Wanted to get my work I did today posted just in case.
This rescales a bunch of human choosen units into natural units I found inside the constants.
import math
# --- Define Constants with SI values and units as lists of (unit, power) ---
constants = {
"speed_of_light_c": {
"value": 299792458,
"units": [("m", 1), ("s", -1)], # m/s
"symbol": "c"
},
"1 Hz": {
"value": 1,
"units": [("Hz", 1) ],
"symbol": "Hz"
},
"planck_constant_h": {
"value": 6.62607015e-34,
"units": [("kg", 1), ("m", 2), ("s", -1)], # J*s = kg*m^2/s^2 * s = kg*m^2/s
"symbol": "h"
},
"boltzmann_constant_k": {
"value": 1.380649e-23,
"units": [("kg", 1), ("m", 2), ("s", -2), ("K", -1)], # J/K = kg*m^2/s^2 / K = kg*m^2/s^2/K
"symbol": "k"
},
"gravitational_constant_G": {
"value": 6.67430e-11,
"units": [ ("m", 3), ("kg", -1), ("s", -2)], # N*m^2/kg^2 = (kg*m/s^2)*m^2/kg^2 = kg^-1*m^3*s^-2
"symbol": "G"
},
"coulombs_constant_k_e": {
"value": 8.987551787e9,
"units": [("kg", 1), ("m", 3), ("s", -2), ("C", -2)], # N*m^2/C^2 = kg*m^3/(s^2*C^2)
"symbol": "k_e"
},
#Wien wavelength displacement law constant 2.897 771 955... e-3
"Wien wl d law": {
"value": 2.897771955e-3,
"units": [("m", 1), ("K", 1) ],
"symbol": "?"
},
#neutron Compton wavelength 1.319 590 905 81 e-15 0.000 000 000 75 e-15 m
"neutron Compton wavelength": {
"value": 1.31959090581e-15,
"units": [("m", 1) ],
"symbol": "?"
},
"elementary_charge_e": {
"value": 1.602176634e-19,
"units": [("C", 1)], # Coulomb is treated as a base unit here for simplicity
"symbol": "e"
},
"avogadro_constant_Na": {
"value": 6.02214076e+23,
"units": [("mol", -1)], # 1/mol is mol^-1
"symbol": "Na"
},
"electron_mass_me": {
"value": 9.1093837015e-31,
"units": [("kg", 1)],
"symbol": "me"
},
"proton_mass_mp": {
"value": 1.67262192369e-27,
"units": [("kg", 1)],
"symbol": "mp"
},
"neutron_mass_mn": {
"value": 1.67492749804e-27,
"units": [("kg", 1)],
"symbol": "mn"
},
"Angstrom star": {
"value": 1.00001495e-10,
"units": [("m", 1)],
"symbol": "?"
},
"vacuum_permittivity_epsilon0": {
"value": 8.8541878128e-12,
"units": [("C", 2), ("kg", -1), ("m", -3), ("s", 2)], # F/m = C^2/J / m = C^2 / (kg*m^2/s^2) / m = C^2*s^2 / (kg*m^3)
"symbol": "ε₀"
},
"vacuum_permeability_mu0": {
"value": 1.25663706212e-6,
"units": [("kg", 1), ("m", 1), ("s", -2), ("C", -2)], # H/m = V*s/A / m = (J/C)*s/(C/s) / m = J*s^2/C^2 / m = (kg*m^2/s^2)*s^2/C^2 / m = kg*m/C^2
"symbol": "μ₀"
},
"rydberg_constant_Rydberg": {
"value": 10973731.568160,
"units": [("m", -1)], # 1/m is m^-1
"symbol": "Rydberg"
},
"bohr_radius_a0": {
"value": 5.29177210903e-11,
"units": [("m", 1)],
"symbol": "a₀"
},
"hartree_energy_Eh": {
"value": 4.359744722071e-18,
"units": [("kg", 1), ("m", 2), ("s", -2)], # J = kg*m^2/s^2
"symbol": "E_h" # E_h
},
"electron_radius_re": {
"value": 2.8179403262e-15,
"units": [("m", 1)],
"symbol": "r_e" # r_e
},
"klitzing_constant_Rk": {
