The energy-momentum vector

Next, let us consider the case when the velocities of objects are close to the speed of light c, and the Lorentz transformation must be used for relating observations from different inertial frames.

Assume that a baseball which was initially at rest is accelerated to half the speed of light by an impact with a bat at point A on the spacetime diagram. The questions we wanted answers for in Chapter 11 were:

As in the Newtonian case, let's represent the “state of motion” of an object with a vector on the spacetime diagram. First, to represent the “state in which the object is at rest,” we follow the Newtonian case and use a vector pointing vertically up from the spacetime origin with length proportional to the object's mass. (See the figure on the opposite page, top-left.) Next, the “state in which the object is moving with velocity v” is the same as “the state in which the object is at rest” but observed from an inertial frame moving at velocity –υ relative to the first.