The first postulate of the special theory of relativity is that there are no preferred inertial frames. This postulate is nothing more than a statement of the principle of relativity that we associated with Galileo. Thus the first postulate is "old hat." The second postulate can be stated in two, equivalent ways. In can be stated as "light (or any electromagnetic radiation) does not require a medium in which to propagate" or "the speed of light is the same in all inertial frames." These statements are equivalent. For example, if the speed of light is the same in all inertial frames, then light must propagate without a medium; otherwise the medium would affect the speed of light as viewed from different inertial frames. This second postulate is the "nonintuitive" one and leads to all the "weird" effects of special relativity. For mechanical waves, such as sound or water waves, a medium is essential for wave propagation. The medium carries along the waves and there are no surprising results. For electromagnetic waves, no medium is needed and we are led to new conclusions about the nature of space and time. Of course, the postulates can be tested only by experiment. The experimental confirmations of the special theory of relativity are overwhelming.

Once we have the postulates, we would like to see how to determine some of the consequences. I will do this two ways. First, I will describe some thought experiments from which we can deduce some properties of space and time. Then I will repeat the same discussion using some mathematical equations known as the Lorentz transformation. Whatever the method, remember it is the postulates (especially the second postulate) that is dictating the results.

The first step is to decide how we will make measurements. In each inertial frame, imagine we have an infinite number of observers, each located at a specific point in the inertial frame with a clock. The observers know where they are because they have measured their distance from the origin of their coordinate system using meter sticks. The role of each observer is to record events. An event is something that happens at a position in the inertial frame at a given time in that frame. Thus an event is located by three position coordinates and one time in each inertial frame. Of course, the coordinates of the events will be different in different inertial frames moving relative to one another at constant velocity, but the event itself is absolute. Examples of events are birth, death, explosions, detectors going off, etc. In other words, if you are born in one inertial frame, you are also born in any other inertial frame – the time and location of your birth may be different in different frames, but the fact of your birth is absolute.

There remains the question of how we can be sure that all the observers clocks in a given inertial frame are synchronized. One way of doing this is to have all observers in a given frame get together, set their clocks and move slowly to their locations. However, there is a better way to accomplish this that will guarantee that all observers in any inertial frame will have their clocks synchronized (although there is no guarantee that clocks of observers in different inertial frames will be synchronized). Imagine there is a flash of light. A spherical ripple of light will propagate out in all directions in all inertial frames. Let us arbitrarily denote the location of this event (flash of light) as occurring at the origin of all inertial frames and take the time of this event equal to zero in all inertial frames. Clearly we can do this since the point we call the origin in any inertial frame is arbitrary and the time we call "zero" is also arbitrary. However, we must now set the clocks of all other observers in a prescribed fashion. In any inertial frame, an observer who is 186,000 miles from the origin in that frame sets her clock at 1.00 sec when the ripple of light passes by her, the observer at 93,000 miles from the origin sets his clock at 0.500 sec, etc. Note that we can do this in each inertial frame, using the same technique, since the speed of light is the same in all inertial frames. When we are done, the clocks in each inertial frame will be synchronized, but the only clocks in different inertial frames that are guaranteed to read the same time are the ones at the origins of the inertial frames.

The method for deducing the consequences of the special theory of relativity then consists of viewing a series of events from different inertial frames and comparing the results. Some examples of this are given on the "Special Relativity" notes.