# Temporal Energy: An Extension of Classical Gravity and Nuclear Interaction Theory

Андрей Викторович Лемешко

Temporal Energy: An Extension of Classical Gravity and Nuclear Interaction Theory

Lemeshko Andriy Viktorovich

Doctor of Philosophy, Associate Professor

Taras Shevchenko National University of Kyiv, Ukraine

ORCID: 0000-0001-8003-3168

1. Introduction

Gravity and nuclear forces are fundamental interactions that define the structure of matter and the evolution of the universe. In classical physics, gravity is explained by the curvature of spacetime in General Relativity (GR), while nuclear forces are described by Quantum Chromodynamics (QCD).

The proposed model considers gravity as a manifestation of the redistribution of temporal energy-a physical property of matter associated with its movement through time. Local variations in the temporal flow can explain both gravitational attraction and nuclear binding mechanisms.

2. Temporal Energy and Its Analogy with a River

Temporal energy is a fundamental property of matter, ensuring its movement through time. In the proposed model, it plays the role of an internal impulse that directs matter's evolution from the past to the future.

Temporal caverns are regions in spacetime where the temporal flow is significantly slowed down or accelerated. In this model, such caverns form near massive objects and within nuclear structures, affecting particle interactions and the redistribution of binding energy.

Analogy with a River Flow:

Imagine that time is a vast river, carrying all matter along with it.

-- Smooth flow: If the water moves uniformly, objects are carried effortlessly without resistance. This is analogous to a stable temporal flow, where matter evolves naturally without external interference.

-- Vortices and currents: In areas with altered flow speed, whirlpools and eddies arise, where water accelerates or decelerates. This corresponds to temporal caverns, where temporal energy redistributes, creating gravitational and nuclear effects.

-- Dense areas: Some parts of a river have strong water pressure, increasing flow intensity. Similarly, temporal gradients can modify the temporal stream, causing matter to accelerate or decelerate.

Physical Analogy: Temporal Flow as an Inertial Source

Time can be seen as a "temporal stream" similar to a river current. In regions where time slows down, objects experience additional influence-analogous to gravitational force.

-- River vortices: Create zones where the flow captures objects. Similarly, massive bodies redistribute temporal energy, producing gravitational attraction.

-- Change in flow speed: If a river slows down in one area, objects are "pulled" into regions of slower movement, just as gravity attracts bodies.

-- River depth: Comparable to gravitational potential; the deeper the region (the stronger the time slowdown), the greater the effect on objects.

Thus, the redistribution of temporal energy can be compared to changes in river flow: in areas with strong temporal gradients, matter is "pulled in," whereas in areas with uniform time, it continues its natural motion. This explains why gravity and inertial effects can both be manifestations of a single mechanism-the redistribution of time.

3. Connection of Temporal Energy with Modern Physics

Analogy with 4-Momentum in General Relativity

In relativistic mechanics, four-momentum is given by:

[ p^\mu = \left( \frac{E}{c}, \vec{p} \right) ]

where:

-- (E) is the system's energy,

-- (c) is the speed of light,

-- (\vec{p}) is spatial momentum.

This equation shows that energy represents the temporal component of momentum. In the proposed model, temporal energy ((E_{\text{temp}})) is seen as a natural extension of this definition:

[ E_{\text{temp}} = mc^2 ]

This alternative description incorporates gravitational potential energy in curved spacetime.

Connection with Gravitational Time Dilation

General Relativity predicts that gravity slows down the passage of time, expressed as:

[ T = T_0 \sqrt{1 - \frac{2GM}{Rc^2}} ]

where:

-- (T_0) is the initial time,

-- (G) is the gravitational constant,

-- (M) is the object's mass,

-- (R) is the distance from the center,

-- (c) is the speed of light.

Near massive objects, part of the movement energy along the time axis transforms into other forms (e.g., potential binding energy).

4. Temporal Gradient and Its Connection to Matter Motion

The temporal gradient ( \nabla T ) defines how the passage of time changes in space. In regions with a strong temporal gradient, matter undergoes redistribution of temporal energy, affecting its trajectory.

If time flows slower near a massive object, this creates an effect analogous to gravitational attraction:

[ F_{\text{gravity}} \approx \eta \cdot \nabla_\alpha (\sqrt{-g} T^\alpha) ]

where ( \eta ) is the temporal energy redistribution coefficient.

This effect is comparable to changes in the density of water in a river: if the flow speed decreases, objects experience additional resistance, similar to gravitational attraction.

5. Formalism of Temporal Energy Redistribution

Classically, gravity is explained as the curvature of spacetime under the influence of mass (GR). However, in the proposed model, the redistribution of temporal energy plays a key role in generating gravitational effects.

The temporal gradient ( \nabla T ) is central to energy redistribution, creating effects analogous to gravity:

[ F_{\text{inertia}} = \eta \cdot \nabla_\alpha (\sqrt{-g} T^\alpha) ]

where ( \eta ) is the temporal energy redistribution coefficient, and ( T^\alpha ) is the temporal flow in spacetime.

Gravitational time dilation in GR is expressed through the Schwarzschild metric:

[ T = T_0 \sqrt{1 - \frac{2GM}{Rc^2}} ]

where ( G ) is the gravitational constant, ( M ) is the mass of the gravitating object, ( R ) is the radius, and ( c ) is the speed of light.

6. Temporal Caverns and Their Impact on Gravity

If massive bodies cause the redistribution of temporal energy, their gravitational influence can be interpreted as the formation of temporal caverns (zones with local time slowdown):

[ \nabla T = \frac{E_{\text{binding}}}{R_{\text{cav}} c^2} ]

Here, ( E_{\text{binding}} ) is the binding energy of matter in the cavern zone, and ( R_{\text{cav}} ) is the radius of the temporal well.

