flies, cathedrals, springs and finding nature

Ok - it is nearly the new year, so let's have a bit of fun.  

 

Find a somewhat elastic cord or a spring.  Something that can stretch out to perhaps 15 feet or so.  You need something that can be stretched fairly tight.  You'll also need a wall to attach it to or, better yet a friend and some cookies.  I'll assume you are going with cookies and a friend.

 

Have a few cookies to get in the right mood and in an open space each grab and end and walk backwards until the spring is fairly taunt.  With a bit of wrist action start shaking your end up and down a bit.  The goal is to have each end mostly fixed in space but shaking just a bit to get the spring moving.  You'll see a lot of chaotic motion.  

 

Good.  Now pump a bit more and you find a rhythm where the middle of the spring is going up and down with the ends still mostly fixed.  Something like this:

The mostly fixed endpoints are nodes and the point with the maximum longitudinal motion, cleverly, the antinode.  Now, and this is where having another person and some sugar fuel comes in handy, pump a bit more.  

 

The spring becomes chaotic agin for awhile, but suddenly a new pattern emerges.  Three nodes and two antinodes.  Like this:

Pushing on keep increasing the frequency of your pumping. Calling out a rhythm can be useful and laughter - a lot of it - is a an ever-present and real danger.  Chaos returns, but if you are good at it another pattern will emerge - four nodes and three antinodes:

If this came easy why not push on? The next pattern is a bit difficult unless you have a nice spring, but you should be able to get to five nodes and four antinodes.  Keep going if you like.  The best I've done is five antinodes and about five minutes of solid hyperventilation.

 

This turns out to be a standing wave. You and your friend are adding energy to the spring, but the constraints of the fixed endpoints conspire to allow only a few stable patterns.  Put a wave in a box, nail the ends down, and it responds to added energy in very discrete levels.  The only acceptable levels are discretely spaced - one antinode, two antinodes, three antinodes and so on ...

 

It turns out this is a nice way to think about atoms.  Think about the simplest case - the hydrogen atom with a proton at the nucleus and one electron.  The positive charge of the nucleus effectively traps the negatively charged electron in a tiny (at least to us) atomic sized box about three tenths of a nanometer across.¹  

 

In the early part of the 20th century it was discovered that matter, at a very tiny scale, behaved like a particle and a wave.  It may seem a bit strange at first, but that's the way nature is and it is one of the most solid scientific results ever. Much of our modern world is built on it.

 

Assume the electron behaves like a wave.  It is trapped in this tiny little box defined by the electric field produced by the nucleus.  Since it is trapped it can't move at the edges of the box and standing waves are the only acceptable wave forms it can make.  They turn out to be more complex than the spring example, but they are just standing ways.  If you add energy to the system the atom can only accept certain amounts of energy.  The energy is "quantized".    It can only give off discrete amounts of energy too.  Getting energy in and out is usually done with particles of light.  So light of a certain fixed energy can be absorbed by the hydrogen atom and light of certain fixed energies can be emitted.  This turns out to be really useful!  

 

If you have made it this far you have learned a fundamental bit of quantum mechanics with no math or equations.

 

But the title mentions flies and cathedrals...  

 

One of the early experimenters, Ernest Rutherford, discovered that atoms are mostly nothing inside - that the nucleus is tiny and electrons are tiny.  He poetically said the nucleus is like a fly in a cathedral.²  It turns out the size of the standing wave - that three tens of a nanometer box - is about a quarter of a million times larger than the nucleus of the atom.  The atom isn't truly empty as the electron that is spread throughout it with a low density at any given point.  But it is still a pretty empty space.

 

There are so many interesting directions to go from here.  I'll leave you with the thought that you never really touch anything.  The electric fields from the electron "clouds" of your atoms repel the electric fields of whatever you are "touching".  They get very strong as the distance gets close, but never really touch.  So if you fall out of a plane you never really hit the ground.  But the close approach deforms both you and the ground.

 

______

¹ A rough number.  A nanometer is a billionth of a meter.  It is really difficult to appreciate the scale of this, but a thin blonde human hair is about fifty microns in diameter and somewhat difficult for us to see clearly.  This is fifty thousand nanometers in diameter.  If you were two nanometers tall (probably a bit more than a billionth of your height) the hydrogen atom would be about the size of a volleyball to you and the thin hair would be nearly thirty one miles in diameter.

The model of an atom that most of us were taught in K12 of electrons orbiting a nucleus is horribly wrong.  It is amazing it is still taught nearly 100 years after it was solidly disproven - less correct than the notion of a flat Earth (which has some semblance to reality at a certain scale ... there is no scale where the solar system model of the atom works)

² This may be a misquote.  Napier writes:

According to Faust in Copenhagen by Gino Segre (p.25) and The Fly in the Cathedral by Brian Cathcart (p.6) Rutherford did NOT himself call it a "fly in the cathedral" but "a gnat in the Albert Hall"

That turns out to be a more accurate description of the ratio of sizes