Single-Atom Electron Paramagnetic Resonance and Modal Objectivity

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.