#1. Are all the (measurable) dimensionless parameters that characterize the physical
Universe calcuable in principle, or are some merely determined by historical or
quantum mechanical accident, and calcuable?
Einstein put it more crisply: Did God have a choice in creating the Universe?
Imagine the Creator-of-All sitting at His control console, preparing to set off
the Big Bang. 'How fast should I set the speed of light?' 'How much charge
should I give this little speck called an electron?' 'What value should I give
to Planck's constant, the parameter that determines the size of the tiny packets -
the quanta - in which energy shall be parceled?' Was He randomly dashing off
numbers to meet a deadline? Or do the values have to be what they are because
of a deep, hidden logic?
These kinds of questions come to a point with a conundrum involving a mysterious number
called alpha. If you square the charge of the electron and then divide it by the
speed of light times Planck's constant, all the dimensions (mass, time, and distance)
cancel out, yielding a so-called 'pure number' - alpha, which is just slightly over
1/137, But why is it not precisely 1/137 or some other value entirely? Physicists
and even mystics have tried in vain to explain why....