M. Fabbrichesi , SISSA

Lorentz's transformations

While Newton's law is invariant under Galileian transformations, the wave equation is not as shown in the first part of this lesson. The transformations that preserve the wave equation are then derived by imposing the condition to leave unchanged the wave front i.e. the quantity x^{2 }+y^{2 }+z^{2 }-ct^{2 }[Jackson, sec. 11.3]. These transformations are called "Lorentz's transformations" and in particular, the *boost *transformations are here discussed. The concept of Minkowski metric is introduced and discussed with the help of a two dimensional space-time model. Next, twins paradox is illustrated as an example of time-dilation. Similarly the Lorentz contraction is discussed and examples are mentioned (e.g. ladder paradox ).