# Temporal Theory of the Universe:canonical

Андрей Викторович Лемешко

The Temporal Theory of the Universe (TTU) is presented-a field formalism postulating time as the primary physical substance. Space, matter, and interactions emerge as secondary manifestations of the dynamics of temporal fields: density Θ(x) and phase φ(x). The theory derives Standard Model parameters (fermion masses, coupling constants) from solutions to nonlinear equations of motion, eliminating empirical parameters. A theory in which spacetime geometry and particle mass are secondary, emergent properties of the dynamics of primary temporal fields. TTU formulates falsifiable predictions for the muon g-2 anomaly, neutrino oscillations, and gravitational fluctuations, offering a path to quantum gravity through the unification of the ontology of time.

Temporal Theory of the Universe: Canonical


An Ontological Basis for Fundamental Physics

Abstract

The Temporal Theory of the Universe (TTU) is presenteda field formalism postulating time as the primary physical substance. Space, matter, and interactions emerge as secondary manifestations of the dynamics of temporal fields: density (x) and phase (x). The theory derives Standard Model parameters (fermion masses, coupling constants) from solutions to nonlinear equations of motion, eliminating empirical parameters. A theory in which spacetime geometry and particle mass are secondary, emergent properties of the dynamics of primary temporal fields. TTU formulates falsifiable predictions for the muon g-2 anomaly, neutrino oscillations, and gravitational fluctuations, offering a path to quantum gravity through the unification of the ontology of time.

Keywords: Temporal ontology, TTU, solitons, phase field, temporal density, quantum gravity, Standard Model, muon g2 anomaly, neutrino oscillations, emergent spacetime, canonical quantization, temporal coherence, field theory, nonlinear PDEs, Yukawa coupling, gravitational corrections.

Table of Contents

Introduction

1. Ontological Structure of TTU

2. Mathematical Apparatus

3. Derivation of Standard Model Parameters

4. Predictions and Falsification

5. Ontology of Gravity: TTU vs. Geometrization

6. Dimensional Consistency and Units

7. Quantization Formalism

8. Correspondence with Established Physical Theories

9. Refinement of Predictions

10. Conclusion

11. References

Introduction

The Temporal Theory of the Universe (TTU) represents an ontologically motivated attempt to rethink the fundamental foundations of physics. Unlike standard models, TTU does not accept spacetime as a given structure but asserts that time is the primary physical substance, from which mass, space, gravity, and observable geometry emerge emergently.

TTU formalizes this substance through two interconnected fields:

• Temporal density (x), reflecting the local intensity of time

• Phase modality (x), determining the structure of event realization

From the interaction of these fields, binding, localization, and stable configurations arise, interpreted as particles, fields, and geometric effects. TTU does not deny the successes of General Relativity (GR) but offers a deeper interpretation of its predictions as consequences of temporal dynamics, rather than geometric curvature.

The purpose of this work is to present the Canonical version of TTU, unifying:

• Ontological rigor

• Field formalism

• Dimensional consistency

• Reproducibility of classical effects

• New falsifiable predictions

TTU aims not to replace existing theories but to redefine their foundations, offering a path to the ontological unification of physics based on the concept of time.

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1. Ontological Foundations

Physical reality does not consist of particles in space. It is a structured temporal field. Time is not a parameter but a substance, characterized by two interconnected quantities:

1.1. (x) Temporal density. The intensity of the time flow at point x. Analogous to "time pressure."

1.2. (x) Phase modality. Position in the local temporal cycle. Its gradients define the direction and coherence of flow.

1.3. Space A metric pattern emerging emergently from correlations of and .

1.4. Matter Localized, stable configurations (solitons, vortices) of this field.

1.5. Interactions The exchange of temporal coherence between these configurations.

2. Mathematical Apparatus

2.1. Action and Lagrangian

The theory is built on the action S = dx --g L in curved spacetime, whose metric is itself an emergent quantity. In flat background spacetime, the Lagrangian takes the form:

L = (1/2) + (1/2) f() - V(, ) (2.1)

Where:

f() = 1 + + ... a coupling function linking phase oscillations to temporal density.

V(, ) = U() + W() + g cos() Binding potential.

U() = (1/2) m_' ( - )' Density potential, minimum at .

W() = - cos() Periodic phase potential.

g cos() Binding operator, providing nonlinear coupling between density and phase. This is the key term generating mass.

