A couple people have pointed me to an article at New Scientist that requires another edition of This Week’s Hype. According to Nuclear clock could steal atomic clock’s crown:
Such clocks could shed light on string theory. The frequency of the jumps in a nuclear clock will depend on the strong nuclear force, while the jumps by electrons in atomic clocks depend on a different fundamental force. So together they could reveal if the relative strength of the forces changes, as string theory has it.
The amusing thing about the string theory “prediction” that relative strengths of forces change over time is that many string theorists promote as a “prediction” exactly the opposite: according to this argument, change in these strengths would imply large changes in the vacuum energy, which we don’t see, so a prediction of the landscape is constancy. See for example here.