The phase of an oscillator in quantum theory. What is it 'in reality'?

F. Cros

Yurii I. Vorontsov

An analysis of the current theory of the quantum oscillator phase is presented. Predictions using existing approaches to the phase problem differ not only quantitatively but also qualitatively. The question in the title has not yet been given a generally accepted answer. However, it is logical to argue that all the theoretically predicted properties of the phase are physically meaningful if appropriate measurements are possible. Current phase measurement methods either involve the simultaneous (approximate) measurement of the amplitude and the phase or rely on the simultaneous measurement of quadrature amplitudes.

ten Napel, Rob

This paper proposes a physical interpretation of the imaginary unit i in the Schrödinger equation, arguing that its complex structure is not a mathematical artifact but a direct signature of the zero field’s internal phase dynamics. In standard quantum mechanics, i enables oscillatory, unitary time evolution—yet its physical meaning remains unaddressed. Within the framework of R-theory (Resonance Theory), the universe is understood as a coherent resonant field with two inseparable components: a real, space-time-manifested aspect and an imaginary, non-local phase domain. This paper identifies i as the mathematical projection of this hidden imaginal axis. The wavefunction’s complex nature—traditionally viewed as formal—is reinterpreted as a physical necessity. The real amplitude corresponds to manifested energy, while the imaginary component expresses the latent coherence through which all energy oscillates between potential and presence. In this view, the Schrödinger equation becomes a dynamical law describing rotations within the zero field, where i functions as the operator of coherence rather than an abstract algebraic device. The implications are significant: Quantum oscillation reflects the continuous exchange between real and imaginal components of the zero field. Complexity is elevated from a mathematical convenience to an ontological principle. Consciousness emerges as the experiential side of the same imaginal phase that maintains physical coherence. Reality itself is intrinsically complex—built from orthogonal dimensions of manifestation and potential. This paper reframes the imaginary dimension as the fundamental axis through which the universe sustains resonance. What physics calls “imaginary” is revealed as the inner structure of reality, the phase without space that allows energy, matter, and awareness to exist as coherent oscillations within the zero field.

Mathieu Valentin Rondet

Summary: Why does reality remain stable?Physics successfully describes how systems evolve, yet a more fundamental question remains largely unexplored: why do stable structures exist at all?Why does one informational configuration become a persistent physical object while countless alternative possibilities never stabilize? This paper proposes a common stabilization mechanism underlying quantum decoherence, Fourier analysis, machine learning, recursive systems, biological regulation, logical exclusion and language. This work may be of interest to researchers in: quantum foundations information theory complex systems logic computational physics machine learning philosophy of physics This manuscript develops the NNO operator step by step, examines its structural parallels across multiple disciplines, and discusses its implications for observer-relative reality, antimatter, and quantum spin. Description: The NNO Stabilization Operator This paper introduces the NNO operator (Negation–Negation–Oscillation), a minimal conceptual mechanism describing how informational configurations become stable and persistent through observation. Its central idea is straightforward: reality does not emerge simply because information accumulates. It emerges because informational configurations repeatedly survive confrontation with incompatible alternatives relative to the observer. Any direct interaction introduces orientation and polarity, which in turn generate a conjugate alternative. A single negation leaves an active ambiguity relative to the informational evolution of an observer. Stabilization therefore requires two inseparable and complementary mechanisms combined into one conceptual operator: Double Negation — a two-step exclusion process requiring a configuration to remain coherent after confrontation with its logical inverse and that of the observer. Oscillation — phase alternation that progressively removes dependence on origin, scale, and monotonic accumulation, leaving only phase-invariant informational structures. Within this framework, stable reality corresponds to informational patterns that remain invariant under repeated exclusion and phase alternation relative to an observer, validating informational structures across successive observations rather than merely selecting a local configuration. Background Although developed independently, remarkably similar stabilization processes appear throughout science and mathematics. Examples include: quantum decoherence and phase scrambling signal processing and Fourier phase integration renormalization and universality logical systems based on exclusion (NAND, NOR, intuitionistic logic) machine learning optimization, convergence and loss-driven exclusion recursive dynamical systems and fractal invariants biological regulation through oscillatory turnover and selective instability semantic stabilization in language and cognition Despite their different formalisms, all of these mechanisms progressively eliminate unstable possibilities until only robust, observer-relative structures remain.This work argues that these apparently unrelated phenomena may represent different manifestations of the same underlying informational principle. Main implications Within this framework, the NNO operator provides an informational interpretation of: observer-relative reality quantum decoherence phase-dependent emergence and stabilization of physical structures phase invariance exclusion-based stabilization persistence of informational structures A companion paper extends these ideas to quantum spin and phase-dependent observer effects. The paper further examines orientation-reversed invariants as a necessary boundary case for any stabilization operator, showing that NNO stabilization remains valid under inverted informational orientation. Within this perspective, antimatter can be described as the stabilization of the same informational structure under inverted orientation. This proposition is consistent with CPT symmetry and the Feynman–Stueckelberg interpretation, without invoking literal backward time propagation. Scope of this work This article is intentionally conceptual. It does not propose a new mathematical formalism or seek to replace established physical theories. Instead, it identifies a minimal stabilization mechanism that appears implicitly across numerous successful theoretical frameworks and proposes a unified informational interpretation of their common logic. The objective is to provide a conceptual foundation for future: mathematical formalization computational modeling independent verification cross-disciplinary investigation As such, the author welcomes constructive discussion, independent verification, mathematical formalization, and interdisciplinary collaboration. Relation to other work This publication constitutes the second major conceptual component of the Universal Theory of Information (TUI) research program. The current sequence consists of: The Universal Theory of Information (TUI): Emergence of Physics from Informational DynamicsInformational foundations of space, time, mass, gravity, and physical reality. Doi: 10.5281/zenodo.15106945 The NNO OperatorStabilization of informational structures through double negation and oscillation. Spin as a Signature of Information ExclusionInformational interpretation of quantum spin and observer-dependent phase stabilization. (Doi: 10.5281/zenodo.18443042 This paper can be read independently, but reaches its full coherence when considered as part of the TUI–NNO–SPIN conceptual sequence.Together, these works propose a unified informational framework in which physical reality emerges from discrete informational interactions, while stable structures arise through recursive stabilization rather than accumulation alone. About the author Mathieu Valentin Rondet is an independent researcher investigating the informational foundations of physical reality through the Universal Theory of Information (TUI) research program. He holds two master's degrees in molecular biology, developmental biology, genetics, and biochemistry, completed in France and the United States. His academic background is complemented by more than twenty years of professional experience developing physically based simulations, procedural systems, and complex dynamic environments for the visual effects industry. His research combines concepts from information theory, complex systems, computational modeling, logic, and physics to investigate observer-relative informational structures and the emergence of stable physical phenomena. If the proposed stabilization mechanism does capture a genuine cross-domain invariant, it could provide a common conceptual foundation linking informational persistence across logic, computation, biology, and fundamental physics.

R. Shepard Scott