Special relativity

By Alessio Mangoni

This book is dedicated to Einstein's special relativity. The main topics are: postulates of relativity, events and Minkowski space-time, Lorentz transformations, metrics in scalar products (with an analysis on the metric tensor in an Euclidean and Minkowski space), intervals and their classification, effects of relativity such as time dilation and length contraction, speed transformations, equation of motion in relativistic dynamics, relativistic Lagrangian, kinetic, mass and total energy and their non-relativistic limits, four-momentum conservation.

• Language: English
• Publisher: Dr. Alessio Mangoni
• Release date: Aug 16, 2020
• ISBN: 9788835879916

Book preview

2020

Contents

Contents

Introduction

Notations

The basis of relativity

Postulates

Event

Interval

Lorentz transformations

Length contraction

Time dilation

The metric tensor

Transformation of velocities

Equation of motion

Total relativistic energy

Conservation laws

Introduction

This book is dedicated to Einstein's special relativity. The main topics are: postulates of relativity, events and Minkowski space-time, Lorentz transformations, metrics in scalar products (with an analysis on the metric tensor in an Euclidean and Minkowski space), intervals and their classification, effects of relativity such as time dilation and length contraction, speed transformations, equation of motion in relativistic dynamics, relativistic Lagrangian, kinetic, mass and total energy and their non-relativistic limits, four-momentum conservation.

Notations

Generally we will use the Greek letters to indicate the indices that take values 0,1,2,3 and the Latin ones for the indices that assume values 1,2,3. We will use the Minkowski metric tensor with signature (+, -, -, -), i.e.



and the Einstein convention that implies summation over two repeated indices, one contravariant and one covariant, such as:



Finally we will use the natural units, i.e.



The basis of relativity

Postulates

The theory of special relativity is based on the following postulates:

Principle of relativity. Same form for physical laws in any inertial reference frame;

Constant speed of light. The speed of light in vacuum, called c, is constant in all inertial reference frames.

The value of the speed of light in vacuum is



or also