The Kyiv Interpretation (KI) of Quantum Mechanics (Киевская интерпретация квантовой механики) represents a natural continuation of the mathematical tradition of the Kyiv school of nonlinear dynamics. In the works of Nikolai Bogolyubov and Nikolai Krylov, nonlinear resonance served as a powerful analytical tool for describing complex macroscopic systems. Within KI, resonance acquires a fundamental ontological status, becoming the physical mechanism underlying the formation of material objects.

In contrast to the Copenhagen interpretation, which treats the wavefunction as an epistemic construct and assigns a privileged role to the observer, KI is based on temporal realism: time is postulated as a fundamental physical field. Quantum states are interpreted as real dynamical configurations of this field defined on an extended manifold that includes an additional cyclic temporal dimension (hypertime).

Within this framework, the wavefunction emerges as a temporal resonance mode of the fundamental timefield in hypertime . Quantum probabilities arise as effective projections of deterministic dynamics in the extended temporal manifold onto fourdimensional spacetime. Measurement is described not as a collapse of the wavefunction, but as phase synchronization (resonant locking) between interacting temporal structures.

This approach provides a consistent physical reinterpretation of key conceptual problems of quantum mechanics including the measurement problem, Schrdingers cat, and EPR correlations without modifying the standard mathematical formalism. By reinterpreting time from a passive parameter t into a physical substance , the Kyiv Interpretation offers a constructive continuation of Einsteins realist program and establishes a unified temporal ontology linking quantum mechanics and gravitation.

Keywords: quantum mechanics, interpretation of quantum theory, temporal realism, deterministic dynamics, wavefunction ontology, hyper-time, Kyiv Interpretation

1. Introduction: From Nonlinear Dynamics to Temporal Realism

The Kyiv Interpretation (KI) of Quantum Mechanics is not proposed as an isolated alternative framework, but as a natural continuation of the mathematical tradition of the Kyiv school of nonlinear dynamics. In the seminal works of Nikolai Bogolyubov and Nikolai Krylov, nonlinear resonance functioned as a powerful analytical tool for describing the emergence of stable behavior in complex macroscopic systems. Within the Kyiv Interpretation, this concept is elevated from a methodological instrument to a foundational ontological principle: resonance becomes the physical mechanism through which material structures themselves are formed.

Since its inception, quantum mechanics has achieved extraordinary predictive success, yet its ontological foundations remain unresolved. Standard interpretations treat the wavefunction either as an epistemic construct or as an abstract element of formalism, while assigning a privileged role to measurement or observation. Einsteins objection to fundamental randomness was not directed at the mathematical structure of quantum theory, but at the absence of an underlying physical reality capable of restoring causality and objectivity. However, within the conventional framework, no such substrate has been identified.

The Kyiv Interpretation addresses this gap by reexamining the physical status of time itself. Whereas classical and relativistic mechanics treat time as an external parameter t, KI postulates time as a physical substance, described by a dynamical temporal field possessing density, elasticity, and topological structure. In this view, matter is not situated within time; rather, matter emerges as a stable dynamical configuration of time.

This ontological shift enables a unified conceptual framework in which quantum phenomena are no longer fundamentally probabilistic, but arise as deterministic processes unfolding in an extended temporal continuum. Apparent randomness and waveparticle duality are interpreted as effective projections of higherdimensional temporal dynamics onto the fourdimensional observational interface. In this sense, the Kyiv Interpretation does not modify the formal machinery of quantum mechanics, but reinterprets its meaning by embedding it within a deeper, temporally realist ontology.

2. Ontological Foundations: Time as a Physical Field

In the Kyiv Interpretation (KI), the hierarchy of physical reality is inverted: time ceases to be a passive parameter or external stage for events and becomes the primary physical substance. This section formalizes the transition from time-as-a-parameter to time-as-a-field and establishes the ontological basis for the subsequent dynamical interpretation of quantum phenomena.

2.1. The Field and the 5D Temporal Continuum

The mathematical foundation of KI is a real scalar temporal field (x, ), where x denotes the standard four spacetime coordinates and represents an additional cyclic temporal dimension (hypertime). The physical arena of the theory is therefore a fivedimensional temporal continuum rather than conventional spacetime.

The dynamics of the system are not postulated heuristically but follow from the principle of least action applied to this extended temporal manifold. The simplest freefield Lagrangian density for the field is:

L = (M )(M )

where the index M = 0,,4 runs over all five temporalspatial coordinates. In the absence of external sources, the EulerLagrange equations yield the fundamental wave equation:

(1 / v') ' / ' = 0

where is the fourdimensional dAlembert operator and v is the characteristic propagation velocity along the hypertime dimension .