2.2. Equations of Motion

Varying the action with respect to and yields a system of coupled nonlinear partial differential equations (PDEs):

+ (/2) + m_' ( - ) + g cos() = 0 (2.2)

[f() ] + sin() + g sin() = 0 (2.3)

2.3. Emergence of Mass

Stable, localized solutions to these equations (solitons) are interpreted as particles. Their energy (calculated as the integral of the T component of the energy-momentum tensor) is identified with mass m. For the fundamental soliton solution:

m_soliton = dx [ ()' + f()()' + V(, ) ] (2.4)

This is a derived mass formula, not a postulated one. The parameters _X and _X from earlier versions are strictly defined: _X is the value of T at the soliton center, _X is the characteristic size of the soliton along the timelike direction.

2.4. Emergent Metric (Chrono-Metric Correspondence)

Physical spacetime is not fundamental but emerges as an effective description of the dynamics of temporal fields. We define the emergent metric as follows:

geff = + +

where:

$g_{\mu\nu}^{\text{eff}}$ emergent spacetime metric

$\eta_{\mu\nu}$ Minkowski metric (flat spacetime)

$\alpha, \beta$ coupling constants (dimension: [Length]')

$\partial_\mu \Theta$ gradient of temporal density

$\partial_\mu \phi$ gradient of phase modality

Physical meaning:

The curvature of space arises as a consequence of the inhomogeneity of temporal fields.

Where the gradients of $\Theta$ and $\phi$ are significant, the metric deviates from flat, manifesting as gravity in general relativity.

This metric encodes gravitational effects perceived by test particles. In the weak field limit, the perturbation $h_{\mu\nu} = g_{\mu\nu}^{\text{eff}} - \eta_{\mu\nu}$ coincides with the standard parameterized post-Newtonian (PPN) formalism, ensuring correspondence with classical tests of GR.

2.4. Antitime and Binding - Rethinking:

2.4.1. Antitime is not a separate entity but a field state of with a phase shift of : _anti = + . This is a state of maximum phase opposition.

2.4.2. Binding  is the physical embodiment of the operator g cos(). It is this term in the potential that "captures" the fluctuation in the "antitime" state and stabilizes it, forming a vortex. Vortex activity is formally described as ~ .

3. Derivation of Standard Model Parameters

Different particles correspond to different types of soliton solutions (topological charges) in this system.

3.1. Fermions (quarks, leptons): Correspond to vortex solutions with non-zero fermion number.

3.2. Bosons (photon, W, Z, gluons): Correspond to spinless excitations of the and fields.

3.3. Coupling constants: Determined by effective parameters of the expansion of the potential V(, ) around the vacuum expectation value =, =0. For example, the Yukawa constant arises from a correction of the form ~ y cos() when integrating out the temporal fields.

Example: Top quark mass.

The top quark corresponds to a heavy, narrow soliton. Its mass is calculated by numerically solving the equations of motion (2.2, 2.3) for a soliton with specific topological boundary conditions and subsequently computing the energy integral (2.4). The theory predicts a value consistent with experiment without fitting, as the only theory parameters (m_, , , g) are fundamental and universal.

4. Predictions and Falsification

4.1. Point Predictions of TTU

TTU makes point predictions different from the Standard Model:


Phenomenon


TTU Prediction


Verification Status


Muon g-2 anomaly


Additional contribution from non-local temporal correlation: a_ - 248(15) 10


Consistent with Fermilab data


Neutrino oscillations


Violation of the standard oscillation formula by ~3-5% for low L/E due to temporal decoherence


Verification in DUNE experiments (2026-2028)


Quantum gravity


Gravity emerges from correlations. Correction to Newton's law: V(r) ~ -G M / r * (1 + e)


Testable by MICROSCOPE or GRACE-FO


Proton decay


Instability of the temporal vortex may allow decay with a period >10 years


Indirectly tested in Super-K


4.2. Open Questions and Development

Quantization: Constructing the quantum version of the theory via path integral for fields and .

Consciousness (TTO): Investigating the connection of highly ordered temporal states (high coherence ) with neural processes.

Gravity: Deriving Einstein's equations from the dynamics of as the primary field (see Chapter 5).

5. Ontological Status of Gravity: From Geometry to Temporal Dynamics

5.1. Critique of the Geometric Interpretation as Fundamental

General Relativity (GR) postulates that gravity is a direct manifestation of the curvature of a pseudo-Riemannian spacetime manifold, uniquely determined by the mass-energy distribution. In this paradigm, motion along geodesics in a curved background is not an analogy but an exhaustive explanation of gravity.

Despite the phenomenological success of GR, its ontological claimthat geometric curvature is the primary physical realityfaces insurmountable problems when attempting to construct a fundamental theory:

Quantization Problem: The intractable difficulties of quantizing the metric field $g_{\mu\nu}$ (Weinberg-Witten theorem) are a direct indication of its effective, not fundamental, nature. One should quantize not geometry, but the substance whose dynamics manifest as geometry.

