The Physical and Mathematical Foundations of the Theory of Relativity by Antonio Romano & Mario Mango Furnari

Author:Antonio Romano & Mario Mango Furnari
Language: eng
Format: epub
ISBN: 9783030272371
Publisher: Springer International Publishing

(8.1.2)

relating the coordinates of an event in the Lorentz frame to the coordinates of the same event in the Lorentz frame , provided that the matrix satisfies the conditions

(8.1.3)

Since in every Lorentz frame the square of the distance s between two events and assumes the form

(8.1.4)

we can say that the Lorentz transformations are orthogonal transformations of , provided that the orthogonality is evaluated by the scalar product . Owing to (8.1.3) or (8.1.4), we conclude that the set of all these transformations is a group.

The norm of a 4-vector can be positive, negative, or zero. In the first case, we say that is a spacelike 4-vector. In the second case, is said to be a timelike 4-vector. Finally, if , then is said to be a lightlike vector or a null 4-vector. At every point , the set of events such that the 4-vectors are null, i.e., the set of the events P satisfying the condition

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