The document introduces the Lorentz transformations, which relate spatial and temporal coordinates between different inertial reference frames according to Einstein's theory of special relativity. The Lorentz transformations were originally derived by Lorentz and others to make Maxwell's laws of electromagnetism invariant. They describe how an event that is specified by its coordinates (x, y, z, t) in one reference frame would be specified by transformed coordinates (x', y', z', t') in another reference frame. At low velocities, the Lorentz transformations reduce to the classical Galilean transformations.

1. Chapter 1Chapter 8
Introduction to Lorentz trasformation

2. The Lorentz equations are transformations of the spatial coordinates and the
time as a result of a change of the reference frame.
They are in accordance with special relativity, but were derived before Einstein
created the special relativity.
They were the result of attempts by Lorentz and others to make invariant the
Maxwell laws of electromagnetism.
The Lorentz transformations mix somehow space and time.
The three spacial coordinates x, y, z, and the coordinate time t describe what is
called EVENT.
So you consider no more three-dimensional space but a four-dimensional
space called SPACE-TIME
Lorentz trasformation equations

3. If you know the event in a reference frame S (x, y, z, t) and you want to
determine the event in an inertial reference frame S '(x', y ', z', t ') apply:
Lorentz trasformation
S S’

4. Conversely, if you know the event S '(x', y ', z', t ') and we want to determine
S (x, y, z, t) apply:
At small values of v, v<<c, where velocities are within the normal range of
human experience, Lorentz trasformation Equations easily reduced to
traditional Galilean Trasformations Equations as follow:

5. These transformations relate to the classical
mechanics, when v<<c . Otherwise, they
must be replaced by Lorentz transformation
that, in particular, anticipate that the time
"flows" in a different way in reference
systems in relative motion

6. These transformations relate to the classical
mechanics, when v<<c . Otherwise, they
must be replaced by Lorentz transformation
that, in particular, anticipate that the time
"flows" in a different way in reference
systems in relative motion