WARNING In order to understand the following slides you should first understand how to construct, for a given observer, an equitemp corresponding to a given equiloc.
• For a given observer all equilocs are parallel • For a given observer all equitemps are parallel • Different observers have different equilocs (they are not parallel) • Different observers have different equitemps (they are not parallel)
• The concept of parallelism in not metric dependent • The orthogonality concept is metric dependent • This means that “perpendicular” depends on the observer • Euclidean orthogonality (like stating that horizontal is perpendicular to vertical) is not applicable to special relativity • In special relativity and, for a given observer, any equitemp is orthogonal to any equiloc
A universal story, valid for any observer (see next slide): • Two particles were created at events A and B and then these two particles annihilate each other, after colliding at event C. • After the collision at event C, two photons are created: one is propagating to the left (from C to D); the other one is propagating to the right (from C to E). So, any valid story cannot state that event C may occur before A or before C. Otherwise, causality would be violated.