Add testing scripts
This commit is contained in:
Andre Heinecke
parent
ae28bdc658
commit
07a88e4502
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import numpy as np
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import matplotlib.pyplot as plt
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from scipy import constants as const
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# Core concept: Mass is information projected from higher dimensions
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# As velocity increases, projection angle changes, reducing observable mass
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# Constants
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c = const.c # speed of light
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hbar = const.hbar
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e = const.e
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k_e = 1/(4*np.pi*const.epsilon_0)
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alpha = const.alpha
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def classical_gamma(v):
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"""Classical Lorentz factor - mass increases"""
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return 1/np.sqrt(1 - (v/c)**2)
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def information_projection_factor(v, n_dims=4):
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"""
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Information projection from n_dims to (n_dims-1)
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As v→c, the object rotates out of our dimensional slice
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"""
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# Angle of rotation in higher-dimensional space
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theta = np.arcsin(v/c) # rotation angle out of our 3D slice
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# Projection factor: how much of the higher-D object we see
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projection = np.cos(theta)**(n_dims-3)
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return projection
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def observed_mass(m0, v, n_dims=4):
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"""Mass as seen in our 3D slice of higher-D spacetime"""
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gamma = classical_gamma(v)
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projection = information_projection_factor(v, n_dims)
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# Key insight: observed mass is rest mass times projection
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# divided by gamma (not multiplied!)
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return m0 * projection / gamma
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def information_density_2d(E, r):
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"""
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Information density on a 2D surface (from our ℏ² analysis)
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E: energy (information content)
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r: radius (information spread)
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"""
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# From our equation: γ = c²ℏ²/(ke²Er)
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# Information area = ℏ² (quantum of area-information)
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# Information density = E/(πr²) in natural units
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area = np.pi * r**2
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info_density = E / area
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# Relate to our gamma factor
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gamma = (c**2 * hbar**2) / (k_e * e**2 * E * r)
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return info_density, gamma
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# Visualization
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fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(12, 10))
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# 1. Mass vs velocity comparison
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velocities = np.linspace(0, 0.999*c, 1000)
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m0 = 1 # normalized rest mass
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classical_masses = m0 * classical_gamma(velocities)
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info_masses_3d = observed_mass(m0, velocities, n_dims=3)
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info_masses_4d = observed_mass(m0, velocities, n_dims=4)
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info_masses_5d = observed_mass(m0, velocities, n_dims=5)
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ax1.plot(velocities/c, classical_masses, 'r-', label='Classical (m₀γ)', linewidth=2)
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ax1.plot(velocities/c, info_masses_3d, 'b--', label='Info projection (3D→2D)', linewidth=2)
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ax1.plot(velocities/c, info_masses_4d, 'g--', label='Info projection (4D→3D)', linewidth=2)
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ax1.plot(velocities/c, info_masses_5d, 'm--', label='Info projection (5D→4D)', linewidth=2)
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ax1.set_xlabel('v/c')
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ax1.set_ylabel('Observed mass / m₀')
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ax1.set_title('Classical vs Information Projection Theory')
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ax1.legend()
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ax1.grid(True, alpha=0.3)
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ax1.set_ylim(0, 5)
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# 2. Projection factor visualization
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projections_3d = information_projection_factor(velocities, n_dims=3)
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projections_4d = information_projection_factor(velocities, n_dims=4)
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projections_5d = information_projection_factor(velocities, n_dims=5)
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ax2.plot(velocities/c, projections_3d, 'b-', label='3D→2D', linewidth=2)
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ax2.plot(velocities/c, projections_4d, 'g-', label='4D→3D', linewidth=2)
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ax2.plot(velocities/c, projections_5d, 'm-', label='5D→4D', linewidth=2)
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ax2.set_xlabel('v/c')
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ax2.set_ylabel('Projection factor')
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ax2.set_title('Information Shadow vs Velocity')
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ax2.legend()
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ax2.grid(True, alpha=0.3)
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# 3. Connection to quantum time dilation
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# Show how projection relates to our γ factor
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energies = np.logspace(-3, 6, 100) * const.eV # meV to MeV
