How constants c, h, k, act as unit scaling factors.

 

import math

# Define the constants

c = 299792458.0  # m/s

h = 6.62607015e-34  # J*s

k = 1.380649e-23  # J/K

# This code calculates unit scaling factors derived from the fundamental constants

# of physics (c, h, k). These scaling factors demonstrate the relationships

# between different units (e.g., kilograms and Joules, Hertz and Kelvin)

# in the context of natural units.

# the unit scaling factors have the format of in_out for the unit conversions

# with the units of out/in

# Calculate the unit scaling factors

kg_J = c**2  # J/kg

J_kg = 1 / kg_J  # kg/J

Hz_kg = h / kg_J  # kg/Hz

kg_Hz = 1 / Hz_kg  # Hz/kg

# Calculate the derived constants

K_Hz = k / (Hz_kg * kg_J)  # Hz/K

Hz_K = 1 / K_Hz            # K/Hz

Hz_J = Hz_kg * kg_J        # J/Hz

J_Hz = 1 / Hz_J            # Hz/J

K_J = K_Hz * Hz_kg * kg_J  # J/K

J_K = 1/K_J                # K/J

K_kg = K_Hz * Hz_kg  # kg/K

kg_K = 1 / K_kg  # K/kg

# Print the values with at least 12 digits of accuracy

print()

print()

print()

print(f"   How constants c, h, and k act as unit scaling factors.")

print()

print()

print(f"   E=mc^2   E=m kg_J where kg_J = c^2 with units of J/kg")

print(f"   kg_J  = {kg_J:.12g} J/kg      J_kg = {J_kg:.12g} kg/J")

print(f"   This unit scaling exists because there are {c} meters in each light second.")

print()

print(f"   E=hf    h = Hz_kg kg_J  therefore Hz_kg = h/kg_J")

print(f"   Hz_J  = {Hz_J:.12g} J/Hz         J_Hz = {J_Hz:.12g} Hz/J")

print(f"   Hz_kg = {Hz_kg:.12g} kg/Hz     kg_Hz = {kg_Hz:.12g} Hz/kg")

print(f"   Hz_kg exists because there are {Hz_kg} kg in each Hz.")

print()

print(f"   E=kT    k = K_Hz Hz_kg kg_J therefore K_Hz = k/(Hz_kg kg_J)")

print(f"   K_J   = {K_J:.12g} J/K            J_K = {J_K:.12g} K/J")

print(f"   K_Hz  = {K_Hz:.12e} Hz/K     Hz_K = {Hz_K:.12g} K/Hz")

print(f"   K_Hz exists because there are {K_Hz} Hz in each Kelvin.")

print()

print()

print(f"   The constants (c, h, k) have the values they do because SI units are defined far")

print(f"   from natural units, where these scaling factors would be unity.") # Clarified to include h and k

print(f"   In natural units (where 1 Hz = 1 kg = 1 K = 1 J), these scaling factors (kg_J, Hz_J, K_J) would all be 1.") 

print(f"   It is only by rescaling our units of measure to unity with each other that c=h=k=1 is true.")

print(f"   This shows that c, h, and k's SI values are solely unit conversion artifacts,") 

print(f"   not indicators of mysterious 'quantum magic' or deeply fundamental values beyond unit scaling.") 

print(f"   This does not diminish the constants, understanding their true nature makes them more important.")

print()

print()