What is physics??
Physics attempts to formulate the "laws" of nature in terms of the precise language of mathematics, so that one can make quantitative predictions about the outcome of simple experiments. Agreement between predictions and experiments is the true test of a physical theory.
Physics can be divided into two types of investigation. In one, we are interested in uncovering the basic laws which tell how the various elementary forms of matter interact which each other. These fundamental laws can be divided into two parts:
Mechanics tells how an object will move when it is acted upon by an external force. Newton's Law's of Classical Mechanics, describe the motion of objects on the scale of everyday life: baseballs, cars, etc. Schrodinger's Equation of Quantum Mechanics, describes the motion of objects on the atomic scale: electrons, protons, etc.
Once one has the laws of mechanics, expressing the motion of particles in response to forces, one next needs to know what are the fundamental interactions between particles which give rise to the forces. So far, four fundamental interactions have been discovered: Gravitation is the attraction between two objects due to the mass of the objects. This is the oldest known interaction, discovered from the study of the motion of astronomical objects beginning in the 1600's. Famous names in the theory of gravitation are Galileo, Newton, and more recently Einstein. Electromagnetism is the interaction between objects which carry electric charge. Electromagnetism is responsible for "static cling", refrigerator magnets, electric motors, light waves, radio waves, TV, etc. Most of the forces we encounter in everyday life have their source in electromagnetic interactions. Classical electromagnetic theory was for the most part developed in the 1800's. Some famous names in the theory of electromagnetism are Ampere, Faraday, and Maxwell. The Strong interaction and the Weak interaction are important when one studies the behavior of sub-atomic particles, such as the neutrino, the electron, or quarks (protons and neutrons are made up of more fundamental parts called quarks). The weak interaction has only become well understood within the last 30 years or so. The strong interaction is still incompletely understood. Elegant theories exist, but they are so mathematically complicated that we have not learned yet how to make many predictions with them.
So one type of physics investigation is concerned with uncovering and understanding the basic laws of motion and interaction, as discussed above. But a second type of physics investigation is concerned with the following type of question: Suppose I have a system in which I understand completely all the basic laws of motion and interaction governing the behavior of the various pieces which make up the system. Do I then understand, and can I predict, what the behavior of the system as a whole will be? To illustrate that this is not a trivial question, consider the fact that Quantum Mechanics and Electromagnetism together, both more or less completely understood and successful theories, are all it takes to describe how electrons, protons, and neutrons combine to form atoms, and how atoms then interact with each other. Yet atoms can combine together to form a rich diversity of different materials, with dramatically different properties: metals, insulators, semiconductors, ferromagnets, glasses, plastics, jello. Even a given material, such a water, can exist in completely different forms: water, ice, vapor. How does all this great diversity and complexity arise from the well understood basic theories of Quantum Mechanics and Electromagnetism? How do we go from an understanding of the basic "microscopic" laws of an individual atom, to derive simple "macroscopic" laws for the behavior of systems consisting of billions and billions of atoms? More generally, how does varied or complicated behavior arise from simple basic rules? Such questions form the subject of Condensed Matter Physics, or Statistical Physics. Topics that appear in such studies include the notions of temperature, entropy, phase transitions.
It is this second type of investigation which will form the foundation of this course.
To give a flavor of this type of investigation, we will start with an example of a system with the simplest of possible basic rules: when you flip a fair coin, it is equally likely to come down heads as it is tails. We then want to see how this simple basic rule can be used to answer some more complicated question such as:
If I flip a coin 10 times, how many heads should I expect to get? On average I expect to get 5 heads. But if I get only 4, is this unreasonable? How about if I get only 3? or only 2? If I flip the coin 100 times, how many heads would be reasonable?