3 ms·
No, because defined this way, the absolute precision to which distance can be defined is ~10^-11 meters. So 1 meter is known within +/- (10^-11) meters. If you
by gh02t 11y ago
No, because defined this way, the absolute precision to which distance can be defined is ~10^-11 meters. So 1 meter is known within +/- (10^-11) meters. If you convert (10^-11) meters to nanometers that's 10^-2 nanometers, which is 1% of a nanometer.
You don't divide the uncertainty when you scale it because the error is in the actual definition of distance itself. The uncertainty in for example 1 meter is the same as the uncertainty in 1 nanometer (=10^-11 meters), which is a correspondingly much larger fraction. It's kind of weird and perhaps counter-intuitive, but that's how it works.
Phrased differently, the idea of a meter is exact and it's our ability to measure distance that is uncertain. The error isn't in saying "a meter is some specific fraction of the distance light travels in a second", it's in determining what physical distance in the world is represented by our definition of the meter.