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

 Semester Herbstsemester 2022 Dozierende T. Zambelli Periodizität jährlich wiederkehrende Veranstaltung Lehrsprache Englisch

KurzbeschreibungMaxwell’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.
LernzielD-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.
Inhalt• 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
SkriptNo 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) !!!!!
Literatur• (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
Voraussetzungen / BesonderesNotions 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!
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