The Theorem of Time(ТТU): Ontology of Time as a Primary Substance

Abstract

The Temporal Theory of the Universe (TTU) proposes a radical reconstruction of physics: time is considered not as a parameter but as a primary substance described by a scalar field ( \rho_T(x) \in \mathbb{R} ). On this basis, a Lagrangian is formulated, allowing phase transitions between states of time and anti-time, preserving CPT invariance and solution stability. TTU demonstrates that space, matter, and interactions are derivative structures against the background of ( \rho_T ), and gravity arises as an effect of phase dynamics. In the limiting case ( \rho_T = \text{const} ), the theory reproduces Einstein's equations, absorbing General Relativity as a limiting case. Experimentally verifiable effects are predicted: anomalous cooling (( \Delta m / m < 0 )), CP violation as phase interference, elimination of singularities through wormholes, and quantum foam of time detectable in gravitational observatories. TTU completes the reductionist program, turning time into the source of all physical phenomena. Keywords: temporal field; anti-time; phase structure of time; ontology of physics; quantization of duration; CPT invariance; wormholes; quantum foam; anomalous cooling; CP violation; time Lagrangian; instanton transitions; metric as derivative; falsifiability; fundamental constants as phase functions

1. Introduction: Crisis of Reductionism

• 1.1. Dissatisfaction with "time-as-parameter"
• 1.2. TTU as a radical solution
• 1.3. Goal: to prove the ontological fundamentality of ( \rho_T(x) )

1. Mathematical Framework of TTU

• 2.1. Lagrangian of the temporal field
• 2.2. Equations of motion
• 2.3. Instanton transitions

1. Birth of Physics from Time

• 3.1. Space-time as a derivative structure
• 3.2. Matter and interactions as phase vortices
• 3.3. Recovery of General Relativity as a limiting case

1. Physics of Time Phases

• 4.1. Anti-time domains
• 4.2. Experimental signatures of phases
• 4.3. Table of phases and effects

1. Ontological Theses

• 5.1. Time as the only substance
• 5.2. Physical constants as phase functions
• 5.3. Quantization as a property of phase transitions

1. Experimental Tests of TTU

• 6.1. Mass shifts during heating
• 6.2. Gravitational micro-signals
• 6.3. Quantum foam of time
• 6.4. CP asymmetry and temperature gradients
• 6.5. Table of key TTU tests

1. Conclusion: A New Paradigm

• 7.1. TTU absorbs General Relativity and the Standard Model
• 7.2. Empirical verification: 20252027
• 7.3. Philosophical conclusion: physics as time dynamics
• 7.4. Epilogue: Poetic formula of TTU

1. Sources and Historical Contexts
2. Acknowledgments.
3. Appendices

• A. Glossary of Temporal Concepts
• B. TTU Formula Compendium

1. Introduction: Crisis of Reductionism Modern physics has achieved exceptional precision in describing interactions but retains ontological ambiguity regarding time. Time remains an external parameter, lacking its own dynamics, structure, or substantial status. This is a fundamental crisis of reductionism: a theory claiming universality relies on an undescribed background.

1.1. Dissatisfaction with "time-as-parameter" Throughout the history of physics, time has remained a strange exception: it participates in equations but not in ontology. Its role is a parameter, a coordinate, an external label, but not a physical entity. In classical mechanics, time acts as Newton's absolute parameter, independent of matter and unaffected by changes. It is the background on which events unfold but not their cause. In quantum mechanics, time is not an operator, not quantized, not observable. It does not enter the algebra of physical quantities, remaining an external parameter of evolution. In General Relativity, time becomes a coordinate in the metric but lacks its own phase or dynamics. It is geometrized but not activated. In the Standard Model, time does not enter the Lagrangian as a field, does not interact with other fields, does not fluctuate, does not quantize. As a result: Time remains a silent witness, not a participant in physical reality. It has no own dynamics, is not subject to fluctuations, does not interact with matter. This is a fundamental gap between formalism and ontology.

Historical Attempts to Overcome the Gap Nevertheless, there have been bold attempts to turn time from a parameter into a physical entity: N.A. Kozyrev (195060s) proposed considering time as an active cause capable of transmitting energy and influencing physical processes. His experiments with asymmetric gyroscopes and telescopes sparked heated debates but remained outside the mainstream. V.M. Miroshnikov (1990s) developed ideas of "physics of time," suggesting that time has its own substance and can be a source of new interactions. His approach was philosophically rich but lacked strict formalization. A. Whitehead, I. Prigogine, G. Meyer, D. Bohm in various contexts raised the question of time as an internal structure of processes but failed to integrate it into operational formalism.