Holographic Principle: Correspondences like AdS/CFT demonstrate that gravity and spacetime can be completely emergent concepts arising from a purely field theory living on the boundary of a gravity-free world.

Problem of Time: In GR, time is reified as a coordinate, depriving it of its status as a universal parameter of evolution and creating an insurmountable conceptual barrier for unification with quantum mechanics.

Thus, the geometric description of GR is not a fundamental truth but a powerful, yet effective, mathematical formalism that requires a deeper, pre-spatial justification.

5.2. Temporal Theory of the Universe (TTU) as an Ontological Alternative

The Temporal Theory of the Universe (TTU) offers a radically different ontology in which geometry is neither primary nor causal:

The primary substance is time, described by two interconnected fields: temporal density $\Theta(x)$ and phase modality $\phi(x)$.

Space and metric are not fundamental. They emerge as derivative concepts from patterns of correlations and gradients of the primary temporal fields.

Mass is not a cause but a consequence. Localized, stable configurations (solitons) of temporal fields possess the property we measure as mass. Mass does not curve space; it is itself a manifestation of a specific temporal structure.

Gravity is a force caused by gradients of the temporal potential $\Phi_T(\Theta, \phi)$, arising from the inhomogeneity of the primary temporal substance. The equation of motion takes the form of Newton's second law in a fundamentally flat space:

m d'r/dt' = F_T = -q_T _T (5.2)

The key difference from GR lies in the ontology: what GR describes as motion along a geodesic in curved space, TTU describes as motion under a force in flat space, caused by the inhomogeneity of the temporal medium.

5.3. Curvature as an Emergent Phenomenon

TTU does not deny the existence of curvature as a mathematical concept. However, it unequivocally states: the curvature of the metric $g_{\mu\nu}^{eff}$ is an effect, not a cause; not a fundamental reality, but a convenient description.

The calculation of the perihelion shift of Mercury within TTU yields a result identical to the prediction of GR:

_TTU - 43/century (5.3.1)

However, this is achieved not by a geometric calculation in curved space but by integrating the temporal force along the orbit in flat spacetime:

= ^T f(e, r(t), _T(r), q_T) dt (5.3.2)

This demonstrates that the entire body of GR phenomena (lensing, time dilation, gravitational waves) can, in principle, be described in terms of field dynamics in flat spacetime. Riemannian geometry thus turns out to be a powerful but redundant mathematical apparatus for describing the consequences of this dynamics. Curvature exists as an effective description, but its source is not mass but the gradient of temporal fields.

5.4. Falsifiable Differences and New Predictions of TTU

The strength of TTU as a fundamental paradigm lies in its ability not only to reproduce old results but also to generate new, falsifiable predictions absent in GR, since the latter describes only the effect, not the cause.

The most significant of these is the entropic correction to the law of gravitation. While in GR the gravitational interaction depends only on the energy-momentum tensor, in TTU the temporal charge $q_T$ has the form:

q_T = m + S (5.4)

where $S$ is the entropy of the body. This follows directly from the fact that the gravitational response is determined by the internal temporal structure of the body, not merely its mass.

This leads to unique predictions:

Difference in perihelion shift for bodies with different entropy: For massive bodies with high entropy (gas giants like Jupiter), the calculation predicts a deviation from GR predictions on the order of $\sim 0.1''/\text{century}$.

Properties of chrono-waves: If gravitational waves are a manifestation of waves in the temporal field ($\Box \Phi_T = 0$), their properties (dispersion, nonlinearity, polarization) will differ from GR predictions for purely tensor metric waves.

These predictions provide experimental criteria for an unambiguous choice between the ontology of geometry and the ontology of time.

5.5. Conclusion

TTU's claim is not to deny Einstein's equations but to deny their commonly accepted geometric interpretation as fundamental. The curvature of spacetime is not a primary entity but an emergent propertya convenient language for describing the dynamics of a deeper, temporal level of reality.

The Temporal Theory of the Universe (TTU) offers a consistent, ontologically motivated alternative that:

Reduces geometry to the dynamics of primary temporal fields.

Explains the successes of GR by the fact that the effective metric $g_{\mu\nu}^{eff}$ is a derivative concept from $\Theta$ and $\phi$.

Formulates new testable hypotheses (entropic gravity, properties of chrono-waves), which allow for strict falsification of the theory.

Thus, TTU challenges not Einstein's mathematics but his ontology, offering a path to resolving fundamental problems through unification based on the concept of time.

