The 1995 article by Achim Kempf, Gianpiero Mangano, and Robert B. Mann, “Hilbert Space Representation of the Minimal Length Uncertainty Relation,” constitutes one of the most important formal constructions through which a nonzero minimal uncertainty in position can be incorporated into quantum mechanics. Rather than representing a fundamental length merely as a discrete lattice imposed upon ordinary space, Kempf, Mangano, and Mann modify the canonical commutation relation and construct a Hilbert- space representation in which arbitrarily precise physical localization is excluded. Their framework yields a minimal position uncertainty, modifies the mathematical status of exact-position states, introduces maximally localized states and a quasi-position representation, and, in multidimensional formulations, leads to noncommuting position coordinates. The original article was published in Physical Review D, volume 52, pages 1108–1118, DOI https://doi.org/10.1103/PhysRevD.52.1108 (Kempf, Mangano, and Mann, 1995). This article develops a critical–propositional analysis of that framework in dia- logue with the Theory of Objectivity (TO), particularly its Seven Absolute Truths, its interpretation of logical Nothingness, the concept of individualizing fields, the onto- logical status attributed to infinity, the role of boundaries and interfaces, nonhuman relational observation, compositional emergence, and the transcendent element under- stood in TO as knowledge or information produced in atomic relations and considered equivalent to atomic radiation. Special attention is given to the foundational TO work A Esfera Perfeita (The Perfect Sphere), because the KMM minimal-localization structure provides an especially useful mathematical dialogue partner for a TO conception of a limiting physical scale. The central thesis developed here is deliberately restricted. Kempf, Mangano, and Mann do not demonstrate the Theory of Objectivity, do not derive its cosmogony, do not establish the individual magnetic field asserted by its Second Absolute Truth, and do not reproduce the triadic relational condition associated with its Fifth Absolute Truth. Nevertheless, their work provides a productive structural analogy for several TO concepts: finite physical localizability, distinction between formal mathematical objects and physically realizable states, existence of a forbidden domain below a localization threshold, generation of geometrical properties by fundamental algebraic relations, and conversion of fundamental constraints into potentially observable consequences. The strongest scientific use of KMM by TO would therefore not consist in claiming retrospective confirmation. TO should instead attempt to derive, from its own modal and cosmogonic architecture, an effective deformation parameter and a nonzero localization scale. If such a derivation were independently obtained, the resulting theory could produce quantitative deviations from ordinary quantum mechanics and could thereby enter genuine empirical contact. The analysis consequently proposes a formal research program in which modal axioms are connected to operator algebra, spectral corrections, propagation relations, information constraints, and experimentally bounded parameters. Later developments in generalized uncertainty principle research are also considered, including qualifications of the KMM algebra concerning Jacobi identities and spin (Fadel and Maggiore, 2022). KMM should therefore be understood as a historically and mathematically impor- tant model of minimal-length quantum mechanics, rather than as an experimentally established universal description of fundamental physics. Keywords: Theory of Objectivity; minimal length; generalized uncertainty principle; Kempf–Mangano–Mann algebra; modal ontology; Perfect Sphere; quantum gravity; physical localizability; information; atomic radiation; noncommutative geometry; In- ductive Effects; cosmology; modal necessity; operational bridges.