Motivation of TTU TTU (Temporal Theory of the Universe) proposes a radically different approach: time as the primary physical entity determining the structure of matter, fields, and interactions. TTU does not continue speculative traditions but reinterprets them ontologically, offering strict mathematical formalization, operationalization, and experimental testability.

1.2. TTU as a Radical Solution

The Temporal Theory of the Universe (TTU) proposes a paradigm shift: Time is a scalar field ( \rho_T(x) \in \mathbb{R} ) possessing phase structure. Phases of time ( \rho_T > 0, \rho_T < 0 ) are physically distinguishable. Transitions between phases are quantum events allowed by the Lagrangian. Space, matter, and interactions are derivatives of the configuration ( \rho_T(x) ) TTU does not modify existing theories it absorbs them as limiting cases.

1.3. Goal: to prove the ontological fundamentality of ( \rho_T(x) )

The goal of the work is to show that: ( \rho_T(x) ) is the only substance from which all physical structures arise The Lagrangian ( \mathcal{L}[\rho_T] ) allows stable, CPT-invariant solutions Phase transitions ( \rho_T \to -\rho_T ) are the source of quantization TTU predicts falsifiable effects different from the Standard Model

1. Mathematical Framework of TTU

The Temporal Theory of the Universe (TTU) describes time as a scalar field ( \rho_T(x) \in \mathbb{R} ), possessing its own dynamics, phase structure, and quantum transitions.

2.1. Lagrangian of the Temporal Field

The field of time is described by a scalar-type Lagrangian: [ \mathcal{L} = \frac{1}{2} (\partial_\mu \rho_T)^2 - V(\rho_T), \quad V(\rho_T) = |\mu_T|^2 \rho_T^2 + \lambda_T \rho_T^4 ] ( \mu_T ) temporal mass, determining the scale of field time excitation ( \lambda_T ) self-interaction coefficient, regulating the nonlinearity of the potential The potential is symmetric with respect to sign reversal: [ V(-\rho_T) = V(\rho_T) ]

Phase Structure of Time The zero points of the potential determine possible phase states of the field ( \rho_T(x) ): ( \rho_T > 0 ): Ordinary temporal phase corresponding to standard causality and entropy growth direction ( \rho_T < 0 ): Anti-temporal phase characterized by inversion of temporal density and change in entropy flow direction

Definition of Anti-Time Anti-time is a field regime where ( \rho_T < 0 ). In TTU, this is not just a reversal of the time arrow but an ontologically distinct phase of physical reality, possessing its own dynamics, causality, and experimental consequences. Anti-time can manifest as: local phase transitions, inversion of entropy gradient (( \Delta S < 0 )), changes in interaction and mass structure.

Table 2.1 Phase States of the Temporal Field ( \rho_T(x) )

Note: The anti-temporal phase does not violate the laws of physics but expands their interpretation within TTU. The oscillating phase can be interpreted as quantum foam, manifesting in non-local metric fluctuations.

2.2. Equations of Motion

From the principle of least action follows the EulerLagrange equation: [ \Box \rho_T + \frac{\partial V}{\partial \rho_T} = 0 \quad \Rightarrow \quad \Box \rho_T + 2|\mu_T|^2 \rho_T + 4\lambda_T \rho_T^3 = 0 ] This nonlinear wave equation allows three types of solutions: ( \rho_T > 0 ): ordinary time ( \rho_T < 0 ): anti-time ( \rho_T(\tau) ): transition between phases Stability of solutions at ( \rho_T < 0 ) is proven through linearization: [ \Box (\delta\rho) + \left( 2|\mu_T|^2 + 12\lambda_T \rho_0^2 \right) \delta\rho = 0 ] ( \to ) positive frequency ( \to ) oscillations ( \to ) stability

2.3. Instanton Transitions Transition between phases ( \rho_T = -\rho_0 \to +\rho_0 ) is described by the Euclidean equation: [ \frac{d^2 \rho_T}{d\tau^2} = \frac{\partial V}{\partial \rho_T} ] with boundary conditions: [ \rho_T(\tau \to -\infty) = -\rho_0, \quad \rho_T(\tau \to +\infty) = +\rho_0 ] The solution represents an instanton quantum tunneling between phases of time. The action is quantized: [ \Delta S_T = \hbar \cdot n, \quad n \in \mathbb{Z} ]

Addition: Each instanton transition corresponds to a discrete jump in action, leading to quantization of physical quantities. This is expressed through the integral over Euclidean time: [ S_T = \int d\tau \left( \frac{1}{2} \left( \frac{d\rho_T}{d\tau} \right)^2 + V(\rho_T) \right) ] Interpretation: Formula (2.8) defines the instanton action as a functional of the configuration ( \rho_T(\tau) ). Quantization ( \Delta S_T = \hbar \cdot n ) arises from the topological structure of the phase transition, not from a postulate. Thus, TTU interprets quantization as an ontological consequence of time dynamics.

