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Nonlocal Unification as the Completion of Mermin's QBism

Aman Chawla

Published Mar 27, 2026• 0 citations
Publisher

Abstract

Quantum Bayesianism (QBism), as articulated most prominently by Mermin, Fuchs, and Schack, reframes quantum theory as a user-centered framework in which probabilities represent an agent’s personal degrees of belief about the outcomes of interventions. While QBism successfully dissolves several foundational paradoxes by rejecting the objectivity of the quantum state, it deliberately refrains from positing an underlying ontological substrate. In this work, we propose that a theory of Nonlocal Unification (NU), grounded in a universal informational field and biologically mediated sampling processes, provides a natural completion of QBism. We argue that agents are not abstract entities but physically instantiated samplers whose structureis shaped by genetic and neural constraints. Spacetime itself emerges as a derived construct from the sampling of nonlocal informational correlations. In this sense, NU preserves QBism’s participatory ethos while extending it into a coherent ontological framework.

DOI
10.5281/zenodo.19243262

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Measured responses to quantum Bayesianism

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Mermin replies: Robert Griffiths takes my joke about an undergraduate collapsing a wavepacket to be an attempt to solve the measurement problem. The actual QBist solution—versions of which predate QBism (see, for example, reference 11. J. B. Hartle, Am. J. Phys. 36, 704 (1968). https://doi.org/10.1119/1.1975096)—is that a quantum state is not an objective property of the world but a compendium of probabilities constructed by an agent. When an agent updates her state assignment, nothing changes in her external world. The only change is in the agent’s expectations for her subsequent experience of that world, and therefore there is no measurement problem. Consistent historians agree that collapse is not a physical process, but for entirely different reasons.QBism takes the “mysterious whatever-it-is” that Griffiths criticizes in quantum orthodoxy to be the experience induced in an agent by the world. That, and the fact that different agents may have different experiences, drains the swamp, slays the dragon, and quiets the maddening paradoxes.QBists hold that any agent can indeed apply quantum mechanics to her own external world, from quarks to quasars. Only an agent’s personal, directly perceived experience is boxed off from the domain of applicability. That exclusion disagrees with most versions of the many-worlds interpretation, but it does not limit the scope of science: Alice can apply quantum mechanics to the experience of another agent, Bob, as represented through his words, writings, or drawings, all of which do belong to her external world.The way in which Bob’s experience impinges on Alice resonates with Niels Bohr’s emphasis on the need to state results of experiments in ordinary language. It also addresses Ching Hung Woo’s question of how different agents can come to agreement on their state assignments.Griffiths correctly notes that QBism violates the first desideratum he quotes from my 15-year-old “Ithaca interpretation.” Like Barack Obama’s view of marriage, my thinking about quantum foundations has evolved. But Griffiths wrongly claims that QBism rejects the other desideratum he quotes: locality. Actually, QBism insists on it. The absurdity of quantum nonlocality provides an independent argument that quantum states cannot be objective internal properties of the systems they describe, whether or not one regards probabilities as subjective. Griffiths is probably right, however, that John Bell would not have been pleased with how QBists fix his shifty split.I would not call QBism an “antiquated approach.” It is younger than Griffiths’ consistent histories and, as I have remarked upon elsewhere,22. M. Schlosshauer, ed., Elegance and Enigma: The Quantum Interviews, Springer, Berlin (2011), pp. 177, 280. taking reality itself to be relative to what he calls a framework, is vastly more radical than taking quantum state assignments to be relative to an agent.But foreshadowings of QBism can indeed be found in antiquity. Since writing my commentary, I came across another striking anticipation in a 1931 letter from Erwin Schrödinger to Arnold Sommerfeld:33. K. von Meyenn, ed., Eine Entdeckung von ganz außerordentlicher Tragweite: Schrödingers Briefwechsel zur Wellenmechanik und zum Katzenparadoxon, Springer, Berlin (2011), p. 490. “Quantum mechanics forbids statements about what really exists—statements about the object. It deals only with the object–subject relation. Although this holds, after all, for any description of nature, it appears to hold in a much more radical and far-reaching sense in quantum mechanics” (translated by N. D. Mermin and Ruediger Schack).When Bell and Michael Nauenberg wrote their delightful article in 1966, there was indeed much less interest in quantum foundations than there is