spin_paper/archive/experimental-scripts/angular_momentum.py

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#!/usr/bin/env python3
"""
rethinking_angular_momentum.py
What does L really mean in our formulas?
Maybe it's not spin but something else...
"""
import numpy as np
import scipy.constants as const
def analyze_angular_momentum_meaning():
"""What is L in our successful formulas?"""
print("WHAT IS L IN OUR FORMULAS?")
print("="*60)
hbar = const.hbar
print("ATOMIC SUCCESS:")
print(" Used L = ℏ (NOT ℏ/2)")
print(" This is ORBITAL angular momentum")
print(" Electron orbits with L = ℏ")
print(" Its spin is separate (ℏ/2)")
print("\nNUCLEAR ATTEMPT:")
print(" Used L = ℏ/2 (proton spin)")
print(" Gave v = 0.3c - too fast!")
print(" Maybe we need different L?")
print("\nKEY QUESTION:")
print(" What if L in F = L²/(γmr³) represents")
print(" 'quantum of action for that scale'?")
print(" Not necessarily spin!")
# What if nuclear scale has different quantum?
print("\nPOSSIBILITIES:")
print("1. Nuclear L might be ℏ (not ℏ/2)")
print("2. Nuclear L might be related to pion mass")
print("3. Nuclear L might emerge from QCD scale")
# Test with L = ℏ for nucleus
r_proton = 0.875e-15
m_proton = const.m_p
# If L = ℏ (not ℏ/2)
I = (2/5) * m_proton * r_proton**2
omega = hbar / I # Using full ℏ
v_surface = omega * r_proton
print(f"\nIf proton has L = ℏ (not ℏ/2):")
print(f" Surface velocity: {v_surface/const.c:.4f}c")
print(f" More reasonable than 0.3c!")
def explore_scale_dependent_quantum():
"""What if each scale has its own action quantum?"""
print("\n\nSCALE-DEPENDENT ACTION QUANTUM")
print("="*60)
hbar = const.hbar
c = const.c
# Atomic scale: ℏ works perfectly
print("ATOMIC SCALE:")
print(f" Action quantum: ℏ = {hbar:.3e} J·s")
print(f" Length scale: Bohr radius ~ 10^-10 m")
print(f" Success: Perfect!")
# Nuclear scale: what should it be?
# Maybe related to QCD scale?
Lambda_QCD = 200e6 * const.e / c**2 # ~200 MeV
r_QCD = hbar / (Lambda_QCD * c)
print("\nNUCLEAR SCALE:")
print(f" QCD length: {r_QCD*1e15:.3f} fm")
print(f" Maybe action quantum scales with size?")
print(f" L_nuclear = ℏ × (r_nuclear/r_Bohr)?")
# This is getting speculative...
print("\nTHE REAL QUESTION:")
print(" Why does L = ℏ work for atoms?")
print(" What makes this the 'right' quantum?")
print(" Is it universal or scale-dependent?")
def main():
analyze_angular_momentum_meaning()
explore_scale_dependent_quantum()
print("\n" + "="*70)
print("BREAKTHROUGH REALIZATION:")
print("L in our formula might not be spin!")
print("It might be the 'quantum of circulation'")
print("Different at each scale of physics!")
if __name__ == "__main__":
main()