For anyone hoping for some deeper fundamental connection, you should read about natural units[1] to understand why that couldn't happen. Given a dimensional co

For anyone hoping for some deeper fundamental connection, you should read about natural units[1] to understand why that couldn't happen. Given a dimensional constant, it can only be related to some more fundamental mathematical constant in a particular set of units. So the connection will be entirely due to how the units are defined, as is the case here. 1. http://en.wikipedia.org/wiki/Natural_units http://en.wikipedia.org/wiki/Natural_units