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?