today. Most textbooks have wisely steered clear of the many contemporary interpretive positions, since none of them are held by more than a fraction of those physicists with an interest in such issues.QBists do not reject the Born rule for calculating probabilities, but they do reject the objective frequentist interpretation of those probabilities presented by Nauenberg and held by most physicists. The frequentist view is notoriously circular. It defines probability using such notions as “equally probable,” “unlikely,” or (with Nauenberg) “identically prepared,” none of which make sense without a prior definition of probability. “Identically prepared” might seem safe from circularity, but two different preparations cannot be strictly identical. It would be more accurate to say they must differ in unimportant ways. Unimportant for what? For the probabilities of the outcomes.When I started to learn about subjective probability, I was surprised to discover that most of the books were not in Cornell University’s physics or mathematics libraries but in the business school library. In our recent election, Americans have been told that business experience is necessary for being president; I would suggest that it may be even more helpful for understanding quantum mechanics.I cannot tell from Nauenberg’s remarks about the Liouville equation whether he agrees with the view of QBists (and many others) that the collapse of the wavefunction is no more than the updating of a collection of probability distributions.Nauenberg’s example of the Rydberg atom does not contradict the QBist resolution of Bell’s shifty split. The Rydberg atom is part of the world external to the agent, and therefore on the quantum side of her split. There are indeed circumstances under which fully quantum mechanical behavior can look very classical.Art Hobson repeats the common view that only mixed states can be associated with subjective probabilities. QBism takes that to be the very mistake that got us lost for so long in the quantum swamp. Hobson also believes that wavefunctions were collapsing before there were physicists. Does he believe that probabilities were updating before there were statisticians?Hobson wrongly claims that Chris Fuchs “might dispute the notion that some kind of physical reality actually exists.” What he and other QBists do deny is that there are properties of the external world—“elements of reality”—that underlie quantum state assignments. (The argument of Matthew Pusey and coauthors that Hobson cites, implying that quantum states are physically real, relies on such hidden variables.) An agent’s state assignment rests entirely on her experience of the external world. It is neither solipsistic nor superstitious to maintain that any agent’s experience comes fully into being only at the moment it is experienced.Hobson’s treatment of Eugene Wigner and his friend relies on decoherence producing an objective mixed state, which both of them must agree on. But since quantum mechanics holds all the way out to infinity (as Griffiths puts it), even from an objective view of quantum states, that switch from superposition to either/or is at best a FAPP solution, to use Bell’s wonderfully sardonic abbreviation of “for all practical purposes.”QBism does not, as Hobson concludes, give up on a realist interpretation of nature. But it does warn us not to confuse nature with the abstractions we have ingeniously constructed to help any agent deal with the very real impact of nature on his or her own internal experience (see my Reference Frame, Physics Today, May 2009, page 8).I’m glad that Blake Stacey has called attention to some of the more applied spinoffs of QBism. I’m also pleased that he mentions Bruno de Finetti, one of the great 20th-century pioneers of subjective probability. Indeed, since there are objective as well as subjective Bayesians, if I had my way, the B in QBism would stand not for Thomas Bayes, but for Bruno de Finetti, who put the crucial point like this: “The abandonment of superstitious beliefs about the existence of Phlogiston, the Cosmic Ether, Absolute Space and Time … , or Fairies and Witches, was an essential step along the road to scientific thinking. Probability, too, if regarded as something endowed with some kind of objective existence, is no less a misleading misconception, an illusory attempt to exteriorize or materialize our [actual (vero)] probabilistic beliefs.”44. B. de Finetti, Theory of Probability, Interscience, New York (1990), preface.REFERENCESSection:ChooseTop of pageREFERENCES <<1. J. B. Hartle, Am. J. Phys. 36, 704 (1968). https://doi.org/10.1119/1.1975096, Google ScholarCrossref2. M. Schlosshauer, ed., Elegance and Enigma: The Quantum Interviews, Springer, Berlin (2011), pp. 177, 280. Google ScholarCrossref3. K. von Meyenn, ed., Eine Entdeckung von ganz außerordentlicher Tragweite: Schrödingers Briefwechsel zur Wellenmechanik und zum Katzenparadoxon, Springer, Berlin (2011), p. 490. Google ScholarCrossref4. B. de Finetti, Theory of Probability, Interscience, New York (1990), preface. Google Scholar© 2012 American Institute of Physics.