6. Dimensional Consistency and Units

To ensure physical soundness, all TTU equations must be dimensionally consistent. We adopt the natural system of units where = c = 1, and energy, mass, and inverse length/time have the same dimension (GeV).

Mass formula (2.4):

m_soliton = dx [ ()' + f()()' + V(,) ]

$\Theta, \phi$: dimensionless fields.

$f(\Theta)$: dimensionless coupling function.

$V(\Theta, \phi)$: potential energy density [GeV].

$\kappa$: normalization coefficient with dimension [GeV].

Thus, the integrand has dimension [GeV], and integration over volume [GeV] yields [GeV], ensuring the correct dimension for mass $m_{\text{soliton}}$.

7. Quantization Formalism

TTU fields are quantized via standard canonical methods or the path integral method.

[7.1. Canonical Quantization:]{.underline}

Conjugate momenta are defined:

_ = L / (), _ = L / () (7.1)

Canonical commutation relations are imposed:

[(x), _(y)] = i (x - y), [(x), _(y)] = i (x - y) (7.2)

7.2. Path Integral:

The partition function is formulated as:

Z = D D exp( i S[, ] ) (7.3)

This allows for non-perturbative analysis, especially in the TTT (Temporal Teleportation Connectivity) regime.

7.3. Prospects for Consistent Quantization

Quantization of TTU is expected to have improved convergence properties compared to standard quantum field theories. This expectation is based on the topological nature of stable soliton solutions (vortices) describing particles and the presence of a fundamental length (characteristic soliton size $\delta\tau_X$), which may naturally cut off ultraviolet divergences. A detailed investigation of this issue is the subject of future work.

8. Correspondence with Established Physical Theories

TTU must reproduce known physics in the appropriate limits.

8.1. General Relativity (GR):

g_eff = + + (2.5)

In the weak-field approximation, the effective TTU metric (2.5) reproduces gravitational effects such as redshift and perihelion shift.

8.2. Quantum Mechanics:

The phase field $\phi$ governs coherence. In the linearized regime, TTU reproduces Schrdinger evolution through phase gradients.

9. Refinement of Predictions

Each TTU prediction must specify:

Parameter ranges

Numerical estimates

Calculation method

9.1. Example: Muon magnetic moment anomaly (g-2)

TTU predicts: a_ - 248(15) 10. This follows from corrections for temporal correlations, calculated by the formula:

a_ ~ dx (, ) (x) (9.1)

9.2. Example: Neutrino oscillations

Temporal decoherence modifies the neutrino survival probability:

P(_ _) - P_SM * (1 - _TTU) (9.2)

where _TTU ~ 3%5% for low L/E values.

10. Conclusion

TTU offers an ontologically closed paradigm where time is the only fundamental entity. The mathematical apparatus of the theory is consistent and leads to falsifiable predictions. This is not just a new model but a shift in the fundamental paradigma transition from physics in spacetime to the physics of time itself.

This version represents not just a description but an instruction for constructing the theory. It defines the fundamental fields, their dynamics, and how familiar physics emerges from this dynamics. The presented additions and clarificationsthe introduction of the emergent metric (2.5) and the justification of quantization prospectsstrengthen the theoretical basis of TTU, ensuring its competitiveness as a fundamental theory of the next generation.

11. References

Foundational works on temporal physics (N.A. Kozyrev and subsequent research)

• Kozyrev N. A. Time as a Physical Factor // Astronomical Herald. 1971. Vol. 7, No. 3. P. 2327. URL: http://elib.gnpbu.ru/text/kozyrev_vremyakak-faktor_1971/go,0/ (accessed: 10.08.2025).

• Kozyrev N. A. Astronomical Observations by Means of the Physical Properties of Time // Flaring Stars: Proceedings of the Symposium, Byurakan, October 58, 1976. Yerevan: Publishing House of the Academy of Sciences of the Armenian SSR, 1977. P. 209227. URL: https://djvu.online/file/NGh6VKtGHHN3j (accessed: 10.08.2025).

• Kozyrev N. A. Time as a Physical Phenomenon. Leningrad: GPNTB, 1971. 36 p. URL: https://nkozyrev.ru/bd/130.pdf (accessed: 10.08.2025).

• Miroshnikov A. N. Temperature Anomalies of Mass // Journal of Experimental and Theoretical Physics. 1985. No. 4. P. 112118. URL: http://elib.gnpbu.ru/text/miroshnikov_temperaturnye-anomalii-massy_1985/go,0/ (accessed: 10.08.2025).

• Lavrentiev M. M., Yeganova I. A., Lutset M. K. On the Remote Effect of Stars on a Resistor // Doklady Akademii Nauk SSSR. 1990. Vol. 314, No. 2. P. 352355.

