## May 11, 2005

### part 2 - catastrophe!

First, a quick definition of classical physics. Classical physics is comprised of 2 things - laws of fields and laws of motion. Laws of fields describe how magnetic fields or gravity fields change - primarily Maxwell's equations. Laws of motion describe how objects move - primarily Newton's laws (and Einstein's relativity corrections). Fields influence how objects move. Objects create and influence fields. Straight forward.

Also note that Maxwell's field laws describe waves. The form of the equations are wave-like in nature. Maxwell's laws describe light fields. Not only that but light does wave-ish things experimentally like constructively and destructively interfere with itself. Therefore up until then scientists had thought of light and fields as waves. Fine. Fields are wavelike and Objects are particlelike.

So what's this catastrophe I mention in the title? This catastrophe occurred with black body radiation. A black body is an ideal object - one that absorbs all electromagnetic energy (no reflection). It also must emit radiation as it heats up. Just like it absorbs at all frequencies it also emits at all frequencies. If you use classical mechanics to calculate the emitted energy you get a strange answer - infinite.

This is because it emits at all frequencies (infinite) and each frequency contains an identical amount of energy (finite). Infinite times a constant equals infinite. This is clearly wrong.

This was dramatically known as the Ultraviolet Catastrophe.

So how did scientists overcome this? Planck ended up guessing an answer. Namely that there are not an infinite number of frequencies emitted (a logical place to start). There are only some frequencies emitted. Namely those with minimum energies that are below the energy of the radiating body. They either have enough energy to radiate or they don't. Out of this work came the concept of quantized energy (minimum energy) and Planck's constant, h.

Side note: A friend who took undergraduate quantum courses with me hated the classes so much that he and I would write songs about quantum theory in the guise of a love song or story about a femme fatale to keep from falling asleep in class. The fake band was named Neils Bohr and the Eigenvectors.  Later we regrouped and called ourselves the Rigid Rotators.  I recall one funny line related to this topic:
Ultraviolet catastrophe
She emits at every frequency
I can't handle this much radiation
Where's Planck? I need salvation
There was still one problem. No one knew why the theory worked. It was pure guesswork. Enter Einstein in 1905. Einstein writes a paper that uses Planck's constant and quantization of energy to explain the photoelectric effect.

The photoelectric effect occurs when you shine light on a metal. Let's say our lamp emits a red color and is dim. We shine it on the metal. Nothing happens. Let's turn our light intensity up. Nothing happens. Turn the intensity back down. Let's change the color from red to blue. Now some electrons start popping out of the metal plate. Let's turn the intensity up. More electrons start popping off. Let's change the 'color' to ultraviolet. The same amount of electrons are popping off but they are ejected at a faster velocity.

This is not intuitive. Compare to a more understandable example - water waves. It suggests that a big tsunami (higher light intensity) wouldn't throw you out of the water with more force. It would just throw more swimmers out. But small quick ripples would throw you out of the water with much greater force. The phenomena above is clearly not 'classical' in nature.

Einstein explained this by saying light behaves like individual ‘coins’ of energy. The higher the coin value the more energy it imparts to an electron and the faster it is ejected. Below a certain coin value, light cannot dislodge an electron from the metal. Increase the intensity (number of coins) and you still cannot dislodge them. Increase the denomination of the coin (increase the frequency or change the color from red to blue) and the light kicks out the electrons with greater speed. Light is behaving distinctly like an individual particle (dubbed the photon) and it has a certain denomination of energy that is related to the frequency. More photons doesn't lead to greater energy per se.

Understand the strangeness of this. Light is electromagnetic radiation. It is described by Maxwell's laws. Maxwell's laws (by the form of the equations) describe a field with wave behavior. Einstein is saying this field of waves is actually behaving like a bunch of individual particles in this situation. Light behave likes a wave in some cases and a particle in others.

A clearer way to see this particle attribute of light is through the Compton effect. Send a light beam through a gas and some light goes right through, some gets slightly deflected, and some actually bounces back. All of this occurs just like light was a cue ball shot into a 'gas' of billiard balls. Distinctly particle like in nature.

DeBroglie was doing the opposite. He claimed that particles behaved like waves. It was his graduate thesis. His advisor thought he was nuts but sent it to Einstein who gave it his blessing. How’s that for a way to seal the deal on your defense. Davison and Germer eventually showed electrons (thought of as particles) behave like waves by actually measuring their wavelength.

So waves behave like particles and particles behave like waves. Is this a problem? Not necessarily. Water waves are made of water particles (molecules). The difference here is that individual particles are behaving in wave-like ways. It's like an individual water molecule can bob up and down on its own. That is weird and not accounted for by classical physics since field/wave laws and motion laws are separate and thus waves and particles are separate things.
Some people get stuck on this point. Just let it go. It's not intuitive and you can't quite visualize it. All things have particle-like attributes under certain conditions and wave-like attributes under other conditions. You never see both at the same time. It's just part of quantum theory and it'll be a little easier to see why later. It won't be easier to swallow but that's why I say let it go. There is no real understanding how something could be a particle and a wave.

Clearly a new theory was needed. It is now 1925. Enter Heisenberg, Dirac, and Schrodinger...