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The QBist and Relational Quantum Mechanics (RQM) informational readings of quantum theory have long lacked a clear account of what kind of physical system qualifies as an “agent” or “observer.” Fuchs, Mermin, and Schack often treat the agent as a human physicist or Bayesian decision-maker; Rovelli suggests that any physical system may serve as a relational observer; Healey abstracts the agent into a Bayesian role without specifying its substrate; and the Khrennikov-Schack-Zwirn exchange sharpens, but does not resolve, the intersubjectivity problem. This paper argues that the QBism/RQM informational reading is best understood as substrate-flexible: any physical system whose input-output statistics exhibit quantum-probability structure, including non-trivial Contextuality-by-Default (CbD) signatures resistant to simplex-embeddable ontological models, is a candidate epistemic agent. This condition is necessary but not sufficient: agency also requires state-sensitive updating across measurement contexts. The argument preserves QBism’s rejection of view-from-nowhere objectivity while removing the assumption that agents must be human or conscious, and disciplines Rovelli’s “any physical system” claim by tying observerhood to measurable non-triviality. Engineered cortical wetware systems such as CL1 and DishBrain offer controllable, non-human, and not clearly conscious testbeds for evaluating this claim, without requiring phenomenal consciousness or quantum-coherent biological dynamics. The paper distinguishes substrate flexibility from Pienaar’s extension of the QBist agent, which expands the agent’s senses rather than its substrate; engages neo-Everettian objections; and rejects Edwards’s attempts to fold classical large language models into QBist formalism. Classical AI token-generation systems remain simplex-embeddable and therefore fail the non-triviality requirement. Substrate flexibility is thus narrower than proposals that include current AI systems.

