Now that we have stated the Principle of Relativity we can examine its implications, and almost immediately we find reason to worry.
Maxwell's equations (the equations of electromagnetism, see page ) contain a quantity we called c, the speed of light, which is given without reference to any inertial observer. So, if we accept the Principle of Relativity and trust Maxwell's equations, we must conclude that c is the same for all inertial observers. So if Jack measures the speed of a beam of light while sitting at the top of the hill, and Jill also measures the speed of the same beam of light while running up the hill, they should get exactly the same answer, no matter how fast Jill runs. It is often said that Einstein ``proved that everything is relative'' but, in fact, his first conclusion was that the speed of light is absolute.
This property of light is very different from, say, the properties of peas as described by the mechanics of Newton: if a person rides on a scooter and shoots peas, these move faster than the peas shot by a person standing by (see Sect. 5.4.1). In contrast if the person on the scooter turns on a laser and the person standing by does the same when they coincide on the street, these two laser beams will reach Pluto at the same time (Fig. 6.5); this happens even if the scooter moves at 99% of the speed of light.
Newton would be horrified by this behavior of light beams: according to his mechanics velocities add, so that the laser beam from the scooter should reach Pluto sooner.
Thus, once Einstein adopted his Principle of Relativity, he was faced with a choice: either dismiss Newtonian mechanics or dismiss Maxwell's equations. It was impossible for them both to be right. Newton's mechanics had survived for about 250 years, it was universally accepted in the physics community, and its predictions agreed with all experiments (done up to 1905). Maxwell's equations, in contrast, were rather new, were not tested as thoroughly as Newton's, and were not universally accepted. Nonetheless Einstein took the daring path of siding with Maxwell and so challenged the whole edifice of the Newtonian theory. He was right.
Having chosen sides, Einstein assumed that Newton's mechanics were not a good description of Nature under all circumstances: it must then be only a good approximation. Einstein's work was then cut out for him: he needed to find a generalization of Newton's mechanics which is consistent with the Principle of Relativity, and which agrees with experiment as well as (or better than) Newton's theory. He was successful.
Significant discrepancies between Newton's and Einstein's mechanics become noticeable only at speeds close to c which explains why no problems were detected with Newton's theory before 1905: all experiments were done at speed very small compared to c. In this century a wealth of experimental evidence has been gathered which supports Einstein's mechanics in favor of Newton's. The best examples appear in experiments done since the 1950's using subatomic particles which are relatively easily accelerated to speeds approaching c. The behavior of such experiments completely vindicates Einstein's approach while being inexplicable from the Newtonian viewpoint.
Concerning the addition of velocities, Newton's formula is, strictly speaking, not correct even for slow moving obejcts. The corrections are, however, very samll when the speeds are small compared to that of light. For example for the case of the passenger in a train in 5.7) if the speed of the ball is u and that of the train is v the speed measured from the platform is not u + v as Newton would claim, but
In conclusion: the Principle of Relativity together with Maxwell's equations imply that there is a universal speed whose value is the same to all inertial observers. This fact required several fundamental changes in the manner we understand the world.