 0 bits of information. The act of reading actualizes the information.” 2.4 Assumptions of ODL Three ideal assumptions for ODL to hold: Assumption 1. (Maintenance of Unitarity): ρS(t) = ˆ U(t)ρS(0) ˆ U†(t),ˆ U(t)=e−iˆ Ht/ℏ Assumption 2. (Boundary Condition): Information reflectivity at the system-environment boundary is 100% Rinfo = 1 −Tinfo = 1 Assumption 3. (Singularity of Observation): Observation is the only non-unitary process of the system t=Tobs ⇒evolution is unitary 7 2.5 Relation of ODL to Existing Theories ODL has various relationships with several existing theories. Regarding the Copenhagen interpretation, it shares the acknowledgement of non-unitary collapse at the moment of measurement, but differs in that ODL admits the “potential reality” of information before measurement. With the Many-Worlds Interpretation, it shares the aspect of unitary evolution before measurement, but ODL denies branching and instead upholds the actualization of a single outcome. It also acknowledges the role of the environment in decoherence theory. However, ODL explores perfect isolation as a theoretical extreme. With relational quantum mechanics [17], ODL is closest in its explanation of the relational nature of information, but it explores the limiting case of relational QM (all relations severed). 3 Thought Experiment: “The Near-Infinite Battery” 3.1 Motivation for the Experiment Design ODL is still abstract. To make it concrete, an intuitive and dramatic thought experiment is needed. For this thought experiment, the author proposes the “Near-Infinite Battery.” This thought experiment visualizes the core of ODL (entropy deferral), connects it with an everyday concept (energy), and effectively reveals the theoretical extreme through unrealistic consequences. 3.2 System Specifications Device: Optical cavity (Fabry-Pérot type) •Length: L= 20 m •Mirror reflectivity: R= 100% (ideal assumption) •Operation period: T= 1 year ≈3.15 ×107s Energy input: •Continuous laser: P= 100 MW •Photon wavelength: λ= 500 nm •Photon energy: Eγ=hc λ≈3.97 ×10−19 J Implementation of ODL assumptions: •Mirror = perfect information boundary (Assumption 2) •Cavity interior = isolated quantum system (Assumption 1) •Photoelectric measurement = only observation (Assumption 3) 3.3 System Evolution Initial state (t= 0): |ψ0⟩=|0⟩(vacuum) Laser injection (0< t < T): at each moment ∆t ∆N=P∆t Eγ 8 Under ODL assumptions, the system remains in a pure state: |ψ(t)⟩= N(t) X n=0 Cn(t)|n⟩, where |n⟩is the Fock state (photon number eigenstate). Total photon number: Ntotal =PT Eγ =108×3.15 ×107 3.97 ×10−19 ≈7.9×1033 Stored energy: Estored =Ntotal ·Eγ=PT = 3.15 ×1015 J Energy scale comparison: the battery is about 50 times the Hiroshima atomic bomb (∼6.3×1013 J). 3.4 Observation Moment: Entropy Explosion At t=T, measurement is performed with a photoelectric device. Before measurement (T−): •State: pure superposition |ψ(T−)⟩ •Entropy: S(T−)=0 •Information: potential state At measurement: wavefunction collapse. Each photon is either detected or not. After measurement (T+): •State: mixed state (specific photon number determined) •Entropy: S(T+)>0 •Information: actualized If each photon represents independent binary information: ∆S∼Ntotal ·kBln 2 ≈7.9×1033 ×10−23 ×0.69 ≈5.5×1011 J/K Physical meaning: •Entropy “frozen” for 1 year •Suddenly appearing at the moment of measurement •Entropy growth rate: dS dt → ∞ (delta function) 3.5 Meaning of the “Near-Infinite Battery” Why “battery”? A conventional battery stores chemical energy and releases it gradually. Thus entropy increases continuously with time, unlike ODL. However, the ODL battery leads to “freezing” of 9 and entropy increase. 6.3 Relativity of Reality: Reality for Whom? One of the most profound implications of ODL is that the timing of information actualization is relative to the observer. Consider the “near-infinite battery” thought experiment with two observers, Alice and Bob. If Alice measures the system at time T1, then from her reference frame the information is actualized. But to Bob, who does not know Alice’s result, the system may still remain in superposition. Only when Bob performs his own measurement at a later time T2does the information actually become available to him. Unlike objective collapse theories, this resonates with the perspective of Relational Quantum Mechanics. The actualization of information is not an absolute event, but one relative to each observer-system pair [6]. In terms of conditional entropy, immediately after Alice’s measurement, the system’s entropy for Alice is S(S|A)(t=T1)>0, but for Bob, who does not know the result of Alice, it remains S(S|B)(t=T1)=0. Reality is not a single universal event, but is constituted within relationships. 