1. Birth of Physics from Time In TTU, time is not a parameter but a substance.

All physical objects and laws are derivatives of the configuration of the field ( \rho_T(x) ). Space, interactions, matter, and even gravity arise as phase effects of the temporal fabric.

3.1. Space-Time as a Derivative Structure

The space-time metric arises as a functional of time field gradients: [ g_{\mu u}(x) = \eta_{\mu u} + \kappa \cdot \partial_\mu \rho_T(x) \partial_ u \rho_T(x) + \mathcal{O}(\rho_T^2) ] ( \eta_{\mu u} ) flat Minkowski metric ( \kappa ) coefficient of temporal geometrization Curvature ( R_{\mu u} ) secondary effect of ( \rho_T ) nonlinearity Space-time is not a fundamental entity it arises from the phase structure of time.

3.2. Interactions as Phase Vortices

Gauge fields are interpreted as phase vortices of the temporal field. In the first approximation, their local structure is given by the expression: [ A_\mu(x) \sim \rho_T^{-1}(x) \cdot \partial_\mu \rho_T(x) ] Comment: This is not a definition but an asymptotic approximation reflecting the behavior of the field ( A_\mu(x) ) in the region of weak fluctuations ( \delta\rho_T(x) ). It illustrates how the gradient of the phase state of time can generate a gauge structure. The complete dynamics of ( A_\mu(x) ), including the Lagrangian, symmetries, and conjugate currents, will be presented in the next work (in print). The specific form of the functional dependence between the temporal field and emergent geometric and gauge structures is denoted as: [ A_\mu[\rho_T], \quad g_{\mu u}[\partial \rho_T] ] Comment: This is not an equation but a designation of functional dependence, indicating that the fields ( A_\mu ) and ( g_{\mu u} ) are derivatives of the configuration ( \rho_T(x) ) and its gradients. Their exact form depends on the TTU Lagrangian and will be revealed in subsequent publications.

3.3. Recovery of General Relativity as a Limiting Case

At ( \rho_T(x) = \text{const} ), derivatives disappear: [ \partial_\mu \rho_T = 0 \quad \Rightarrow \quad \delta g_{\mu u} = 0 ] ( \to ) The metric becomes fixed ( \to ) Einstein's equations are restored as a phase approximation: [ R_{\mu u} - \frac{1}{2} R g_{\mu u} = 8\pi G T_{\mu u} ] TTU does not contradict General Relativity it includes it as a phase limit Gravity in TTU is the dynamics of time phases, not the geometry of space

Section Conclusion: TTU asserts: physics is born not from space but from time as a substance. Everything else is an epiphenomenon.

1. Physics of Time Phases

The phase structure of the field ( \rho_T(x) ) allows the existence of various causality regimes, each possessing unique physical properties. TTU predicts observable effects arising in anti-temporal and oscillating phases.

4.1. Anti-Time Domains

Regions with ( \rho_T(x) < 0 ) are interpreted as anti-temporal phases. Their properties: Reverse causality: [ \frac{\partial S}{\partial t} < 0 ] ( \to ) processes develop in the direction of decreasing entropy Decreasing entropy: [ \Delta S_{\text{anti-temp.}} < 0 ] ( \to ) local violations of the second law of thermodynamics are possible Geometry regularization: In the Schwarzschild solution at ( \rho_T(r) < 0 ), the singularity is eliminated ( \to ) a wormhole arises Mass change during cooling: Phase transition ( \rho_T \to -\rho_T ) leads to a decrease in the effective mass of the body

4.2. Experimental Signatures

TTU predicts effects absent in the Standard Model:

