Gravitation fundamental fields

[computAI]

All the most known theories of gravity are built on the principle of long-range action. When approximately "point" body or mass density (also electromagnetic energy) distributed in space creates gravitational potential. This article attempts to substantiate gravitational phenomena on the principle of proximity (locality). The cause of interactions is some spatial state of fundamental fields, the consequence is change of these fields over time (first derivative in time at point of continuum).

Presumably, following fundamental gravitational fields exist:
(SI units in parentheses are m-metre, s-second, k-kilogram, A-Ampere)
scalar potential g (m^2/s^2)
vector potential G (m/s)
scalar strain f (m^2/s^3)
vector strain F (m/s^2)

The gravitational constant g0 = 6.6742^-11 (m^3/s^2/k) is also used,
local energy density u (k/m/s^2), for example electromagnetic = ε0/2 • E^2 + μ0/2 • H^2
and Poynting vector S (k/s^3) = [E × H]

Time derivatives are expressed as follows:
g' = - f - c^2 • div G
G' = - F - grad g
f' = - c^2 • div grad g + fu • u
F' = c^2 • rot rot G - fs • S

The constants fu (m^3/s^2/k) and fs (m/k) are positive, signs are selected so that scalar potential g
becomes negative in presence of positive density u in vicinity of point.

The equations are similar to electromagnetic equations expressed in potentials:
a' = - c^2 • div A
A' = - E - grad a
E' = c^2 • rot rot A

In stationary state, for example, during formation of gravitational fields by stable elementary particle
or single celestial body:
S = 0, G = 0, f = 0
F = - grad g
div grad g = fu • u / c^2 = 4 • π • g0 • ρ, according to Newton's potential

Hence we get at ρ = u / c^2: fu = 4 • π • g0
The effect of gravitational fields on other fundamental ones can manifest itself as a curvature of space, and direct effect on velocity vector V, mentioned in this topic:
Hypothesis about the formation of particles from fields | Sciforums

With zero u and S, following types of "pure" gravitational waves can exist:
1. Longitudinal potential-potential: g' = - c^2 • div G, G' = - grad g
2. Longitudinal with phase shift of 90 degrees: g' = - f, f' = - c^2 • div grad g
3. Transverse: g' = - c^2 • div G, G' = - F - grad g, F' = c^2 • rot rot G
Transverse ones are probably easier to detect in experiments.

 

[origin]

It sure would be helpful if you would use LaTex.

 

[computAI]

Not all computers support LaTex. It would be better to use [sup][/sup] tags or HTML format. Other thing, in LaTex many indices are too small to view conveniently. I would try to add LaTex version also, but I see no button to insert tag in text redactor. Have it to start from [math]$ and end with $[/math] ?

 

[origin]

Not all computers support LaTex.

LaTex has nothing to do with your computer. It only depends on the site supporting LaTex or actually Tex in this case.

$$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

The above equation is from this ( I left out the first bracket on 'tex' so you can see it).

tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

One other thing after you initially post your tex you need to hit refresh to see the equation and not the tex.

 

[computAI]

All the most known theories of gravity are built on the principle of long-range action. When approximately "point" body or mass density (also electromagnetic energy) distributed in space creates gravitational potential. This article attempts to substantiate gravitational phenomena on the principle of proximity (locality). The cause of interactions is some spatial state of fundamental fields, the consequence is change of these fields over time (first derivative in time at point of continuum).
Presumably, following fundamental gravitational fields exist:
(SI units in parentheses are m-metre, s-second, k-kilogram, A-Ampere)
scalar potential $$g \frac{m^2}{s^2}$$
vector potential $$G \frac{m}{s}$$
scalar strain $$f \frac{m^2}{s^3}$$
vector strain $$F \frac{m}{s^2}$$
The gravitational constant $$g_0 = 6.6742^{-11} \frac{m^3}{s^2 \cdot k}$$ is also used,
local energy density u $$\frac{k}{m \cdot s^2}$$, for example electromagnetic $$= \frac{\varepsilon0}{2} \cdot E^2 + \frac{\mu0}{2} \cdot H^2$$
and Poynting vector $$S \frac{k}{s^3} = [E × H]$$
Time derivatives are expressed as follows:
$$g' = - f - c^2 \cdot div(G)$$
$$G' = - F - grad(g)$$
$$f' = - c^2 \cdot div grad(g) + fu \cdot u$$
$$F' = c^2 \cdot rot rot(G) - fs \cdot S$$
The constants $$fu \frac{m^3}{s^2 \cdot k}$$ and $$fs \frac{m}{k}$$ are positive, signs are selected so that scalar potential $$g$$
becomes negative in presence of positive density u in vicinity of point.
The equations are similar to electromagnetic equations expressed in potentials:
$$a' = - c^2 \cdot div(A)$$
$$A' = - E - grad(a)$$
$$E' = c^2 \cdot rot rot(A)$$
In stationary state, for example, during formation of gravitational fields by stable elementary particle
or single celestial body:
$$S = 0, G = 0, f = 0$$
$$F = - grad(g)$$
$$div grad(g) = fu \cdot \frac{u}{c^2} = 4 \cdot π \cdot g_0 \cdot ρ$$, according to Newton's potential
Hence we get at $$ρ = \frac{u}{c^2}: fu = 4 \cdot π \cdot g_0$$
The effect of gravitational fields on other fundamental ones can manifest itself as a curvature of space, and direct effect on velocity vector V, mentioned in this topic:
Hypothesis about the formation of particles from fields | Sciforums
With zero $$u$$ and $$S$$, following types of "pure" gravitational waves can exist:
1. Longitudinal potential-potential: $$g' = - c^2 \cdot div(G), G' = - grad(g)$$
2. Longitudinal with phase shift of 90 degrees: $$g' = - f, f' = - c^2 \cdot div grad(g)$$
3. Transverse: $$g' = - c^2 \cdot div(G), G' = - F - grad(g), F' = c^2 \cdot rot rot(G)$$
Transverse ones are probably easier to detect in experiments.

 

[James R]

[tex]\nabla[/tex] gives $$\nabla$$.

Hence:
[tex]\nabla \cdot \vec{v}[/tex] is $$\nabla\cdot \vec{v}=\text{div}(\vec{v})$$ etc.