Unlike most mathematical systems derived to show simple single variable solutions, the Z_{0} Theory involves the complex relationship between the elements of charge, space, time, and the observation that gravity is a property of nature based on inter-related characteristics of permittivity and permeability related to energy flow.

Z_{0} states that the energy in space is self-organizing based on the energy content. A result is that if energy is quantized, gravity is also quantized.

The following equations, the basis for Z_{0}, describe quantum gravity in terms of classical physics:

**A critical insight:**

As Galileo learned, acceleration due to gravity doesn’t depend on the mass of an object:

*“All objects behave in the same way regardless of their mass.” *

This implies that gravity is unlike any other force in the universe, therefore:

“**Theories relating gravity to mass are flawed.**“

**Relating energy to mass**

This is Einstein’s famous equation of mass-energy equivalence. It states that energy (E) is equal to mass (m) multiplied by the speed of light squared (c²). This means that mass and energy are two different forms of the same thing.

**E = mc ^{2 }**

Where:

**E** is the concentration of energy, **m** is mass, **c** is the speed of energy.

E = mc² is one of the most important equations in physics. It is the basis of nuclear energy and it has been used to explain a wide range of phenomena, including the formation of stars. The relationship between mass and energy is a fundamental property of the universe. It is a property that is responsible for the existence of matter.

In the context of Z_{0}, the relationship between mass and energy can be used to explain the relationship between gravity and energy. Z_{0} suggests that gravity is a manifestation of the change in the speed of energy. A change in the speed of energy can be caused by a change in the mass of a system. Therefore, the relationship between mass and energy can be used to explain the relationship between gravity and energy.

**The speed of electromagnetic energy**

The Z_{0} math bases “equivalent” gravity on the change of speed of electromagnetic energy using Maxwell’s formula for the speed of energy:

**c = 1/√μ _{0}ε_{0} **

Where: **c** is the speed of energy, **ε _{0}** is the permittivity or dielectric constant,

**μ**is the permeability.

_{0}A change in the speed of energy through space creates a force. This is because space has an impedance, which is like a resistance to the flow of energy. The higher the impedance, the slower the energy moves. Charged particles are affected by this force because they have an electric field. The electric field is stronger around a charged particle with more energy. The potential energy of a charged particle is the energy it has due to its electric field. The higher the potential energy, the stronger the electric field. Therefore, the force on a charged particle is proportional to the product of its charge and the potential energy of the space around it.

**Relating electromagnetic energy to impedance of space**

Z_{0} begins with an understanding of the behavior of electromagnetic energy based on the following Maxwell formula:

**Z _{0} = √μ_{0}/ε_{0}**

Where: **Z _{0}** is the impedance of space,

**ε**is the permittivity or dielectric constant,

_{0}**μ**is the permeability.

_{0}**Lorentzian time distance**

**Δ**_{s}** = √(Δt ^{2}) – (Δx/c^{2})**

Where: **Δ _{s}** is Lorentzian distance,

**t**is time interval,

**x**is the difference in Euclidean distance,

**c**is the speed of energy.

The distance in the above equation is the distance measured in Lorentzian time. Lorentzian time is the time which occurs in the standard equations of physics, with a different status than a spatial coordinate x. Euclidean time is obtained from Lorentzian time by a Wick rotation in the complex t plane, and enters into the resulting equations exactly in the same way as a spatial coordinate x

In Minkowski space—the mathematical model of spacetime in special relativity—the Lorentz transformations preserve the spacetime interval between any two events.

In the Z_{0} Theory Lorentz’s “proper time” becomes “proper distance”.

**Gravity at altitude above sea level on earth**

Newton’s Second Law of Motion and Law of Universal Gravitation are used to calculate the acceleration due to gravity at various heights above the earths surface:

**g _{h} = g(r/(r+h))^{2}**

Where: **g** is the baseline gravitational constant, **r** is the Earth’s radius, and **h** is the altitude above the Earth’s surface.

**Baseline speed of light in free space**

Based on the Pound-Rebka experiment. the calculation for c_{fs} is derived from the difference between the speed of light as measured on Earth’s surface at sea level (c_{msl}) and the gravitational constant (g):

**c _{fs} = c_{msl} + g**

Where: **c _{msl}** is the SI unit for the measured speed of light on earth at sea level = 299792458.26 m/s and

**Gv**is the SI gravitational constant = 9.80665 m/s

^{2}.

It should be noted the difference in the speed of light from free space to that at the surface of the earth is only 1.00000000024692.

Therefore: The speed of light in the far reaches of deep void space is 299,792,468.07 m/s

**Theory Z _{0} relates gravity to energy**

In Z0 models, gravity manifests as the instantaneous change, or acceleration, in the speed of light (energy):

**G _{v} = -Δ_{c}/Δ_{x}**

This model illustrates the relationship between the speed of energy density and gravitational effects. It recognizes that, beyond the impedance of space depending on the permeability and permittivity of space, these parameters also influence the concentration of energy reciprocally.

