# Agent Inaccessibility as a Fundamental Principle in Quantum Mechanics: Objective Unpredictability and Formal Uncomputability

## Abstract

**:**

## 1. Introduction

## 2. Many-World and Single-World Quantum Interpretations

## 3. Restricting Agent Access to Ontological Quantum States and Quantum Information

#### 3.1. On the Reality of an Indefinite Quantum Ontology: Contextuality and Relationality

#### 3.2. The Inaccessible Universe and the Limits of Science

#### 3.2.1. On No-Hidden-Variables Theorems in Ontological Quantum Mechanics

#### 3.3. Hidden-Variables in Quantum Mechanics are Agent-Inaccessible Variables

## 4. Defining the Experimenter Agent

#### 4.1. The Quantum Measurement Problem

#### 4.2. An Early Definition of the Experimenter Agent: “Maxwell’s Demon”

#### 4.3. Recent Definition of the Experimenter Agent: “Epistemic Agency”

“Agency is generally defined as the capacity of humans or other entities to act in the world. Put differently, an agent is defined initially by possessing the capacity to influence causal flows in nature. By prefacing “agent” with the term “epistemic”, attention is drawn to the fact that a complete definition of agency represents more than the mere “capacity to influence causal flows”: an agent possesses knowledge-based, i.e., epistemic, capacity for predictably directing, and redirecting, causal flows, and thus for directing, and redirecting, information flows as well. That is, an epistemic agent holds the power to (statistically) control physical activity based upon an ability to predict the outcome of specific actions on targeted processes in reference to a known standard or goal. In short, an epistemic agent thus manifests in the world a genuine source of operational control”.

## 5. How does Nature Prohibit Access to the Experimenter Agent?

#### 5.1. Orthodox Quantum Mechanics: “Universal Indeterminism”

#### 5.1.1. On the Impossibility of Proving the Truth of Quantum Indeterminism

#### 5.2. Ontological Quantum Mechanics: “Effective Ignorance in Global Determinism”

#### 5.2.1. Understanding John Bell’s Concept of “Free Variables” for Quantum Mechanics

“Consider the extreme case of a ‘random’ generator which is in fact perfectly deterministic in nature—and, for simplicity, perfectly isolated. In such a device the complete final state perfectly determines the complete initial state—nothing is forgotten. And yet for many purposes, such a device is precisely a ‘forgetting machine’. A particular output is the result of combining so many factors, of such a lengthy and complicated dynamical chain, that it is quite extraordinarily sensitive to minute variations of any one of many initial conditions. It is the familiar paradox of classical statistical mechanics that such exquisite sensitivity to initial conditions is practically equivalent to complete forgetfulness of them.”