•Aug 11, 2026•0 citations
Quantum Bayesianism (QBism), as articulated most prominently by Mermin, Fuchs, and Schack, reframes quantum theory as a user-centered framework in which probabilities represent an agent’s personal degrees of belief about the outcomes of interventions. While QBism successfully dissolves several foundational paradoxes by rejecting the objectivity of the quantum state, it deliberately refrains from positing an underlying ontological substrate. In this work, we propose that a theory of Nonlocal Unification (NU), grounded in a universal informational field and biologically mediated sampling processes, provides a natural completion of QBism. We argue that agents are not abstract entities but physically instantiated samplers whose structureis shaped by genetic and neural constraints. Spacetime itself emerges as a derived construct from the sampling of nonlocal informational correlations. In this sense, NU preserves QBism’s participatory ethos while extending it into a coherent ontological framework.
Schack, Brun, and Caves derived a quantum Bayes rule for exchangeable quantum states by showing that, under generalized measurements, the posterior state of unmeasured systems may be represented as a Bayesian update over density operators. The present article proposes a Nonlocal-Unification-informed extension of that rule. In Nonlocal Unification (NU), an observer is not only an abstract user of probabilities, but an embodied sampling function acting on a nonlocal informational substrate. The proposed update therefore acts on a joint model of quantum state and observer function. The ordinary quantum Bayes rule is recovered when the sampling architecture is fixed. The article further examines NU information conservation, Frechet convergence of observer functions to a limiting observer, and a two-observer toy universe in which one observer reconstructs the internal spacetime of another. The resulting framework connects Bayesian inference, observer-relative spacetime reconstruction, and the informational field-equation side of NU.
The completeness problem in quantum mechanics concerns whether the formalism constitutes a logically closed and ontologically complete description of physical reality. Historically, this led to a persistent tension between operational success and ontological clarity. This note argues that the Nonlocal Unification (NU) framework can provide the necessary conceptual ingredients to resolve this problem. Specifically, we show that if information is taken as a fundamental and conserved quantity, then quantum mechanics may emerge as an operationally complete theory while simultaneously being conceptually incomplete as a base ontology. This reframing might dissolve the classical tension between completeness and hidden-variable extensions by replacing the ontology of states with an informational geometry governed by conservation.
Mermin replies: Robert Griffiths takes my joke about an undergraduate collapsing a wavepacket to be an attempt to solve the measurement problem. The actual QBist solution—versions of which predate QBism (see, for example, reference 11. J. B. Hartle, Am. J. Phys. 36, 704 (1968). https://doi.org/10.1119/1.1975096)—is that a quantum state is not an objective property of the world but a compendium of probabilities constructed by an agent. When an agent updates her state assignment, nothing changes in her external world. The only change is in the agent’s expectations for her subsequent experience of that world, and therefore there is no measurement problem. Consistent historians agree that collapse is not a physical process, but for entirely different reasons.QBism takes the “mysterious whatever-it-is” that Griffiths criticizes in quantum orthodoxy to be the experience induced in an agent by the world. That, and the fact that different agents may have different experiences, drains the swamp, slays the dragon, and quiets the maddening paradoxes.QBists hold that any agent can indeed apply quantum mechanics to her own external world, from quarks to quasars. Only an agent’s personal, directly perceived experience is boxed off from the domain of applicability. That exclusion disagrees with most versions of the many-worlds interpretation, but it does not limit the scope of science: Alice can apply quantum mechanics to the experience of another agent, Bob, as represented through his words, writings, or drawings, all of which do belong to her external world.The way in which Bob’s experience impinges on Alice resonates with Niels Bohr’s emphasis on the need to state results of experiments in ordinary language. It also addresses Ching Hung Woo’s question of how different agents can come to agreement on their state assignments.Griffiths correctly notes that QBism violates the first desideratum he quotes from my 15-year-old “Ithaca interpretation.” Like Barack Obama’s view of marriage, my thinking about quantum foundations has evolved. But Griffiths wrongly claims that QBism rejects the other desideratum he quotes: locality. Actually, QBism insists on it. The absurdity of quantum nonlocality provides an independent argument that quantum states cannot be objective internal properties of the systems they describe, whether or not one regards probabilities as subjective. Griffiths is probably right, however, that John Bell would not have been pleased with how QBists fix his shifty split.I would not call QBism an “antiquated approach.” It is younger than Griffiths’ consistent histories and, as I have remarked upon elsewhere,22. M. Schlosshauer, ed., Elegance and Enigma: The Quantum Interviews, Springer, Berlin (2011), pp. 177, 280. taking reality itself to be relative to what he calls a framework, is vastly more radical than taking quantum state assignments to be relative to an agent.But foreshadowings of QBism can indeed be found in antiquity. Since writing my commentary, I came across another striking anticipation in a 1931 letter from Erwin Schrödinger to Arnold Sommerfeld:33. K. von Meyenn, ed., Eine Entdeckung von ganz außerordentlicher Tragweite: Schrödingers Briefwechsel zur Wellenmechanik und zum Katzenparadoxon, Springer, Berlin (2011), p. 490. “Quantum mechanics forbids statements about what really exists—statements about the object. It deals only with the object–subject relation. Although this holds, after all, for any description of nature, it appears to hold in a much more radical and far-reaching sense in quantum mechanics” (translated by N. D. Mermin and Ruediger Schack).When Bell and Michael Nauenberg wrote their delightful article in 1966, there was indeed much less interest in quantum foundations than there is today. Most textbooks have wisely steered clear of the many contemporary interpretive positions, since none of them are held by more than a fraction of those physicists with an interest in such issues.QBists do not reject the Born rule for calculating probabilities, but they do reject the objective frequentist interpretation of those probabilities presented by Nauenberg and held by most physicists. The frequentist view is notoriously circular. It defines probability using such notions as “equally probable,” “unlikely,” or (with Nauenberg) “identically prepared,” none of which make sense without a prior definition of probability. “Identically prepared” might seem safe from circularity, but two different preparations cannot be strictly identical. It would be more accurate to say they must differ in unimportant ways. Unimportant for