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r_bohr = 0.529e-10 # Bohr radius
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info_densities = []
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gammas = []
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for E in energies:
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density, gamma = information_density_2d(E, r_bohr)
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info_densities.append(density)
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gammas.append(gamma)
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ax3.loglog(energies/const.eV, gammas, 'k-', linewidth=2)
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ax3.axhline(y=1, color='r', linestyle='--', label='γ = 1 (classical limit)')
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ax3.axvline(x=511e3, color='b', linestyle='--', label='Electron rest mass')
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ax3.set_xlabel('Energy (eV)')
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ax3.set_ylabel('γ (time dilation factor)')
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ax3.set_title('Quantum Time Dilation as Information Spreading')
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ax3.legend()
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ax3.grid(True, alpha=0.3)
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# 4. 2D plane visualization
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# Two observers running orthogonally on a plane
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t_points = np.linspace(0, 1, 100)
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v_max = 0.9 * c
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# Observer trajectories
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x1 = v_max * t_points
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y1 = np.zeros_like(t_points)
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x2 = np.zeros_like(t_points)
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y2 = v_max * t_points
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# Their observed masses
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m1 = observed_mass(m0, v_max * t_points, n_dims=4)
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m2 = observed_mass(m0, v_max * t_points, n_dims=4)
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ax4.scatter(x1[::5]/c, y1[::5], s=100*m1[::5], c=t_points[::5],
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cmap='Reds', alpha=0.6, label='Observer 1')
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ax4.scatter(x2[::5], y2[::5]/c, s=100*m2[::5], c=t_points[::5],
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cmap='Blues', alpha=0.6, label='Observer 2')
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ax4.arrow(0, 0, 0.5, 0, head_width=0.05, head_length=0.05, fc='red', ec='red')
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ax4.arrow(0, 0, 0, 0.5, head_width=0.05, head_length=0.05, fc='blue', ec='blue')
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ax4.set_xlabel('x position (light-seconds)')
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ax4.set_ylabel('y position (light-seconds)')
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ax4.set_title('Orthogonal Observers: Size = Observed Mass')
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ax4.set_xlim(-0.1, 1)
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ax4.set_ylim(-0.1, 1)
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ax4.legend()
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ax4.grid(True, alpha=0.3)
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plt.tight_layout()
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plt.savefig('information_projection_theory.png', dpi=150)
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# Key calculations
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print("=== INFORMATION PROJECTION THEORY ===")
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print("\nAt v = 0.9c:")
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v_test = 0.9 * c
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gamma_classical = classical_gamma(v_test)
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proj_4d = information_projection_factor(v_test, n_dims=4)
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m_observed = observed_mass(m0, v_test, n_dims=4)
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print(f"Classical γ = {gamma_classical:.3f}")
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print(f"Classical mass increase: m = {gamma_classical:.3f} m₀")
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print(f"Information projection (4D→3D): {proj_4d:.3f}")
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print(f"Our theory mass: m = {m_observed:.3f} m₀")
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print(f"Mass DECREASES by factor of {1/m_observed:.3f}!")
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# Connection to E=mc²
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print("\n=== E=mc² AS INFORMATION ON 2D SURFACE ===")
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print("If mass is information shadow, then E=mc² means:")
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print("Energy = (Information content) × (Maximum info processing rate)²")
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print("Where c² is the speed of information propagation squared")
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print("\nThis explains why E ∝ c²:")
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print("- c: speed of 1D information (along a line)")
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print("- c²: speed of 2D information (on a surface)")
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print("- Energy spreads as 2D information on spacetime surfaces!")
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# Superconductivity connection
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print("\n=== SUPERCONDUCTIVITY CONNECTION ===")
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E_cooper = 1e-3 * const.eV # 1 meV Cooper pair binding
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r_cooper = 1000e-10 # 1000 Å coherence length
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_, gamma_cooper = information_density_2d(E_cooper, r_cooper)
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print(f"Cooper pair: E = 1 meV, r = 1000 Å")
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print(f"γ = {gamma_cooper:.2e}")
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print("Electrons are 'frozen' in higher dimensions!")
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print("No projection into time dimension = no resistance!")
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# Mathematical framework
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print("\n=== MATHEMATICAL FRAMEWORK ===")
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print("1. Mass is information projected from n-dimensions to (n-1)")
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print("2. Projection factor: P(v) = cos^(n-3)(arcsin(v/c))")
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print("3. Observed mass: m_obs = m₀ × P(v) / γ(v)")
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print("4. At v→c: P→0, so m_obs→0 (not ∞!)")