#### 5.2.2. Criticizing the Weak Option Interpretation

#### 5.3. Ontological Quantum Mechanics: “Objective Ignorance in Global Determinism”

## 6. In Search of Incomputable Nature: Quantum Reality and Quantum Randomness

#### 6.1. Computational Approaches to Quantum Theory Invoking Nonlinear Interactions

#### 6.2. Quantum Ontology and the Information-Theoretic Paradigm in Quantum Mechanics

#### 6.3. Could Hidden Variables Represent Uncomputable Variables Such as Turing-Incomputable Variables?

#### 6.4. The Non-Signaling Theorem and Effective versus Objective Computational Constraints

#### 6.5. Quantum Randomness and Turing Incomputability

## 7. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Bohm, D. A suggested interpretation of the quantum theory in terms of “hidden” variables. I. Phys. Rev.
**1952**, 85, 166–179. [Google Scholar] [CrossRef] - Bohm, D. A suggested interpretation of the quantum theory in terms of “hidden” variables. II. Phys. Rev.
**1952**, 85, 180–193. [Google Scholar] [CrossRef] - Bohm, D.; Hiley, B.J. The Undivided Universe: An Ontological Interpretation of Quantum Theory; Routledge: London, UK, 1993. [Google Scholar]
- Holland, P.R. The Quantum Theory of Motion; Cambridge University Press: Cambridge, UK, 1993; ISBN 0-521-35404-8. [Google Scholar]
- Bricmont, J. Making Sense of Quantum Mechanics; Springer: Heidelberg, Germany, 2016. [Google Scholar]
- Norsen, T. Foundations of Quantum Mechanics; Springer: Heidelberg, Germany, 2018. [Google Scholar]
- Dürr, D.; Teufel, S. Bohmian Mechanics; Springer: Heidelberg, Germany, 2009. [Google Scholar]
- Tumulka, R. Bohmian mechanics. In The Routledge Companion to the Philosophy of Physics; Wilson, A., Ed.; Routledge: London, UK, 2018. [Google Scholar]
- Harrigan, N.; Spekkens, R.W. Einstein, incompleteness, and the epistemic view of quantum states. Found. Phys.
**2010**, 40, 125–157. [Google Scholar] [CrossRef] - Pusey, M.F.; Barrett, J.; Rudolph, T. On the reality of the quantum state. Nat. Phys.
**2012**, 8, 475–478. [Google Scholar] [CrossRef][Green Version] - Leifer, M.S. Is the quantum state real? An extended review of ψ-ontology theorems. Quanta
**2014**, 3, 67–155. [Google Scholar] [CrossRef] - Leifer, M.S.; Pusey, M.F. Is a time symmetric interpretation of quantum theory possible without retrocausality? Proc. R. Soc. A
**2017**, 473, 20160607. [Google Scholar] [CrossRef] [PubMed][Green Version] - Wharton, K. A new class of retrocausal models. Entropy
**2018**, 20, 410. [Google Scholar] [CrossRef] - Adlam, E.C. Quantum mechanics and global determinism. Quanta
**2018**, 7, 40–53. [Google Scholar] [CrossRef] - Adlam, E.C. Spooky action at a temporal distance. Entropy
**2018**, 20, 41. [Google Scholar] [CrossRef] - Argaman, N. A lenient causal arrow of time? Entropy
**2018**, 20, 294. [Google Scholar] [CrossRef] - Grössing, G.; Fussy, S.; Mesa Pascasio, J.; Schwabl, H. Vacuum landscaping: Cause of nonlocal influences without signaling. Entropy
**2018**, 20, 458. [Google Scholar] [CrossRef] - Wolfram, S. Undecidability and intractability in theoretical physics. Phys. Rev. Lett.
**1985**, 54, 735–738. [Google Scholar] [CrossRef] [PubMed] - Wolfram, S. A New Kind of Science; Wolfram Media: Champaign, IL, USA, 2002; ISBN 1-57955-008-8. [Google Scholar]
- Church, A. An unsolvable problem of elementary number theory. Am. J. Math.
**1936**, 58, 345–363. [Google Scholar] [CrossRef] - Turing, A. On Computable Numbers, with an Application to the Entscheidungsproblem. Proc. Lond. Math. Soc.
**1936**, 42, 230–265. [Google Scholar] - Everett, H. Relative state formulation of quantum mechanics. Rev. Mod. Phys.
**1957**, 29, 454–462. [Google Scholar] [CrossRef] - Vaidman, L. All is ψ. J. Phys. Conf. Ser.
**2016**, 701, 012020. [Google Scholar] [CrossRef] - Schiff, J.; Poirier, B. Quantum mechanics without wave functions. J. Chem. Phys.
**2012**, 136, 031102. [Google Scholar] [CrossRef] [PubMed] - Hall, M.J.W.; Deckert, D.-A.; Wiseman, H.M. Quantum phenomena modeled by interactions between many classical worlds. Phys. Rev. X
**2014**, 4, 041013. [Google Scholar] [CrossRef] - Ghadimi, M.; Hall, M.J.W.; Wiseman, H.M. Nonlocality in Bell’s theorem, in Bohm’s theory, and in many interacting worlds theorising. Entropy
**2018**, 20, 567. [Google Scholar] [CrossRef] - Walleczek, J.; Grössing, G. Nonlocal quantum information transfer without superluminal signalling and communication. Found. Phys.
**2016**, 46, 1208–1228. [Google Scholar] [CrossRef] - Bell, J.S. On the Einstein Podolsky Rosen paradox. Physics
**1964**, 1, 195–200. [Google Scholar] [CrossRef][Green Version] - Sutherland, R.I. Bell’s theorem and backwards-in-time causality. Int. J. Theor. Phys.
**1983**, 22, 377–384. [Google Scholar] [CrossRef] - Price, H. Time’s Arrow & Archimedes’ Point: New Directions for the Physics of Time; Oxford University Press: Oxford, UK, 1997. [Google Scholar]
- Wharton, K. Quantum states as ordinary information. Information
