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Heisenberg's uncertainty principle states that the uncertainty in the position of the particle times the uncertainty in its velocity times the mass of the particle can never be smaller than a certain quantity (Planck’s constant). i.e. It is impossible to assign definite values of certain pairs of variables, such as position and momentum, with arbitrary precision for any type of sub-atomic particle using any method of measurement
DE position x (DE velocity x mass) = h = Planck's constant
In order to measure the current position of a particle, the obvious way is to shine light on the particle. Some of the waves of light will be scattered by the particle and this will indicate its position. However, one will not be able to determine the position of the particle more accurately than the distance between the wave crests of light, so one needs to use light of a short wavelength in order to measure the position of the particle precisely. Now, by Planck’s quantum hypothesis, one cannot use an arbitrarily small amount of light; one has to use at least one quantum. This quantum will disturb the particle and change its velocity in a way that cannot be predicted. Moreover, the more accurately one measures the position, the shorter the wavelength of the light that one needs and hence the higher the energy of a single quantum. So the velocity of the particle will be disturbed by a greater amount. In other words the more accurately you try to measure the position of the particle, the less accurately you can measure its speed, and vice versa.
Heisenberg's uncertainty principle is important in that it proves that the first premise in the theory of determinism is false. Laplace in his Philosophical Essay on Probabilities (1814) described determinism thus:
"An intellect which at any given moment knew all the forces that animate Nature and THE MUTUAL POSITIONS OF THE BEINGS THAT COMPRISE IT, if this intellect were vast enough to submit its data to analysis, could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom: for such an intellect nothing could be uncertain; and the future just like the past would be present before our eyes."
Heisenberg proved that "the mutual positions of the beings that comprise it" could never be found.
To put another way, determinism states that all future positions can be predicted if:
1) The current position and momentum (velocity x mass) at any one point is known and
2) All the laws of nature are known.
Heisenberg's uncertainty principle says that premise 1 can never be know with absolute accuracy.
To see how Heisenberg's uncertainty principle relates to Schrödinger's cat, quantum theory and the concept of true randomness visit the Randomness? debate.
Or see how this affects freewill?
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