(5-15) If we take Cormorant’s professed uncertainty in his velocity (± 0.008 ms-1) as being a standard deviation in the distribution of a series of measurements, we can apply the uncertainty principle:
Momentum: p = mv, so uncertainty in momentum sp = msv = 2.5 x 0.008 = 0.02 kgms-1
Now Heisenberg tells us that sx = h / 4πσp
= 6.626 x 10-34 kgm2s-1 / (4π x 0.02 kgms-1) = 2.6 x 10-33 m
What this means is that no matter how hard Cormorant works to improve his GPS, he can never avoid an uncertainty in his in-flight position which amounts to about a millionth of a billionth of a billionth of the radius of a hydrogen atom. “I can live with that” he concedes.