VIOLATION OF A LEGGETT–GARG INEQUALITY WITH IDEAL NON-INVASIVE MEASUREMENTS

This article develops an expanded critical–propositional analysis of George C. Knee et al.’s experiment, “Violation of a Leggett–Garg Inequality with Ideal Non-Invasive Measurements,” published in Nature Communications, in systematic dialogue with the Theory of Objectivity (TO) formulated by Vidamor Cabannas and Denivaldo Silva. Knee et al. implemented a Leggett–Garg test using phosphorus donors in isotopically enriched silicon, with the phosphorus-31 nuclear spin serving as the primary system and the associated electron spin functioning as an ancillary measuring degree of freedom. Their experimental protocol employed ideal negative-result measurements, selective microwave and radio-frequency control, a strong static magnetic field, low- temperature preparation, hyperpolarization, post-selection, and population tomography. The electron–nuclear hyperfine interaction was approximately 117.5 MHz, while the experiment operated near a static magnetic field of 3.357 T. The authors reported Leggett–Garg function values including f = −0.031 and f = −0.296, with final-state population fidelities no lower than approximately 98.9 percent (Knee et al. 2012). Under the assumptions explicitly adopted in the experiment, these results falsified the conjunction of macrorealism and non-invasive measurability for the investigated cold nuclear-spin system. The present analysis does not interpret this outcome as a direct confirmation of the complete ontology of TO. Instead, it asks whether the experimental architecture, empirical findings, and conceptual consequences of Knee et al. provide operational domains in which particular propositions of TO may be confronted with contemporary physics. Special attention is devoted to the Second, Fourth, Fifth, Sixth, and Seventh Absolute Truths. The Fifth Absolute Truth is especially relevant because, in TO, observation is not fundamentally a human or conscious act. According to the formulation adopted in the theory, an element possesses logical existence only when it is observed by, or lies within the relevant frequency of, at least two other elements. Knee et al.’s system– ancilla architecture offers a concrete physical example in which information concerning a nuclear spin is obtained through relations involving another microscopic system, electromagnetic fields, conditional transformations, and physical readout, without attributing a constitutive physical role to human consciousness. The analysis also examines the TO proposition that the transcendent element consists of knowledge or information produced in atomic relations and that such information is equivalent, in the ontology of TO, to atomic radiations. Knee et al. demonstrate that recoverable information can indeed be encoded in controlled relations among atomic degrees of freedom and that electromagnetic radiation participates in producing and reading these correlations. However, this operational fact does not by itself establish the stronger ontological identity among information, knowledge, transcendence, and atomic radiation. A central conclusion of the present study is that violation of a Leggett–Garg inequality must not be equated with the destruction of objectivity. What is challenged experimentally is a particular conjunction of macrorealism and non-invasive measurabil- ity, not every conceivable realist ontology. This distinction is particularly important for TO, whose concept of objectivity may be understood as relational, field-dependent, modal, compositional, and informational rather than as a simple restatement of classical macrorealism. Knee et al. therefore provide substantial indirect empirical dialogue with the TO program concerning non-anthropocentric observation, physical relationality, fields, frequencies, boundaries, and information. At the same time, the experiment leaves TO’s cosmogenic claims, the modal necessity attributed to its Seven Absolute Truths, and its proposed cosmological Eras largely outside the experimental domain. Keywords: Theory of Objectivity; Leggett–Garg inequality; macrorealism; non-invasive measurability; ideal negative-result measurement; quantum measurement; nuclear spin; phosphorus in silicon; ancilla; relational ontology; information; modal necessity; Inducing Effects; quantum foundations.