The fact is that platinum atoms are bound together by the electromagnetic force, so if c = 1/sqrt(mu_0 epsilon_0) changes their distance changes too. (Who the hell is downvoting the entire thread, anyway?)
Equally a problem with the fine structure constant, since it directly measures the strength of the electromagnetic force. However, while the length of a platinum bar would, as you say, change under a change in the speed of light, it would not change linearly; so you can measure ratios of lengths and presumably pinpoint the constant that changed. The curvature of the Earth, for example, presumably depends on the strength of gravity in addition to the electromagnetic repulsion of its constituent particles, so it should change more slowly than the platinum bar’s length.
The fact is that platinum atoms are bound together by the electromagnetic force, so if c = 1/sqrt(mu_0 epsilon_0) changes their distance changes too. (Who the hell is downvoting the entire thread, anyway?)
Equally a problem with the fine structure constant, since it directly measures the strength of the electromagnetic force. However, while the length of a platinum bar would, as you say, change under a change in the speed of light, it would not change linearly; so you can measure ratios of lengths and presumably pinpoint the constant that changed. The curvature of the Earth, for example, presumably depends on the strength of gravity in addition to the electromagnetic repulsion of its constituent particles, so it should change more slowly than the platinum bar’s length.
But the fine structure constant is dimensionless, so you don’t need to find a standard to measure it which doesn’t change when it changes.
Ah, now I see what you’re saying. Good point.