81786 - Relativistic Physics (A-L)

Learning outcomes

At the end of the course, students will be familiar with the fundamental principles of special relativity and their applications to mechanics and electromagnetism. They will have acquired proficiency with the essential mathematical tools required for the subject and will be able to solve elementary problems in special relativity. They will also be familiar with the key experiments that require a relativistic description, particularly those that led to the formulation of the theory and subsequently provided experimental confirmation of its validity.

Course contents

Brief review of mechanics. Relative and absolute quantities. Inertial and non-inertial reference frames. The equivalence of inertial frames and the Galilean principle of relativity. Galilean transformations. Transformations of the main mechanical quantities and of the laws of motion.

Brief review of electromagnetism. The interpretation of electromagnetism within the concept of the luminiferous ether. The main implications: the failure of the Galilean principle of relativity and the composition law for the speed of light. The Michelson interferometer and the Michelson–Morley experiment.

Einstein's proposal: the postulates of the theory of special relativity. The derivation of the new transformations: Lorentz transformations. Time dilation, relativity of simultaneity, length contraction, the limiting speed, and the principle of causality. Velocity addition and the Doppler effect.

The geometric formulation of special relativity. Covariant and contravariant vector components. The spacetime interval between events. Spacetime and four-vectors. Lorentz transformations as "rotations" in spacetime. The geometric interpretation of relativistic effects. The principle of covariance.

Relativistic mechanics. Derivation of the equations of motion. Momentum, energy, and four-momentum. Power of a force, conservative forces, the work–energy theorem, the inertia of energy. Selected applications.

Relativistic electrodynamics. Covariant formulation of Maxwell's equations. Transformations of electric and magnetic fields. Formulation of electromagnetism in terms of potentials and the four-potential. Gauge invariance of electromagnetism.

Experimental evidence. Lifetime of cosmic muons and muons in particle accelerators, the Sagnac effect, clocks in motion around the Earth, the Compton effect, and binding energy.

Readings/Bibliography

Lecture notes made available on the platform virtuale.

The Special Theory of Relativity, Vincenzo Barone, Ed. Bollati Boringhieri.

Teaching methods

Lectures on the blackboard and exercises.

Assessment methods

General information about the examination

• The examination consists of a written exam and an oral exam.
• There are six examination sessions per academic year: three during the summer session, one during the autumn session, and two during the winter session. No extraordinary examination sessions are offered.
• To take either the written or the oral exam, students must register through the AlmaEsami platform.
• The written exam consists of three problems to be completed within two hours.
• The grade obtained in the written exam remains valid for the entire academic year. Students wishing to improve their written grade may retake the written exam only once.
• The oral exam may be taken in any examination session following the one in which the written exam was passed. It consists of questions covering the course syllabus.
• The final grade is approximately the average of the written and oral exam grades (30 cum laude is treated as 31/30for the purpose of the average).
• If a student fails the oral exam or declines the proposed final grade, the decision to retain the written exam grade is at the discretion of the examination committee. Please note that, according to University regulations, the instructor is required to allow a student to decline a proposed grade at least once; any subsequent refusal is subject to the instructor's discretion.

Teaching tools

Didactic material provided by the teacher and made available on VIRTUAL platform.

Office hours

See the website of Angelo Carbone