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print("5. Information cannot be destroyed, only rotated out of view")
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plt.show()
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import numpy as np
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import scipy.constants as const
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from scipy.optimize import fsolve
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# Physical constants in SI units
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c = const.c # speed of light: 299792458 m/s
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e = const.e # elementary charge: 1.602176634e-19 C
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k = 1 / (4 * np.pi * const.epsilon_0) # Coulomb constant: 8.9875517923e9 N⋅m²/C²
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hbar = const.hbar # reduced Planck constant: 1.054571817e-34 J⋅s
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m_e = const.m_e # electron mass: 9.1093837015e-31 kg
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m_p = const.m_p # proton mass: 1.67262192369e-27 kg
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alpha = const.alpha # fine structure constant: ~1/137
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print("=== DIMENSIONAL ANALYSIS ===")
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print(f"ℏ = {hbar:.6e} J⋅s = kg⋅m²/s")
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print(f"ℏ² = {hbar**2:.6e} J²⋅s² = kg²⋅m⁴/s²")
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print(f"Units of ℏ²: [M²L⁴T⁻²]")
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print(f"\nInteresting: L⁴ = (L²)² - suggesting 2D area squared!")
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print(f"So ℏ² relates mass², area², and time² fundamentally")
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print("\n=== OUR EQUATION: c² = ke²γEr/(ℏ²) ===")
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print("Rearranged forms:")
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print("γ = c²ℏ²/(ke²Er)")
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print("E = c²ℏ²/(ke²γr)")
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print("r = c²ℏ²/(ke²γE)")
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# Case 1: Hydrogen-antihydrogen annihilation
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print("\n=== CASE 1: H + anti-H annihilation ===")
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E_annihilation = 2 * (m_e + m_p) * c**2 # Total rest mass energy
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r_bohr = const.physical_constants['Bohr radius'][0] # 5.29e-11 m
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# Solve for gamma at Bohr radius
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gamma_annihilation = (c**2 * hbar**2) / (k * e**2 * E_annihilation * r_bohr)
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v_from_gamma = c * np.sqrt(1 - 1/gamma_annihilation**2) if gamma_annihilation > 1 else 0
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print(f"Total annihilation energy: {E_annihilation:.6e} J = {E_annihilation/const.eV:.3f} eV")
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print(f"At Bohr radius r = {r_bohr:.3e} m:")
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print(f" γ = {gamma_annihilation:.6f}")
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print(f" Implied velocity: {v_from_gamma/c:.6f}c")
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# Case 2: Ground state hydrogen (binding energy)
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print("\n=== CASE 2: Ground state hydrogen ===")
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E_binding = 13.6 * const.eV # Hydrogen ionization energy
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gamma_ground = (c**2 * hbar**2) / (k * e**2 * E_binding * r_bohr)
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print(f"Binding energy: {E_binding:.6e} J = 13.6 eV")
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print(f"γ = {gamma_ground:.3e}")
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print(f"This huge γ suggests we're probing quantum regime!")
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# Case 3: What if we set γ = 1 (non-relativistic)?
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print("\n=== CASE 3: Non-relativistic case (γ = 1) ===")
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gamma_nr = 1
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E_nr = (c**2 * hbar**2) / (k * e**2 * gamma_nr * r_bohr)
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print(f"Energy when γ = 1: {E_nr:.6e} J = {E_nr/const.eV:.3f} eV")
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print(f"This is {E_nr/E_binding:.1f}× the actual binding energy")
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# Explore the meaning of the equation parts
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print("\n=== EQUATION COMPONENTS ===")
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quantum_term = hbar**2
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em_term = k * e**2
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print(f"Quantum term (ℏ²): {quantum_term:.6e} J²⋅s²")
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print(f"EM term (ke²): {em_term:.6e} J⋅m")
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print(f"Ratio c²ℏ²/(ke²) = {(c**2 * quantum_term)/em_term:.6e} J⋅m")
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print(f"This has units of [Energy × Length]")
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# The fine structure connection
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print("\n=== FINE STRUCTURE CONSTANT CONNECTION ===")
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# α = ke²/(ℏc) in SI units
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calculated_alpha = (k * e**2) / (hbar * c)
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print(f"α calculated: {calculated_alpha:.10f}")
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print(f"α known: {alpha:.10f}")
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print(f"Our equation can be rewritten using α:")
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print(f"γ = c/(αEr/ℏ)")
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# Exploring unit independence
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print("\n=== UNIT INDEPENDENCE CHECK ===")
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# In natural units where c = ℏ = 1
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print("In natural units (c = ℏ = 1):")
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print("γ = 1/(αEr)")
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print("This shows γ depends only on:")
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print(" - The fine structure constant α (dimensionless)")
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print(" - Energy × distance (action units)")
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# What this means for spacetime
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print("\n=== SPACETIME INTERPRETATION ===")
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print("Since γ = dt/dτ (time dilation factor):")
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print("Our equation suggests coordinate time / proper time = c²ℏ²/(ke²Er)")
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print("\nThis means time dilation emerges from the balance between:")
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print(" - Quantum action (ℏ²) pushing toward uncertainty")
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print(" - EM binding (ke²Er) pulling toward classical behavior")
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print("\nAt high energies or small distances, γ becomes huge,")
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print("suggesting extreme time dilation in the quantum regime!")