This equation defines time not as a background parameter but as a dynamical medium capable of sustaining propagating modes, resonances, and stable configurations.

2.2. The Schrdinger Equation as a Low-Energy Projection

A central claim of KI is that the Schrdinger equation is not fundamental but emerges as a low-energy, phase-averaged projection of the underlying five-dimensional temporal dynamics.

Assuming a compact topology of the hyper-time dimension, the temporal field admits a mode decomposition of the form:

(x, t, ) = (x, t) " e^(i n )

where is the fundamental frequency associated with the cyclic dimension and n Z.

Substitution of this ansatz into the 5D wave equation shows that gradients along generate an effective mass-like contribution in the four-dimensional dynamics. Averaging over the extremely rapid oscillations in which are inaccessible to direct observation yields an effective evolution equation for the slowly varying envelope (x, t).

Within this framework, the quantum Hamiltonian is interpreted as a manifestation of the hyper-time gradient of the fundamental temporal field. The Schrdinger equation does not describe intrinsic probabilistic waves but rather the evolution of a resonant envelope of a real, deterministic temporal vibration. A detailed derivation of this projection is provided in Appendix A.

2.3. Core Ontological Postulates The temporalfield formulation of KI rests on the following ontological postulates:

1. Substantiality of Time. Time is a nonlinear, elastic physical medium. The local density of this medium determines the intrinsic rates of all physical processes. The vacuum corresponds to a uniform, minimalenergy configuration of the field rather than an empty void.
2. Emergent Geometry. Spatial distance is not fundamental but corresponds to phase delays and signal propagation effects within the temporal medium. Geometry emerges as a macroscopic interface describing variations in temporal density and phase structure.
3. Matter as Knotted Time. Elementary particles are stable, selfsustaining topological configurations (solitons or knots) of the field. Mass measures the internal tension and energy concentration of these configurations, primarily associated with gradients in the hypertime dimension .

2.4. From Amplitudes to Vibrations

The essential conceptual shift of KI lies in redefining the ontological status of quantum objects. In the Copenhagen interpretation, the wavefunction is an epistemic construct encoding information about measurement outcomes. In KI, the same mathematical object is reinterpreted as a real dynamical feature of the temporal substrate:

• Wavefunction : a physically real envelope (modulation) of the fundamental temporal field on the fourdimensional observational interface.
• Quantum state: a resonance mode of the field sustained by the cyclic hypertime dimension .
• Local intensity ||': a phaseaveraged measure of the local oscillation intensity of the field and, consequently, of the effective energy stored in the corresponding temporal vibration mode. This interpretation is grounded in the existence of a welldefined energy density for the field derived from its quadratic Lagrangian; upon averaging over the fast phase, the dominant hypertime contribution scales proportionally to ||'.

Under this interpretation, waveparticle duality is replaced by a unified field picture. A particle corresponds to a localized, dynamically stable concentration of the field (the soliton core of a temporal knot), while the wave is the surrounding field configuration propagating and oscillating through hypertime .

2.5. Gravity as the Geometry of the Field

The preceding analysis leads naturally to a unified interpretation of quantum mechanics and gravitation. Since matter corresponds to localized concentrations of temporal density, gravity arises as a largescale manifestation of the same underlying field:

• Quantum mechanics describes the highfrequency resonant modes (acoustics) of the field.
• Gravitation describes the largescale gradients and geometric structure of that field.

Spatial curvature is thus reinterpreted as a variation in the effective refractive properties of the temporal medium. Increased temporal density slows internal cycles in , providing a direct physical mechanism for gravitational time dilation:

t = t -(1 / c')

where is the gravitational potential derived from the local density of the field.

In this sense, KI supplies a common ontological denominator for quantum mechanics and general relativity: they represent, respectively, the dynamical and geometrical regimes of a single fundamental temporal substrate.

3.The Wavefunction as a Temporal Resonance

The Kyiv Interpretation (KI) departs fundamentally from the statisticaloperational reading of quantum mechanics by assigning a direct physical meaning to the wavefunction. Rather than treating as an abstract vector in Hilbert space or a bookkeeping device for probabilities, KI identifies it as a real dynamical manifestation of the underlying fivedimensional temporal field. Within this framework, quantum mechanics is reinterpreted as an effective description of resonant structures and modulation patterns of time itself.

