Mathematics

Gravitational Acceleration: Two Complementary Perspectives

In QA theory, gravity arises from small variations in the speed of energy (c) as it propagates through space. These variations are influenced by the impedance and viscosity of space, both of which are determined by the electromagnetic properties of the vacuum, represented by μ0​ and ​ε₀​.

Rate of Change Perspective: Gravitational acceleration can be described by the rate of change in the speed of energy with respect to distance, encapsulated by the Quantum Admittance Gravitational Acceleration Vector:

G_v​ = – d_c/ d_x

Where:

G_v represents the rate of gravitational acceleration,

d_c represents the change in speed of energy,

d_x represents the change in distance.

This equation emphasizes how gravitational acceleration emerges from the spatial gradient of energy speed, showing a dynamic interaction over distance.

Instantaneous Difference Perspective: As a complementary view, gravitational acceleration can also be understood through the instantaneous difference between the speed of energy in open space (cmax​) and the local speed of energy (cl​):

G_a = 1/(c_max​−c_l​)

Where:

G_a represents the rate of gravitational acceleration,

c_max​ is the speed of energy in open space,

c_l​ is the local speed of energy, which varies depending on the gravitational potential in that region.

This expression captures the gravitational acceleration as an immediate consequence of the difference in energy speeds, providing a snapshot of the gravitational effect at a specific point in space.

Equivalence and Veracity

These two equations, though derived from different perspectives, describe the same gravitational acceleration. The consistency between the rate of change in energy speed over distance and the instantaneous difference in energy speeds reinforces the validity of the Quantum Admittance framework. Together, they provide a comprehensive understanding of gravity, demonstrating how it can be understood both as a continuous process and an instantaneous effect within the same theoretical structure.

Clarifying the Acceleration: To relate this to gravitational phenomena, we can express the gravitational constant (G_v) in terms of these energy dynamics. If we denote the gravitational acceleration by G_v​= – d_x/d_{√(ε0​μ0)} where gravity is defined as distance with respect to the change in the speed of energy. This can be reduced to G_v​=d_c/d_x​. This formulation implies that gravitational effects can be directly linked to variations in the propagation speed of energy within the context of Charge Admittance.

Explanation of the Transition: To connect the change in the speed of energy with gravitational acceleration, consider that: The change in the speed of energy (d_c) over a distance (d_x) reflects an acceleration. In classical mechanics, acceleration is defined as the change in velocity over time. Here, dc serves as a proxy for velocity changes in the energy flow, with d_x corresponding to either time or a spatial dimension (or both).

Verification of Correctness: In traditional physics, c² is a significant term in both energy-mass equivalence and electromagnetism. Here, G_v²​ could be interpreted as relating to changes in the energy propagation squared: G_v²= – (d_c/d_x)², However, simplifying to: G_v​= – d_x/d_c aligns with the interpretation of gravitational acceleration as a first-order derivative of the energy speed with respect to distance, making it consistent with classical mechanics and the principles of Admittance.

The Reciprocity of Z₀ and Energy Concentration:

∂_E/∂Y₀ = -k*E

Where:

Y₀ is the admittance of space,

E is the concentration of energy,

k is a constant of proportionality.

This equation states that the rate of change of the concentration of energy with respect to the admittance is equal to the negative of the product of the constant of proportionality and the density of energy. There are similarities between the force of gravity and the force produced by the energy speed gradient and are proportionate. This is an important link in not only showing the organizing energy but also in the relationship of that organization.