The 1995 article by Achim Kempf, Gianpiero Mangano, and Robert B. Mann, “Hilbert Space Representation of the Minimal Length Uncertainty Relation,” constitutes one of the most important formal constructions through which a nonzero minimal uncertainty in position can be incorporated into quantum mechanics. Rather than representing a fundamental length merely as a discrete lattice imposed upon ordinary space, Kempf, Mangano, and Mann modify the canonical commutation relation and construct a Hilbert- space representation in which arbitrarily precise physical localization is excluded. Their framework yields a minimal position uncertainty, modifies the mathematical status of exact-position states, introduces maximally localized states and a quasi-position representation, and, in multidimensional formulations, leads to noncommuting position coordinates. The original article was published in Physical Review D, volume 52, pages 1108–1118, DOI https://doi.org/10.1103/PhysRevD.52.1108 (Kempf, Mangano, and Mann, 1995). This article develops a critical–propositional analysis of that framework in dia- logue with the Theory of Objectivity (TO), particularly its Seven Absolute Truths, its interpretation of logical Nothingness, the concept of individualizing fields, the onto- logical status attributed to infinity, the role of boundaries and interfaces, nonhuman relational observation, compositional emergence, and the transcendent element under- stood in TO as knowledge or information produced in atomic relations and considered equivalent to atomic radiation. Special attention is given to the foundational TO work A Esfera Perfeita (The Perfect Sphere), because the KMM minimal-localization structure provides an especially useful mathematical dialogue partner for a TO conception of a limiting physical scale. The central thesis developed here is deliberately restricted. Kempf, Mangano, and Mann do not demonstrate the Theory of Objectivity, do not derive its cosmogony, do not establish the individual magnetic field asserted by its Second Absolute Truth, and do not reproduce the triadic relational condition associated with its Fifth Absolute Truth. Nevertheless, their work provides a productive structural analogy for several TO concepts: finite physical localizability, distinction between formal mathematical objects and physically realizable states, existence of a forbidden domain below a localization threshold, generation of geometrical properties by fundamental algebraic relations, and conversion of fundamental constraints into potentially observable consequences. The strongest scientific use of KMM by TO would therefore not consist in claiming retrospective confirmation. TO should instead attempt to derive, from its own modal and cosmogonic architecture, an effective deformation parameter and a nonzero localization scale. If such a derivation were independently obtained, the resulting theory could produce quantitative deviations from ordinary quantum mechanics and could thereby enter genuine empirical contact. The analysis consequently proposes a formal research program in which modal axioms are connected to operator algebra, spectral corrections, propagation relations, information constraints, and experimentally bounded parameters. Later developments in generalized uncertainty principle research are also considered, including qualifications of the KMM algebra concerning Jacobi identities and spin (Fadel and Maggiore, 2022). KMM should therefore be understood as a historically and mathematically impor- tant model of minimal-length quantum mechanics, rather than as an experimentally established universal description of fundamental physics. Keywords: Theory of Objectivity; minimal length; generalized uncertainty principle; Kempf–Mangano–Mann algebra; modal ontology; Perfect Sphere; quantum gravity; physical localizability; information; atomic radiation; noncommutative geometry; In- ductive Effects; cosmology; modal necessity; operational bridges.
This article develops an expanded critical–propositional analysis of Daniel Salart, Augustin Baas, Cyril Branciard, Nicolas Gisin, and Hugo Zbinden’s 2008 experiment, “Testing the Speed of ‘Spooky Action at a Distance’,” published in Nature, in systematic dialogue with the Theory of Objectivity (TO) developed by Vidamor Cabannas and Denivaldo Silva. Salart et al. performed an energy–time entanglement experiment between two receiving stations separated by approximately 18 km in the Geneva region and used the rotation of the Earth to constrain hypothetical finite-speed influences that might be invoked to reproduce quantum correlations in a privileged reference frame. Under a representative assumption concerning the Earth’s velocity relative to such a frame, their analysis produced lower bounds exceeding 104 c, with a reported bound of approximately 54,000c in a particular geometrical configuration. These quantities are not measurements of an actually detected superluminal signal; they are conditional lower bounds applying to hypothetical hidden influences. The present study asks whether this experimental structure can be placed in meaningful dialogue with the modal axioms of the Theory of Objectivity, especially the First Absolute Truth concerning primordial Nothingness as a logical, mathematical, and eternal essence; the Second Absolute Truth concerning an element-specific individualiz- ing field; the TO treatment of infinity; and, most importantly, the Fifth Absolute Truth, according to which an element acquires logical existence through elementary relational observation involving at least two other elements. In this framework, “observation” does not signify human consciousness but an objective relation among physical elements. The article argues that Salart et al. provide no direct empirical test of the First or Second Absolute Truths and no direct confirmation of TO’s cosmogonic theorem or cosmological eras. The strongest dialogue concerns relational ontology, the Fifth Absolute Truth, and the TO concept of the transcendent element as knowledge or information produced through atomic relations and associated, within TO, with atomic radiation. Nevertheless, quantum information in a Bell experiment cannot simply be identified with a controllable signal propagating between distant systems. This distinction becomes theoretically decisive. If the TO transcendent element is construed as an ordinary finite-speed physical carrier responsible for Bell correlations, strong conceptual difficulties arise. If, instead, it is formulated as relationally constituted information whose manifestation cannot be reduced to classical signal propagation, the dialogue with quantum nonlocality becomes substantially stronger. The article further examines criticisms of the 2008 Franson-type implementation, subsequent loophole-reduced and loophole-free Bell experiments, and theoretical results showing difficulties for finite-speed hidden-influence models. It concludes that Salart et al. may be treated as an indirect empirical bridge for developing TO’s relational propositions, but not as a unique experimental confirmation of TO. A scientifically decisive future program requires the Theory of Objectivity to derive an observable probability distribution or correlation function that differs quantitatively from the predictions of standard quantum mechanics. An appendix formulates such a research program in a TO-style modal–empirical structure. Keywords: Theory of Objectivity; quantum nonlocality; Bell inequalities; Salart exper- iment; entanglement; relational ontology; modal necessity; information; transcendent element; quantum foundations; empirical corroboration; cosmology.