3.1. Ontological Status of : Temporal Realism In KI, the wavefunction is an objective physical entity whose properties follow from the dynamics of the fundamental temporal medium :

1. Physical Modulation. The function (x, t) represents the slowly varying spatialtemporal envelope of highfrequency oscillations of the field occurring along the hypertime dimension . It is therefore a real modulation of the temporal field rather than an abstract probability amplitude.
2. Energetic Interpretation. Unlike the standard Born interpretation, where ||' is postulated as a probability density, KI interprets ||' as a phaseaveraged measure of the local oscillation intensity of the field. Through the welldefined energymomentum tensor of the underlying scalar field, this intensity is proportional to the effective local energy density stored in the corresponding temporal vibration mode. A particle is detected where this temporal energy density becomes locally concentrated, forming a stable resonant core.
3. Independence from Observation. Since is a physical state of the field, it exists and evolves deterministically regardless of whether a measurement is performed. The wavefunction does not encode an observers knowledge; it encodes the actual dynamical state of the temporal substrate.

This ontological reassignment removes the need for a privileged observer and restores objectivity to the quantum state.

3.2. The Origin of Quantization: Topology and Resonance Structure

In KI, quantization is not introduced as a fundamental axiom but emerges from the global topology of the temporal manifold.

• Compact HyperTime Topology. The hypertime dimension is assumed to be compact, with topology S. Consequently, any physically admissible configuration of the field must satisfy periodic boundary conditions:

() = ( + 2R)

• Discrete Resonance Modes. As in any system with compact geometry, only discrete standingwave configurations are dynamically stable. The field can therefore sustain only a discrete set of resonance modes in , analogous to harmonics on a vibrating string or cavity.
• Physical Meaning of Quantization. The familiar quantum condition:

E = n

is reinterpreted as a closure condition: an integer number of temporal oscillation cycles must fit consistently into the hypertime loop. Quantization thus reflects a topological constraint on temporal vibrations rather than an intrinsic granularity of nature.

Within this view, quantum mechanics becomes the effective theory of nonlinear temporal acoustics governed by resonance selection rules.

3.3. Projection from the 5D Temporal Field to Schrdinger Dynamics

The link between the fundamental fivedimensional field and the standard Schrdinger equation is established through a controlled lowenergy projection.

Starting from the fundamental wave equation:

(1 / v') ' / ' = 0

one applies separation of variables:

(x, t, ) = (x, t) " e^(i n )

where the exponential factor represents a fast oscillation along the compact hypertime dimension.

Substitution into the 5D equation shows that the derivative produces a term proportional to n', which acts as an effective restenergy contribution in the fourdimensional dynamics. Averaging over the extremely rapid oscillations unresolvable at the observational level yields an effective evolution equation for the slowly varying envelope (x, t).

In this picture, the complex nature of is not a mathematical artifact but a direct representation of the phase of a real temporal oscillation in the hidden dimension. The Schrdinger equation thus emerges as the governing equation for the propagation and interference of resonant envelopes of the field on the fourdimensional observational interface.

3.4. Conceptual Consequences

This reinterpretation has several immediate consequences:

• The waveparticle duality is replaced by a single-field ontology: localized soliton-like resonances appear as particles, while extended oscillatory configurations appear as waves.
• Probabilities enter the theory only at the level of phase-averaging over unresolved hyper-time dynamics, not as fundamental indeterminism.
• The standard mathematical formalism of quantum mechanics is preserved, while its ontological meaning is radically clarified.

4. Measurement Without Collapse: The Resonant Locking Mechanism

The Kyiv Interpretation (KI) replaces the metaphysical notion of wavefunction collapse with a concrete dynamical process: phase synchronization (resonant locking) between interacting temporal structures. Measurement is thus reinterpreted not as a probabilistic rupture of unitary evolution, but as a continuous and deterministic reconfiguration of the underlying temporal field.

Within this framework, the apparent discontinuity associated with measurement arises solely from projecting higher-dimensional temporal dynamics onto the four-dimensional observational interface.

4.1. Resonant Interpretation of Measurement

In standard quantum mechanics, the transition from a superposition to a single outcome is postulated as an instantaneous and fundamentally stochastic event. In KI, the same transition is described as a nonlinear dynamical process governed by resonance selection.

