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Examples of Natural Unit Conversion

    There are five examples below to show how to run a reversed conversion from natural unit to cgs units (see Table) :

  1. Electromagnetic Wave Equation -
    In natural unit of [cm] (the natural unit is enclosed within the bracket [ ]) this equation is in the form :
    2E - E = 0
    Conversion back to cgs units in this case is very simple by substituting the natural unit [cm] with the cgs conversion factor c for the time variable. There is no conversion involved with the spatial variables. Then the equation in cgs units is recovered as:
    2E - (1/c2)E = 0

  2. Total Energy -
    E = (m2 + p2)1/2
    In natural unit of [erg], m is converted back to cgs by c2, while the conversion for p is c. Therefore the formula in cgs is :
    E = (m2c4 + p2c2)1/2

  3. Schrodinger Equation -
    In natural unit it has the form : -(1/2m) = i
    In converting from the natural unit of [erg], the left-handed side produces a factor of (1/c2)(c)2=2. On the right-handed side the converting factor is . Combining everything together, we recovered the equation in cgs :
    -(2/2m) = i
    Incidentally, for all cases, the same form in cgs units will be recovered whether the natural unit is in [cm] or [erg].

  4. Traveling (quantum) Wave -
    In natural unit with the energy E in [erg] : = exp[i(kx-Et)]. Backward conversion to cgs becomes = exp[i(kx-Et/)].

  5. Scales of the Universe - The formulas for the various scales (see table) are expressed in natural units. The following demonstrates the procedure of converting them back to the cgs units and in the process reproduces the numerical values quoted in the table.