#!/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()