1. Interaction as Coupling. When a microscopic temporal structure (the system) interacts with a macroscopic temporal structure (the apparatus), the interaction is mediated by the common field. Dynamically, this interaction is modeled as the coupling of nonlinear oscillatory modes within a shared temporal medium.
2. Phase Synchronization. Measurement corresponds to the evolution of the coupled system toward a stable synchronized state in the hypertime dimension . Analogously to wellstudied synchronization phenomena in nonlinear dynamics, initially independent oscillators tend to lock into a common phase once the coupling exceeds a critical threshold.
3. Deterministic Outcome Selection. The specific measurement outcome (e.g., a particular spin projection) is uniquely determined by the relative phases of the interacting temporal modes at the moment of coupling. No stochastic element is introduced at the fundamental level; the selection is fixed by the initial conditions in the extended (x, t, ) manifold.
4. Apparent Discontinuity. The synchronization process is smooth and continuous in the full fivedimensional temporal manifold. However, because observers have access only to the fourdimensional projection and cannot resolve the fast dynamics, the transition appears as an instantaneous jump, conventionally interpreted as wavefunction collapse.

4.2. The Role of the Apparatus: Macro-Temporal Stability

In KI, a measurement apparatus is not ontologically distinct from the system it measures. It is a macroscopic temporal structure characterized by a high degree of internal phase coherence and stability.

• Classicality as Phase Stiffness. A macroscopic object possesses a temporally stiff phase configuration: its many internal degrees of freedom collectively stabilize a small set of robust resonance modes. When coupled to a microscopic system, this stability biases the interaction toward synchronization with one of these modes.
• Emergence of Born Statistics. Although the dynamics are deterministic, the precise hypertime phase of the macroscopic apparatus is practically uncontrollable and unobservable. As a result, experimental statistics arise from averaging over an enormous ensemble of unresolved phases. Borns rule is thus reinterpreted as a phaseaveraged selection law, not as a fundamental postulate of randomness.

This interpretation preserves the empirical success of quantum statistics while grounding them in deterministic temporal dynamics.

4.3. No Privileged Observer: The End of Subjectivity

The Kyiv Interpretation restores objectivity to quantum theory by removing any special ontological role assigned to the observer.

• Observers as Temporal Structures. Whether the interaction involves a photodetector, a crystal lattice, or a biological organism, the underlying physics is identical: a resonant coupling between temporal field configurations.
• Independence from Consciousness. Conscious awareness does not induce state reduction. The outcome of a measurement is fixed by the temporal field dynamics prior to and independent of any act of perception. Consciousness merely registers the result of an already completed physical synchronization process.
• Symmetry of Interaction. Measurement is not a oneway act. In KI, the system and the apparatus mutually influence each other through the field, forming a symmetric process of phase locking within the universal temporal medium.

4.4. Conceptual Implications

By replacing collapse with resonant locking, KI resolves the measurement problem without modifying the linear structure of quantum dynamics. The apparent randomness of measurement outcomes is traced to unresolved hyper-time phases rather than to intrinsic indeterminism, thereby preparing the ground for the deterministic reinterpretation of probability developed in the following section.

5. Determinism and Probability: The Emergence of Borns Rule

The Kyiv Interpretation (KI) rejects the assumption that randomness is a fundamental property of nature. Instead, it postulates that the underlying dynamics of the universe are strictly deterministic, while quantum probabilities arise as an effective description resulting from limited access to the full temporal degrees of freedom.

Within this framework, probability is not ontological but emergent, reflecting systematic phase-averaging over unresolved hyper-time dynamics.

5.1. Deterministic Dynamics in the Extended Temporal Manifold In the fivedimensional temporal manifold (x, t, ), the evolution of the temporal field is governed by a continuous and causal field equation. Given complete information about the configuration of and its hypertime phase at an initial moment t, the subsequent evolution of the system would, in principle, be uniquely determined.

• Role of the Phase. The effective hidden variable in KI is not a localized particle coordinate but the phase of the temporal oscillation along the hypertime dimension . This phase encodes dynamical information that is inaccessible to fourdimensional observation.
• Continuous Trajectories. Quantum processes correspond to continuous trajectories in the extended phase space of the temporal field. The formal alternatives of branching worlds or stochastic state reductions are replaced by smooth rotations and deformations of in hypertime.

At the fundamental level, therefore, KI restores causal completeness without altering the linear mathematical structure of quantum dynamics.

5.2. The Origin of Probability: Phase Averaging and Coarse Graining While the underlying dynamics are deterministic, observable quantum statistics arise from systematic loss of information when higherdimensional dynamics are projected onto the fourdimensional observational interface.

