Can we accurately measure the momentum of a particle?

[kini.Amith]

Is there any law that prevents us from accurately measuring the momentum of a particle , just like the energy time uncertainty principle makes us observe the system for an infinite amount of time before we can be certain about its energy? I got this doubt because if we can do it, we will collapse the wave function into the eigenstate of momentum, which is not a normalisable state. I know that practically, measurements always come with some uncertainty, but at least in theory can we do it?

 

[mfb]

If you have enough time, the measurement can get as precise as you like (in theory). Just set up a detector light years away and measure when and where the particle arrives.

 

[kini.Amith]

If you have enough time, the measurement can get as precise as you like (in theory). Just set up a detector light years away and measure when and where the particle arrives.

Reminds me of the energy time uncertainty Principle. So is this true of all observables? And is there any formula that tells to what accuracy we can measure the observable given the amount of time we observe it?

 

[mfb]

That is not an accident as momentum and energy are related - measure one precisely and you get the other precisely. I guess you can use the energy/momentum relationship to set a lower bound on the measurement time.