Dear Marc,
As you know, in the MKS system of units the ampere is defined as a constant current present in empty space in each of two parallel conductors infinite in length, one meter apart, and experiencing a force of 2x10-7 newtons per meter of conductor lengths. This definition refers an ampere to a measure of force at a measure of distance. The ampere then is established by empirical measurements. These measurements firmly establish the value of the constant current.
Also in the MKS system of units the coulomb is defined as the quantity of charge in a constant current of one ampere which crosses a section of a conductor in one second. The ampere is a firmly established constant current. The definition of the coulomb includes a property called electric charge. The existence of electric charge is taken for granted. The property of electric charge is not itself defined. However, it is known that particles of matter are flowing in the conductors and that they are the physical representation of current. For the purpose of this message, the property of electric charge will be taken for granted and its nature will not be challenged.
In my essay, however, I show that the value of electric charge of one of the particles of the hydrogen atom is numerically close to the magnitude of the period of time it takes for light to travel the length of the radius of the hydrogen atom. The model used is the Bohr model.
You questioned that a different definition of a second would cause the two magnitudes to no longer be close. It is accepted that one is free to define the second differently. However, it is claimed by me that the magnitudes of the two values will remain just as close. The reason for this claim is contained in the definition of a coulomb. Specifically the part "...the quantity of charge in a constant current of one ampere which crosses a section of a conductor in one second." If the unit of second is cut in half the quantity of charge in a constant current of one ampere which crosses a section of a conductor in one new second will be cut in half.
If the coulomb's definition is unchanged then the quantity of charge of the electron will be twice its old value. The reason for this result has to do with dividing the coulomb by the number of particles that make it up. The number of particles is cut in half. Dividing one coulomb by their new number establishes their quantity of charge as 2x1.602x10-19 coulombs.
The speed of light is the number of meters traveled per second. The new value of second cuts that number of meters in half. The new value of the speed of light has a magnitude of one half that of the previous speed of light. The result is that it will require twice the number of new seconds for light to travel the radius of the hydrogen atom. That time period is twice as large but the charge of one of the particles of the hydrogen atom is also twice as large. The close relationship between their magnitudes remains.
I apologize for writing this out so deliberately detailed. I had other potential readers in mind and wrote it out to be understood by the maximum number of readers.