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Why is it impossible to simultaneously measure the position and velocity of a particle with infinite accuracy?

User Maechler
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Step-by-step explanation:

Heisenberg uncertainty principle.

the thing about velocity is that it is about movement :

DISTANCE / time (difference between start and end)

so, to measure velocity you need to observe the object during a period of time (even if it is a tiny period).

what you get is a mean value of the velocity the object was moving with while going from point A to B during the observed time period.

now, at what point between A and B did it have exactly that velocity ? we can't say, due to the nature of velocity.

no matter how tiny we make the distance between A and B and the time interval, it has to be a measurable distance and time interval. they cannot be 0.

otherwise we would have a velocity 0/0. and that is undefined.

the other direction is to identify the position of a moving body. once we have the velocity, we are dealing with a distance and not a point. the velocity of an object at a point is

0/time = 0

so, for a given object we can only determine the exact position at a given time OR the exact velocity it has during a given time interval.

both is simply impossible.

User Jyo Banerjee
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