**2014**, 5, 190–208. [Google Scholar] [CrossRef] - Price, H.; Wharton, K. Disentangling the quantum world. Entropy
**2015**, 17, 7752–7767. [Google Scholar] [CrossRef] - Frauchiger, D.; Renner, R. Quantum theory cannot consistently describe the use of itself. Nat. Commun.
**2018**, 9, 3711. [Google Scholar] [CrossRef] [PubMed] - Brukner, C. A no-go theorem for observer-independent facts. Entropy
**2018**, 20, 350. [Google Scholar] [CrossRef] - Bub, J. In defense of a “single-world” interpretation of quantum mechanics. arXiv, 2018; arXiv:quant-ph/1804.03267v1. [Google Scholar] [CrossRef][Green Version]
- Lazarovici, D.; Hubert, M. How single-world quantum mechanics is consistent: Comment on Frauchiger and Renner. arXiv, 2018; arXiv:quant-ph/1809.08070v1. [Google Scholar]
- Zwolak, M.; Zurek, W. Complementarity of quantum discord and classically accessible information. Sci. Rep.
**2013**, 3, 1729. [Google Scholar] [CrossRef] - Einstein, A.; Podolsky, B.; Rosen, N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev.
**1935**, 47, 777–780. [Google Scholar] [CrossRef] - Kochen, S.; Specker, E.P. The problem of hidden variables in quantum mechanics. J. Math. Mech.
**1967**, 17, 59–87. [Google Scholar] [CrossRef] - Abbott, A.A.; Calude, C.S.; Conder, J.; Svozil, K. Strong Kochen-Specker theorem and incomputability of quantum randomness. Phys. Rev. A
**2012**, 86, 6. [Google Scholar] [CrossRef] - Abbott, A.A.; Calude, C.S.; Svozil, K. Value-indefinite observables are almost everywhere. Phys. Rev. A
**2014**, 89, 032109. [Google Scholar] [CrossRef] - Abbott, A.A.; Calude, C.S.; Svozil, K. A quantum random number generator certified by value indefiniteness. Math. Struct. Comput. Sci.
**2014**, 24, e240303. [Google Scholar] [CrossRef] - Koberinski, A.; Müller, M.P. Quantum Theory as a Principle Theory: Insights from an Information-theoretic Reconstruction. In Physical Perspectives on Computation, Computational Perspectives on Physics; Fletcher, S.C., Cuffaro, M.E., Eds.; Cambridge University Press: Cambridge, UK, 2018; pp. 257–280. [Google Scholar]
- Fuchs, C. Quantum mechanics as quantum information, mostly. J. Mod. Opt.
**2003**, 50, 987–1023. [Google Scholar] [CrossRef] - ’t Hooft, G. The Cellular Automaton Interpretation of Quantum Mechanics; Fundamental Theories of Physics; Springer: Berlin/Heidelberg, Germany, 2016; Volume 185. [Google Scholar]
- Elze, H.-T. Quantum features of natural cellular automata. J. Phys. Conf. Ser.
**2016**, 701, 012017. [Google Scholar] [CrossRef][Green Version] - Palmer, T.N. Experimental non-violation of the Bell inequality. Entropy
**2018**, 20, 356. [Google Scholar] [CrossRef] - Mermin, N.D. Hidden variables and the two theorems of John Bell. Revs. Mod. Phys.
**1993**, 65, 803–815. [Google Scholar] [CrossRef][Green Version] - Maudlin, T. Quantum Non-locality and Relativity: Metaphysical Intimations of Modern Physics; Wiley-Blackwell: West Sussex, UK, 2011. [Google Scholar]
- Maudlin, T. Ontological clarity via canonical presentation: Electromagnetism and the Aharonov–Bohm effect. Entropy
**2018**, 20, 465. [Google Scholar] [CrossRef] - Lazarovici, D.; Oldofredi, A.; Esfeld, M. Observables and unobservables in quantum mechanics: How the no-hidden-variables theorems support the Bohmian particle ontology. Entropy
**2018**, 20, 381. [Google Scholar] [CrossRef] - Passon, O. On a common misconception regarding the de Broglie–Bohm theory. Entropy
**2018**, 20, 440. [Google Scholar] [CrossRef] - Tumulka, R. On Bohmian mechanics, particle creation, and relativistic space-time: Happy 100th birthday, David Bohm! Entropy
**2018**, 20, 462. [Google Scholar] [CrossRef] - Norsen, T. On the explanation of Born-rule statistics in the de Broglie-Bohm pilot-wave theory. Entropy
**2018**, 20, 422. [Google Scholar] [CrossRef] - De Gosson, M.A. The symplectic camel and Poincaré superrecurrence: Open problems. Entropy
**2018**, 20, 499. [Google Scholar] [CrossRef] - Khrennikov, A. Contextual Approach to Quantum Formalism; Springer: Berlin/Heidelberg, Germany; New York, NY, USA, 2009. [Google Scholar]
- Khrennikov, A. Classical probability model for Bell inequality. J. Phys. Conf. Ser.
