The idea of imagining a universe with different constants is not new, but, in my opinion,
the early literature is very confusing. For example, Vol'berg [17] and Gamow [18] imagine a universe in which the velocity of light is different from ours, say by ten orders of magnitude, and describe all sorts of weird effects hat would result:
Gamow said:
The initials of Mr. Tompkins originated from three fundamental physical constants: the velocity of light c; the gravitational constant G; and the quantum constant h, which have to be changed by immensely large factors in order to make their effect easily noticeable by the man on the street."
In this one sentence, Gamow manages to encapsulate everything I am objecting to!
First, he takes it as axiomatic that there are three fundamental constants. Second, he
assumes a change in these constants can be operationally defined, I for one am mystified
by such comparisons. After all, an inhabitant of such a universe (let us identify him with
Feynman's alien) is perfectly free to choose units in which c = 1, just as we are. To use
the equation
k = E/c
to argue that in his universe, for the same energy E, the photon emitted by an atom would have a momentum k that is ten orders of magnitude smaller than ours is, to my mind, meaningless. There is no experimental information that we and the alien could exchange that would allow us to draw any conclusion.