6.4 The Arrow of Time: Directionality of Information Actualization ODL also offers a new perspective on the long-standing “arrow of time” problem since Boltzmann. Why does the entropy of the universe increase only in one direction? ODL suggests that the arrow of time is the arrow of information actualization. Fundamental microscopic laws (quantum mechanics) are time-symmetric and do not increase entropy in isolated systems (dS/dt = 0). But the macroscopic thermodynamic laws we experience are asymmetric (dS/dt > 0). ODL explains the gap as arising from “observation”—interaction with the environment. The early universe was like a vast low-entropy quantum system where most information existed in potential state. As the universe evolved and structures formed, interactions among subsystems increased, leading to gradual actualization of information—manifested as entropy growth. The final heat death state of the universe would be one where all potential information has been fully actualized, leaving no room for new information to emerge. From this viewpoint, the low entropy of the early universe may not have been a special initial condition, but simply the natural state of information not yet actualized—an ironic yet intriguing conclusion. 7 Physical Limitations and Future Directions 7.1 Physical Limitations of ODL Why is ODL unrealizable? ODL represents a theoretical extreme. The assumption of perfect information isolation is elegant, but in the actual physical world, several fundamental mechanisms obstruct it. The inevitability of decoherence is the first obstacle. Interaction with the environment cannot be avoided in principle. The decoherence time achievable with current technology varies greatly depending on the system: for optical cavities τD∼10−8s, for state-of-the-art superconducting qubits τD∼10−3s, and the longest record in ion traps is about τD∼103s. However, the 1 year (τD∼107s) required by ODL demands an improvement of more than 104times beyond current capabilities. The more fundamental issue is not merely technical. Cosmic microwave background radiation (T∼ 2.7 K) cannot be completely blocked. Tiny fluctuations of spacetime due to quantum gravity effects, as well as quantum fluctuations of the vacuum itself, always exist. These constitute environments that are 16 in principle unavoidable, and no matter how sophisticated the isolation techniques, perfect isolation is unattainable. The finite duration of measurement is another important limitation. In ODL’s ideal limit, measurement is assumed to occur instantaneously (∆t→0), causing the entropy increase rate to diverge to infinity. In reality, measurement takes finite time. For the photoelectric effect, this is about τPE ∼10−15 s. Considering this, the entropy increase rate is dS dt ∼1034kB 10−15 ∼1049 J/(K ·s) which is still astronomically large, but not mathematically infinite. The energy-time uncertainty principle also presents a fundamental limit. According to Heisenberg’s uncertainty relation ∆E·∆t≳ℏ, for a system isolated for 1 year (∆t∼107s), the energy uncertainty is ∆E≲10−41 J. This is 1022 times smaller than the photon energy Eγ∼10−19 J. In other words, it is so small that even verifying whether energy conservation holds is impossible in principle. This implies that ODL’s assumption of “perfect” energy conservation is physically untestable. 7.2 Partial Realization: Possibility of Weak ODL Perfect ODL is impossible, but “weak ODL” may be partially realizable. Three specific proposals are as follows. The first is short-time ODL, which drastically lowers the target. Instead of one year, aim for coherence maintenance of about one hour (τD∼1 hour). Combining cryogenic environments, superconducting cavities, and active decoupling techniques may make this possible in principle. Even this would suffice to test the principle of “entropy deferral” itself. The second is few-qubit ODL, an approach to reduce system size. Instead of 1034 photons, aim for around 10 qubits, maintaining coherence for about one day (τD∼1 day). With ion trap technology and dynamic decoherence suppression methods, this could be accessible. This would allow observation of the stepwise process of information actualization. The third is an analog system. Instead of directly studying black holes, use analogous systems. Examples include acoustic black holes (supersonic flow in BECs) or vortices in superfluids, where “information deferral” phenomena may be found. This would be an indirect test of the ODL-black hole analogy [19]. 