**2014**, 504, 012019. [Google Scholar] [CrossRef][Green Version] - Hiley, B.J.; Van Reeth, P. Quantum trajectories: Real or surreal? Entropy
**2018**, 20, 353. [Google Scholar] [CrossRef] - Flack, R.; Hiley, B.J. Feynman paths and weak values. Entropy
**2018**, 20, 367. [Google Scholar] [CrossRef] - Walleczek, J. The super-indeterminism in orthodox quantum mechanics does not implicate the reality of experimenter free will. J. Phys. Conf. Ser.
**2016**, 701, 012005. [Google Scholar] [CrossRef][Green Version] - Gisin, N. Why Bohmian mechanics? One- and two-time position measurements, Bell inequalities, philosophy, and physics. Entropy
**2018**, 20, 105. [Google Scholar] [CrossRef] - Valentini, A. Signal-locality in hidden-variables theories. Phys. Lett. A
**2002**, 297, 273–278. [Google Scholar] [CrossRef][Green Version] - Bendersky, A.; Senno, G.; de la Torre, G.; Figueira, S.; Acin, A. Non-signaling deterministic models for non-local correlations have to be uncomputable. Phys. Rev. Lett.
**2017**, 118, 130401. [Google Scholar] [CrossRef] [PubMed] - Bell, J.S. Einstein-Podolsky-Rosen experiments. In Speakable and Unspeakable in Quantum Mechanics; Cambridge University Press: Cambridge, UK, 1987; pp. 81–92. [Google Scholar]
- Bell, J.S. La nouvelle cuisine. In Speakable and Unspeakable in Quantum Mechanics; Cambridge University Press: Cambridge, UK, 2004; pp. 232–248. [Google Scholar]
- Bohm, D. Quantum Theory; Prentice-Hall: Englewood Cliffs, NJ, USA, 1951. [Google Scholar]
- Fuchs, C.A.; Schack, R. QBism and the Greeks: Why a quantum state does not represent an element of physical reality. Phys. Scr.
**2015**, 90, 015104. [Google Scholar] [CrossRef] - Maxwell, J.C. Theory of Heat; Reprinted Dover: New York, NY, USA, 2001. [Google Scholar]
- Szilard, L. Über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen (On the reduction of entropy in a thermodynamic system by the intervention of intelligent beings). Zeitschrift für Physik
**1929**, 53, 840–856. [Google Scholar] [CrossRef] - Von Neumann, J. Mathematische Grundlagen der Quantenmechanik; Springer: Berlin, Germany, 1932. [Google Scholar]
- ‘t Hooft, G. Time, the arrow of time, and quantum mechanics. Front. Phys.
**2018**, 6, 81. [Google Scholar] [CrossRef] - Colbeck, R.; Renner, R. A short note on the concept of free choice. arXiv, 2013; arXiv:quant-ph/1302.4446. [Google Scholar]
- Plotnitsky, A. What is complementarity? Niels Bohr and the architecture of quantum theory. Phys. Scr.
**2014**, 163, 014002. [Google Scholar] [CrossRef] - Conway, J.; Kochen, S. The free will theorem. Found. Phys.
**2006**, 36, 1441–1473. [Google Scholar] [CrossRef] - Conway, J.; Kochen, S. The strong free will theorem. Not. AMS
**2009**, 56, 226–232. [Google Scholar] - Bera, M.N.; Acín, A.; Kuś, M.; Mitchell, M.; Lewenstein, M. Randomness in Quantum Mechanics: Philosophy, Physics, and Technology. Rep. Prog. Phys.
**2017**, 80, 124001. [Google Scholar] [CrossRef] - Landsman, K. Foundations of Quantum Theory: From Classical Concepts to Operator Algebras; Fundamental Theories of Physics; Springer: Berlin/Heidelberg, Germany, 2017; Volume 188, ISBN 978-3-319-51777-3. [Google Scholar]
- Bell, J.S. The theory of local beables. Epistemol. Lett.
**1976**, 9, 11, reprinted in Dialectica**1985**, 39, 85–96. [Google Scholar] - Bell, J.S. Free variables and local causality. Epistemol. Lett.
**1977**, 15, 15, reprinted in Dialectica**1985**, 39, 103–106. [Google Scholar] - Bell, J.S. De Broglie-Bohm, delayed-choice, double-slit experiment, and density matrix. Int. J. Quantum Chem.
**1980**, 14, 155–159. [Google Scholar] [CrossRef] - Bell, J.S. On the impossible pilot wave. Found. Phys.
**1982**, 12, 989–999. [Google Scholar] [CrossRef] - Bell, J.S. Speakable and unspeakable in quantum mechanics. In Speakable and Unspeakable in Quantum Mechanics; Cambridge University Press: Cambridge, UK, 1987; pp. 169–172. [Google Scholar]
- Walleczek, J.; Grössing, G. The non-signalling theorem in generalizations of Bell’s theorem. J. Phys. Conf. Ser.
