metric of orthogonal infinitesimal forces

[AntonioLao]

as a follow-up to post#22 of gravity and light

[math]d_{m,n,l}=\sqrt{m^2+n^2+l^2} [/math]

where m,n, and l are the indices for the 3-orthogonal planes of each quandrant and the 3-plane with indices of (0,0,0) is defined as passing thru the point itself at (0,0,0), which is considered as the origin of a particular coordinate system.

[Guille]

Is gravity an orthogonal force?

is there any orthogonal force known?

what is the orthogonal force concept used for?

[AntonioLao]

Is gravity an orthogonal force?

orthogonal forces can be used to describe quantum gravity as what i'm trying to develop.

The continuation of this thread will subsequently describe what are orthogonal forces. According to me, it can be used to quantize spacetime coordinate systems.

[AntonioLao]

the constancy of these forces forms constant absolute accelerations at the infinitesimal region of spacetime. These accelerations vanish when the metric is exactly zero. To make the metric zero, a quantity of [math]c^2t^2[/math] must be subtracted from [math]d_{mnl}[/math]. The new expression is equivalent to the spacetime interval of Einstein's special theory of relativity.

[math]d_{mnl-t}=\sqrt{m^2+n^2+l^2-c^2t^2}[/math]

but [math]c^2=\mathbf{a}\cdot\mathbf{r}[/math] and [math]a_m r_m + a_n r_n + a_l r_l [/math] is not identically zero. Two of the indices can be zero, (1,0,0), (0,1,0),(0,0,1). For n=0 and l=0 then

[math] d_{m00}=\sqrt{m^2-ma_m t^2}[/math]

[AntonioLao]

to complete the structure of spacetime, the following metric is needed:

[math]d_{0,n,0}=sqrt{n^2-na_n t^2}[/math]

the two metrics formed a Hopf ring. A 3rd metric [math] d_{0,0,l} [/math] exists and by nature's random selections, the maximum permutation given as 3! is six forming two distinct topologies of the dynamic Hopf rings.

[AntonioLao]

because there can only be two distinct metrics ( [math]\psi_E [/math] and [math]\psi_B [/math] ), there should be only two fundamental orthogonal forces ([math]\phi_E [/math] and [math]\phi_B [/math] ). In optimization of min-max configuration, these are equivalent to the electric force and magnetic force of the vacuum. The nonzero values of magnetic permeability and electric permittivity are proofs that these forces do exist.

the vector and scalar products of these metrics and forces give the square of energy as the quantum of spacetime.

[math]E^2=\psi_E \times \phi_E \cdot \psi_B \times \phi_B [/math]

[AntonioLao]

the double actions integral of [math]E^2[/math] is given

[math]A^2 = \int\int E^2 dt dt [/math]

[AntonioLao]

if a quantum of mass can be defined then the double actions integral is equal to the square of Planck's constant of action or angular momentum and the square of the quantum of mass is defined as follows

[math] m^2 = \left( \frac{h}{ac} \right)^2 [/math]

where [math]h[/math] is Planck's constant, [math]a[/math] is Planck length, and [math]c [/math] is the speed of light in vacuum.

[Guille]

what's the formula for the planck length?

[AntonioLao]

the formula for Planck length is given at the following website.
http://scienceworld.wolfram.com/phys...nckLength.html