Uncertainty Principle

Uncertainty Principle:
Classical physics was on loose footing with problems of wave/particle duality, but was
caught completely off-guard with the discovery of the uncertainty principle.

The uncertainty principle, developed by W. Heisenberg, is a statement of the effects of
wave-particle duality on the properties of subatomic objects. Consider the concept of
momentum in the wave-like microscopic world. The momentum of wave is given by its
wavelength. A wave packet like a photon or electron is a composite of many waves.
Therefore, it must be made of many momentums. But how can an object have many
momentums?
Of course, once a measurement of the particle is made, a single momentum is observed.
But, like fuzzy position, momentum before the observation is intrinsically uncertain.
This is what is know as the uncertainty principle, that certain quantities, such as
position, energy and time, are unknown, except by probabilities. In its purest form, the
uncertainty principle states that accurate knowledge of complementarity pairs is

impossible. For example, you can measure the location of an electron, but not its
momentum (energy) at the same time.

Mathematically we describe the uncertainty principle as the following, where `x' is
position and `p' is momentum:

This is perhaps the most famous equation next to E=mc2 in physics. It basically says
that the combination of the error in position times the error in momentum must always
be greater than Planck's constant. So, you can measure the position of an electron to
some accuracy, but then its momentum will be inside a very large range of values.
Likewise, you can measure the momentum precisely, but then its position is unknown.
Also notice that the uncertainty principle is unimportant to macroscopic objects since
Planck's constant, h, is so small (10-34). For example, the uncertainty in position of a
thrown baseball is 10-30 millimeters.
The depth of the uncertainty principle is realized when we ask the question; is our
knowledge of reality unlimited? The answer is no, because the uncertainty principle
states that there is a built-in uncertainty, indeterminacy, unpredictability to Nature.