The only non-arbitrary length unit is the Planck length. The Planck length is the smallest possible unit of distance that makes any physical sense in our universe. It is derived from the universal gravitational constant, the speed of light, and Planck's constant. Physically it represents the shortest possible wavelength for a photon of light. Since the wavelength is inversely proportional to the energy of the photon, a smaller wavelength means a larger energy. The Planck length is the wavelength at which a single photon would have so much energy it would spontaneously collapse into a black hole. Thus nothing can exist at a smaller size.

Unfortunately Planck lengths are too small to be of much practical use in everyday life. But I have a solution! Let's just take some multiple of the Planck length, and use that instead! The multiple will still be arbitrary, but the foundation it is based upon would not be. I suggest multiplying it by 6.25*10^34. I shall call this new semi-natural unit the Meeter! It is about equivalent to 1.0 meters.