"value": 25812.80745,
"units": [("kg", 1), ("m", 2), ("s", -3), ("C", -2)], # Ohm = kg*m^2/(s^3*A^2) = kg*m^2/(s^3*C^2/s^2) = kg*m^2/(s*C^2)
"symbol": "R_K" # R_K
},
"weber_per_kelvin": { # Example of a derived unit combination, not a fundamental constant, but illustrative
"value": 1.0, # Arbitrary value for demonstration
"units": [("kg", 1), ("m", 2), ("s", -1), ("C", -1), ("K", -1)], # Weber per Kelvin, Wb/K = kg*m^2/(s^2*A) / K = kg*m^2/(s^2*C/s) / K = kg*m^2/(s*C*K)
#"units": [("Wb", 1), ("K", -1)], # Weber per Kelvin, Wb/K = kg*m^2/(s^2*A) / K = kg*m^2/(s^2*C/s) / K = kg*m^2/(s*C*K)
"symbol": "Wb/K"
},
"faraday_constant_F": {
"value": 96485.33212,
"units": [("mol", -1), ("C", 1)], # C/mol
"symbol": "F"
},
"stefan_boltzmann_constant_sigma": {
"value": 5.670374419e-8,
"units": [("kg", 1), ("s", -3), ("K", -4)], # W/(m^2*K^4) = (J/s)/(m^2*K^4) = (kg*m^2/s^2)/s / (m^2*K^4) = kg/(s^3*K^4)
"symbol": "σ"
},
"magnetic_flux_quantum_Phi0": {
"value": 2.067833848e-15,
# Wb = V*s = (J/C)*s = (kg*m^2/s^2)/C * s = kg*m^2/(s*C)
"units": [("kg", 1), ("m", 2), ("s", -1), ("C", -1)],
"symbol": "Φ₀"
},
"josephson_constant_KJ": {
"value": 483597.8484e9,
# Hz/V = 1/s / (J/C) = C / (s*J) = C / (s * kg*m^2/s^2) = C*s / (kg*m^2)
"units": [("kg", -1), ("m", -2), ("s", 1), ("C", 1)],
"symbol": "K_J"
},
"conductance_quantum_G0": {
"value": 7.748091729e-5,
# Siemens (S) = 1/Ohm = A/V = (C/s) / (J/C) = C^2 / (s*J) = C^2 / (s * kg*m^2/s^2) = C^2*s / (kg*m^2)
"units": [("kg", -1), ("m", -2), ("s", 1), ("C", 2)],
"symbol": "G₀"
},
"molar_gas_constant_R": {
"value": 8.314462618,
# J/(mol*K) = (kg*m^2/s^2) / (mol*K)
"units": [("kg", 1), ("m", 2), ("s", -2), ("mol", -1), ("K", -1)],
"symbol": "R"
},
"atomic_mass_unit_u": {
"value": 1.66053906660e-27,
"units": [("kg", 1)],
"symbol": "u"
},
"bohr_magneton_muB": {
"value": 9.2740100783e-24,
# J/T = (kg*m^2/s^2) / (kg/(s*C)) = m^2*C/s
"units": [("m", 2), ("s", -1), ("C", 1)], # Units are actually A⋅m² = (C/s)⋅m²
"symbol": "μ_B"
},
"nuclear_magneton_muN": {
"value": 5.0507837461e-27,
# J/T, same units as Bohr Magneton
"units": [("m", 2), ("s", -1), ("C", 1)], # Units are actually A⋅m² = (C/s)⋅m²
"symbol": "μ_N"
},
"electron_compton_wavelength_lambda_eC": {
"value": 2.42631023867e-12,
"units": [("m", 1)],
"symbol": "λ_e,C"
},
"planck_mass_mP": {
"value": 2.176434e-8,
"units": [("kg", 1)], # Derived from sqrt(hbar*c/G)
"symbol": "m_P"
},
"planck_length_lP": {
"value": 1.616255e-35,
"units": [("m", 1)], # Derived from sqrt(hbar*G/c^3)
"symbol": "l_P"
},
"planck_time_tP": {
"value": 5.391247e-44,
"units": [("s", 1)], # Derived from sqrt(hbar*G/c^5)
"symbol": "t_P"
},
"planck_temperature_TP": {
"value": 1.416784e+32,
"units": [("K", 1)], # Derived from sqrt(hbar*c^5/(G*k^2))
"symbol": "T_P"
},
"standard_gravity_g0": {
"value": 9.80665,
"units": [("m", 1), ("s", -2)], # m/s^2
"symbol": "g₀"
