Postulates of Special Relativity

As we learned previously, the principle of relativity states that the laws of physics are the same in all inertial reference frames. The principle of relativity applies to Einsteinian relativity just as it applies to Galilean relativity.

Notice that the constancy of the speed of light in all reference frames is consistent with the principle of relativity. However, as noted above, it is inconsistent with our notions as to how velocities add, or alternatively, how we think the world should look from reference frames moving at different speeds. We have called the classical way of understanding the view from different reference frames Galilean relativity. The new way that reconciles the behavior of objects moving at very high speeds is called Einsteinian relativity. Einstein's great contribution was to discover the laws that tell us how the world looks from reference frames moving at high speeds relative to each other. These laws constitute a geometry of spacetime, and from them all of special relativity can be derived.

All of the observed facts about spacetime can be derived from two postulates:

Figure 4.4: Triangle for Pythagorean theorem in spacetime.

• Whether two events are simultaneous depends on the reference frame from which they are viewed.
• Spacetime obeys a modified Pythagorean theorem, which gives the distance, $I$, in spacetime as
  

  $$I^2 = X^2 - c^2 T^2 ,$$ (5.3)

  
  
  where $X$, $T$, and $I$ are defined in figure 4.4.

Let us discuss these postulates in turn.