This article presents a critical–propositional analysis of Ming Cheng’s work, The Structural Origin of Heisenberg’s Uncertainty Principle: Infinite-Dimensional Reality and Its Analytic, Functional, Geometric, and Algebraic Foundations (2026), in confrontation with the Theory of Objectivity (TO), developed by Vidamor Cabannas and Denivaldo Silva. The study examines Cheng’s central thesis that Heisenberg’s uncertainty principle does not arise primarily from limitations of measurement, but from the very infinite-dimensional structure of physical reality and its mathematical representation through four convergent layers: analytic non-commutativity, Fourier duality, symplectic geometry, and algebraic rigidity. From this reconstruction, the article identifies both compatibilities and points of tension between Cheng’s proposal and the modal axioms of TO. Among the compatibilities are the critique of simplistic instrumentalism, the emphasis on deep structures, and the understanding of the phenomenon as derived from prior compositions. Among the tensions are the ontological status of infinity, the absence of an originary cosmogonic treatment, and the insufficient treatment of the auratic singularity of the element. In a propositional framework, the text interprets the uncertainty principle as a derived phenomenic element, articulating it with the Inductive Effects, the Reductive Inductive Effect, the cosmogonic theorem of TO, and the cosmological Eras of the Theory of Objectivity. The article also develops the hypothesis that the transcendent element corresponds to the knowledge or information produced in atomic relations, equivalent to atomic radiations, which allows uncertainty to be reread not merely as a limit, but as an index of the non-saturation of the quantum and of reality’s openness to the production of knowledge. Thus, the study argues that Cheng’s article offers a strong and philosophically fertile structural description of the quantum domain, but that its full ontological intelligibility requires subordination to the modal, relational, and cosmogonic discipline of the Theory of Objectivity. The result is a rigorous dialogue between contemporary mathematical physics and modal ontology, reaffirming that TO does not seek to replace modern physics, but to provide it with a logical, ontological, and scientific foundation compatible with a possible universe. Keywords Theory of Objectivity; uncertainty principle; Heisenberg; Ming Cheng; modal ontology; infinite-dimensionality; Hilbert space; Fourier duality; symplectic geometry; Stone–von Neumann; Reductive Inductive Effect; phenomenic elements; information-radiation; cosmogony; quantum physics
This article develops an expanded critical-propositional analysis of S. L. N. Hermans et al.’s 2022 experimental study, “Qubit Teleportation between Non-Neighbouring Nodes in a Quantum Network,” published in Nature, in systematic dialogue with the Theory of Objectivity (TO) developed by Vidamor Cabannas and Denivaldo Silva. Hermans et al. realized quantum teleportation between stationary, non-neighbouring nodes of a three-node quantum network composed of solid-state spin qubits associated with nitrogen-vacancy centers in diamond. The experimental architecture involved remote entanglement generation on two elementary links, entanglement swapping at an intermediate node, preservation of previously generated quantum correlations through nuclear-spin quantum memories, Bell-state measurement at the sending node, classical communication, and conditional feed-forward at the receiving node. The experiment is examined here not as a direct confirmation of the complete ontology of the Theory of Objectivity but as an unusually rich operational domain in which several TO concepts may be confronted with controlled empirical phenomena. Particular attention is devoted to the Fourth, Fifth, Sixth, and Seventh Absolute Truths: boundary and interface; objective and non-anthropocentric observation; composition from previous elements and relations; and the transcendent element understood within TO as knowledge or information produced in atomic relations and considered equivalent to atomic radiation. The First Absolute Truth is also examined according to its specific formulation in TO: before the emergence of the Universe there was Nothing, although such Nothing was not absolute non-being but a logical, mathematical, and eternal essence. The article maintains a strict methodological distinction between modal necessity and empirical corroboration. If the Absolute Truths are claimed to possess modal necessity, no finite experiment can by itself establish that necessity. Experiments may instead test derived consequences, operational bridges, quantitative predictions, and physical interpretations of the axioms. In this sense, the three-node Alice-Bob-Charlie network displays a strong structural analogy with TO’s emphasis on relational and triangular observation. Nevertheless, compatibility is not equivalent to proof. Standard quantum mechanics predicts the experiment without requiring the complete modal ontology of TO. The analysis further proposes operational bridges through which TO could move from modal axioms toward experimentally distinguishable predictions. These include formalization of triadic relational conditions, information-memory relations, boundary- mediated composition, and the distinction