7.3 Four Directions of Theoretical Extension ODL is not a finished theory but a starting point. Four main directions of extension exist. First, a theory of partial actualization would be closer to reality. If information is not actualized “all at once” but gradually, how should it be described? A simple model is exponential actualization: S(t) = Smax 1−e−t/τD The key question here is: what is the mathematical structure of partially actualized states? How does it connect with weak measurement theory? How can “gradual acquisition” of information be quantified? In contrast, a dynamics of information actualization speed is a more ambitious goal. If the “speed” of actualization can be controlled, what parameters matter? Candidate factors include measurement strength, environmental coupling constants, and temperature. The goal is to establish a general 17 function dIactual dt =f(parameters) If established, this could lead to technologies for actively controlling information actualization. Third, ODL in quantum gravity represents the most fundamental extension. If spacetime itself is quantized, how would ODL be modified? Could spacetime itself exist in a “potential” state? How can ODL be formulated within the Wheeler-DeWitt equation? Could spin networks of loop quantum gravity be related to information deferral? One bold speculation is that near the black hole singularity, spacetime geometry exists in a quantum superposition, with information encoded in this superposed geometry as potential. Finally, cosmological application extends ODL to the largest scale. What was the information state of the universe just after the Big Bang? Perhaps almost all information existed in potential state, gradually actualizing through cosmic expansion and structure formation. The CMB observation may be a partial actualization of early-universe information. At the opposite extreme, how should heat death be interpreted? It may be the state in which all information is fully actualized, making any “new” observation impossible. 7.4 Experimental Verification Proposals Three experiments may partially test the core predictions of ODL. Experiment 1: Entropy Deferral Measurement. The goal is to confirm dS dt ≈0for short times. Inject a single photon into a superconducting cavity, isolate it for time tusing active decoupling, and measure purity via quantum state tomography. The key is how long Tr(ρ2)stays close to 1. ODL predicts Tr(ρ2)≈1for t≲τD. Confirming this would verify the principle of “entropy deferral.” Experiment 2: Discontinuous Actualization. The goal is to observe the “burst” of entropy increase. Prepare a superposed state, perform a sudden strong measurement, and compare entropy before and after: ∆S=Safter −Sbefore. ODL predicts that this ∆Soccurs on a timescale much shorter than the measurement time. By measuring the time profile of entropy increase with high precision, one could test ODL’s claim of “discontinuity.” Experiment 3: Page Curve in Acoustic Black Holes. This would indirectly test the ODL-black hole connection. Create an acoustic horizon in a Bose-Einstein condensate (BEC) and generate “Hawking radiation.” Then trace the entanglement entropy between the inside and outside of the horizon over time. ODL predicts that entropy will begin to decrease around tPage. Acoustic Hawking radiation has already been observed, so the next step is to observe the temporal unfolding of information actualization. 8 Conclusion: Insight Through the Impossible 8.1 ODL as a Theoretical Tool This paper has proposed a new interpretative framework, Observational Deferral Logic (ODL). The core proposition is clear: in a perfectly isolated quantum system, the actualization of information and entropy can be deferred until the moment of observation. This proposition is physically unrealizable, but precisely this impossibility reveals the value of ODL. Looking back at the history of physics, the most important conceptual tools were often unattainable extremes. The ideal gas assumes molecules with no volume, yet it became the starting point for understanding real gases. Reversible processes assume no entropy increase, yet they provided the foundation 18 for Carnot efficiency and the laws of thermodynamics. Absolute zero is unreachable, yet it became the reference point for quantum statistics and low-temperature physics. ODL stands in the same tradition. Perfect information isolation is impossible, but it can serve as a theoretical tool for understanding the extremes of the quantum-classical boundary and information actualization. 