},
}
# --- Calculate Scaling Factors ---
c_value = constants["speed_of_light_c"]["value"]
h_value = constants["planck_constant_h"]["value"]
k_value = constants["boltzmann_constant_k"]["value"]
#k_value = 1.380649e-23
# --- Rescaling Factors ---
# natural units
rescale_factors = {
"m": c_value,
"kg": h_value / (c_value**2),
"K": h_value / k_value,
"s": 1.0,
"Hz": 1.0,
"mol": 1/6.02214076e+23,
"C": 1.602176634e-19,
}
'''
rescale_factors = {
"m": 1.0,
"kg": 1.0,
"K": 1.0,
"s": 1.0,
"Hz": 1.0,
"C": 1.0,
}
'''
'''
rescale_factors = {
"m": 1.0,
"kg": h_value / (c_value),
"K": h_value / k_value *c_value,
"s": 1/c_value,
"Hz": c_value,
"C": 1.602176634e-19,
}
'''
'''
# scaling units to powers of 10 for constants
rescale_factors = {
"m": c_value/1e10,
"s": 1.0,
"Hz": 1.0,
"kg": h_value / (c_value**2) *1e10 ,
#"kg": h_value / (c_value**2) * 1e51 ,
"K": 1.0 ,
#"K": h_value / k_value ,
"C": 1.602176634e-19,
}
'''
# --- set time to 1000 second, changes Hz, keep speed limit the same but with meters now 1km ---
'''
rescale_factors = {
"m": 1000.0,
"s": 1000.0,
}
'''
# --- Function to Rescale a Value based on Unit List ---
def rescale_value_by_units_a(constant_data, rescale_factors):
original_value = constant_data["value"]
unit_list = constant_data["units"]
rescaled_value = original_value
for unit_symbol, power in unit_list:
if unit_symbol in rescale_factors:
rescaled_value /= (rescale_factors[unit_symbol] ** power) # Divide for numerator, multiply for denominator due to power
print (f"{unit_symbol} {power} ", end="")
print()
return rescaled_value
# --- Function to Rescale a Value based on Unit List ---
def rescale_value_by_units(constant_data, rescale_factors):
original_value = constant_data["value"]
unit_list = constant_data["units"]
rescaled_value = original_value
units_applied_list = [] # Store the units that were actually scaled
for unit_symbol, power in unit_list:
if unit_symbol in rescale_factors:
rescale_factor = rescale_factors[unit_symbol]
rescaled_value /= (rescale_factor ** power) # Divide original value by the scaling factor raised to the power
units_applied_list.append(f"{unit_symbol}^{power}") # Record the unit and power applied
return rescaled_value, units_applied_list # Return both value and list of units applied
# --- Display Original and Rescaled Constants Side-by-Side ---
print(f"{'Constant':<30} {'Original Value':<25} {'Rescaled Value':<25}")
print("-" * 80)
for name, data in constants.items():
original_value = data["value"]
rescaled_value, units_applied = rescale_value_by_units(data, rescale_factors)
units_applied_str = " ".join(units_applied)
print(f"{data['symbol']:<10} {name:<35} {original_value:<20} {rescaled_value:20.10} {units_applied_str}")
print("\n--- Scaling Factors Used ---")
for unit_symbol, factor_value in rescale_factors.items():
print(f"{unit_symbol:<10} {factor_value:.20e}")