Where: **G _{v}** is the gravitational acceleration,

**is the change in speed of energy,**

**Δ√ε**_{0}μ_{0}**is the change of temporal distance at Z**

**Δ**_{x}_{0}referenced to c.

using **c = 1/√ε _{0}μ_{0} becomes:**

**G _{v} = -Δx/Δ√ε_{0}μ_{0}**

Given that the velocity pertains to both the physical and temporal planes—Lorentzian’s “proper time”—the notation is revised to:

**G _{s} = -Δ_{s}/Δ√ε_{0}μ_{0}**

This equation is analogous to the equation F = qE, which describes the force on a charged particle in an electric field.

**The reciprocity of Z _{0} and energy concentration**

*This elegant insight is as important as Maxwell’s 4th equation, which shows the reciprocity of charge and magnetic flux.*

**∂Z _{0}/∂_{E} = -k*E** — The reciprocity of Z

_{0}and energy concentration.

Where:

**Z _{0}** is the impedance of space,

**E**is the concentration of energy,

**k**is a constant of proportionality.

This equation states that the rate of change of the impedance of space with respect to the concentration of energy is equal to the negative of the product of the constant of proportionality and the concentration of energy.

There are similarities between the force of gravity and the force produced by the energy speed gradient. This is because the force of gravity and the potential energy gradient are both proportionate.

This is an important link in not only showing the organizing energy but also in the relationship of that organization based on its quantum nature.

**Dynamic gravity between two energy densities in time **

**Newton:**

**F = ma**

Where: **F** is force, **m** is mass, **a** is acceleration

Then:

**F = GM _{1}M_{1}/r^{2}**

Where: **F** is force, **G** is the acceleration of gravity, **M** is a mass, **m** is second mass, **a** is acceleration.

Then, adding in the first equation:

**F = ma = GM_{1}M_{1}/r^{2}**

Where: **F** is force, **G** is the acceleration of gravity, **M** is a mass, **m** is second mass, **a** is acceleration, **r ^{2}** is the distance between the masses.

Then, adding in the equation for energy = mass:

**F = G_{v} [(1/ε_{0}μ_{0}E_{1}) (1/ε_{0}μ_{0}E_{2})]/(d-t/√ε_{0}μ_{0})^{2}**

Adding in Gv from above:

**F = -Δ_{x}/Δ√ε_{0} [(1/ε_{0}μ_{0}E_{1}) (1/ε_{0}μ_{0}E_{2})]/(d-t/√ε_{0}μ_{0})^{2}**

Where: **F _{t}** is the gravitational force between two masses at time

**t**,

**[Δ**is the gravitational gradient (Gv from above),

**/Δ√ε**_{x}_{0}μ_{0}]**(1/ε**are the relative mass densities,

_{0}μ_{0}E_{1}) (1/ε_{0}μ_{0}E_{2})**is the distance between their centers of attraction, the speed of c is represented by**

**(d-t/√ε**_{0}μ_{0})**t/√ε**.

_{0}μ_{0}Reducing the terms:

**F = G_{v} * [E_{1}E_{2} / d^{2}**] — Apparent force of energy seeking equilibrium at the rate of c — Newton revised.

Z_{0} models calculate the force that drives the speed of energy is due to differences of energy density in areas of space:

This is the apparent force of energy seeking equilibrium at the rate of c. – Note the similarity between this equation and Newton’s formula for gravitational force replacing mass with energy:

**F = GM_{1}M_{1}/r^{2}**

**The energy wavelength relationship**

**E = hc/λ**

Where: **E** is the electric field, **h** is Planck’s constant, **c** is the speed of energy, **λ** is the wavelength of energy.

The energy-wavelength relationship shows that photons with shorter wavelengths have higher energies. This means that photons with shorter wavelengths will interact more strongly with the impedance of space. This is why photons with shorter wavelengths are more likely to be bent by gravity.

The energy of a photon is also related to its momentum. This can be seen from the equation E = pc, where p is the momentum of the photon. This relationship is important because it shows that photons have both energy and momentum.

Here is the sequence of equations that links Z_{0} to quantized gravity:

**1. E = mc²**

**2. c = 1/sqrt(μ _{0}ε_{0})**

**3. Z _{0} = √μ_{0}/ε_{0}**

**4. ∂Z _{0}/∂_{E} = -k*E**

**5. G _{v} = -∂c/∂x**

**6. E = hc/λ = hf**

Combining the equations 1 and 4 we get:

**∂Z _{0}/(mc^{2}) = −k⋅(mc^{2})**

This can be rearranged to isolate mass:

**∂Z _{0}∂_{m} = −k⋅c^{2}**

Here, ∂Z_{0}/∂_{m} represents how the ε_{0}μ_{0} field changes with respect to mass (m).

If we combine Equations 4 and 5, we get the following wave equation:

**G _{v} = -k*(∂_{E}/∂_{x})**

This means that gravity can propagate through space in the form of waves. This is a very important result, as it suggests that gravity is a fundamental force of nature.

**Quantum implications**

Z_{0} has a number of quantum implications. One can see that the stepping of energy density at the quantum level provides the basis for the quantum impedance of space. With this, ** the rate of change in speed of energy is quantized**, and thus, with Z

_{0}, equivalent gravity is quantized based on the steps in the impedance of space.

One implication is that the quantization of physical properties is not a fundamental property of the universe but rather an emergent property of the self-organizing system that underlies the universe.

According to the Z_{0}, the universe is ordered and subject to the laws of physics rather than being chaotic and unpredictable.