8.2 Five Contributions of ODL First, conceptual clarification. ODL clarifies the relationship between information, entropy, and observation. Information passes through three stages—potential, leakage, actual—and each stage has physically distinguishable characteristics. Entropy emerges when information is actualized. Observation is not passive “seeing” but an active process of actualization. This clarity offers a new angle on the quantum measurement problem. Second, the role as a limiting theory. Just as the ideal gas is the theoretical extreme for real gases, ODL is the limiting case for understanding decoherence in real quantum systems. With decoherence times currently achievable at τD∼103s, the τD∼107sdemanded by ODL means an improvement by a factor of 104. This gap itself is educational. By exploring the “boundary of the possible,” we understand why that boundary exists—cosmic microwave background, vacuum fluctuations, quantum gravity effects. Third, a new perspective on paradoxes. The traditional question in the black hole information paradox was “where is the information?” ODL poses a different question: “when does the information actualize?” This temporal shift reinterprets the Page curve not as spatial information transfer but as a process of temporal actualization. Soft hair becomes not a storage mechanism but a deferral mechanism. The firewall paradox may find resolution through the observer-dependence of information actualization. These reinterpretations may not be final answers, but they open new routes where discussion had stalled. Fourth, an interdisciplinary bridge. ODL connects quantum information theory, thermodynamics, and gravity. Information actualization unifies von Neumann entropy (S=−Trρln ρ), Landauer’s principle (∆E≥kBTln 2), and Bekenstein-Hawking entropy (SBH =A 4l2 P ) into a single narrative. It further engages in dialogue with ontology in philosophy—Aristotle’s dynamis/energeia, Heidegger’s Sein/Dasein. Such connections remind us that physics is not merely a science of calculation but also a philosophy probing the essence of reality. Fifth, the stimulation of new questions. How can partial actualization be quantified? What is the general form of the dynamics of actualization speed, dIactual dt =f(parameters)? Could spacetime itself exist in a potential state in quantum gravity? Cosmologically, was the Big Bang a potential state of information and Heat Death complete actualization? These questions have no immediate answers, but they serve as a compass for future research. Science sometimes advances more from good questions than from definitive answers. 8.3 The Legacy of the “Near-Infinite Battery” The starting point of this paper, the “near-infinite battery,” was a provocative and dramatic metaphor. A device storing 3.15 ×1015 J(equivalent to about 50 atomic bombs) for a year and then releasing it all at once is unrealistic. But the very unreality was the point. Just as Maxwell’s demon appeared to “violate” the second law and revealed the link between information and entropy, and Schrödinger’s cat dramatized the absurdity of macroscopic superposition, the near-infinite battery visualizes the extreme consequences of information deferral. Its value lies in three aspects. First, intuitive communication: it transforms the abstract idea of “information actualization deferral” into the concrete image of “energy storage and sudden release.” 19 Second, the dramatic effect of entropy explosion: the mathematical expression dS dt → ∞ becomes vivid through the image of dozens of atomic bombs exploding simultaneously. Third, pedagogical usefulness: it can serve as a memorable tool for students learning about the relationship between quantum measurement and entropy. Of course, this is not a proposal for a practical energy device. It does not violate energy conservation—it merely recovers the energy invested. What is unrealistic is not the amount of energy, but the storage duration and sudden release. And it is precisely this impossibility that highlights ODL’s extreme character. 8.4 The Black Hole Information Paradox: Contributions and Limits of ODL ODL’s contributions to the black hole information paradox can be summarized in four points. 