between radiation as a physical carrier or mediator and information as a physically instantiated relational structure. The study also connects the experiment with TO’s phenomenic elements, Inducing Effects, the cosmogenic theorem, cosmological Eras, foundational works of Cabannas and Silva, recent TO publications, and supporting literature from quantum mechanics, relativity, cosmology, philosophy of physics, and scientific methodology. The principal conclusion is that Hermans et al. provide substantial indirect empirical support for relational, compositional, memory-based, and non-anthropocentric observational principles compatible with important sectors of TO. The experiment, however, neither establishes the modal necessity of the Seven Absolute Truths nor confirms the specific cosmological narrative of TO. Its strongest scientific value for TO lies in offering an advanced experimental platform from which operational and potentially falsifiable consequences may be developed. Keywords: Theory of Objectivity; quantum teleportation; quantum networks; entan- glement; information; quantum memory; modal necessity; objective observation; atomic relations; radiation; boundaries; Inducing Effects.
This article presents an expanded critical–propositional analysis of Taeyoung Choi et al.’s 2017 experiment, “Atomic-Scale Sensing of the Magnetic Dipolar Field from Single Atoms,” published in Nature Nanotechnology 12: 420–424, DOI 10.1038/nnano.2017.18, in systematic dialogue with the Theory of Objectivity (TO) developed by Vidamor Cabannas and Denivaldo Silva (Choi et al. 2017; Cabannas and Silva 2016, 2025). Choi et al. used individual iron atoms as electron-spin-resonance sensors in a scanning tunnelling microscope to detect the magnetic fields generated by nearby individual magnetic atoms. In artificially constructed Fe–Co atomic structures on mag- nesium oxide, the measured interaction energy followed an inverse-distance dependence of Eint ∝ r −3.01±0.04 , consistent with magnetic dipole–dipole coupling, which the authors found to dominate at separations greater than approximately one nanometre (Choi et al. 2017). The experiment therefore provides an unusually precise empirical domain in which atomic individuality, magnetic fields, physical boundaries, relational interaction, measurement, and information can be jointly examined. The central thesis developed here is not that Choi et al. experimentally prove the Theory of Objectivity. Rather, the experiment provides a strong regional empirical bridge to specific propositions of TO, most notably the Second Absolute Truth, according to which every existing element possesses a magnetic field proper to itself that participates in its individuation. The experiment also permits substantial dialogue with the Fourth Absolute Truth concerning boundaries and differentiation, the Fifth Absolute Truth concerning non-human relational observation, the Sixth concerning composition, and the Seventh concerning information or knowledge generated through atomic relations and identified in TO with atomic radiation as the transcendent element. The analysis distinguishes modal necessity from empirical corroboration. TO presents its Absolute Truths as necessary components of an axiomatic ontology; lab- oratory experiments operate instead through contingent physical arrangements and inductive inference. Consequently, an experiment on Fe and Co atoms cannot logically establish the universal proposition that every element in existence possesses an indi- vidual magnetic field. It can, however, substantiate an operational consequence in a well-defined physical domain: an individual atom can produce a spatially extended mag- netic field that alters the measurable state of another individual atom, and information concerning the source atom can be reconstructed through that relation. This distinction is used to formulate a methodological framework connecting TO’s modal ontology to experimentally discriminable hypotheses. The article further examines TO’s phenomenic elements, its Expansive and Reductive Inductive Effects, its cosmogonic theorem, and its cosmological Eras. Choi et al. are interpreted not as testing primordial cosmogenesis, but as investigating a late and highly structured physical regime in which some relational consequences predicted by TO can be operationally represented. The article finally proposes criteria for transforming compatibility into stronger empirical support: universalization tests across different species and states of matter; op- erational definitions of “individual field”; quantitative models of radiation–information; tests of TO’s relational observation requirement; and predictions capable of distinguish- ing TO from standard quantum mechanics and electromagnetism. In this sense, Choi et al. constitute an important experimental interlocutor for TO precisely because their work exposes both the potential empirical strength of magnetic individuality and the methodological boundaries that a modal theory must cross to become a distinctive physical research program. Keywords: Theory of Objectivity; atomic magnetometry; magnetic dipole field; elec- tron spin resonance; scanning tunnelling microscopy; magnetic individuality; relational observation; atomic information; modal ontology; radiation-information; phenomenic elements; inductive effects; cosmogonic theorem; scientific testability.
