The Derivation of the Laws of Nature

I will be short and sweet.

This is the 4D Diagram used to derive the Laws:

The horizontal lines are actually 3D hyperplanes. This means that those vectors have three components…:) and represent a direction within our 3D space. The distance traversed vertically is the distance traversed by our universe (traveling at the speed of light perpendicularly to our 3D hypersurface - here represented locally as a hyperplane).

The time for that to happen is R0/c, where R0 is the initial distance between two bodies or charges. Notice that the final dependence will be on r_{23} or the position where the body 1 will be after the time R0/c.

This is what bothered Lagrange and everyone with a Brain about Gravity. The force depends upon the CURRENT INSTANTANEOUS POSITION. This has been used to justify considering Gravity an instantaneous force or a non-local force. Of course, that is wrong.

Later, I will recover the Radial Law of Gravitation. Gravitation and Electromagnetism are Lorentz Forces. That said, anything within a galaxy can be approximated to be in the Absolute Reference Frame (ARF). To recover the Radial Gravitation Formula, one just has to make v_2 = 0 (consider the reference frame to be on the Sun or on the center of mass).

Notice that when v_2=0, r_{43} becomes v1*R0/c - R0

That is exactly the instantaneous position of body 1. In other words, Lagrange and everyone who understands physics was always bothered by the dependence on instantaneously correct distances. Notice that the dependence is actually upon r_23, but if v2=0, then r_23=r_43

Here are them:

HU FORCE EM

HU GRAVITATIONAL FORCE

Notice that the two values for N are different. For Electromagnetism, N is the number of electrons in one Coulomb, and for Gravity, it is the number of hydrogen atoms in one kilogram. ?? is 81489.699.

So, Gravitation is also a Lorentz Force, one that is always attractive. Notice that because of its dependence upon the 4D radius of the Universe, it is also epoch-dependent.

WHAT ABOUT THE GRAVITATION FORCE BEING RADIAL?

That is due to placing the Absolute Reference Frame on the Sun or its center of mass. Under those conditions, v2 =0.

Notice that the dependence is upon “instantaneous distance,” as Gravitation has traveled from the Sun to the planets while the planets traversed some distance v1*R0 /c. The reason is that gravitation is carried by the dilaton field, which is always on. So, the gravitation planets are sensing right now, which was created R0/c seconds before.

This puzzled Laplace, who considered that Gravitation speed should be instantaneous.

Where one used the CMB-based Milky Way velocity of 0.2% c for calculating ?.

NOTICE THAT THIS IS THE NATURAL FREQUENCY OF SPACE DEFORMATIONS AND THE SOLUTION TO MANKIND PROBLEMS.

HEY… WHERE IS THE DERIVATION?

import sympy as sp

def cleanForce(Force):

???Force_latex = sp.latex(Force)

???Force_latex = Force_latex.replace("V_{1 hat}", "\hat{V}_1")

???Force_latex = Force_latex.replace("V_{2 hat}", "\hat{V}_2")

???Force_latex = Force_latex.replace("R_{0 hat}", "\hat{R}_0")

???Force_latex = Force_latex.replace("r_{hat}", "\hat{r}")

???# Force_latex = Force_latex.replace("+ 0 \hat{r}", "")

???Force_latex = Force_latex.replace("^{T}", "")

???print(Force_latex)

# Define symbols

pi, m_0, x, Q, lambda1, R0, c, N, v1, v2, gamma_v1, gamma_v2, P1, P2, delta, R_4D, P1_hat, P2_hat, G0, kg, h? = sp.symbols(

???'pi m_0 x Q lambda1 R0 c N v1 v2 gamma_v1 gamma_v2 P1 P2? delta R_4D P1_hat P2_hat G0 kg h',

???real=True, positive=True)

alpha = sp.symbols('alpha', real=True, positive=True)

# Define MatrixSymbols for arbitrary unit vectors

V1_hat = sp.MatrixSymbol('V1_hat', 3, 1)? # 3x1 Matrix Symbol for Unit vector along V1

V2_hat = sp.MatrixSymbol('V2_hat', 3, 1)? # 3x1 Matrix Symbol for Unit vector along V2

