Two events 1 and 2 that take place at different positions and but at the same time , as measured in some reference frame, are said to be simultaneous in that reference frame. Simultaneity is determined by when the events actually happen, not when they are seen or observed. In general, simultaneous events are not seen at the same time because of the difference in light travel times from the events to an experimenter.
An experimenter in reference frame S stands at the origin looking in the positive x-direction. At she sees firecracker 1 explode at . A short time later, at she sees firecracker 2 explode at . Are the two explosions simultaneous? If not, which firecracker exploded first?
MODEL Light from both explosions travels toward the experimenter at .
SOLVE The experimenter sees two different explosions, but perceptions of the events are not the events themselves. When did the explosions actually occur? Using the fact that light travels at , we can see that firecracker 1 exploded at and firecracker 2 also exploded at . The events are simultaneous.