1. MacroTemporal Complexity. A macroscopic measuring apparatus consists of an enormous number (10') of interacting temporal degrees of freedom, each characterized by its own hypertime phase. Although each degree of freedom evolves deterministically, their collective behavior effectively forms a dense distribution of phases.
2. ProjectionInduced Information Loss. When an interaction between a microscopic system and a macroscopic apparatus is described only in fourdimensional terms, the rapidly varying dependent information is eliminated. This projection acts as a coarsegraining procedure over hypertime phases.
3. Statistical Limit and Borns Rule. In this coarsegrained limit, the probability of a particular measurement outcome corresponds to the measure of hypertime phases for which resonant locking between the system and the apparatus occurs. Since the local oscillation intensity of the field determines the stability domain of synchronization, the resulting detection statistics scale as:

P(x) |(x, t)|'

Borns rule thus emerges as a temporal density law: it quantifies the phaseaveraged likelihood of resonance between deterministic temporal structures.

Importantly, no stochastic postulate is introduced at the fundamental level; probability arises solely from averaging over unresolved hypertime degrees of freedom.

5.3. Restoring Causality: A Realist Completion By deriving quantum probabilities from deterministic temporal dynamics, KI fulfills the longstanding requirement for a causally complete description of physical reality.

• Causal Origin of Events. Every individual quantum event such as a detector click is determined by a specific configuration of temporal phases of the system and the apparatus at the moment of interaction. Apparent randomness reflects ignorance of these phases, not indeterminacy of nature.
• Effective Stochasticity. Probabilistic methods remain indispensable in practice because direct experimental access to the hypertime phase is currently unavailable. Nevertheless, within KI this limitation is technological rather than fundamental.

In this sense, KI reconciles the empirical success of probabilistic quantum mechanics with a deterministic and realist ontology: chance is not a basic ingredient of the universe, but an emergent feature of temporal coarse graining.

5.4. Transition to Paradox Resolution

The reinterpretation of probability as phase-averaged deterministic dynamics prepares the ground for resolving the traditional paradoxes of quantum mechanics. In the following section, this framework is applied to Schrdingers cat, EPR correlations, and related conceptual puzzles, demonstrating how temporal realism eliminates their apparent contradictions without modifying the standard formalism.

6. Resolution of Classical Quantum Paradoxes

Within the Kyiv Interpretation (KI), the traditional paradoxes of quantum mechanics are not treated as fundamental inconsistencies of nature, but as artifacts arising from an incomplete ontological picture. Once time is recognized as a physical field with its own dynamics, the apparent weirdness of quantum phenomena is replaced by well-defined temporal processes.

6.1. Schrdingers Cat: Metastability Instead of Superposition

In the standard formulation of quantum mechanics, Schrdingers cat is described as existing in a linear superposition of macroscopically distinct states until an act of observation occurs. In KI, this description is replaced by a physically grounded account based on temporal dynamics.

1. Metastable Temporal States.
   The radioactive atom triggering the experiment is not simultaneously decayed and undecayed. It occupies a specific, well-defined phase of its oscillation in hyper-time \Theta. What is conventionally described as a superposition corresponds, in KI, to a metastable temporal configuration that has not yet transitioned to the next dynamically stable state.
2. Objective Temporal Relaxation.
   The transition from alive to dead occurs when the temporal phase of the decaying system enters a stability domain that allows resonant locking with the macroscopic detectorcat system. This transition is a process of temporal relaxation, driven by the dynamics of the \tau-field toward a lower-energy, more stable configuration.
3. Observer Independence.
   At every value of hyper-time , the macroscopic state of the cat is uniquely determined by the configuration of the temporal field. The presence or absence of an observer has no influence on this physical fact. Observation merely records the outcome of a temporal transition that has already taken place.

Thus, the paradox dissolves: macroscopic superpositions are replaced by dynamically evolving metastable states of a real temporal medium.

6.2. EPR Correlations and Nonlocality: The Common Temporal Substrate

The EinsteinPodolskyRosen (EPR) paradox highlights the tension between quantum correlations and classical notions of locality. In KI, this tension is resolved by shifting the explanatory framework from spatial separation to temporal coherence.

1. Unity in the Temporal Field.
   Entangled particles are not independent objects that later exchange information. They are two localized manifestations of a single, continuous deformation of the temporal field . Spatial separation does not imply ontological separation at the level of the temporal substrate.
2. Shared Temporal Phase Structure.
   The hyper-time dimension provides a global phase structure for the entangled configuration. Correlations observed in spatially separated measurements reflect the fact that both outcomes are constrained by a common temporal phase history established at the moment of entanglement.
3. Preservation of Relativistic Locality.
   No signal or causal influence propagates faster than the speed of light through three-dimensional space. Measurement outcomes at each location are generated locally through interaction with the measuring apparatus. The observed correlations arise because the local interactions are conditioned by a shared temporal structure, not because of superluminal communication.
4. Reinterpretation of Nonlocality.
   From the KI perspective, quantum correlations do not represent spooky action at a distance. They express the persistence of a globally coherent temporal configuration whose effects become manifest only when projected onto the four-dimensional observational interface.

