PHY 042: Electricity and Magnetism Introduction Prof. Pierre-Hugues Beauchemin

The Structure of Sciences I  E&M offers a clear way to see how physics laws are obtained from simple experimental setups, and how they evolve and get generalized following new experimental results and richer mathematical formalism  This is a great opportunity to understand, at least partly, how sciences work, and how an established theory is structured  Studying E&M has an high epistemological value  In this class, I will heavily insist on the elucidation of the connections between theoretical ideas, formalism and instrumental setups.  These connections are generally applicable to other field of physics, and often demystify a theory  For example, quantum mechanics is not describing a bizarre reality, it proceeds from a similar interplay between experiments, math and physics concepts as in E&M.

The Structure of Sciences II  We will see that:  Every laws or equations in physics have CONDITIONS OF APPLICABILITY  They are valid only under certain circumstances;  Theoretical statements serve to describe or make predictions for experimental setups or technological devices to which the laws can be applied;  Laws of physics are often generalized by some more powerful mathematical and conceptual apparatus;  Concepts are not really equivalent, even if one formula converts one into another; they express different empirical conditions  Generalization means an extension of the conditions of applicability of the laws, which, in turn, will describe new experiments, new devices and provide new phenomena

The Structure of Sciences III  No physics law or equation of state is meaningful without an experimental context  This experimental context may or may not be actually realized, but it must at least be conceivable  The same equation might be applicable to various incompatible experimental contexts, but in this case they have different meaning and often the identity of formula is just a simplification  The narrative of the course will be organized in a way to make such structure obvious!

Context in physics I  In mechanics, you learned to quantify the motion of an object:  Description (kinematic)  Effects of forces on the kinematic of an object (dynamic)  Symmetry of the system in motion  conserved quantity  The mathematical framework of classical mechanics is inadequate in describing the motion of systems which:  Travel closed to the speed of light  Are microscopic

Context in physics II Classical mechanics (Newton) Quantum mechanics (Bohr, Heisenberg, Schrödinger, Fermi) Special and general Relativity (Einstein ) Quantum field theory (Dirac, Schwinger, Feynman) Where does E&M fit?

Fundamental forces  The electromagnetism is the interaction between matter particles that we describe in mechanics.  It is the cause of a change in the state of motion of a system  There are 4 fundamental forces in Nature:  Gravitational  Long range, very weak classical and relativistic description  Nuclear Weak and Strong  Short range, quantum and relativistic description  Electromagnetic  Long range, can be described in all 4 realms This course focus on the non-relativistic classical description of the E&M interaction

Unification  Special relativity description of E&M contains a fundamental feature:  The complete unification of the E and B fields  Lorentz transformations leave Maxwell equations invariant  Light is also an E&M wave (crucial to relativity too)  Unification of E, M and optics  Further unification?  Kaluza-Klein, Glashow-Salam-Weinberg, GUT?, Superstring?  Unification is not a formal or epistemological requirement for physics theories, but provides theories with rich structures extending the known laws of physics to a broader range of phenomena.  Unification also serve as guiding principle for theory development, and provide a simple and beautiful picture of the world

Crucial Concepts in E&M I  Fields:  The space around an electric charge is permeated by electric and magnetic fields which are responsible for transmitting the effects of a set of charges on another  Destroy the idea of distant action  Keep causality  Mediator of an interaction  Fields are not passive:  They carry energy, momentum and angular momentum  They can be a system (radiation)  Extend the concept of force to the concept of interaction

Crucial Concepts in E&M II  Charges :  Property of matter that is responsible for the interaction via a field  It is related to the very powerful concept of symmetry  0 net charge does not mean no E&M interaction…  Each fundamental interaction comes from a fundamental symmetry of Nature and thus with a charge associated  Noether’s theorem  They are quantized  They are involved in the experimental aspects of probing E&M :  Preparation  produce a field  Observation  detect test charges