1. Posing new questions: shifting from “where is the information?” to “when does the information actualize?” reframes the issue from spatial to temporal/ontological. This is not mere wordplay. If the attempt to track the location of information has reached a dead end, exploring the timing of actualization opens a new path. 2. Potential for integrative interpretation: the soft hair hypothesis provided a storage mechanism but left unclear how information is read. ODL offers a complementary perspective. Soft hair + ODL = information stored in BMS charges in potential form, then gradually actualized through Hawking radiation. While not a complete answer, it could form a unifying conceptual framework. 3. Indirect testability: full black hole evaporation takes 1067 years, making direct observation impossible. But ODL offers detours for partial testing: measuring short-time information deferral in quantum optics, searching for Page-like transitions in acoustic black holes, or testing consistency within frameworks like AdS/CFT. These are indirect but meaningful verifications. 4. Conceptual clarification: the phrase “information loss” is misleading. Is information really “lost,” or merely inaccessible? ODL presents a third possibility: information exists in potential form and gradually actualizes. This is neither loss nor concealment but a change in mode of existence. Yet the limitations are also clear. ODL does not provide specific mechanisms. How exactly is information encoded in BMS charges, correlated with Hawking radiation, or why transitions occur at the Page time remain unresolved. ODL is a phenomenological framework, not a microscopic theory. Without a complete theory of quantum gravity, final judgment cannot be made. Thus, ODL is not a “solution” to the black hole information paradox but a “new perspective.” 8.5 Testability: A Realistic Assessment Frankly, testing ODL in its complete form is nearly impossible. Maintaining perfect quantum coherence for one year, or observing full black hole evaporation, far exceeds the scale of current technology and civilization. However, indirect testability exists. •Analog systems: In BEC-based acoustic black holes, Hawking radiation analogues have already been observed. The next step is to measure the entanglement entropy evolution inside and outside the horizon to look for Page-like transitions. 20 •Quantum optics experiments: In superconducting cavities, entropy deferral could be measured for about one hour, or discontinuous entropy increase upon measurement could be observed. This would not fully verify ODL but would confirm its core principle. •Theoretical consistency: Testing how well ODL interpretations align with frameworks like AdS/CFT correspondence, island formula, and holographic entanglement entropy. Most importantly, ODL provides conceptual clarity. Whether ultimately right or wrong, the question it raises—“when does information actualize?”—forces us to look at the black hole information paradox from a new angle. In the history of science, sometimes false theories advanced progress by asking the right questions. The phlogiston theory was wrong but triggered inquiries into the essence of combustion. The ether theory was wrong but prompted exploration of light propagation. ODL may play a similar role. Sometimes a good question is more valuable than a correct answer. 8.6 Final Reflection: The Value of the Impossible This paper has seriously explored the impossible—perfect quantum isolation. Some may see this as a waste of time. Why study what cannot be realized? But the history of physics is the story of those who imagined the impossible. Galileo imagined frictionless inclined planes. Newton calculated gravity at infinite distances. Einstein wondered about running at the speed of light. Schrödinger devised a half-dead cat. All these “impossibilities” advanced physics. ODL stands in the same tradition. Perfect information isolation is impossible. But by exploring that impossibility, we gain deeper understanding of information, entropy, observation, and the nature of reality. We discover the “boundary of the possible” and learn why it exists. The “near-infinite battery” cannot be built. But by imagining it, we confront the fundamental tension between quantum mechanics and thermodynamics. We cannot directly measure “when” black hole information actualizes. But by asking the question, we discover new routes into the information paradox. Ultimately, ODL’s value lies not in whether