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

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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.

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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

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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!

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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

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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?

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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

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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

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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

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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

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