I understand that the wave function of some system at some point in time can't be an eigen state for both the position and the momentum operators simultaneously. Here is what I am asking about, assume we make an experiment and in this experiment I have two apparatuses, one for a velocity measurement and the other for a position measurement. I let the system undistributed until I decide now to measure the position and the momentum simultaneously, I will be extremely careful to let the two apparatuses start running at the exact same time. So, my question is, which quantity I will measure with indefinite precision and which one I won't and why? My opinion is as far as I understand is that I will measure the two quantities with an indefinite precision, but if I managed to perform 1 million other identical experiment and plotted the value I got for x and p in each of those experiments I will now calculate the standard deviations and I will find that they are in agreement with uncertainty principle, am I wrong?
3
-
$\begingroup$ Just to make it clear, you do know that the uncertainty commonly associated with theoretical quantum mechanics (and maybe especially Heisenberg's uncertainty principle) is a lot more fundamental than just imprecise measurements, right? $\endgroup$– ArthurCommented Sep 1, 2022 at 10:50
-
2$\begingroup$ I am afraid that without a description of the two apparatuses, it is impossible to say anything. As a related remark, I would note that no measurement can be performed in zero time. $\endgroup$– GiorgioP-DoomsdayClockIsAt-90Commented Sep 1, 2022 at 11:08
-
$\begingroup$ I know that how good our measuring apparatuses are is one thing and the inherited uncertainties is another thing $\endgroup$– JackCommented Sep 1, 2022 at 12:20
Add a comment
|