Лемешко Андрей Викторович
Gravity of Time: New Dynamics of Space-Time

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  • Аннотация:
    The paper explores an alternative approach to explaining gravity by integrating thermodynamics and General Theory of Relativity (GTR). The author hypothesizes that the redistribution of temporal energy and localized arrows of time play a key role in shaping gravitational fields. The proposed model examines how temporal gradients influence matter dynamics and inertia, potentially complementing classical gravitational understanding. Experimental validation of this concept can be achieved through astrophysical observations, laboratory experiments, and space studies. Incorporating this idea into an extended mathematical framework of GTR may refine predictions of gravitational phenomena.

Gravity of Time: New Dynamics of Space-Time

   Abstract.
   This article explores the role of temporal gradients in shaping gravitational phenomena and matter dynamics. Departing from traditional mass-centric models, it introduces a framework where localized arrows of time redistribute energy and generate inertial forces. The equivalence between gravitational acceleration derived from space-time curvature and from temporal gradients is demonstrated through comparative modeling. The proposed approach offers a novel interpretation of gravity as a consequence of temporal energy flow, with implications for strong-field environments such as black holes and neutron stars.
   Keywords: temporal gradient, arrow of time, inertial force, gravitational acceleration, energy redistribution, space-time curvature, time dilation, ontological physics, strong gravitational fields, TTU framework.
   Contents
   1. Introduction
   2. Temporal Gradients and Their Influence on Gravity
   3. Localized Arrows of Time and Energy Redistribution
   4. Gravity as a Result of Temporal Energy Redistribution
   5. Mathematical Model: Comparing Methods for Calculating Gravity
   6. Experimental Verification of the Concept
   7. References
   8. Appendixs
   Appendix A: Summary of Key Equations
   Appendix B: Glossary of Symbols
   Appendix C: Dimensional Consistency of Key Equations
   Appendix D: Planetary Gravity Table (Comparison via GR and Time Gradient)
   1.Introduction
   The General Theory of Relativity (GTR), developed by A. Einstein, explains gravity as the curvature of space-time under the influence of mass. However, recent studies indicate that temporal gradients may play a significant role in gravitational processes. This paper examines the hypothesis that the redistribution of temporal energy and localized arrows of time play a key role in shaping gravitational fields.
   While most research focuses on uniting quantum mechanics with GTR, this paper proposes an alternative interdisciplinary approach, integrating thermodynamics and general relativity. The analysis of the impact of temporal gradients and energy redistribution on gravitational phenomena offers a fresh perspective on fundamental physical laws, opening avenues for future research. Gravity cannot be fully explained solely by the time gradient, but its influence can complement classical gravitational theory.
   2. Temporal Gradients and Their Influence on Gravity
   Gravity is traditionally understood as a consequence of space-time curvature, but observations suggest that temporal gradients can affect the dynamics of matter:
   (2.1)"T " ьэьэ ьэ'
   where (G) is the gravitational constant, (M) is the mass of the object, and (r) is the radial coordinate. In strong gravitational fields, the redistribution of temporal energy may modify the traditional gravitational potential:
   (2.2)_grav = "ьэьэ ьэ +  " "T
   where () is the coefficient reflecting the influence of temporal gradients.
   3. Localized Arrows of Time and Energy Redistribution
   Localized arrows of time form in regions with intense temporal gradients, redistributing energy from areas with faster time flow to zones where time slows down. This process contributes to the establishment of energy equilibrium and impacts matter dynamics.
   The relationship between temporal gradients and inertia can be expressed by the following equation:
   (3.1)F_inertia "  " "T
   where () is the coefficient defining the properties of the medium.
   The arrow of time plays a fundamental role in the evolution of matter, guiding it from the past to the future-from regions with a high rate of temporal flow (past) to areas where time moves slower (future). Mass also generates localized modifications of the arrow of time. Near massive objects, branches emerge that locally alter the motion of matter, redistributing it from zones with accelerated time flow to areas where time slows down. This effect may explain the behavior of matter in strong gravitational fields, such as near black holes and neutron stars.
   4. Gravity as a Result of Temporal Energy Redistribution
   The traditional approach associates gravity exclusively with mass effects, but the redistribution of temporal energy may also play a crucial role:
   (4.1)E_eff = E + E_grad
   where (E_grad " "T) describes the contribution of temporal gradients to the total energy of the system.
   5. Mathematical Model: Comparing Methods for Calculating Gravity
   We analyze two approaches to computing gravitational acceleration: space-time curvature (GR) and time gradient.
   5.1. Acceleration via Space-Time Curvature (GR) Gravitational acceleration follows Newton's equation:
   (5.1)g = GM R'
   where:
  -- (G = 6.674 " 10 "") m"/kg"s' - gravitational constant,
  -- (M = 5.972 " 10' ) kg - Earth's mass,
  -- (R = 6.371 " 10 ) m - Earth's radius.
   Substituting values:
   (5.2)g - 9.81 m/s'
   5.2. Acceleration via Time Gradient In this model, local time arrows create inertial forces:
   (5.3)F_inertia =  " "T
   The time gradient relates to gravitational time dilation:
   (5.4)"T " GM R'
   Setting ( = 1):
   (5.5)F_inertia = 9.81 m/s'
   5.3. Conclusion:
  -- Both methods result in (g - 9.81) m/s'.
  -- GR: gravity arises due to space-time curvature.
  -- Time gradient: inertial forces direct matter to slower time zones, equivalent to gravitational attraction.
  -- This principle applies to all planets-gravitational acceleration (g) is determined using the same formula, regardless of the approach.
   6.Experimental Verification of the Concept
   To confirm the proposed hypothesis, several tests are needed:
  -- Astrophysical observations: Analysis of gravitational lenses and anomalies in the motion of cosmic objects.
  -- Laboratory experiments: Modeling of temporal gradients using atomic clocks and interferometry.
  -- Space studies: Examination of trajectory deviations of spacecraft.
   6.1.Compatibility with GTR and Future Research Perspectives
   If temporal gradients significantly impact gravitational processes, they could be integrated into an extended mathematical model of GTR. Incorporating this factor into Einstein's equations could refine predictions of gravitational phenomena.
   6.2.Conclusion
   The proposed hypothesis that temporal gradients serve as an additional factor in gravity does not contradict GTR but rather complements it. Experimental verification will determine the precise role of temporal gradients and energy redistribution in forming gravitational fields, broadening our understanding of fundamental physical laws.
   7.References
      -- Landau L.D., Lifshitz E.M. - Field Theory, Vol. 2, Sections 81-87, 91-95, 99-102.
    A classic textbook on gravity and field theory containing fundamental GTR principles.
      -- Misner C., Thorne K., Wheeler J. - Gravitation.
    A comprehensive work covering key aspects of gravity, including relativistic effects.
      -- Padmanabhan T. - Theoretical Physics of Gravity.
    An exploration of thermodynamic aspects of gravity and their relation to entropy.
      -- Carroll S. - A Special Course on General Relativity.
    A modern textbook explaining core GTR concepts and their mathematical representation.
      -- List of Literature on Gravity - HSE
    A compilation of books and articles on gravity, including works by Landau and Lifshitz.
   8. Appendixs
   Appendix A: Summary of Key Equations