This article develops an expanded critical–propositional analysis of Susanne Baumann et al.’s 2015 experiment, “Electron Paramagnetic Resonance of Individual Atoms on a Surface,” published in Science 350, 417–420, DOI 10.1126/science.aac8703, in systematic dialogue with the Theory of Objectivity (TO) formulated by Vidamor Cabannas and Denivaldo Silva. Baumann et al. combined the high energy resolution of electron paramagnetic resonance with the spatial resolution of scanning tunneling microscopy to observe and manipulate the magnetic resonance of individual iron atoms deposited on a magnesium oxide film. The experiment achieved an energy resolution of approximately 10 neV, drove spin transitions by means of an oscillating electric field in the 20–30 GHz range, and obtained energy-relaxation and phase-coherence times of approximately T1 ≈ 100 µs and T2 ≈ 210 ns, respectively. Of particular relevance to the present analysis, the resonance signals of distinct Fe atoms differed by more than their individual linewidths, thereby exposing atom-specific spectroscopic differences that would appear merely as inhomogeneous broadening in a conventional ensemble measurement (Baumann et al. 2015). The principal question examined here is whether these results can enter into legitimate empirical dialogue with the modal axioms of the Theory of Objectivity, especially its Second Absolute Truth, according to which every existing element possesses a magnetic field proper and exclusive to itself, and its Fifth Absolute Truth, according to which an element requires relational observation or frequency inclusion involving at least two other elements for logical existence, where “observation” is physical and relational rather than specifically human. The article argues that Baumann et al. offer a significant empirical bridge to an operational consequence compatible with the Second Absolute Truth: individual atoms are magnetically addressable and may display experimentally distinguishable resonance signatures. Nevertheless, atom-specific spectral differentiation does not by itself establish an ontologically unique intrinsic magnetic field, since resonance frequencies depend on local bonding, substrate, tip field, applied magnetic field, electronic structure, anisotropy, and other environmental contributions. The analysis therefore distinguishes three epistemic levels: modal necessity internal to TO, empirical compatibility, and discriminating empirical confirmation. This distinction is central to the recent methodological development of TO, particularly its attempt to construct bridges between modal axioms and empirical observables without reducing logical necessity to inductive evidence (Cabannas and Silva 2026a, 2026c). Subsequent ESR-STM experiments strengthen the relevance of this research program. Choi et al. measured the magnetic dipolar field of individual atoms with atomic-scale precision, while Willke et al. showed that the hyperfine interaction of individual surface atoms depends strongly on binding configuration and local atomic environment (Choi et al. 2017; Willke et al. 2018). These developments simultaneously reinforce the experimental accessibility of atomic magnetism and sharpen the main tension for TO: intrinsic magnetic individuality must be distinguished from contextual physical individuality. The article further relates the Baumann experiment, where appropriate, to TO’s phenomenic elements, Inductive Effects, cosmogenic theorem, cosmological Eras, boundaries, composition, and its conception of the transcendent element as knowledge or information generated in atomic relations and regarded in TO as equivalent to atomic radiations. The experimental chain—oscillating field, spin transition, tunneling magnetoresistance, electrical current, and recorded information—is shown to be partic- ularly fertile for a TO-oriented analysis of relational information. Yet no claim is made that Baumann et al. experimentally establish information as a transcendent substance or demonstrate an equivalence between information and atomic radiation. A specific discriminating protocol is proposed: equivalent atoms of the same isotope should be prepared under progressively controlled and replicated environments in order to determine whether a reproducible atom-specific magnetic residual persists after known environmental contributions are removed. Such a residual, if independently replicated and quantitatively predicted by TO, would constitute a substantially stronger empirical bridge to the Second Absolute Truth than presently available evidence. Conversely, convergence of equivalent atoms toward indistinguishable spectra under equivalent environments