4.3. Phase Structure of Time and Observable Effects

The Temporal Theory of the Universe (TTU) asserts that time has a phase structure analogous to the phases of matter. Unlike the classical representation of time as a homogeneous and linear background, TTU considers time as a dynamic medium capable of transitioning between different phase regimes ( \rho_T ). Each phase is characterized by: type of causality (direct, reverse, local), direction of entropy, geometric realization, and observable physical effects. Special attention is paid to transitions between phases, especially between direct (( \rho_T > 0 )) and reverse (( \rho_T < 0 )) phases. It is in these transitions that interference effects arise, capable of explaining: CP symmetry violation, anomalous mass changes, appearance of wormholes, and gravitational signals detected by LIGO/Virgo detectors. As shown in 4.2, CP violation in TTU is interpreted not as a fundamental symmetry violation but as a phase effect arising from interference of temporal regimes. This allows linking quantum anomalies with geometric and thermodynamic transitions within the temporal structure. Below is a summary table of time phases and corresponding observable effects:

TTU makes the phase of time not a philosophical assumption but an experimentally verifiable physical reality. Transitions between phases, especially near phase boundaries, can be sources of observable quantum and gravitational effects previously considered anomalous. Thus, TTU unites geometry, causality, thermodynamics, and quantum effects into a single phase picture of time.

1. Ontological Theses

TTU asserts a new ontology of physics: time is the only substance from which all physical structures emerge.

5.1. Time as the Only Substance

Thesis: Physical reality is reduced to the configuration of the temporal field: [ \rho_T(x) \in \mathbb{R} ] Consequences: Space arises from time gradients: [ g_{\mu u}(x) \sim \partial_\mu \rho_T \cdot \partial_ u \rho_T ] Matter topological defects in the phase structure of ( \rho_T ). Interactions vortices of phase gradients: [ A_\mu(x) \sim \rho_T^{-1} \cdot \partial_\mu \rho_T ] Philosophical conclusion: "There is no empty space only the dynamic fabric of time."

5.2. Physical Constants as Phase Functions

Thesis: Fundamental "constants" depend on the local phase ( \rho_T ): [ G \sim \rho_T^{-1}, \quad \hbar \sim |\rho_T|, \quad m \sim \rho_T^\alpha ] Justification: Gravitational constant ( G ) is inversely proportional to the density of time (in anti-temporal domains ( G \uparrow )). Planck constant ( \hbar ) amplitude of quantum fluctuations ( \rho_T ). Mass ( m ) degree of particle involvement in the local phase of time. Experimental meaning: ( \Delta m / m < 0 ) during cooling direct consequence of ( m(\rho_T) ).

5.3. Quantization as a Property of Phase Transitions

Thesis: Discreteness of physical quantities arises from action quantization during transitions: [ \rho_T \rightarrow -\rho_T \quad \Rightarrow \quad \Delta S_T = \hbar \cdot n ] Mechanism: Transitions ( \rho_T^+ \leftrightarrow \rho_T^- ) instanton events. Energy levels, charges, spins topological invariants of phase dynamics. Example: Particle charge as an integral over the phase contour: [ Q \sim \oint_C \partial_\mu \rho_T , dx^\mu ]

1. Experimental Tests of TTU

TTU asserts: time is not a parameter but a field with phase structure. Its oscillations, inversions, and non-local vortices generate observable effects beyond the Standard Model. Below are key directions for experimental verification.

6.1. Mass Shifts

During Heating If the mass of a body is determined by the phase of time, its change during heating should lead to small but measurable shifts: [ \left| \frac{\Delta m}{m} \right| \sim \alpha \cdot \frac{\Delta \rho_T}{\rho_T} ] For estimation at temperature ( T = 77 , \text{K} ), using ( \rho_0 \sim T_{\text{Planck}} ), we obtain: [ \left| \frac{\Delta m}{m} \right| \sim 10^{-9} ] Mass becomes a function of the temporal environment. Heating is not just thermodynamics but an act of intervention in the phase of time. Methods of verification: precision scales, experiments with heated bodies Historical data: mass anomalies in Soviet experiments (see section 8.2, discussing mass anomalies in Soviet experiments, including Miroshnikov's work (1985))

6.2. Gravitational Micro-Signals

Phase vortices of time can induce gravitational signals at high frequencies. TTU predicts: [ \delta h \sim \kappa \frac{l_c^2}{c^2} \cdot \left( \frac{\partial \rho_T}{\rho_T} \right)^2 ] At ( l_c \sim 10^{-19} , \text{m} ), frequency ( f > 10^{10} , \text{Hz} ), we obtain: [ \delta h \sim 10^{-26} ] Gravity here is not space curvature but resonance of time phases. Waves generated not by mass but by its temporal structure. Methods of verification: high-frequency modes of LIGO, HFGW interferometers Difference from classical: TTU predicts non-local sources not described by the energy-momentum tensor

