In George Gamow's Mr. Tompkins books, Mr. Tompkins ends up, first in a world where the speed of light is so small that time dilation and Lorentz contraction are dominantly present when he rides a bicycle, later in one where Planck's constant is so large that dispersion of wave packets is manifest when he plays billiards (it is a long time ago that I read this book, so I don't remember all details).
In the answers to this question (one of which mentions Mr. Tompkins as well by the way), it is essentially asserted that it doesn't make sense to talk about changing a dimensionful constant. Initially I thought that was nitpicking, because it still is clear what Gamow meant and what Mr. Tompkins experiences, but giving it a bit more thought however, it may not be so clear indeed.
If we just think of our perception of the passing of time, which is what made Mr. Tompkins adventures so interesting, that will probably be closely tied to the strength of the electromagnetic interaction, which governs most of the processes that directly influence us, and which in turn is closely related to the speed of light. On the other hand, for a life form whose physical reality is dominated by the strong interaction, like for the Cheela in Robert Forward's Dragon's Egg who live on a neutron star, and who go on a holiday between the reception of two spoken syllables when communicating with humans, relativistic effects must be omnipresent in daily life without changing any constants of nature.
In any case my question is, how should (a) dimensionless constant(s) be changed so that we would experience the world like Mr. Tompkins in the world with a low velocity of light? Likewise for the large Planck's constant? If that is not possible, why not?