No.

Equation

Explanation

   (2.1)
   "T " GM r'
   Temporal gradient is proportional to gravitational acceleration.
   (2.2)
   _grav = "GM r +  " "T
   Gravitational potential modified by temporal gradient.
   (3.1)
   F_inertia "  " "T
   Inertial force arises from temporal gradient.
   (4.1)
   E_eff = E + E_grad
   Total energy includes contribution from temporal gradient.
   (5.1)
   g = GM R'
   Classical gravitational acceleration (Newton).
   (5.2)
   g - 9.81 m/s'
   Value for Earth.
   (5.3)
   F_inertia =  " "T
   Alternative interpretation via time arrow.
   (5.4)
   "T " GM R'
   Temporal gradient linked to gravitational time dilation.
   (5.5)
   F_inertia = 9.81 m/s'
   Result equivalent to classical g.
   Appendix B: Glossary of Symbols

Symbol

Meaning

   G
   Gravitational constant (6.674 " 10 "" m"/kg"s')
   M
   Mass of the object (e.g., Earth = 5.972 " 10' kg)
   r, R
   Radial coordinate or radius (e.g., Earth = 6.371 " 10 m)
   "T
   Temporal gradient - rate of change of time flow in space
   _grav
   Gravitational potential
   
   Coefficient reflecting influence of temporal gradient
   
   Coefficient describing medium properties
   E
   Classical energy
   E_grad
   Temporal contribution to energy
   E_eff
   Effective energy including "T
   F_inertia
   Inertial force generated by time arrow
   g
   Gravitational acceleration
   Appendix C: Dimensional Consistency of Key Equations

Equation No.

Equation

Dimensional Check

   (2.1)
   "T " GM r'
   ["T] ~ [m""s '"kg "] ! consistent with time gradient units
   (2.2)
   _grav = "GM r +  " "T
   [_grav] ~ [m'"s '] ! both terms match potential energy per unit mass
   (3.1)
   F_inertia "  " "T
   [F] ~ [kg"m/s'] if  absorbs units of mass and spatial scale
   (4.1)
   E_eff = E + E_grad
   [E] ~ [kg"m'/s'] ! total energy remains dimensionally valid
   (5.1)
   g = GM R'
   [g] ~ [m/s'] ! standard gravitational acceleration
   (5.3)
   F_inertia =  " "T
   [F] ~ [kg"m/s'] ! same as Newtonian force
   (5.5)
   F_inertia = 9.81 m/s'
   Interpreted as acceleration per unit mass ! dimensionally valid
   This appendix confirms that all equations maintain internal dimensional consistency, assuming  and  are defined to absorb necessary units.
   Appendix D: Planetary Gravity Table (Comparison via GR and Time Gradient)

Planet

Mass (kg)

Radius (m)

g via GR (m/s')

"T Estimate

g via "T Model

   Earth
   5.972"10'
   6.371"10
   9.81
   "T " GM R'
   - 9.81
   Mars
   6.39"10'"
   3.39"10
   3.71
   "T " GM R'
   - 3.71
   Jupiter
   1.90"10'
   6.99"10
   24.79
   "T " GM R'
   - 24.79
   Moon
   7.35"10''
   1.74"10
   1.62
   "T " GM R'
   - 1.62
   This table shows that both GR and time-gradient approaches yield consistent gravitational acceleration values across planetary bodies, reinforcing the equivalence principle in practical terms.
   Note:
   *This is an early research version of the concept, preceding the full ontological formulation of the Temporal Theory of the Universe (TTU).
   Key differences from the modern TTU framework:
      -- It employs the concept of the temporal gradient ("T) rather than the fundamental fields  and .
      -- The theory is presented as a complement to General Relativity (GR), not as an independent ontology.
      -- It lacks a variational derivation and the fundamental constant C_TTU.
   This document holds historical value for tracing the genesis of the idea.
  
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