Friday, June 18, 2010

Charges Rule!

While gravity is the universal glue that holds together the stars, prevents us from flying off the surface of the Earth, and is the stuff that makes space-time itself; from the perspective of our everyday lives, electromagnetism is the most fundamental force that profoundly affects us. At the heart of everything we are and do are the interactions of electromagnetic fields and charges. Indeed, matter is merely a bag of charges that are held together predominantly by electric fields.

Connoisseurs of the strong force may argue that theirs is the most important since it binds together the neutrons and protons that form the tiny nuclei at the center of every atom; but, alas, the swarm of electrons that buzz around the nuclei shield them from view. We can be thankful that nuclei exist as anchors to the frenetic electrons, but, physicists would agree that our personal interactions with the universe are governed by the affects of electromagnetic fields on electrons.

When our eyes see, its because light - made of wiggling electric and magnetic fields - causes charges to slosh around in our optic nerves, eventually leading to an electrical signal that finds its way to our brains. Similarly, charges communicate with each other by shouting not words, but bursts of light. It's the coordinated symphony of these light bursts that choreograph the dancing collection of charges.

The group of cells that constitute a brain interact with each other through electrical signals. But the animal body is also the host to many chemical reactions and thermodynamic processes. One might therefore defend chemistry as the true seat of life, with charges as essential albeit second-class citizens. But what is chemistry? You've guessed it! Chemistry is no more than interactions between charges.

Quantum Mechanics, as quantified by the Schrodinger Equation, imposes the rule of law that must be obeyed by all particles such as electrons and atoms (as long as they are not moving at nearly the speed of light). The social gathering of atoms form communities called molecules. While there is much shouting and motion within the community - all of which obey the grammar of quantum mechanics, the molecule speaks with one voice. All of these complex interactions within the group leads to an entity that behaves in a well defined way due to the very simple rule that like charges repel and opposite charges attract, and, that the strength of this force gets larger as the charges get closer together. This relationship is called Coulomb's Law. All of chemistry can be explained by applying the crank of the Schrodinger Equation to the tune of Coulomb's Law.

By understanding the social rules of the electrons and nuclei, the complex behavior of the molecular community can be predicted. The rules are communicated through a mathematical language via the Schrodinger Equation. Being a differential equation, it can only be solved exactly for the simplest cases. One of the triumph's of early twentieth-century Physics, a time of explosive discovery the likes of which has yet to be repeated, was the precise prediction of the colors and intensities of light emitted by the scream of an electron in a hydrogen atom when it de-excites after being jarred by a pulse of light or an electric shock.

To go beyond this simplest class of atoms, made of one electron and one nucleus, requires that the Schrodinger Equation be solved using approximation techniques or high-speed computers. Such approaches lead to accurate predictions of more complex systems and helps us to understand the concept of chemical bonds, which connect atoms. Indeed, the order observed in the periodic table of elements, as first arranged by the Russian chemist Dmitry Ivanovich Mendeleyev in the mid to late 1800s, can be understood by the simple concept of interactions between the social charges.

As the complexity of a molecule increases, it becomes more difficult to predict its properties using Quantum Mechanics. It's not that Quantum Mechanics is in any way breaking down, but rather that computer memories are too small and microprocessors too slow to get an accurate answer in a reasonable amount of time.

We get around these issues by extrapolating what we understand for smaller systems. For example, chemists make stick figures of larger molecules by using qualitative rules for making bonds between atoms. This approach allows them to approximately predict the properties of more complicated materials. To put this in the language of Physics, chemistry is a compilation of the myriad number of ways that charges interact with each other. While such empirically-determined rules are not hard and fast (there are always exceptions), this approach has been extremely profitable in designing and synthesizing new molecules, through a process of trial and error, that are useful for a given application.

To illustrate how all this relates to everyday experiences, consider physically touching someone. We might conclude that the force of contact between two objects is a new type of force, and we would be in good company. Even Isaac Newton considered the force of contact distinct from others; but it is not. Newton could be excused for his ignorance of electricity and magnetism, which would not be fully understood until Maxwell came on the seen in the eighteen hundreds.

When the fingers are brought together, the negatively charged electrons repel, leaving the positively charged nuclei behind. As we push harder, the protons get closer together and the shouting match of light bursts swells, yielding greater repulsion. Even when pressing your fingers together with gut-wrenching vigor, a small gap remains. The conclusion is that we can never touch anything. The sensation of touch originates in the electric repulsion between charges.

On one occasion as a young adult, I was annoying my parents - as was my habit, by picking the M\&Ms off the cookies. In response to my persistent disobedience, my mother yelled in anger,``Don't touch the cookies!" In response, I calmly explained to her the Physics underlying her misconception about the physical reality of touch. My smug satisfaction was abruptly interrupted by swat across the head and my indignant protest was returned with a devious smile, ``I didn't touch you either."

So, when you kick a football, kiss your sweetie, hit a nail with a hammer, slide on a patch of ice, use your computer, or float in the heavens on a hang glider, you are relying on the interactions between charges. You would be hard-pressed to find an everyday experience that did not originate in the flicker of light between the charges that form matter.

We might be faulted for ignoring the humblest force of the four, the weak interaction, which is responsible for encounters between ghostly neutrinos and matter. Neutrinos are emitted when a neutron decays into a proton and an electron (more accurately, anti-neutrinos are emitted) and are produced in copious amounts in supernovas. A light year of lead is required to stop one of these tiny sprites. Interestingly, the universe is filled with neutrinos. If we could take a snapshot with a magic camera that stops neutrinos in their tracks, we would find that any volume around us the size of a sugar cube would contain about 1000 neutrinos. But, while they are pervasive and travel near the speed of light, they interact so weakly with matter that over a typical human lifetime, our body captures about one neutrino from this large surrounding sea. We can therefore ignore the affect of the weak interaction on our daily lives. That we are made from stuff that formed in supernova explosions is another matter. It happened so long ago!

All processes in nature can be reduced to the four forces (gravitational, weak, strong, and electromagnetic). The idea that the complexity of the universe is governed by the action of four simple rules is both compact and elegant. While gravity may woo us with its beautiful geometric description of space and time, and the strong force may capture our imagination of how the smallest particles (the quarks) are held together and explains the power source of the sun, life and our existence today is for the most part dominated by electromagnetism.

As a graduate student, I was tempted by and flirted with all four of the forces of nature, but by a fluke of fate ended up concentrating on the force that makes us tick; the most practical of the fundamental forces that governs interactions between charges and electromagnetic waves. Light is a specific case of an electromagnetic wave that occupies the visible part of the spectrum. And this is precisely what makes light so special; we can see it.

Everything that we can know about the interaction between light and matter originates in the interactions between photons, the tiny particles of light, and charges. The interaction of light with a molecule is quantified by a function called the polarizability and the interaction between a beam of light and a collection of molecules is called the susceptibility. As such, these special quantities we call the polarizability and the susceptibility provide us with the code to decipher all of the richness of electromagnetic phenomena in materials that we take for granted. We will need to consider these quantities carefully if we are to understand how we interact with the universe. More pragmatically, understanding what makes the polarizability tick empowers us to use these interactions for the benefit of humanity. That is why I study nonlinear optics.

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