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