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Simply put HUP involves position and momentum, further more consider a mass of 1kg. as momentum is mass X velocity = 1X velocity = velocity for calculation purposes. now for a stationary observer the uncertainty in velocity of the observed mass is some value, if another observer is travelling at the same speed as the mass the relative velocity is zero or at least smaller than what the stationary observer would see the mass travelling at. we now have two values for the uncertainty in the velocity of the mass. they both can't be right, HUP is subject to classical Newtonian relativity?

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  • $\begingroup$ Why would the two observers measure a different uncertainty in the velocity? $\endgroup$ – John Rennie Nov 27 '14 at 10:19
  • $\begingroup$ because one is moving at the same speed as the body. $\endgroup$ – Peter Nov 27 '14 at 10:34
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    $\begingroup$ If I measure a velocity as $v \pm \Delta v$, then the uncertainty is $\Delta v$ and whether $v$ is large or zero makes no difference. From purely practical considerations it's probably easier to measure a velocity accurately if it's small, but the error due to the uncertainty principle is not due to practical considerations. $\endgroup$ – John Rennie Nov 27 '14 at 10:39
  • $\begingroup$ Δv arises from my measurement technique does it not? or are you saying it is more fundamental and not a function of my measurement technique? $\endgroup$ – Peter Nov 27 '14 at 10:43
  • $\begingroup$ Yes, I am saying the uncertainty does not arise from your measurement technique. See Is uncertainty principle a technical difficulty in measurement? for more on this. $\endgroup$ – John Rennie Nov 27 '14 at 10:47