Importantly, KI does not modify the empirical predictions of quantum mechanics or the statistical structure of Bell-type experiments. Instead, it reinterprets the assumptions underlying spatial separability by introducing a temporally holistic substrate that remains consistent with relativistic causality.

6.3. Conceptual Summary

In both the Schrdingers cat and EPR scenarios, paradoxes arise when quantum states are treated as abstract probability assignments disconnected from physical reality. By identifying quantum states with real temporal configurations of the -field, KI removes the need for observer-induced collapse, superluminal influences, or fundamental randomness.

Quantum paradoxes are thus revealed not as failures of nature, but as signals that time itself must be included among the fundamental physical degrees of freedom.

7. Comparative Analysis: Why the Kyiv Interpretation?

The Kyiv Interpretation (KI) does not merely offer a new set of labels for existing equations; it addresses the fundamental "missing link" in quantum theory: the physical substrate. Below is an expanded justification of the differences presented in the comparative matrix.

7.1 Ontological Efficiency (Occams Razor)

• vs. ManyWorlds: While the ManyWorlds Interpretation (MWI) restores determinism, it does so at the cost of an infinite multiplication of universes. KI achieves determinism within a single universe by expanding the geometry of time rather than the number of realities.
• vs. Bohmian Mechanics: Bohmian mechanics requires two distinct entities a point particle and a guiding "pilot wave." KI is more parsimonious: there is no separate particle. The "particle" is simply the localized peak (soliton) of the temporal field itself.

7.2 The Role of the Observer: Physicalization vs. Operationalism

• vs. Copenhagen: The Copenhagen school remains "operational" it works but doesn't explain. By placing the observer at the center, it introduces a dualism between the "quantum world" and the "classical observer." KI removes this "Heisenberg cut." In KI, the observer and the observed are both resonance modes of the same field, governed by the same laws of phase synchronization.

7.3 Expanded Comparative Matrix

7.4 Justification of the "New Time Ontology"

The primary advantage of KI is that it provides New Physics without modifying the Mathematical Results of QM.

1. Phase as the Hidden Variable: In KI, the "hidden variables" are not localized coordinates but the internal phases of the field in hypertime .
2. Compatibility: KI is the only interpretation that naturally bridges the gap to General Relativity, as the field is also the source of the gravitational potential.

7.5 Summary of the KI Advantage

The Kyiv Interpretation represents a shift from Epistemic Probability (what we can know) to Temporal Dynamics (what actually is). It provides a "hard" physical mechanism for quantum behavior, transforming the "mystery" of the waveparticle duality into the "certainty" of nonlinear temporal acoustics.

8. Einstein 2.0: Completing the Realist Program

Albert Einsteins opposition to the Copenhagen interpretation was never a rejection of the empirical success of quantum mechanics, but a principled objection to its ontological incompleteness. His insistence that a physical theory should describe reality independently of observation reflects a demand for causal continuity and objective existence rather than a denial of quantum phenomena themselves. The Kyiv Interpretation (KI) translates this philosophical stance into a concrete physical framework.

8.1. Beyond Hidden Variables: The Five-Dimensional Temporal Substrate

Einsteins historical search for hidden variables remained constrained by the fourdimensional spacetime paradigm. Within KI, realism is restored not by introducing additional parameters attached to particles, but by identifying a deeper physical substrate residing in an extended temporal manifold.

• The Field as Ontological Ground. The fundamental variables of the theory are the configurations and phases of the temporal field (x, ). These variables are not hidden in the sense of being artificially appended to quantum states; they are intrinsic degrees of freedom of a physical field that underlies observable phenomena.
• Deterministic Continuity. The introduction of hypertime restores continuous field evolution at the fundamental level. Quantum transitions correspond to smooth deformations and phase rotations of the field in the fivedimensional temporal manifold, rather than to discontinuous stochastic events.

In this sense, KI realizes Einsteins demand for causal completeness without reverting to prequantum mechanical concepts.

