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.

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