R0_hat = sp.MatrixSymbol('R0_hat', 3, 1)? # 3x1 Matrix Symbol for Unit vector along R0

r_hat = sp.MatrixSymbol('r_hat', 3, 1)? ? # 3x1 Matrix Symbol for general unit vector for position adjustments

# Identity matrix for space dimension

One = sp.MatrixSymbol('One', 3, 3) # Correct usage of Identity Matrix

# Velocity vectors

V1 = v1 * V1_hat

V2 = v2 * V2_hat

R0_vect = R0 * R0_hat

# Position vectors

r1 = V1 R0 / c + x r_hat

r2 = V1 R0 / c - R0_vect + x r_hat

# Projection matrices and Lorentz transformation matrices

# 1+(GAMMA-1)P = (1-P) + GAMMA*P

# P IS THE PROJECTOR TO THE V1 AND V2 DIRECTIONS

M1 = One + (gamma_v1 - 1) V1 V1.T / (v1**2)

M2 = One + (gamma_v2 - 1) V2 V2.T / (v2**2)

# Wave vectors

k1 = (2 pi / lambda1) r1.T* M1? / P1

k2 = (2 pi / lambda1) r2.T * M2 / P2

# P1 is the modulus of r1 or |r1| or |v1 R0/c|

# P2 is the modulus of r2 or |r2| or R0*sqrt (v1**2/c**2 + 1 - 2 dr/dt)

# Fields definitions

k1path = ( k1 * r1 )

Phi1 = sp.cos(k1path)

first_derivative = sp.diff(k1path, x)

second_derivative = sp.diff(first_derivative, x)

# Took the second derivative to extract the coefficient of x

k1path_diff = second_derivative

k1path=k1path.subs(x,0)

k1path

# Derivatives - Here we used diff(cos(k.x) = -ksin(kx) = -k**2x

Phi1_diff = k1path.T*k1path_diff

Phi1_diff

cleanForce(Phi1_diff)

k2path = ( k2 * r2 )

k2path =Q k2path/(2pi)

k2path_diff = sp.diff(k2path,x,2)

Phi2 = N / (1 + k2path[0].subs(x,0))

# Derivatives

Phi2_diff = -N k2path_diff / (k2path.subs(x,0))*2

Phi2_diff

cleanForce(Phi2_diff)

# Display results

dr1dr = P2_hat

x_result = Phi2_diff/Phi1_diff

Force_EM = m_0*c**2*(1-v1**2/c**2)*x_result/lambda1**2

Force_EM = Force_EM.subs(Q, 1/(2*pi*alpha))

Force_EM = Force_EM.subs(x,0).simplify()*dr1dr

Force_EM

# Display results

dr1dr = P2_hat

x_result = Phi2_diff/Phi1_diff

Force_G = m_0*c**2*(1-v1**2/c**2)*delta x_result/lambda1/R_4D(N/kg**2)

Force_G = Force_G.subs(Q, 1/(2*pi*alpha))

Force_G = Force_G.subs(x,0).simplify()*dr1dr

Force_G

# Display results

dr1dr = P2_hat

x_result = Phi2_diff/Phi1_diff

Force_G = m_0*c**2*(1-v1**2/c**2)*delta x_result/lambda1/R_4D(N/kg**2)

# Display results

dr1dr = P2_hat

x_result = Phi2_diff/Phi1_diff

Force_G = m_0*c**2*(1-v1**2/c**2)*delta x_result/lambda1/R_4D(N/kg**2)

Force_G = Force_G.subs(Q, 1/(2*pi*alpha))

Force_G = Force_G.subs(x,0).simplify()*dr1dr

Force_G

Force_G = Force_G.subs(gamma_v2,1).subs(delta, G0*(2*pi*(kg**2)*R_4D)/(N**2*m_0*c**2*alpha*lambda1**2))

Force_G = Force_G.simplify()

print(Force_G)

IN SUMMARY

I provided the derivation of the laws of nature and the sympy code to check the derivation.

The Law of Gravitation passed all tests and provides better prediction than General Relativity:

where you can see where Einstein screwed up (Mercury). His formula is not good enough for Mercury Perihelion Precession Rate Calculation. Everything else in Physics has been corrected.

https://www.researchgate.net/publication/385424751_THE_HYPERGEOMETRICAL_UNIVERSE_THEORY