8.2. Bell-Type Correlations and Temporal Holism

Bells theorem is commonly interpreted as forcing a choice between realism and locality. The Kyiv Interpretation reexamines this tension by shifting the ontological basis of correlations from spatial separation to temporal coherence.

1. Nonlocal Correlations without Superluminal Influence.
   KI is realist in the sense that physical states exist independently of observation. At the same time, correlations between entangled systems arise from the fact that the temporal field \tau forms a single, continuous configuration. Spatially separated subsystems are not independent at the level of the temporal substrate, even though no signals propagate between them through space.
2. Consistency with Relativistic Causality.
   All observable interactions remain local in spacetime and respect the relativistic speed limit ccc. Correlations observed in Bell-type experiments are not mediated by faster-than-light communication, but reflect constraints imposed by a shared temporal phase structure established during the preparation of the entangled state.
3. Reinterpretation of Bell Assumptions.
   KI does not alter the statistical predictions of quantum mechanics. Instead, it reinterprets the assumption of separability by embedding quantum systems in a temporally holistic framework, in which global temporal structure constrains local measurement outcomes.

Thus, Bell-type correlations are accommodated without abandoning realism or relativistic causality.

8.3. Preservation of the Quantum Formalism

Unlike modification-based realist approaches, such as spontaneous collapse models, the Kyiv Interpretation introduces no changes to the mathematical structure of quantum mechanics.

• The linearity of the Schrdinger equation is retained as a fundamental property of the temporal medium.
• The standard formalism of quantum mechanics is understood as an effective description of resonant dynamics of the -field projected onto four-dimensional spacetime.

In this view, quantum mechanics is not incorrect or incomplete in its predictions; it is complete as a calculational framework but ontologically silent with respect to the underlying physical substrate.

8.4. From Philosophical Realism to Physical Ontology

The Kyiv Interpretation represents a transition from philosophical realism to explicit physical ontology. What Einstein lacked was not conceptual clarity, but a concrete physical structure capable of supporting deterministic evolution without contradicting experimental facts.

By identifying the wavefunction with a resonance mode of a real temporal field, KI provides such a structure. Physical reality is described as a self-consistent temporal medium whose dynamics give rise to quantum states, measurement outcomes, and correlations without invoking observer dependence or fundamental randomness.

In this sense, the Kyiv Interpretation may be viewed as a contemporary completion of Einsteins realist program: not by rejecting quantum mechanics, but by supplying it with a physically grounded temporal ontology.

9. Conclusion: The Inevitability of Temporal Realism

The Kyiv Interpretation (KI) proposes a foundational reorientation of quantum theory: from a framework centered on observation and intrinsic uncertainty to one grounded in deterministic temporal dynamics. By embedding the standard quantum formalism within the Temporal Theory of the Universe (TTU), the interpretation establishes a coherent link between quantum behavior and a physically explicit ontology.

9.1. Core Contributions of the Kyiv Interpretation

The principal results of the present work can be summarized as follows:

1. Resolution of the Measurement Problem.
   KI replaces the postulate of wavefunction collapse with a physically defined process of resonant phase synchronization. Measurement is reinterpreted as deterministic temporal locking between interacting field configurations, preserving causal continuity without modifying the linear structure of quantum dynamics.
2. Emergence of Quantum Probabilities.
   Quantum randomness is shown to arise from phase-averaging over unresolved degrees of freedom in the hyper-time dimension . Borns rule emerges as a statistical limit of deterministic temporal dynamics rather than as a fundamental axiom.
3. Unified Field Interpretation of Wave and Particle.
   The traditional waveparticle duality is resolved within a single-field ontology. Localized, stable concentrations of the -field manifest as particles, while extended oscillatory configurations correspond to wave-like behavior.
4. Ontological Bridge to Gravitation.
   The same temporal field that governs microscopic resonant dynamics also defines large-scale gravitational structure. Quantum mechanics and general relativity are thereby interpreted as complementary dynamical and geometrical regimes of a common temporal substrate.

9.2. Conceptual Implications

The Kyiv Interpretation preserves the full empirical content of standard quantum mechanics while addressing its long-standing conceptual difficulties:

• The observer is no longer assigned a privileged or non-physical role, but is treated as an interacting temporal structure governed by the same laws as the measured system.
• Quantum correlations are explained through global temporal coherence rather than through superluminal influences, maintaining consistency with relativistic causality.
• The wavefunction \psi acquires a clear ontological status as a real physical manifestation of temporal dynamics, rather than as a purely epistemic construct.

