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PHY 042: Electricity and Magnetism
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
 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
Quantum mechanics
(Bohr, Heisenberg,
Schrödinger, Fermi)
Special and general
Quantum field theory
(Dirac, Schwinger,
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
 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