7. Gravity: Classical and Alternative Calculations (Earth)

Classical Approach (Newton's Equation)

Gravitational acceleration is determined by the standard Newtonian equation:

[ g = \frac{GM}{R^2} ]

where:

-- ( G ) is the gravitational constant ( (6.674 \times 10^{-11} ) m/kg"s)

-- ( M ) is the mass of the gravitating object

-- ( R ) is the radius of the object

For Earth:

[ g \approx \frac{(6.674 \times 10^{-11}) (5.972 \times 10^{24})}{(6.371 \times 10^{6})^2} \approx 9.81 \text{ m/s}^2 ]

Alternative Approach (Through Temporal Gradient)

If temporal caverns create a local time gradient, inertia can be rewritten as:

[ F_{\text{inertia}} = \eta \cdot \nabla_\alpha (\sqrt{-g} T^\alpha) ]

where ( T ) is the temporal flow associated with spacetime curvature.

Gravitational time dilation is expressed as:

[ T = T_0 \sqrt{1 - \frac{2GM}{Rc\alpha) = \frac{GM}{R^2} ]

Substituting values:

[ g = \eta \cdot \frac{GM}{R^2} ]

If ( \eta = 1 ), we obtain:

[ g \approx 9.81 \text{ m/s}^2 ]

The alternative method based on the redistribution of temporal energy yields the same result as Newton's classical equation.

8. Interaction of Temporal Caverns with Nuclear Forces

In classical physics, strong interactions are explained through the exchange of gluons between quarks. However, if we consider the redistribution of temporal energy, nuclear forces can be interpreted as a result of temporal gradients' influence.

Temporal caverns inside an atomic nucleus modify interaction structures, forming zones with local time slowdowns. In such areas, particle binding energy redistributes similarly to gravitational time dilation:

[ \nabla T = \frac{E_{\text{binding}}}{R_{\text{cav}} c^2} ]

where:

-- ( E_{\text{binding}} ) - the nuclear binding energy,

-- ( R_{\text{cav}} ) - the radius of the temporal cavern,

-- ( c ) - the speed of light.

This effect creates additional particle retention, analogous to classical nuclear forces but within the framework of time redistribution.

Temporal Structure of the Atomic Nucleus:

Inside a nucleus, nucleons are held together by the Yukawa potential:

[ V(r) = -V_0 \frac{e^{-r / r_0}}{r} ]

However, considering temporal caverns, a correction must be made for local time gradients:

[ \nabla_q T = \frac{\hbar}{E_{\text{binding}}} \frac{\partial T}{\partial r} ]

where:

-- ( \hbar ) - Planck's constant,

-- ( E_{\text{binding}} ) - the nuclear binding energy,

-- ( r ) - the distance between nucleons.

This means that the redistribution of temporal energy can affect nuclear interaction strength, creating an analog of quantum confinement zones caused by temporal flow.

9. Nuclear Forces: Classical and Alternative Calculations (Uranus)

Classical Approach (Yukawa Potential):

Strong interactions between nucleons are described by the Yukawa potential:

[ V(r) = -V_0 \frac{e^{-r / r_0}}{r} ]

where:

-- ( V_0 \approx 40 ) MeV,

-- ( r \approx 1.4 ) fm,

-- ( r_0 \approx 1.4 ) fm.

Interaction force:

[ F_{\text{nuclear}} = -\frac{dV}{dr} = \frac{V_0}{r} e^{-r / r_0} \left( \frac{r - r_0}{r_0} \right) ]

This gives an approximate nuclear force of ( 10^{13} ) N.

Alternative Approach (Temporal Gradient):

Time gradient inside the nucleus:

[ \nabla T = \frac{E_{\text{binding}}}{R_{\text{nucleus}} c^2} ]

where:

-- ( E_{\text{binding}} \approx 7.6 ) MeV,

-- ( R_{\text{nucleus}} \approx 7.4 ) fm.

Interaction force through temporal gradient:

[ F_{\text{inertia}} = \eta \cdot \nabla T c^2 ]

Substituting values:

[ F_{\text{inertia}} \approx \frac{7.6 \times 10^{-15} \times (3 \times 10^8){-15}} ]

[ F_{\text{inertia}} \approx 10^{13} \text{ N} ]

Both methods yield comparable numerical results (~( 10^{13} ) N), confirming that the proposed model of temporal energy redistribution explains the mechanisms of gravity and strong interaction through temporal flow modification, integrating relativistic and quantum effects into a unified structure.

10. Conclusions

Unified Mechanism of Interactions

Gravity and nuclear forces can be viewed as manifestations of a single mechanism of temporal energy redistribution. This approach provides an alternative interpretation of fundamental interactions, integrating relativistic and quantum effects.

Consistency Between Alternative and Classical Calculations

Analysis shows that the proposed model produces numerically consistent results with classical theories of Newtonian gravity and Yukawa nuclear forces, confirming the mathematical correctness of the concept. This suggests a profound connection between gravity, inertia, and strong interaction through temporal gradients.

Physical Interpretation of Temporal Energy

Temporal energy acts as a hidden impulse guiding the movement of matter through time. Its redistribution creates effects of gravitational attraction and nuclear binding, analogous to how a river's altered flow creates vortices and turbulence in a water stream.

Experimental Perspectives

-- Gravitational Waves: Investigating possible phase shifts near massive objects.

-- Neutrino Oscillations: Studying mass variations of particles depending on local temporal gradients.

-- Impact on Quark Structure: Evaluating hadron stability under interaction with temporal caverns.

Potential Applications

The proposed concept of time redistribution may have implications for cosmology, astrophysics, and quantum field theory, offering new insights into the nature of fundamental interactions.

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