6.3. Quantum Foam of Time

In oscillating phases ( \rho_T(x) ), quantum foam arises a non-local, dynamic structure manifesting in metric and causality fluctuations. [ \rho_T(x) = \rho_0 + \delta \rho_T(x), \quad \delta \rho_T(x) \sim \sin(\omega t + \phi(x)) ] Foam of time is not noise but the language in which the Universe speaks about its deep structure. Where space is silent, time vibrates. Expected effects: Non-local metric fluctuations Anomalous noise in interferometers Temporal interferences not described by classical field theory Methods of verification: LIGO/Virgo, quantum sensors, analysis of residual noise

6.4. CP Asymmetry and Temperature Gradients (Hypothesis, Requires Data)

TTU allows that phase interference of time may affect symmetries, including CP violation. In particular, dependence is possible: [ A_{CP} \sim \gamma \cdot abla T ] Comment: This is a hypothetical formula reflecting the idea that the local slope of the temporal phase may induce asymmetry. However, experimental data from Belle II, necessary for verification, is not publicly available. Therefore, the formula is not included in Table 6.5 and is considered a theoretical possibility.

6.5. Table of Key TTU Tests

Comment: Formula (6.6) on CP asymmetry is excluded from the table due to the lack of open Belle II data. The quantum foam effect is presented as a qualitative hypothesis awaiting statistical interpretation.

7.Conclusion

The Temporal Theory of the Universe (TTU) proposes a radical shift in the foundation of physics: from space as a stage to time as a substance. In TTU, time possesses its own dynamics, phase structure, and quantum transitions, from which all physical objects and laws emerge. Section 8 systematizes the empirical and historical sources on which TTU is based. It shows that the theory is not only ontologically closed but also historically motivated as an attempt to comprehend forgotten or rejected phenomena.

7.1. Summary of Key

Provisions Time is a scalar field ( \rho_T(x) \in \mathbb{R} ), allowing phase transitions Space, matter, interactions, and gravity are derivatives of the configuration ( \rho_T(x) ) Quantization is a consequence of instanton transitions between time phases TTU includes General Relativity and the Standard Model as limiting cases Falsifiable effects are predicted: ( \Delta m / m ), ( \delta h ), ( A_{CP} )

7.2. Prospects

The theory allows experimental verification: from laboratory masses to gravitational micro-signals Known anomalies can be interpreted as manifestations of temporal dynamics The next step is the analysis of historical data, especially Soviet experiments, in light of TTU

7.3. Epigraph: Poetic Formula of TTU

Compressed expression of the ontological shift: Space is a derivative, Matter is a defect, Interaction is a phase vortex, Quantization is a transition between phases, And time is all there is.

1. Sources and Historical Contexts

8.1. Philosophical Foundations

8.2. Scientific Anomalies and Empirical Signals

8.3. Theoretical Precursors

Acknowledgments

The author expresses gratitude to intellectual assistants used in the process of developing, formalizing, and editorial preparation of this work. In particular, I thank: Microsoft Copilot for participation in text structuring, checking mathematical consistency, formulating ontological theses, and editing sections, including tables of time phases, experimental signatures, and philosophical generalizations. Copilot was used as a dialogical co-author capable of critical analysis, synthesis, and clarification of formulations within the framework of the Temporal Theory of the Universe (TTU). DeepSeek for assistance in generating technical formulas, checking Lagrangians, analyzing Euclidean transitions, and clarifying phase solution parameters. DeepSeek was used as a computational assistant for verifying equations of motion, instanton configurations, and predictions related to action quantization. The participation of AI systems was carried out under the author's control, with adherence to scientific integrity, transparency, and full responsibility of the author for content and interpretations. All conclusions, hypotheses, and interpretations are the result of the author's work, supported by machine intelligence tools.

