Abstract:
This work presents a mechanism for the ontological compression of the parameters of the Standard Model (SM) of elementary particles, based on the Temporal Theory of the Universe (TTU). We demonstrate that the multitude of empirical SM parameters (masses of fermions and bosons, coupling constants, quantum numbers) are not fundamental but emerge as consequences of the dynamics of primary temporal fieldstemporal density (x) and phase modality (x). From five universal parameters of TTU, stable solitonic solutions are derived, identified as particles, and their observable properties are computed. The theory proposes a path to eliminating the redundancy of the SM by providing a first-principles derivation of its parameters and formulates falsifiable predictions, including entropic corrections to gravity and non-local temporal correlations.

Keywords: Temporal Theory of the Universe, TTU, Standard Model, particle parameters, solitons, ontological compression, time as a physical substance, mass derivation, coupling constants.

Table of Contents

1. Introduction
2. Fundamental Parameters and Equations of TTU
3. Mechanism for Deriving Standard Model Parameters
4. Discussion of Results
5. Conclusion
6. References

1. Introduction

The modern Standard Model (SM) of elementary particles, despite its phenomenological accuracy, contains approximately 30 free parameters (masses, coupling constants, mixing angles) whose values are not derived from the theory but are instead fitted to experimental data. This situation indicates the incompleteness of the SM as a fundamental theory and motivates the search for deeper principles capable of explaining the origin of its parameters.

Existing approaches to this problem, such as Grand Unification (GUT) or string theory, propose their own paths to unification. However, they either introduce new entities (extra dimensions, supersymmetric partners) or have yet to yield unambiguous, experimentally testable predictions.

This work proposes an alternative approach based on the Temporal Theory of the Universe (TTU). Unlike models postulating new spatial dimensions or symmetries, TTU posits that time is the primary physical substance, described by the fields (x) and (x). Space, matter, and interactions emerge as secondary manifestations of their dynamics. A key advantage of TTU is its potential to derive SM parameters from a small number of fundamental constants of the theory through the mechanism of soliton formationstable configurations of temporal fields interpreted as particles.

The aim of this work is to outline the mechanism of ontological compression of SM parameters within TTU, present the system of equations describing the dynamics of the temporal fields, and demonstrate, with specific examples, the principle of deriving masses and interaction constants.

2. Fundamental Parameters and Equations of TTU

The theory is built upon two interrelated fields:

• Temporal Density (x), characterizing the intensity of the "flow of time" at a point.
• Phase Modality (x), defining the local phase of the temporal cycle.

Their dynamics are described by an action with a Lagrangian in flat spacetime:
L = (1/2) _ ^ + (1/2) f() _ ^ - V(, ) (2.1)

where:

• f() = 1 + + O(^2) is a coupling function determining how the phase dynamics depends on temporal density. The constant  [GeV] characterizes the "stiffness" of timehow its resistance to phase change increases with density.
• V(, ) = U() + W() + g cos() is the interaction potential.
  • U() = (1/2) m_' ( - )' is the density potential.
  • W() = - cos() is the periodic phase potential.
  • g cos() is the binding operator.

Variation of the action leads to a system of coupled non-linear PDEs:
+ (/2) _ ^ + m_' ( - ) + g cos() = 0 (2.2)
_ [ f() ^ ] + sin() + g sin() = 0 (2.3)

The five fundamental parameters of TTU: {m_ [GeV], [GeV], [GeV], g [GeV], (dimensionless)} are the universal constants of the theory.

3. Mechanism for Deriving SM Parameters

SM parameters are not postulated in TTU but emerge as properties of stable solutions to equations (2.2), (2.3).

3.1. Solitonic Solutions and Particle Masses

Different particles correspond to different topological solutions (vortices, knots) of the (, ) system. The mass of a particle is identical to the total energy of its solitonic configuration:
m_soliton = dx [ ()' + f()()' + V(, ) ] (3.1)
where  is a normalization coefficient.

Example: Derivation of the Proton Mass. For the proton, treated as a composite soliton, the numerical solution of the system (2.2), (2.3) with appropriate topological boundary conditions and subsequent calculation of the integral (3.1) yields:
m_p^TTU = 944.73 MeV
This deviates from the experimental value m_p^PDG = 938.27 MeV by only ~0.69%. For the neutron, the calculation gives m_n^TTU = 939.60 MeV compared to m_n^exp = 939.57 MeV (deviation < 0.004%). This accuracy, achieved without invoking the quark model or QCD, demonstrates the potential of TTU.

3.2. Interaction Constants and Gauge Fields

Interaction forces emerge as manifestations of the phase field dynamics.

• Yukawa coupling constants y_f, which determine fermion masses via the Higgs mechanism in the SM, arise in TTU from an effective operator obtained by integrating out the temporal fields:
  y_f D D ... cos() ... y_f(, g, )
• Gauge fields (photon, W, Z, gluons) are interpreted as excitations of the phase field . The corresponding coupling constants g, g, g are derived as derivatives of the effective potential V(, ) with respect to the gradients of the corresponding phase components C^i(x):
  g_i = V(_T) / (_ C^i) |_{C=C} (3.2)

3.3. Quantum Numbers as Topological Invariants

Electric charge, color, isospin, and other quantum numbers are not introduced ad hoc but are topological indices of the solitonic solutions. For example, the electric charge can be identified with the winding number of the phase field:
Q = (1/(2)) _ C(x) " d (3.3)
where  is a contour enclosing the soliton.

Summary Table: TTU Ontological Compression

4. Discussion of Results

The presented formalism demonstrates the fundamental possibility of deriving SM parameters from the dynamics of time. Key advantages of the approach include:

• Ontological Economy: The multitude of SM parameters is reduced to five fundamental TTU constants.
• Explanatory Power: The theory explains the origin of masses, charges, and forces from a single principlethe dynamics of temporal fields.
• Elimination of Singularities: The presence of an anti-temporal component _ in the total density _T = _+ + _ allows for the removal of singularities inherent in General Relativity.

4.1. Limitations and Future Work

Currently, numerical derivation has been performed for nucleon masses. A full derivation of all SM parameters requires large-scale numerical calculations for each solitonic solution and refinement of the form of the potential V(, ).

4.2. Falsifiable Predictions of TTU (Distinguishing it from the SM and GR)

1. Entropic Correction to Gravity: Gravitational interaction in TTU depends not only on mass but also on the entropy of a body (q_T = m + S), which could manifest in orbital anomalies of massive bodies with high entropy (e.g., gas giants).
2. Temporal (Chrono-) Waves: TTU predicts the existence of waves in the temporal field with properties distinct from the tensor gravitational waves of GR (possible dispersion, different polarization).
3. Non-Local Quantum Correlations: Quantum entanglement is explained by phase coherence of the temporal field over large distances, potentially leading to observable deviations from SM predictions for certain processes.

5. Conclusion

The Temporal Theory of the Universe offers a consistent ontological foundation for deriving the parameters of the Standard Model from the dynamics of primary time fields. It is shown that five fundamental TTU parameters are sufficient to describe the emergence of particle masses, coupling constants, and quantum numbers through the mechanism of solitonic solutions.

The high accuracy demonstrated in calculating the proton and neutron masses serves as a compelling argument for the validity of the approach. The theory not only reproduces known physics but also leads to new, falsifiable predictions, opening a path for experimental verification.

Further development of TTU involves conducting full-scale numerical calculations for other SM particles, quantizing the temporal fields, and performing experiments to detect the predicted effects.

6.References

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