supernova8.py
Assumptions:
- s = seconds
- m = meters
- M = mass
- C = k · M
- m = r
- τG = Ω (situationally)
Force Law:
F = (Ω · C²) / (m · s)
Substitute:
F = (Ω · k² · M²) / (r · s)
Emergent G:
G = (Ω · k² · r) / s
Therefore:
F = G · M² / r²
G is proportional to r/s
So gravity’s strength depends on distance and time scale, consistent with a dynamic, field-based universe where coupling constants emerge from deeper structure.
from sympy import symbols, Eq, solve, simplify
# Define symbols
Omega, k, M, r, s, G, F = symbols('Omega k M r s G F')
# Define charge as proportional to mass
C = k * M
# Define force law
F1 = (Omega * C**2) / (r * s) # From: F = (Ω · C²) / (r · s)
# Define emergent gravitational constant
G_expr = (Omega * k**2 * r) / s
# Define Newtonian form: F = G·M² / r²
F2 = (G_expr * M**2) / r**2
# Simplify and compare
difference = simplify(F1 - F2)
print("Force from field tension model:\nF1 =", F1)
print("\nForce from Newtonian with emergent G:\nF2 =", F2)
print("\nSimplified difference (should be 0):\n", difference)
OUTPUT:
Force from field tension model:
F1 = Omega*k**2*M**2/(r*s)
Force from Newtonian with emergent G:
F2 = Omega*k**2*M**2/(r*s)
Simplified difference (should be 0):
0
from sympy import symbols, Eq, simplify, Function
# ------------------------------------------
# Define Fundamental Symbols
# ------------------------------------------
# Units:
# s = time (seconds)
# r = radial distance (meters)
# M = mass
# Ω = field tension (Ohmic tension, e.g., N·s/m)
# k = proportionality constant between mass and charge
# C = charge (emergent from mass)
# G = emergent gravitational coupling
# F = force
# ------------------------------------------
# Declare symbolic variables
# ------------------------------------------
M, r, s = symbols('M r s', real=True, positive=True) # mass, radius, seconds
k, Omega = symbols('k Omega', real=True, positive=True) # constants
G = symbols('G', real=True) # gravitational coupling
F = symbols('F', real=True) # force
# ------------------------------------------
# Define Core Relationships
# ------------------------------------------
# Assumption 1: Charge is proportional to mass
C = k * M # C ≡ k · M
# Assumption 2: Gravitational field tension is Ohmic-like
# τ_G = Ω
# Step 1: Generalized force law using field tension
F_from_tension = (Omega * C**2) / (r * s) # F = (Ω · C²) / (r · s)
# Step 2: Define emergent gravitational constant
G_emergent = (Omega * k**2 * r) / s # G = (Ω · k² · r) / s
# Step 3: Newtonian form using emergent G
F_newtonian = (G_emergent * M**2) / r**2 # F = G · M² / r²
# ------------------------------------------
# Validate Equivalence
# ------------------------------------------
difference = simplify(F_from_tension - F_newtonian)
# ------------------------------------------
# Output and Verification
# ------------------------------------------
def print_summary():
print("\n--- Emergent Gravity Framework ---")
print(f"Charge: C = {C}")
print(f"Force (tension): F = {F_from_tension}")
print(f"Emergent G: G = {G_emergent}")
print(f"Force (Newton): F = {F_newtonian}")
print(f"Difference: Δ = {difference} (should be 0)")
print("\nConclusion: Newtonian gravity is recovered as a special case.\n")
# Call to display the summary if this file is executed directly
if __name__ == "__main__":
print_summary()
OUTPUT:
--- Emergent Gravity Framework ---
Charge: C = k*M
Force (tension): F = Omega*k**2*M**2/(r*s)
Emergent G: G = Omega*k**2*r/s
Force (Newton): F = Omega*k**2*M**2/(r*s)
Difference: Δ = 0 (should be 0)
Conclusion: Newtonian gravity is recovered as a special case.
This demonstrates that gravity emerges from field tension (Ω) when charge is proportional to mass, and time and distance scales are respected.
This isn’t an end-all be all, rather, it is a departure from something which was thought to be foundational, being disproven as a universal constant. Kindly extrapolate.
