Title Page
"Relativity Theory"
––––––––
SIMONE MALACRIDA
Table of Contents
Table of Contents
Title Page
Relativity Theory
INTRODUCTION
GALILEIAN RELATIVITY
PROBLEMS OF CLASSICAL PHYSICS
SPECIAL RELATIVITY
GENERAL RELATIVITY
ASTROPHYSICS AND RELATIVISTIC COSMOLOGY
ATTEMPTS AT UNIFICATION AND OPEN QUESTIONS
Relativity Theory
The following basic physics topics are presented in this book:
Galilean relativity
crisis of classical physics
theory of special relativity
theory of general relativity
relativistic astrophysics and cosmology
attempts at unification and open questions
––––––––
Simone Malacrida (1977)
Engineer and writer, has worked on research, finance, energy policy and industrial plants.
ANALYTICAL INDEX
––––––––
INTRODUCTION
––––––––
I - GALILEIAN RELATIVITY
The concept of relativity according to Galileo
Newton's vision
––––––––
II -PROBLEMS OF CLASSICAL PHYSICS
Introduction
astronomical observations
The invariant transformations of electromagnetism
––––––––
III -SPECIAL RELATIVITY
Einstein's solution
Revisitation of classical mechanics
Space-time
Aftermath
––––––––
IV - GENERAL RELATIVITY
Introduction
Tensor mathematics
General Theory of Relativity
Experimental confirmations
––––––––
V - ASTROPHYSICS AND RELATIVIST COSMOLOGY
Solutions of Einstein's equations
Singularities and black holes
Relativistic cosmology
––––––––
VI - ATTEMPTS AT UNIFICATION AND OPEN QUESTIONS
Introduction
Attempts at unification
From GUT to The Theory of Everything
INTRODUCTION
INTRODUCTION
In this book the entire theory of relativity is presented, as it has been presented throughout the history of science.
First, space is given to the theory of relativity according to Galileo and according to classical physics.
After having exposed the problems of classical mechanics, a detailed overview of the special theory of relativity is given.
Tensor mathematics introduces the understanding of the theory of general relativity, the consequences of which are highlighted both at an astrophysical and cosmological level.
Finally, attempts at unification between quantum field theory and general relativity are proposed, with the problems still open.
What is set out in this manual is only partially addressed at university level, unless one chooses a course of study strictly related to astrophysics and cosmology.
Knowledge of advanced mathematical analysis is required to understand the manual, at least from the theory of general relativity onwards.
I
GALILEIAN RELATIVITY
GALILEIAN RELATIVITY
The concept of relativity according to Galileo
––––––––
Galileo was the first to scientifically ask himself the question of the validity of physical laws, especially of mechanics, and of the role of different observers in different reference systems.
Galileo started from the hypothesis that the laws of mechanics are always the same for inertial reference systems, ie reference systems that satisfy the principle of inertia.
Simply put, such frames of reference are not accelerated.
These reference systems can be expressed through the formalism of the Cartesian axes in three dimensions (with Cartesian coordinates) and by adopting the rules of Euclidean geometry.
The observer present in the reference system is integral with the reference system, therefore it does not have its own motion, but only that of the system.
The first point that Galileo highlighted is that of the simultaneity of the experiment.
Two observers placed in different inertial frames of reference must perform the same experiment at the same instant in order to have an identical result.
Therefore they will have to exchange information to synchronize this experiment.
Galileo tried to measure the speed of light and deduced that it was so high compared to daily practice, as to make the time necessary for the exchange of information irrelevant.
––––––––
The first conclusion of Galilean relativity was that time remained the same in the passage from one inertial system to another.
––––––––
Since the two reference systems have different speeds, Galileo posed the problem of how to carry out a transformation of the speeds, passing from one system to another.
By applying Euclidean geometry together with Cartesian coordinates, he vectorically composed the velocities according to the well-known law of the parallelogram.
This law, already known by Leonardo, now found an explanation in the Galilean theory of relativity.
Ultimately, given two inertial systems, the passage of space-time coordinates from one system to another according to Galilean relativity is given by:
Where v is the relative speed between the two systems, composed according to the parallelogram rule.
With these scientific assumptions and with the method developed by Galileo, there were the real foundations for starting the path of modern physics, starting right from the mechanical concepts.
––––––––
Newton's vision
––––––––
The publication of Newton's theory coincided not only with the beginning of a scientific study of mechanics in all its forms, but also a general interpretation was given to the theory of gravitation and various astronomical problems, until then explained only by empirical observations or not totally scientific principles.
Newton established that two masses attract each other according to a force proportional to them and decreasing with the square of the distance.
Newton and claimed that the gravitational force is responsible both for the acceleration of gravity on planet Earth (the attraction that pushes the famous apple to fall to the ground) and for the mutual attraction between the planets.
To affirm all this, Newton had to assume two fundamental prerequisites:
––––––––
1) The mass that appears in the second law of dynamics is called inertial mass, the one that appears in the law of universal gravitation is called gravitational. In Newton's theory it remains unclear why these two values always coincide, for any body. On a practical level, Newton took this assumption as valid and did not pose further problems.
––––––––
2) The gravitational force is a force at a distance but which has an immediate effect on bodies, even in the astronomical field. This means that this force does not respect the Galilean principle of relativity. Newton did not ask other questions, syndicating that space and time were absolute.
––––––––
With these assumptions, the so-called classical physics began.
II
PROBLEMS OF CLASSICAL PHYSICS
Imprint
Publisher: BookRix GmbH & Co. KG
Publication Date: 04-19-2023
ISBN: 978-3-7554-3950-9
All Rights Reserved