**2014**, 504, 012001. [Google Scholar] [CrossRef] - Chaitin, G.J. Information, Randomness, and Incompleteness: Papers on Algorithmic Information Theory; Series in Computer Science; World Scientific: Singapore, 1987; Volume 8. [Google Scholar]
- Esfeld, M. Ontic structural realism and the interpretation of quantum mechanics. Eur. J. Philos. Sci.
**2013**, 3, 19–32. [Google Scholar] [CrossRef] - Walleczek, J.; Grössing, G. Is the world local or nonlocal? Towards an emergent quantum mechanics in the 21st century. J. Phys. Conf. Ser.
**2016**, 701, 012001. [Google Scholar] [CrossRef] - Shimony, A. Controllable and Uncontrollable Non-locality. In Foundations of Quantum Mechanics in Light of the New Technology; Kamefuchi, S., Butsuri Gakkai, N., Eds.; Physical Society of Japan: Tokyo, Japan, 1984; pp. 225–230. [Google Scholar]
- Aharonov, Y.; Cohen, E.; Shushi, T. Accommodating retrocausality with free will. Quanta
**2016**, 5, 53–60. [Google Scholar] [CrossRef] - Rozema, L.A.; Darabi, A.; Mahler, D.H.; Hayat, A.; Soudagar, Y.; Steinberg, A.M. Violation of Heisenberg’s measurement-disturbance relationship by weak measurements. Phys. Rev. Lett.
**2012**, 109, 100404. [Google Scholar] [CrossRef] - Walleczek, J. (Ed.) Self-Organized Biological Dynamics and Nonlinear Control; Cambridge University Press: Cambridge, UK, 2000. [Google Scholar]
- Bennett, C.H. Undecidable dynamics. Nature
**1990**, 346, 606–607. [Google Scholar] [CrossRef] - Moore, C. Unpredictability and undecidability in dynamical systems. Phys. Rev. Lett.
**1990**, 64, 2354–2357. [Google Scholar] [CrossRef] - Cooper, S.B.; Odifreddi, P. Incomputability in Nature. In Computability and Models; Cooper, S.B., Goncharov, S.S., Eds.; Kluwer Academic, Plenum Publishers: New York, NY, USA, 2003; pp. 137–160. [Google Scholar][Green Version]
- Lloyd, S. Uncomputability and Physical Law. In The Incomputable: Journeys Beyond the Turing Barrier; Cooper, S.B., Soskova, M.I., Eds.; Springer: Berlin/Heidelberg, Germany, 2017; pp. 95–104. [Google Scholar]
- Rucker, R. An Incompleteness Theorem for the Natural World. In Irreducibility and Computational Equivalence; Zenil, H., Ed.; Springer: Berlin/Heidelberg, Germany, 2013; pp. 185–198. [Google Scholar]
- Cubitt, T.S.; Perez-Garcia, D.; Wolf, M.M. Undecidability of the spectral gap. Nature
**2015**, 528, 207–211. [Google Scholar] [CrossRef] [PubMed] - Cooper, S.B.; Soskova, M.I. (Eds.) The Incomputable: Journeys Beyond the Turing Barrier; Springer: Berlin/Heidelberg, Germany, 2017. [Google Scholar]
- Fletcher, S.C.; Cuffaro, M.E. (Eds.) Physical Perspectives on Computation, Computational Perspectives on Physics; Cambridge University Press: Cambridge, UK, 2018. [Google Scholar]
- Franke, H.W. Cellular Automata: Models of the Physical World. In Irreducibility and Computational Equivalence; Zenil, H., Ed.; Springer: Berlin/Heidelberg, Germany, 2013; pp. 3–10. [Google Scholar]
- French, S. The Structure of the World: Metaphysics and Representation; Oxford University Press: Oxford, UK, 2014; ISBN 9780199684847. [Google Scholar]
- Tzemos, A.C.; Efthymiopoulos, C.; Contopoulos, G. Origin of chaos near three-dimensional quantum vortices: A general Bohmian theory. Phys. Rev. E
**2018**, 97, 042201. [Google Scholar] [CrossRef][Green Version] - Towler, M.D.; Russell, N.J.; Valentini, A. Time scales for dynamical relaxation to the Born rule. Proc. R. Soc. A
**2012**, 468, 990. [Google Scholar] [CrossRef] - Efthymiopoulos, C.; Contopoulos, G.; Tzemos, A.C. Chaos in de Broglie-Bohm quantum mechanics and the dynamics of quantum relaxation. Ann. Fond. Louis Broglie
**2017**, 42, 133–160. [Google Scholar] - Underwood, N.G. Extreme quantum nonequilibrium, nodes, vorticity, drift, and relaxation retarding states. arXiv, 2018; arXiv:quant-ph/1705.06757v2. [Google Scholar] [CrossRef]
- Islam, T.; Wehner, S. Computability limits non-local correlations. Phys. Rev. A
**2012**, 86, 042109. [Google Scholar] [CrossRef] - Calude, C.S. Quantum Randomness: From Practice to Theory and Back. In The Incomputable: Journeys Beyond the Turing Barrier; Cooper, S.B., Soskova, M.I., Eds.; Springer: Berlin/Heidelberg, Germany, 2017; pp. 169–181. [Google Scholar]

