227-0652-00L  Maxwell, Einstein, and the GPS

Courses

Catalogue data

Abstract	Maxwell’s equations are reinterpreted in the framework of Einstein's special relativity theory using the Lagrangian formalism in order to discover the deep interconnection between the electric and magnetic field. Its daily relevance is emphasized by pinpointing how GPS atomic clocks in satellites and on the earth are affected by frequency shifts which can be explained only in terms of relativity.
Learning objective	D-ITET is the depository of the Maxwell’s equations, which are dissected from all perspectives in the courses Physics I, Electromagnetic Fields and Waves, and Advanced Electromagnetic Waves. Only one aspect is left over: the fact that they are not invariant with respect to the classical Galilean transformation… On the contrary, Maxwell’s equations predict that the light speed is the same for every inertial frame of reference. In this course, we will deepen how Einstein solved this clash elaborating the theory of “special relativity”. Maxwell's equations are thus naturally derived in a breath-taking fashion from the principle of stationary action within the Lagrangian formalism. Not only its elegance, but also the daily importance of the relativity theory will be finally highlighted explaining how the GPS can work only if the relativistic view of synchronous clocks is taken into account.
Content	• Galileo-Newton, the Ether, Michelson-Morley's Experiment • Lorentz Transformations • 4-Vectors in Minkowski’s Spacetime: Tensor Calculus • The Lagrangian, the Principle of Stationary Action for Particles and Fields, Noether's Theorem • Maxwell’s Equations and the Energy-Momentum Tensor • Waves • Radiation from Accelerated Charged Particles • Very First Notions of General Relativity: Einstein's Equivalence Principle and Time Dilation • Sagnac's Effect • GPS
Lecture notes	No lecture notes because the proposed textbooks together with the provided supplementary material are more than exhaustive! !!!!! I am using OneNote. All lectures and exercises will be broadcast via ZOOM and correspondingly recorded (link in Moodle) !!!!!
Literature	• (Special Relativity) L. Susskind and A. Friedman, "Special Relativity and Classical Field Theory: The Theoretical Minimum", 2019, Hachette Book Group USA • (Lagrangian Formalism) L. Susskind and G. Hrabovsky, "Theoretical Minimum: What You Need to Know to Start Doing Physics", 2014, Hachette Book Group USA Supplementary material will be uploaded in Moodle. _ _ _ _ _ _ _ + (the classical and probably unsurpassed treatise) L.D. Landau, E.M. Lifshitz, "The Classical Theory of Fields", 1980, Butterworth-Heinemann + (on the GPS) E.D. Kaplan, C. Hegarty, "Understanding GPS/GNSS", 2017, ARTECH HOUSE USA + (as account of that annus mirabilis) J.S. Rigden, "Einstein 1905: The Standard of Greatness", 2006, Harvard University Press
Prerequisites / Notice	Notions of a course on Electromagnetism like D-ITET "Electromagnetic Fields and Waves" are indispensable. Furthermore, a solid base of Analysis I & II as well as of Linear Algebra is really helpful. IMPORTANT: a few Wednesdays are lectures (NOT exercises!), details in Moodle!
Competencies	Subject-specific Competencies Concepts and Theories assessed Techniques and Technologies fostered Method-specific Competencies Analytical Competencies assessed Decision-making assessed Media and Digital Technologies fostered Problem-solving assessed Project Management assessed Social Competencies Communication fostered Cooperation and Teamwork fostered Customer Orientation fostered Leadership and Responsibility fostered Self-presentation and Social Influence fostered Sensitivity to Diversity assessed Negotiation fostered Personal Competencies Adaptability and Flexibility assessed Creative Thinking assessed Critical Thinking assessed Integrity and Work Ethics assessed Self-awareness and Self-reflection assessed Self-direction and Self-management assessed

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits	6 credits
Examiners	T. Zambelli
Type	session examination
Language of examination	English
Repetition	The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examination	written 180 minutes
Written aids	none (closed book)
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

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Offered in

Programme	Section	Type
Electrical Engineering and Information Technology Bachelor	Engineering Electives	W
Electrical Engineering and Information Technology Master	Specialisation Courses	W
Electrical Engineering and Information Technology Master	Specialisation Courses	W