The uncertainty principle was the End of the Classical Physics in its mechanical meaning: "knowing the state of the world today, we can predict with a perfect precision what it will be tomorrow". This reveals to be impossible because even today's state is not known with a sufficient precision.
This rather philosophical than mathematical conclusion was made by Werner Heisenberg not on the basis of theoretical considerations but on observations of water droplets on the electron path in Wilson's chamber - if there is a droplet it is sure that in that place there was also an electron (he had a defined position in the space), if there is a gap between the droplets, we know that on this distance the electron flew-through (he had a defined speed).
More precisely: the product of the position uncertainity and of the speed uncertainty is not less than Planck's constant (divided by 2π)
ΔxΔp ≥ ћ
The uncertainity principle stays, for example that:
1) it is impossible to make "exact" measurement,
2) a wave packet describing the position of an electron diffuses with time,
3) in a similar way the Bose-Einstein's condensate does inflate.
The Heisenberg principle determines also the lowest electronic orbit of the hydrogen atom - in which the uncertainity of the electron speed is equal to that speed2).
1) Such pairs are called non commutating operators: measurements of x and then p or p and then x give two results that differ by ћ.
2 ) Of course, measurements with an error exceeding measured value would have no sense.
