86 lines
2.4 KiB
Python
86 lines
2.4 KiB
Python
#!/usr/bin/env python3
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"""
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test_relativistic_quarks.py - WITH PROPER LORENTZ FACTORS
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Critical fix: Include relativistic effects properly!
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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_with_relativity(name, mass_mev, radius_fm, alpha_s):
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"""Properly include relativistic effects"""
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# Constants
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hbar = const.hbar
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c = const.c
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e = const.e
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mev_to_kg = e * 1e6 / c**2
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# Convert units
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m0 = mass_mev * mev_to_kg # REST mass
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r = radius_fm * 1e-15
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CF = 4.0/3.0
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# This gets tricky - we need to solve self-consistently
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# because v depends on s, but γ depends on v
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# Start with non-relativistic estimate
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s_squared_nr = CF * alpha_s * m0 * c * r / hbar
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s_nr = np.sqrt(s_squared_nr)
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# Iterate to find self-consistent solution
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s = s_nr
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for i in range(10):
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v = s * hbar / (m0 * r) # Using rest mass
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beta = v / c
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if beta >= 1.0:
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print(f"ERROR: v > c for {name}!")
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beta = 0.99
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gamma = 1.0 / np.sqrt(1 - beta**2)
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# Recalculate s with relativistic correction
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# But how exactly? This is the key question!
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s_new = np.sqrt(CF * alpha_s * m0 * c * r * gamma / hbar)
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if abs(s_new - s) < 0.001:
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break
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s = s_new
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# Final forces with proper γ
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F_geometric = (hbar**2 * s**2) / (gamma * m0 * r**3)
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sigma = 0.18 * (e * 1e9 / 1e-15)
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F_total = F_geometric + sigma
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print(f"\n{name}:")
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print(f" Rest mass: {mass_mev} MeV/c²")
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print(f" Velocity: v = {v/c:.3f}c")
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print(f" Lorentz γ = {gamma:.3f}")
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print(f" s factor = {s:.3f}")
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print(f" F_geometric = {F_geometric:.2e} N")
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print(f" F_total = {F_total:.2e} N")
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return s, gamma, F_total
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def main():
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print("RELATIVISTIC QUARK ANALYSIS - PROPER LORENTZ FACTORS")
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print("="*60)
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systems = [
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("Pion (qq̄)", 140, 1.0, 0.5),
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("Light quark", 336, 0.875, 0.4),
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("J/ψ (cc̄)", 3097, 0.2, 0.3),
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]
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for system in systems:
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analyze_with_relativity(*system)
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print("\n" + "="*60)
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print("CRITICAL INSIGHT:")
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print("At v ~ c, relativistic effects DOMINATE!")
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print("This could explain why different systems need different s")
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print("Maybe s encodes relativistic dynamics?")
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if __name__ == "__main__":
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main()
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