The Cosmic Game ( PDFDrive.com )

Cosmic Game © Douglass A. White, 2012 v151207 154
side of a single square, we get the well-known reciprocal of the fine structure constant,
which is approximately 137. We then adjust the scale by 12 orders of magnitude.
(% / λce)(1.054)(100) ≈ α -1 (10 12 ) ≈ 137.
λce ≈ 1.054 α % (10 -10 ).
We can now express the Compton wavelength as a factor among a cluster of constant
component factors with a combined product that is a power of ten.
10 10 = 1.054 α % / λce.
The proton Compton wavelength is λcp = h / Mp c = 1.3214098446×10 −15 m, and is
smaller than the electron's because of the larger proton mass. When we substitute the
formula for the proton mass, we get a very simple expression:
λcp = h / π e = 2 ħ / e = 1.32×10 −15 m.
This is an elegant definition of quantized space. Since the proton is the foundation of all
stable matter, it makes sense to use either the proton's Compton wavelength or the Bohr
radius as a standard for length.
Time: the Second
Once we have a way of determining the meter, the second is automatically determined by
the time it takes light to travel 3e8 meters, and of course any fraction of that distance will
give us the corresponding fraction of a second.
Of course it is fine to use the current standard definition: "the duration of 9,192,631,770
periods of the radiation corresponding to the transition between the two hyperfine levels
of the ground state of the cesium 133 atom," -- provided you have a supply of cesium 133
available. Some areas of the universe may not have such supplies of cesium readily
available, so a person would have to carry his own supply in order to set his clocks.
Another way to measure a second is to set up a standardized LC circuit. "An LC circuit,
also called a resonant circuit, tank circuit, or tuned circuit, consists of an inductor,
represented by the letter L, and a capacitor, represented by the letter C. When connected
together, they can act as an electrical resonator, an analog of a tuning fork, storing energy
that oscillates at the circuit's resonant frequency.
An LC circuit can store electrical energy by oscillating at its resonant frequency. A
capacitor stores energy in the electric field between its plates, depending on the voltage
across it, and an inductor stores energy in its magnetic field, depending on the current
through it.
If a charged capacitor is connected across an inductor, charge will start to flow through
the inductor, building up a magnetic field around it and reducing the voltage on the
capacitor. Eventually all the charge on the capacitor will be gone and the voltage across it