81786 - Relativistic Physics

Learning outcomes

At the end of the course, the student has learned the fundamental laws of special relativity, their application to mechanics and electromagnetism, he has become acquainted with some necessary mathematical tools and is able to solve simple problems. He is finally acquainted with some fundamental experiments that require a relativistic description and, in particular, those that led to the formulation of the theory and then supported it.

Course contents

RELATIVISTIC PHYSICS

Historical preamble and introduction

- The main steps in the development of the special theory of relativity

- The principle of relativity of Galilei. The law of inertia. Inertial frames of reference. The Galilean transformation

- The speed of stellar light

- Newton’s laws of motion. The invariance of Newton’ s second law of motion under the Galilean transformation

- The aberration of stellar light

- The constancy of the speed of stellar light

- Measurements of the speed of light in the laboratory

- The aether and attempts to measure its dragging

- Maxwell’s equations and the wave equation

- The experiment of Michelson and Morley (in-depth study)

- The hypotheses of Lorentz and Poincaré on space contraction and time dilation

- Mass of the electron at relativistic speeds. Experiments of Kaufmann, Bucherer, Guye

- The invariance of Maxwell’ s equations and the Lorentz transformations (in-depth study)

- Einstein and the formulation of the special theory of relativity

Relativistic Kinematics

- Inertial frames of reference

- Synchronization of clocks and the relativity of simultaneity

- The relativity of time and space

-The Lorentz transformation for the coordinates: the contraction of length, the dilation of time

- The transformation of velocity: the gamma Lorentz factor, the speed c as an upper limit

- The transformation of acceleration and proper acceleration

Optical phenomena and relativity

- The aberration of light

- Fizeau’s experiment

- The Doppler effect

- Synchrotron radiation

- The force exerted by light

Relativistic dynamics

- Relativistic formalism for momentum, mass and energy

- The relationship between momentum and energy

- Classical approximations

- Particles with zero mass

- The conservation of momentum and energy

- The equivalence of mass and energy

- The transformation of momentum and energy

- The zero-momentum frame of reference and the transformation of the total momentum and energy of a system of particles

- The collision of two identical particles and experimental tests of relativity

- The transformation of force

- The motion of a charged particle under the influence of a constant force in an electric and in a magnetic field

Electromagnetic phenomena and relativity

- The invariance of electric charge

- The transformations of the electric field and the magnetic field

- Fields produced by a moving electric charge

- The force exerted on a moving charge by an electric current

The world of Minkowski

- Causality, past, present and future

- The Minkowski diagram of the Lorentz transformation, for the effect of length contraction and of time dilation

- A Minkowski diagram for the Doppler effect

- Four-vectors: four-vectorial formalism for position, velocity, acceleration, energy-momentum, force

- The four-vectorial equation of motion

- Maxwell's equations using four-potential and four-current. Electromagnetic field tensor. Covariant formulation

Applications and experimental tests of relativity

- The lifetime of cosmic muons

- The Sagnac effect

- Clocks moving around the Earth

- Einstein's train

- The twin paradox

- The Compton effect

- Particle accelerators

- Nuclear binding energy

Readings/Bibliography

-- The Special Theory of Relativity – Foundations, Theory, Verification, Applications

Costas Christodoulides

(Springer, 2016)

-- Special Relativity

Valerio Faraone

(Springer 2014)

-- Introduction to the Basic Concepts of Modern Physics – Special Relativity, Quantum and Statistical Physics

Carlo Maria Becchi, Massimo D'Elia

(Springer, 2016 - Third Edition)

-- Relativity Matters

Johann Rafelski

(Springer 2017)

Teaching methods

Lectures (40 hours) and exercises (12 hours)

Assessment methods

Written and oral examination

Teaching tools

Slides and video projector

Office hours

See the website of Luisa Cifarelli

See the website of Andrea Alici