Extra Credit: Show that the appropriate condition for forbidding time reversal in (Proper) Lorentz transformations is . Transformations that satisfy this criteria are called orthochronous transformations. One could equally easily derive a condition that picks out all transformations that reverse time, i.e. non-orthochronous transformations. In this case, the condition is . Hint: Consider the Minkowski metric in two coordinate systems related by a generic transformation.