**Figure 1.**Quantum super-indeterminism [60]. The shortcomings of the orthodox view, which are revealed by the simple concept of super-indeterminism, in the attempt to prove, or justify, the metaphysics behind quantum indeterminacy, are recognized increasingly. The fallacy of circular reasoning is illustrated in Figure 1, which arises from the use of the intrinsic randomness assumption in support of the free choice assumption, which—in turn—rationalizes the presumably “free” selection of measurement settings. Bera et al. [76], for example, have confirmed the fact of ‘super-indeterminism’ by noting that there is indeed present “…an unavoidable circulus vitiosus” in any tests for true randomness, because any available tests for “…the indeterministic character of the physical reality” must presume that “…it is, in fact, indeterministic.” Similar arguments have been put forth by, and prior developments were summarized in, Landsman [77].

**Figure 2.**Illustration of the irreducible interdependency of basic assumptions that are implicit in standard interpretations of orthodox quantum mechanics (adapted from Walleczek and Grössing [27,83]). (

**A**) Free choice assumption, (

**B**) Intrinsic randomness assumption, and (

**C**) Axiomatic non-signaling assumption. Importantly, the validity of interpreting the non-signaling theorem as a foundational theorem, or axiom, for quantum mechanics, i.e., one which would imply strict indeterminism as the only viable option for interpreting quantum theory, depends on the independent validity of assumptions (

**A**,

**B**). However, neither assumption (

**A**) nor assumption (

**B**) can be confirmed independently if the possibility of ‘free choice’ depends on the existence of a process that is intrinsically random and vice versa (compare Figure 1). Therefore, for example, the observation of EPR-type nonlocal correlations in the laboratory does not represent empirical proof for the indeterministic nature of the locally observed measurement outcomes, if that proof relies on the employment of an axiomatic non-signaling theorem (for more details see Walleczek and Grössing [27]).

