# On Superposition and Experimental Facts of Life (Lec. 1 & 2)

I didn’t take notes on the first lecture, but essentially the Prof. abstracted certain experiments about electrons which gave way to the theory of superposition which basically means we don’t know what’s going on and that sometimes an electron will keep its state, but other times will become totally random on measurement.

But, what are some fundamental properties that we need to know for quantum physics?

### 1. Atoms exist

“If you can spray them, they exist,” said Ian Hacking. But more precisely, we know electrons exist because we can manipulate them (as with a CRT TV) or even see them (or rather their effects) as in the Gargamelle Bubble Chamber. This experiment revealed that you can actually see electrons and that it’s possible for a neutrino to hit an electron (weak neutral current).

So electrons exist, but what about nuclei? Well, we know we nuclei exist because we can shoot stuff at them!

Actually, this is an experiment done by Rutherford, Geiger and Marsden where they shoot alpha particles at a wall of atoms. Most of the time they go through, and they should. However, once in a while you’d have them bounce back at 120 or 160 degree angles. Rutherford likened this to throwing a bowling ball against a piece of paper and having it bounce back! This indicates that atoms have high density cores where most of the mass is concentrated.

Well now if we strip the electrons away from a metal we’re left with a positively charged nucleus. With classical mechanics, we know if we have a positive and negative charge, we have an inverse r potential ($\frac{q_1 q_2}{r}$) like planets do in a Keplarian orbit. But there’s a problem with this picture? If an electron orbits in this manner, it must radiate to accelerate and keep the orbit. But then it must fall lower down because it radiates. In classical mechanics, atoms cannot thusly exist. BUT THEY DO! WHY? We have to explain that.

#### Side Note on Hard Scattering

Hard scattering is a way by which you shoot a charged particle at something and look at how it deflects. This is used for studying the dense cores of particles. At MIT they also did a series of experiments where you shoot an electron at a proton and look at the deflection. It was found that the proton is itself composite and made out of “3” (more complicated than that) quarks, each of fractional charge. This was led by Kendall, Freedman, and Taylor.

This was continued with the Relativistic Heavy Ion Collider, so you collide two protons at high energy and you get massive shrapnel comming out of the collision instead of them bouncing out. This can be seen here where two Gold nuclei were collided. So how do you interpret that data?

First off, the interior parts of a proton interact very strongly with each other. However, when they collide you actually get a quantum liquid (quark-gluon plasma). But it has very interesting properties: the time it takes for the system to come to thermal equilibrium is over order the time it takes for light to cross the liquid. This is very well modelled by black holes?!?!?!?

### 2. Randomness Exists

Geiger wanted a way to detect radiation that’s obviously hard to see. So he fills a capacitor with a noble gas. When a capacitor is charged to a point, the dialectric in between breaks down and you get a spark. Well if you charge the capacitor to slightly below this point and then a charged particle (like an alpha particle with charge +2) flies through, you get a spark. Hence, the Geiger counter. And if you’ve ever heard a Geiger counter, it goes off kind of randomly. And we cannot predict the decay of atoms because they are random. Hence, randomness exists.

### 3. Atomic Spectra: Discrete, structured

To study atomic spectra, there are a couple of important experiments. You set up a power source and have a spark gap with a gas in between, which will emit a light. Put this light through a prism and you get bands of intensity. There are three groups of lines (Lyman, around 1000 Ang.; Balmer, around 3000 Ang.; Paschen, around $10^4$). For different gasses you’ll get different bands.

The Balmer lines can approximated for Hydrogen gas as:

Rydberg and Ritz went further and theorized that for any number $n > m$ with a Hydrogen gas:

This shows that the atomic spectra are not only discrete, but have a very specific structure. But why?

Stopped @ 23.27

Written on December 30, 2014