Recommended Literature

1. N.A. Kozyrev. Time as a Physical Factor // Astronomical Bulletin. 1971. Vol. 7, No. 3. P. 2327. URL: http://elib.gnpbu.ru/text/kozyrev_vremya-kak-faktor_1971/go,0/ (accessed: 10.08.2025).
2. A.N. Miroshnikov. 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).
3. Experimental Detection of Entropy Gradient // Reports of the USSR Academy of Sciences. 1987. Vol. 297, No. 4. P. 865868.
4. Entropy Aspects of Symmetry in Nonequilibrium Processes // Problems of Universe Research. L.: Nauka, 1991. Issue 15. P. 4559.
5. N.A. Kozyrev. Astronomical Observations through Physical Properties of Time // Flashing Stars: Proceedings of the Symposium, Byurakan, October 58, 1976. Yerevan: Publishing House of the Armenian Academy of Sciences, 1977. P. 209227. URL: https://djvu.online/file/NGh6VKtGHHN3j (accessed: 10.08.2025). Weight Change of Gyroscopes during Vibrations // Technology Youth. 1991. No. 89. P. 1214.
6. N.A. Kozyrev. Time as a Physical Phenomenon. SPb.: GPNTB, 1971. 36 p. URL: https://nkozyrev.ru/bd/130.pdf (accessed: 10.08.2025).
7. Time and Stars: To the 100th Anniversary of N.A. Kozyrev / edited by V.A. Batsiev. SPb.: Asterion, 2008. 256 p. URL: https://archive.org/details/kozyrev (accessed: 10.08.2025).
8. Lemeshko, A. TTU: Temporal Unification Theory [Temporal Theory of Unification], 2025. URL: https://doi.org/10.5281/zenodo.16732254
9. Lemeshko, A. TTU and the Enigmas of Black Holes [Temporal Theory of Everything and the Enigmas of Black Holes], 2025. URL: https://doi.org/10.13140/RG.2.2.25445.10726
10. Lemeshko, A. TTG: Temporal Theory of Gravitation, 2025. URL: https://doi.org/10.5281/zenodo.16044168
11. Lemeshko, A. TTE: Temporal Theory of Everything [Temporal Theory of Everything], 2025. URL: https://doi.org/10.13140/RG.2.2.35468.83847
12. TTU-Group Repository. All materials: https://zenodo.org/communities/ttg-series

Appendix A. Glossary of TTU

Appendix B. TTU Formulas

B.1. Ontology of Time [ \rho_T(x) \in \mathbb{R} ] [ \rho_T > 0, \rho_T < 0 ] [ \mathcal{L}[\rho_T] ] [ \rho_T \to -\rho_T ] [ \rho_T(x) = \rho_0 + \delta \rho_T(x) ]

B.2. Field Dynamics [ \mathcal{L} = \frac{1}{2} (\partial_\mu \rho_T)^2 - V(\rho_T), \quad V(\rho_T) = |\mu_T|^2 \rho_T^2 + \lambda_T \rho_T^4 ] [ V(-\rho_T) = V(\rho_T) ] [ \Box \rho_T + 2|\mu_T|^2 \rho_T + 4\lambda_T \rho_T^3 = 0 ] [ \Box (\delta\rho) + \left( 2|\mu_T|^2 + 12\lambda_T \rho_0^2 \right) \delta\rho = 0 ] [ \frac{d^2 \rho_T}{d\tau^2} = \frac{\partial V}{\partial \rho_T} ] [ \rho_T(\tau \to \pm\infty) = \pm\rho_0 ] [ \Delta S_T = \hbar \cdot n, \quad n \in \mathbb{Z} ]

B.3. Emergence of Physics [ g_{\mu u}(x) = \eta_{\mu u} + \kappa \cdot \partial_\mu \rho_T(x) \partial_ u \rho_T(x) + \mathcal{O}(\rho_T^2) ] [ A_\mu(x) \sim \rho_T^{-1}(x) \cdot \partial_\mu \rho_T(x) ] [ \partial_\mu \rho_T = 0 \Rightarrow \delta g_{\mu u} = 0 ] [ R_{\mu u} - \frac{1}{2} R g_{\mu u} = 8\pi G T_{\mu u} ]

B.4. Phase Effects [ \frac{\partial S}{\partial t} < 0 ] [ \Delta S_{\text{anti-temp}} < 0 ] [ \rho_T \to -\rho_T ]

B.5. Experimental Predictions [ \left| \frac{\Delta m}{m} \right| \sim \alpha \cdot \frac{\Delta \rho_T}{\rho_T} ] [ \left| \frac{\Delta m}{m} \right| \sim 10^{-9} ] [ \delta h \sim \kappa \frac{l_c^2}{c^2} \cdot \left( \frac{\partial \rho_T}{\rho_T} \right)^2 ] [ \delta h \sim 10^{-26} ] [ \rho_T(x) = \rho_0 + \delta \rho_T(x), \quad \delta \rho_T(x) \sim \sin(\omega t + \phi(x)) ] [ A_{CP} \sim \gamma \cdot abla T ]