Measuring Reality

Like many folks, I'm sure you've heard of Werner Heisenberg's uncertainty principle in popular culture. It essentially states that you cannot know the position and momentum of a quantum particle at the same time. This is probably the most widely known principle in quantum physics and the least understood at the same time.

It's understandable that people get the concept mixed up and infuse poor reasoning and strange theology into it because, frankly, the very concept of uncertainty is confusing and seems to cross the border from physics into philosophy. It arrises in quantum physics due to a wave / particle duality of the microscopic world.

The popular model of an atom looks like a miniature solar system with a tough nut of a nucleus at the center and electrons in various energetic states orbiting around it. Physicists know this model is complete bunk in terms of modeling how atoms are put together physically but it's great for mathematically explaining how they function. (Physicists are freaks for building models, most of them are abstract and represented in computers nowadays.)

Instead physicists describe physical systems (such as an atom) using what's called a wavefunction. Before discussing wave functions, a quick reminder of the properties of a wave are in order.

Let's look at a typical example of a wave (drawn with amazing detail with my favorite writing utensil, the Sharpie):

This is an example of a simple wave generated with the cosine function. Wavelength is the length between each peak (or valley) of the wave, amplitude is the measure of how large the wave is at it's peaks and frequency defines how many peaks pass a given point within a period length of time. Generally, wave functions are described using a two dimensional graph in which the Y axis represents probability and the X axis represents position.

So, lets say this wave represents a unit of matter. This unit of matter could be anything from an electron to a molecule or even a snowball. In the example above, the wave repeats an pattern with certain frequency, amplitude, and wavelength. If we over lay this wave on to a two dimensional wave distribution graph described above, several observations are able to made.

First, each point in which the amplitude (Y-axis) is at it's maximum would represent a higher probability an object would be found in a particular position (X-axis). Also, longer wavelengths directly correspond to longer positions in the same amount of time so we can infer that wavelength is a measure of momentum.

Now, imagine attempting to define a single point on this wave where the unit of matter exists. An obvious solution would be at the peaks. If that's the case, which peak do we define as the position of our unit of matter? There is an infinite number of them (remember, the wave is continuous).

Ack! Getting long and I need to go draw more graphs, therefore:

To be continued…