what? For the probabilities of the outcomes.When I started to learn about subjective probability, I was surprised to discover that most of the books were not in Cornell University’s physics or mathematics libraries but in the business school library. In our recent election, Americans have been told that business experience is necessary for being president; I would suggest that it may be even more helpful for understanding quantum mechanics.I cannot tell from Nauenberg’s remarks about the Liouville equation whether he agrees with the view of QBists (and many others) that the collapse of the wavefunction is no more than the updating of a collection of probability distributions.Nauenberg’s example of the Rydberg atom does not contradict the QBist resolution of Bell’s shifty split. The Rydberg atom is part of the world external to the agent, and therefore on the quantum side of her split. There are indeed circumstances under which fully quantum mechanical behavior can look very classical.Art Hobson repeats the common view that only mixed states can be associated with subjective probabilities. QBism takes that to be the very mistake that got us lost for so long in the quantum swamp. Hobson also believes that wavefunctions were collapsing before there were physicists. Does he believe that probabilities were updating before there were statisticians?Hobson wrongly claims that Chris Fuchs “might dispute the notion that some kind of physical reality actually exists.” What he and other QBists do deny is that there are properties of the external world—“elements of reality”—that underlie quantum state assignments. (The argument of Matthew Pusey and coauthors that Hobson cites, implying that quantum states are physically real, relies on such hidden variables.) An agent’s state assignment rests entirely on her experience of the external world. It is neither solipsistic nor superstitious to maintain that any agent’s experience comes fully into being only at the moment it is experienced.Hobson’s treatment of Eugene Wigner and his friend relies on decoherence producing an objective mixed state, which both of them must agree on. But since quantum mechanics holds all the way out to infinity (as Griffiths puts it), even from an objective view of quantum states, that switch from superposition to either/or is at best a FAPP solution, to use Bell’s wonderfully sardonic abbreviation of “for all practical purposes.”QBism does not, as Hobson concludes, give up on a realist interpretation of nature. But it does warn us not to confuse nature with the abstractions we have ingeniously constructed to help any agent deal with the very real impact of nature on his or her own internal experience (see my Reference Frame, Physics Today, May 2009, page 8).I’m glad that Blake Stacey has called attention to some of the more applied spinoffs of QBism. I’m also pleased that he mentions Bruno de Finetti, one of the great 20th-century pioneers of subjective probability. Indeed, since there are objective as well as subjective Bayesians, if I had my way, the B in QBism would stand not for Thomas Bayes, but for Bruno de Finetti, who put the crucial point like this: “The abandonment of superstitious beliefs about the existence of Phlogiston, the Cosmic Ether, Absolute Space and Time … , or Fairies and Witches, was an essential step along the road to scientific thinking. Probability, too, if regarded as something endowed with some kind of objective existence, is no less a misleading misconception, an illusory attempt to exteriorize or materialize our [actual (vero)] probabilistic beliefs.”44. B. de Finetti, Theory of Probability, Interscience, New York (1990), preface.REFERENCESSection:ChooseTop of pageREFERENCES <<1. J. B. Hartle, Am. J. Phys. 36, 704 (1968). https://doi.org/10.1119/1.1975096, Google ScholarCrossref2. M. Schlosshauer, ed., Elegance and Enigma: The Quantum Interviews, Springer, Berlin (2011), pp. 177, 280. Google ScholarCrossref3. K. von Meyenn, ed., Eine Entdeckung von ganz außerordentlicher Tragweite: Schrödingers Briefwechsel zur Wellenmechanik und zum Katzenparadoxon, Springer, Berlin (2011), p. 490. Google ScholarCrossref4. B. de Finetti, Theory of Probability, Interscience, New York (1990), preface. Google Scholar© 2012 American Institute of Physics.
Abstract The idea that the quantum probabilities are best construed as the personal/subjective degrees of belief of Bayesian agents is an old one. In recent years the idea has been vigorously pursued by a group of physicists who fly the banner of quantum Bayesianism (QBism). The present paper aims to identify the prospects and problems of implementing QBism, and it critically assesses the claim that QBism provides a resolution (or dissolution) of some of the long-standing foundations issues in quantum mechanics, including the measurement problem and puzzles of nonlocality.
Abstract QBism is an agent-centered interpretation of quantum theory. It rejects the notion that quantum theory provides a God’s eye description of reality and claims instead that it imposes constraints on agents’ subjective degrees of belief. QBism’s emphasis on subjective belief has led critics to dismiss it as antirealism or instrumentalism, or even, idealism or solipsism. The aim of this paper is to consider the relation of QBism to scientific realism. I argue that while QBism is an unhappy fit with a standard way of thinking about scientific realism, an alternative conception I call “perspectival normative realism” may allow for a reconciliation.
The QBist and Relational Quantum Mechanics (RQM) informational readings of quantum theory have long lacked a clear account of what kind of physical system qualifies as an “agent” or “observer.” Fuchs, Mermin, and Schack often treat the agent as a human physicist or Bayesian decision-maker; Rovelli suggests that any physical system may serve as a relational observer; Healey abstracts the agent into a Bayesian role without specifying its substrate; and the Khrennikov-Schack-Zwirn exchange sharpens, but does not resolve, the intersubjectivity problem. This paper argues that the QBism/RQM informational reading is best understood as substrate-flexible: any physical system whose input-output statistics exhibit quantum-probability structure, including non-trivial Contextuality-by-Default (CbD) signatures resistant to simplex-embeddable ontological models, is a candidate epistemic agent. This condition is necessary but not sufficient: agency also requires state-sensitive updating across measurement contexts. The argument preserves QBism’s rejection of view-from-nowhere objectivity while removing the assumption that agents must be human or conscious, and disciplines Rovelli’s “any physical system” claim by tying observerhood to measurable non-triviality. Engineered cortical wetware systems such as CL1 and DishBrain offer controllable, non-human, and not clearly conscious testbeds for evaluating this claim, without requiring phenomenal consciousness or quantum-coherent biological dynamics. The paper distinguishes substrate flexibility from Pienaar’s extension of the QBist agent, which expands the agent’s senses rather than its substrate; engages neo-Everettian objections; and rejects Edwards’s attempts to fold classical large language models into QBist formalism. Classical AI token-generation systems remain simplex-embeddable and therefore fail the non-triviality requirement. Substrate flexibility is thus narrower than proposals that include current AI systems.