Superposition

Recently, I've been reading Chad Orzel's book "How To Teach Physics To Your Dog" and browsing around the internets in an attempt to gain a better understanding of modern physics, specifically quantum mechanics. I decided to write a few blog posts about my adventures in QM to provide myself study direction.

It's difficult to convey just how unbelievably weird quantum mechanics is. Interactions of the elementry particles of reality are difficult to grasp with a classical understanding of physics.

For example, when throwing a snowball at your neighbor for stealing the day's paper (once again) you expect said snowball to rise at the angle and velocity your hand and arm put it in. You also expect the snowball to begin arcing downward according to Earth's gravitational pull (9.8 m/s^2) and finish it's flight in his face.

You do not expect, however, the snowball to be in a superposition state during the flight and only suffer a small chance of smashing into your neighbor's face. Instead, you feel you know the flight and subsequent termination of the snowball's trajectory because you've dealt with classical physical phenomena all your life.

Personally, I find superposition to be an insanely cool sounding term. Unfortunately, the concept is outside of our "normal" physical understanding and can be difficult to grasp. What makes it so different from everyday life? Unlike the simple model of an atom usually imagined as a tiny solar system, electrons don't orbit around a nucleus like planets around a star. Generally, when folks in the know refer to electrons in an atom, they are imaging something similar to a cloud of potential electron states surrounding the atom's nucleus.

You may say, "Wait a minute, what does state mean?" A particle's state refers to it's position and energy level (momentum) around a nucleus. So when you say an electron exists in all states at once, you're essentially saying that it's at all energy levels and positions around the nucleus at once. This is very counterintuitive especially considering we don't see a haze of Jupiter's, Saturn's or Neptune's when we look up into the night sky.

So, let's look at hydrogen as an example. We know that the hydrogen atom has one electron. The electron cloud surrounding hydrogen's nucleus is made up of (usually) one electron in a superposition state. That is to say, the electron exists in all possible states at once. Very strange, eh? To describe the position of the electron isn't too difficult and describing the energy level (momentum) of the electron isn't too difficult either. However, woe is the person who attempts to find both at once.

Finding both position and momentum of a particle in superposition is impossible due to constraints of not our quantum mathematical model, but reality itself. I'll explain why in my next post.

Most of the information in this post was gathered from Dr. Orzel's book and Wikipedia.