Comment by dooglius
2 years ago
The fine structure constant is dimensionless and would be different if c were different. When doing a unit conversion, one also has to alter other constants so as to be consistent with observed reality; whether one alters other constants or not is the difference between talking about a change in units and a change in c.
From Wikipedia https://en.wikipedia.org/wiki/Fine-structure_constant and following further links:
e is the charge, h is the Planck constant, ε_0 is the electric constant
However, h is heavily related to c with
where λ is wavelength. And,
where μ_0 is the magnetic constant, and is determined experimentally as 4π × 1.00000000055(15)×10−7 H⋅m−1.
A Kibble balance (dog food?) has become an instrument for measuring weight from a known current, rather than measuring current from a known weight.*
It looks like this still doesn't cancel out? It's an interesting point as to whether our hypothetical change in c would affect the relationship between photon energy and wavelength, but either way we get a nonzero power of c.