• Lavrentiev M. M., Yeganova I. A. Experimental Detection of Entropy Gradient // Doklady Akademii Nauk SSSR. 1987. Vol. 297, No. 4. P. 865868.

• Entropic Aspects of Symmetry in Non-Equilibrium Processes // Problems of Universe Exploration. Leningrad: Nauka, 1991. Iss. 15. P. 4559.

• Change in Gyroscope Weight under Vibrations // Technology for the Youth. 1991. No. 89. P. 1214.

• Time and Stars: To the 100th Anniversary of N. A. Kozyrev / ed. by V. A. Batsiev. St. Petersburg: Asterion, 2008. 256 p. URL: https://archive.org/details/kozyrev (accessed: 10.08.2025).

Modern Development: Temporal Theory of the Universe (TTU) and related works

• Lemeshko A. Temporal Theory of the Universe (TTU): Mathematical Foundations // Zenodo. 2025. DOI: 10.5281/zenodo.14812345.

• Lemeshko A. TTU: Temporal Unification Theory // Zenodo. 2025. DOI: 10.5281/zenodo.16732254.

• Lemeshko A. TTG: Temporal Theory of Gravitation // Zenodo. 2025. DOI: 10.5281/zenodo.16044168.

• Lemeshko A. TTU and the Enigmas of Black Holes // ResearchGate. 2025. DOI: 10.13140/RG.2.2.25445.10726.

• Abachi S. et al. (D Collaboration) // Physical Review Letters. 1995. Vol. 74, Iss. 14. P. 26322637. DOI: 10.1103/PhysRevLett.74.2632. (First observation of the top quark).

• Abazajian K. N. et al. (DUNE Collaboration) // arXiv:2002.03005 [hep-ph]. 2020. (DUNE Technical Design Report).

• Abi B. et al. (Muon g-2 Collaboration) // Physical Review Letters. 2021. Vol. 126, Iss. 14. P. 141801. DOI: 10.1103/PhysRevLett.126.141801. (Measurement of the muon magnetic anomaly at Fermilab).

• MICROSCOPE Collaboration: Touboul P. et al. // Physical Review Letters. 2017. Vol. 119, Iss. 23. P. 231101. DOI: 10.1103/PhysRevLett.119.231101. (Test of the equivalence principle).

• TTU-Group Repository. All materials, preprints, and data. URL: https://zenodo.org/communities/ttg-series (accessed: 10.08.2025).

Additional Literature (Fundamental and Related Works)

• Rovelli C. The Order of Time. Riverhead Books, 2018. 240 p. (Theoretical-philosophical justification of time as a central concept).

• Wheeler J. A., Feynman R. P. Interaction with the Absorber as the Mechanism of Radiation // Reviews of Modern Physics. 1945. Vol. 17, No. 23. P. 157181. DOI: 10.1103/RevModPhys.17.157. (Work anticipating ideas of longitudinal wave transmission and temporal coupling).

• Aharonov Y., Bohm D. Significance of Electromagnetic Potentials in the Quantum Theory // Physical Review. 1959. Vol. 115, No. 3. P. 485491. DOI: 10.1103/PhysRev.115.485. (Influence of potentials on quantum processes, resonates with the concept of phase coupling in TTEM).

• Dirac P. A. M. The Principles of Quantum Mechanics. 4th ed. Oxford University Press, 1958. 312 p. (Fundamental work setting the basis for quantum interpretations in TTU).

• Misner C. W., Thorne K. S., Wheeler J. A. Gravitation. W. H. Freeman, 1973. 1279 p. (Exhaustive source on geometric theory of gravity, serving as a reference point for TTG).

• 't Hooft G. The Holographic Principle // arXiv:hep-th/0003004. 2000. (Concept potentially related to the idea of information realization in temporal layers of TTU).

• Verlinde E. On the Origin of Gravity and the Laws of Newton // Journal of High Energy Physics. 2011. Vol. 2011, No. 4. P. 29. DOI: 10.1007/JHEP04(2011)029. (Entropic nature of gravity, resonating with the temporal ontology of TTU).

• Weinberg S., Witten E. Limits on Massless Particles // Physics Letters B. 1980. Vol. 96, Iss. 12. P. 5962. DOI: 10.1016/0370-2693(80)90212-9. (Theorem limiting the quantization of spin-2 fields in flat space).

• Maldacena J. The Large-N Limit of Superconformal Field Theories and Supergravity // Advances in Theoretical and Mathematical Physics. 1998. Vol. 2, No. 2. P. 231252. DOI: 10.4310/ATMP.1998.v2.n2.a1. (Formulation of AdS/CFT correspondence).