1. Understand the fundamental principles of special relativity, such as the constancy of the speed of light, the relativity of time and space, and the equivalence of mass and energy.
2. Develop the necessary mathematical tools to analytically treat relativity (Lorentz transformations and notes on tensor calculus)
3. Apply special relativity to simple physical problems relating to kinematics and relativistic dynamics.
2. Develop the necessary mathematical tools to analytically treat relativity (Lorentz transformations and notes on tensor calculus)
3. Apply special relativity to simple physical problems relating to kinematics and relativistic dynamics.
teacher profile teaching materials
– Recalls of Newtonian physics
Principle of Galilean relativity. Galilean space-time transformations. Newtonian dynamics. Laws of electromagnetism.
Michelson-Morley experiment. Lorentz-Fitzgerald contraction hypothesis. Hypothesis of ether dragging. Light aberration.
– Relativistic Kinematics
Einstein's postulates. Events and methods of clock synchronization. Relativity of simultaneity. Time dilation. Length contraction. Clock desynchronization in motion.
Lorentz transformations. Law of velocity composition. Rigidity, incompressibility, and mechanical resistance. Relativistic Doppler effect. Invariance of the electromagnetic wave equation under Lorentz transformations. Twin paradox and barn paradox. Invariant intervals.
Space-time diagrams: worldline and its length. Principle of maximum aging. Angular worldline; revisited twin paradox and barn paradox. Calibration hyperbolas. Light cone: time-like, space-like, and light-like intervals.
• Notes on tensor calculus
– Lorentz transformations in matrix form, four-vectors, metric. Lorentz group. Tensor calculus in Minkowski space-time. Properties of the metric tensor.
• Relativistic dynamics
– Energy-momentum four-vector. Four-velocity and four-force. Energy-momentum conservation. Two-body decay. Maxwell's equations in covariant form. Motion of a charged particle in an electric field.
• Manuale di relativita’ ristretta, M. Gasperini. Springer
Programme
• Kinematics– Recalls of Newtonian physics
Principle of Galilean relativity. Galilean space-time transformations. Newtonian dynamics. Laws of electromagnetism.
Michelson-Morley experiment. Lorentz-Fitzgerald contraction hypothesis. Hypothesis of ether dragging. Light aberration.
– Relativistic Kinematics
Einstein's postulates. Events and methods of clock synchronization. Relativity of simultaneity. Time dilation. Length contraction. Clock desynchronization in motion.
Lorentz transformations. Law of velocity composition. Rigidity, incompressibility, and mechanical resistance. Relativistic Doppler effect. Invariance of the electromagnetic wave equation under Lorentz transformations. Twin paradox and barn paradox. Invariant intervals.
Space-time diagrams: worldline and its length. Principle of maximum aging. Angular worldline; revisited twin paradox and barn paradox. Calibration hyperbolas. Light cone: time-like, space-like, and light-like intervals.
• Notes on tensor calculus
– Lorentz transformations in matrix form, four-vectors, metric. Lorentz group. Tensor calculus in Minkowski space-time. Properties of the metric tensor.
• Relativistic dynamics
– Energy-momentum four-vector. Four-velocity and four-force. Energy-momentum conservation. Two-body decay. Maxwell's equations in covariant form. Motion of a charged particle in an electric field.
Core Documentation
• Fisica dello spazio tempo, Edwin F. Taylor, John Archibald Wheeler. Medea• Manuale di relativita’ ristretta, M. Gasperini. Springer
Attendance
Attendance is not mandatory but is strongly recommendedType of evaluation
The exam will take place through a written test, the grade obtained will be recorded unless you choose to also take the oral test (which, therefore, is optional) to try to improve the result of the written test. In the case that both the oral and written tests are taken, the recorded grade will be given by a weighted average between the two tests.