One of the most difficult and misunderstood concepts in the space section of the current NSW HSC Physics syllabus is simultaneity. Listed below are some tutorial points on this concept. Two sentences from Einstein's own popular exposition on relativity, Relativity, the Special and General Theory, Methuen, 1920, are given italics.
- A frame of reference is a measurement system (coordinate system) where time and position values of an event can be determined. A railway platform is a frame of reference. A moving train is a frame of reference. A person on the platform makes measurements in the platform reference frame. A passenger on the train makes measurements in the reference frame of the train.
- Two events are simultaneous in a reference frame if each has the same time coordinate in this reference frame.
- Every reference body (coordinate system) has its own particular time; unless we are told the reference body to which the statement of time refers, there is no meaning in a statement of the time of an event.
- Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity).
- Suppose that two simultaneous events (such as lightning strikes) occur at the different points x1 and x2 in the reference frame of the platform. The times at which these events occur in the reference frame of the train are not the same as those in the reference frame of the platform. The time interval between these events in the platform reference frame is zero. The time interval between these events in the reference frame of the train is -v/c2(1-v2/c2)-1/2(x2-x1). This expression shows that the time interval between two events depends on the location of the events and the relative speed of the reference frames. The factor c is the speed of light in a vacuum, this being the same in all inertial (non accelerating) frames of reference.