**Figure 3.**Agent inaccessibility as a function of (

**A**) Intrinsic randomness versus (

**B**) Effective ignorance (adapted from Walleczek [60]). Intrinsic randomness represents the orthodox interpretation of quantum mechanics, which is universal indeterminism. There, the presence of the experimenter agent introduces an apparent metaphysical dualism between agent and world (see the main text for additional explanations), which is indicated by the closed line that encloses the presence of the experimenter agent (Figure 3A). By contrast, in universal or global determinism, agents and the physical universe are subject to the same fundamental determinism, whereby, there, the experimenter agent is an integral element of the physical universe, i.e., agent and universe together constitute a lawful, physical continuum (e.g., Szilard [69]), as is indicated by the open line (see Figure 3B). In this picture, the experimenter agent constitutes an entity possessing distinct ‘epistemic’ as well as ‘agentic’ properties (for definitions see Section 4.3). For a detailed explanation of an axiomatic (Figure 3A) versus an effective (Figure 3B) non-signaling constraint—in the context of Bell’s nonlocality theorem—consult Walleczek and Grössing [27]. Briefly, an axiomatic non-signaling constraint (see also Figure 2) is compatible with the violation of measurement outcome independence, which is the standard violation in the context of orthodox quantum theory; by contrast, an effective non-signaling constraint is thought to be compatible with the violation of setting or parameter independence (Shimony [87]), which is the standard violation in the context of an ontological quantum mechanics such as dBB-theory in a universally deterministic universe (Section 3.3).

**Figure 4.**Agent inaccessibility as a function of (

**A**) Intrinsic randomness versus (

**B**) Objective ignorance (adapted from Walleczek [60]). Intrinsic randomness represents the orthodox interpretation of quantum mechanics, which is universal indeterminism (see legend to Figure 3 for an explanation of the nature of the experimenter agent). Objective ignorance, by contrast, advances the alternative proposal that quantum mechanics in a universally deterministic universe (i.e., global determinism) could account for (objective) quantum unpredictability as defined by an in-principle limit (Figure 4B). Please note that a prior report referred to a related proposal by the term ‘intrinsic complexity’ [60] due to the fact that such an option is available for complex systems dynamics. An objective non-signaling constraint, which is proposed here as an option that may underlie the non-signaling theorem of quantum mechanics, is equally governed by an objective, in-principle constraint; that is, the capacity for operational control by the experimenter agent (for definition see Section 4.3) of, for example, time-symmetric, or nonlocal, ontic influences, or information transfers, is formally and objectively limited by the unavailability to the agent of either (i) infinitely precise knowledge about (time-symmetric) initial conditions, or (ii) infinite computational, or generally technological, resources, or a combination of (i) and (ii). For an overview, see Table 1.

**Table 1.**Two types of self-referential dynamics are considered as a basis for the proposed physics of agent inaccessibility. For the proposal of an AIP as a fundamental principle in quantum mechanics (objective ignorance), the objective unpredictability of an individual measurement outcome as part of a typical quantum random sequence is a function of formal uncomputability; both, dynamical chaos as well as undecidable dynamics posit “infinity”—the lack of infinite resources—as a fundamental limit on computability. Regarding the limit of infinite precision detection in relation to the concept of formal uncomputability, note that—in computational predictions of chaotic dynamics—an arbitrarily small difference in initial conditions may lead to a vastly different future outcome state. Note also that the concept of undecidable dynamics underpins both computational irreducibility [18,19] as well as the halting problem in the Church-Turing thesis [20,21].

Self-Referential Dynamics | Formal Uncomputability |
---|---|

Dynamical chaos | Infinite precision detection of initial conditions is impossible in-principle |

Undecidable dynamics | Infinite computational resources are unavailable in-principle |

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Walleczek, J.
Agent Inaccessibility as a Fundamental Principle in Quantum Mechanics: Objective Unpredictability and Formal Uncomputability. *Entropy* **2019**, *21*, 4.
https://doi.org/10.3390/e21010004

**AMA Style**

Walleczek J.
Agent Inaccessibility as a Fundamental Principle in Quantum Mechanics: Objective Unpredictability and Formal Uncomputability. *Entropy*. 2019; 21(1):4.
https://doi.org/10.3390/e21010004

**Chicago/Turabian Style**

Walleczek, Jan.
2019. "Agent Inaccessibility as a Fundamental Principle in Quantum Mechanics: Objective Unpredictability and Formal Uncomputability" *Entropy* 21, no. 1: 4.
https://doi.org/10.3390/e21010004