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# Function to explore different scenarios
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def explore_scenario(E, r, label):
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gamma = (c**2 * hbar**2) / (k * e**2 * E * r)
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print(f"\n{label}:")
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print(f" E = {E/const.eV:.3e} eV, r = {r:.3e} m")
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print(f" γ = {gamma:.3e}")
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if gamma > 1 and gamma < 1e6:
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v = c * np.sqrt(1 - 1/gamma**2)
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print(f" v/c = {v/c:.6f}")
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# Explore various energy/distance scales
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print("\n=== EXPLORING DIFFERENT SCALES ===")
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explore_scenario(1*const.eV, 1e-9, "1 eV at 1 nm")
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explore_scenario(1*const.eV*1000, 1e-12, "1 keV at 1 pm")
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explore_scenario(511*const.eV*1000, const.physical_constants['classical electron radius'][0],
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"Electron rest mass at classical radius")
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explore_scenario(const.m_e * c**2, const.physical_constants['Compton wavelength'][0]/(2*np.pi),
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"Electron at reduced Compton wavelength")
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import math
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from scipy import constants as const
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# Konstanten aus scipy.constants
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c = const.c # Lichtgeschwindigkeit in m/s
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hbar= const.hbar # ℏ in J·s
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e = const.e # Elementarladung in Coulomb
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k_e = 1/(4*math.pi*const.epsilon_0) # Coulomb-Konstante in N·m²/C²
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def gamma_quantum_time(E_joule, r_meter):
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"""Berechnet γ = c^2 ℏ^2 / (k e^2 E r)."""
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return c**2 * hbar**2 / (k_e * e**2 * E_joule * r_meter)
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# Beispielszenarien (E in eV, r in m):
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scenarios = [
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("Wasserstoff Grundzustand", 13.6, 0.529e-10), # E=13,6 eV, r = 0,529 Å
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("Wasserstoff angeregt (n=2)", 3.4, 2.116e-10), # E≈3,4 eV, r≈2,116 Å (n=2)
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("Chemische Bindung (~C–H)", 4.5, 1.10e-10), # E≈4-5 eV, r≈1,1 Å
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("Thermische Energie (300 K)", 0.025, 5.0e-10), # E≈0,025 eV, r≈5 Å (Raumtemperatur, Atomgitter)
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("Kernbindung (typisch)", 8.0e6, 5.0e-15), # E≈8 MeV, r≈5 fm (Bindung in mittelschwerem Kern)
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("Starke Kernkraft (extrem)", 2.0e8, 1.0e-15), # E≈200 MeV, r=1 fm (starke Bindung im Kern)
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("H–Anti-H Annihilation", 1.88e9, 0.529e-10), # E≈1,88 GeV, r=0,529 Å (H mit Anti-H Abstand ~ Bohr)
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("Kritischer Punkt (γ=1)", 5.11e5, 0.529e-10) # E=511 keV, r=0,529 Å (Elektron-Ruheenergie)
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]
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print(f"{'Szenario':30} | {'Energie E':>15} | {'Abstand r':>12} | γ (berechnet)")
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print("-"*75)
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for name, E_eV, r in scenarios:
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E_J = E_eV * const.e # eV -> Joule
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gamma_val = gamma_quantum_time(E_J, r)
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print(f"{name:30} | {E_eV:9.2e} eV | {r:8.2e} m | {gamma_val:9.3e}")
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