it is “true” but whether it is “useful.” Does it inspire new experiments? Does it stimulate theoretical connections? Does it spark the imagination of the next generation of physicists? Time will answer these questions. For now, what we can do is put this idea out into the world and subject it to critique and debate within the scientific community. That is the way of science: not pretending to have perfect answers, but posing interesting questions and seeking answers together. "Reality is not a collection of facts, but a process of actualization." This is the spirit of Observational Deferral Logic, and the message this paper seeks to leave with its readers. Information does not merely “exist,” it “becomes.” Reality is not a noun but a verb. And we, as observers, are part of that process. Through the impossible, we understand the possible. This is the paradox of theoretical physics, and the legacy of ODL. References [1] A. Almheiri, D. Marolf, J. Polchinski, and J. Sully. Black holes: Complementarity or firewalls? Journal of High Energy Physics, 2013(2):062, 2013. 21 [2] N. Bohr. The quantum postulate and the recent development of atomic theory. Nature, 121(3050):580–590, 1928. [3] L. Boltzmann. Über die beziehung zwischen dem zweiten hauptsatze der mechanischen wärmetheorie und der wahrscheinlichkeitsrechnung. Wiener Berichte, 76:373–435, 1877. [4] R. Clausius. Üeber verschiedene für die anwendung bequeme formen der hauptgleichungen der mechanischen wärmetheorie. Annalen der Physik und Chemie, 125(7):353–400, 1865. [5] P. A. M. Dirac. The Principles of Quantum Mechanics, 4th edition. Oxford University Press, Oxford, UK, 1958. First edition 1930. [6] C. A. Fuchs. Qbism, the perimeter of quantum bayesianism, 2010. 83 pages, v1 submitted March 26, 2010. [7] G. C. Ghirardi, A. Rimini, and T. Weber. Unified dynamics for microscopic and macroscopic systems. Physical Review D, 34(2):470–491, 1986. [8] S. W. Hawking. Black hole explosions? Nature, 248(5443):30–31, 1974. [9] S. W. Hawking. Breakdown of predictability in gravitational collapse. Physical Review D, 14(10):2460–2473, 1976. [10] S. W. Hawking, M. J. Perry, and A. Strominger. Soft hair on black holes. Physical Review Letters, 116(23):231301, 2016. [11] H. Everett III. ’relative state’ formulation of quantum mechanics. Reviews of Modern Physics, 29(3):454–462, 1957. [12] E. T. Jaynes. Information theory and statistical mechanics. Physical Review, 106(4):620–630, 1957. Part II: Physical Review 108(2): 171–190 (1957). [13] E. Joos, H. D. Zeh, C. Kiefer, D. J. W. Giulini, J. Kupsch, and I.-O. Stamatescu. Decoherence and the Appearance of a Classical World in Quantum Theory, 2nd edition. Springer-Verlag, Berlin, 2003. [14] J. M. Maldacena. The large n limit of superconformal field theories and supergravity. Advances in Theoretical and Mathematical Physics, 2(2):231–252, 1998. Also published in International Journal of Theoretical Physics 38(4): 1113–1133 (1999). [15] D. N. Page. Information in black hole radiation. Physical Review Letters, 71(23):3743–3746, 1993. [16] G. Penington. Entanglement wedge reconstruction and the information paradox. Journal of High Energy Physics, 2020(9):002, 2020. [17] C. Rovelli. Relational quantum mechanics. International Journal of Theoretical Physics, 35(8):1637– 1678, 1996. [18] E. Schrödinger. Die gegenwärtige situation in der quantenmechanik. Naturwissenschaften, 23:807– 812, 823–828, 844–849, 1935. English translation: "The Present Situation in Quantum Mechanics", Proc. Am. Phil. Soc. 124, 323–338 (1980). [19] J. Steinhauer. Observation of quantum hawking radiation and its entanglement in an analogue black hole. Nature Physics, 12(10):959–965, 2016. [20] L. Susskind, L. Thorlacius, and J. Uglum. The stretched horizon and black hole complementarity. Physical Review D, 48(8):3743–3761, 1993. 22 [21] G. ’t Hooft. Dimensional reduction in quantum gravity. In A. Ali, J. Ellis, and S. Randjbar-Daemi, editors, Salamfestschrift, pages 284–296. World Scientific, 1993. [22] John von Neumann. Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton, NJ, 1955. Original German edition: Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932). [23] J. A. Wheeler. The ’past’ and the ’delayed-choice’ double-slit experiment. In A. R. Marlow, editor, Mathematical Foundations of Quantum Theory, pages 9–48. Academic Press, New York, 1978. [24] W. H. Zurek. Decoherence, einselection, and the quantum origins of the classical. Reviews of Modern Physics, 75(3):715–775, 2003. 23