would favor the conventional contextual explanation of the observed individuality. The study concludes that Baumann et al. constitute a strong experimental interlocutor for the microphysical dimension of TO, especially concerning individual magnetic addressability, relational observation, interfaces, frequency conditions, and physically encoded information. The experiment does not establish the complete ontology or cosmogony of TO, but it provides a technologically mature domain in which some of its propositions can be translated into increasingly discriminating empirical questions. Keywords: Theory of Objectivity; electron paramagnetic resonance; ESR-STM; scan- ning tunneling microscopy; individual atoms; magnetic fields; atomic individuality; modal necessity; empirical testability; Absolute Truths; relational observation; informa- tion; atomic radiation; Inductive Effects; phenomenic elements; cosmogenic theorem; Vidamor Cabannas; Denivaldo Silva; Baumann; quantum measurement.
This article develops an expanded critical-propositional analysis of Marissa Giustina et al.’s 2015 experiment, “Significant-Loophole-Free Test of Bell’s Theorem with Entangled Photons,” published in Physical Review Letters, in systematic dialogue with the Theory of Objectivity (TO) developed by Vidamor Cabannas and Denivaldo Silva. Giustina et al. performed a photonic Bell experiment designed to close simultaneously the most significant locality and detection-related loopholes that had historically allowed restricted local-realist explanations of earlier tests. By employing an optimized entangled- photon source, rapid physically generated measurement settings, spatially separated measurement stations, and high-efficiency superconducting detectors, the experiment produced a statistically overwhelming violation of a Bell inequality. Under the local- realist null hypothesis considered by the authors, the probability of obtaining results at least as extreme as those observed did not exceed 3.74 × 10−31, corresponding to approximately 11.5 standard deviations (Giustina et al., 2015). The present article does not treat this result as a direct proof of the Theory of Objectivity. Instead, it distinguishes three epistemic levels: empirical fact, structural compatibility, and theory-specific confirmation. This distinction is indispensable because Bell experiments constrain broad classes of local hidden-variable descriptions while not uniquely selecting the ontology proposed by TO. The article nevertheless argues that Giustina et al. provide an exceptionally fertile empirical domain for examining several elements of TO. Particularly significant are the Fourth Absolute Truth, concerning boundaries and interfaces; the Fifth Absolute Truth, according to which logical existence requires physical observation or relational frequency involving at least two other elements and where observation is explicitly non-anthropocentric; and the Seventh Absolute Truth, interpreted within TO as the informational or transcendent element generated in atomic relations and physically associated with atomic radiation. The analysis also addresses the First Absolute Truth, according to which prior to the universe there was Nothing, although this Nothing is not absolute absence but an eternal logical and mathematical essence; the Second Absolute Truth, according to which every existing element possesses its own exclusive magnetic field that individualizes it; the Third and Sixth Absolute Truths; the phenomenic elements; the Expansive and Reductive Inductor Effects; the cosmogenic theorem; and the cosmological Eras of TO. Particular attention is paid to points at which the experimental facts are neutral toward TO, points of genuine structural compatibility, and points of tension requiring further mathematical development. The central proposal is that Bell experiments should become an operational benchmark for TO. If TO is to move from modal axioms to empirical contact, it must derive a probability structure for entangled measurements, recover Bell-inequality violations without reducing its relational ontology to local predetermined properties, preserve operational no-signalling, and ultimately identify at least one experimentally accessible regime in which a TO prediction differs from standard quantum mechanics. In this sense, Giustina et al. offer strong indirect empirical compatibility with the relational and informational dimensions of TO, but not an exclusive empirical confirmation of the theory. Keywords: Theory of Objectivity; Bell theorem; Bell nonlocality; entanglement; local realism; modal ontology; observation; information; radiation; boundaries; quantum foundations; testability.