9.3. Outlook

By providing a concrete physical basis for the wavefunction and for quantum probabilities, the Kyiv Interpretation suggests that determinism and realism are compatible with the established mathematical structure of quantum theory. In this framework, quantum mechanics is neither paradoxical nor incomplete; it is an effective description of resonant processes occurring within a deeper temporal medium.

Temporal realism thus appears not as an optional philosophical stance, but as a natural consequence of extending the ontological foundations of physics to include time itself as a dynamical field. From this perspective, the apparent indeterminacy of quantum phenomena reflects the limits of observational access rather than a fundamental feature of nature.

10. Limitations and Future Directions

While the Kyiv Interpretation provides a coherent ontological framework for quantum mechanics, several aspects of the theory remain to be developed further. In the present formulation, the hyper-time dimension is treated at an effective level, and its direct experimental accessibility has not yet been established. Consequently, parameters associated with temporal dynamicssuch as characteristic hyper-time frequencies or coupling scalesare introduced phenomenologically and await independent empirical constraints. In addition, the current analysis focuses primarily on non-relativistic quantum mechanics; a fully covariant formulation within quantum field theory remains an open task.

Future work will concentrate on extending the temporal-field framework to relativistic and many-body regimes, as well as on identifying experimentally testable signatures that could distinguish temporal realism from other interpretations. Promising directions include controlled phase-coherence experiments, precision tests of temporal synchronization effects in mesoscopic systems, and the exploration of possible deviations from standard quantum statistics under conditions of engineered temporal stability. Such developments would allow the Kyiv Interpretation to move beyond conceptual resolution toward quantitative falsifiability.

Suggested citation

Lemeshko, A.
The Kyiv Interpretation of Quantum Mechanics: Temporal Realism and Deterministic Resonance Dynamics.
Preprint, 2026. https://doi.org/10.13140/RG.2.2.30240.24326

Appendix A. From the 5D Field Equation to the Effective Schrdinger Dynamics

We start from the free fivedimensional Lagrangian density for the temporal field:

L = M M,M = 0,1,2,3,4

where the index M runs over the four spacetime coordinates x = (t, x) and the additional hypertime coordinate .

Variation of this Lagrangian yields the fundamental field equation:

(1 / v') ' / ' = 0

where is the fourdimensional dAlembert operator and v denotes the characteristic propagation speed along the hypertime dimension.

A.1. Compact HyperTime and Mode Decomposition

Assume that hypertime is compact with topology:

+ 2R

so that the temporal field admits a discrete Fourier expansion along .

Consider a single hypertime mode:

(x, t, ) = [ (x, t) " e^(i n / R) ],n

The second derivative with respect to is then:

' / ' = [ (n / R)' (x, t) " e^(i n / R) ]

Substitution into the fivedimensional field equation yields an effective equation for the slowly varying envelope :

+ ' = 0,' (1 / v')(n / R)'

This equation has the form of a KleinGordon equation, where the effective mass scale originates entirely from gradients along the compact hypertime dimension. No independent mass parameter is introduced at this stage.

A.2. NonRelativistic Limit and Envelope Dynamics

To access the nonrelativistic regime, we separate the fast carrier oscillation associated with the effective rest energy by writing:

(x, t) = e^(i t) " (x, t), c

where the envelope (x, t) varies slowly on time scales much longer than .

Retaining only the leading terms in the slowenvelope (lowenergy) approximation, the KleinGordon equation reduces to:

i _eff / t = (_eff' / 2m_eff) ' + V_eff

The effective parameters are determined by the hypertime scales:

m_eff c' _eff , (c / v)(n / R)

Higherorder relativistic corrections are suppressed by powers of and are neglected in the present lowenergy treatment, consistent with the effectivefieldtheory character of the construction.

A.3. Physical Interpretation

In this framework, the complex wavefunction is not postulated as a fundamental entity. It arises naturally as the envelope representation of a real fivedimensional temporal field oscillating with an extremely high carrier frequency along the hypertime dimension.

The Schrdinger equation therefore appears as an effective, lowenergy, phaseaveraged description of deterministic temporal dynamics projected onto the fourdimensional observational interface. This construction provides a direct physical origin for:

• the complex structure of the wavefunction,
• the emergence of effective mass,
• and the validity of standard quantum dynamics,

without modifying the established mathematical formalism of quantum mechanics.

CrossReferences in the Main Text

• See Section 2.2 for the conceptual interpretation of the Schrdinger equation as a lowenergy projection of temporal dynamics.
• See Section 3.3 for the ontological role of the envelope as a temporal resonance mode of the field.