will appear the same as they would if the system were standing still. Let us first investigate whether Newtons laws appear the same in the moving sys Suppose that Moe is moving in the x-direction with a uniform velocity u, and he measures the position of a certain point, shown in Fig. 15-1. He designates the x-distance"of the point in his coordinate system as x'. Joe is at rest, and measures the position of the same point, designating its x-coordinate in his system as x The relationship of the coordinates in the two systems is clear from the diagram After time t Moe's origin has moved a distance ut, and if the two systems originally coincided y =y, (152) X,y12) x If we substitute this transformation of coordinates into Newton 's laws we find that these laws transform to the same laws in the primed system; that is, the laws Fig. 15-1. Two coordinate systems of Newton are of the same form in a moving system as in a stationary system, and in uniform relative motion along the therefore it is impossible to tell, by making mechanical experiments, whether the x-axes. system is moving or not. The principle of relativity has been used in mechanics for a long time. It was employed by various people, in particular Huygens, to obtain the rules for the collision of billiard balls, in much the same way as we used in Chapter 10 discuss the conservation of momentum. In the past century interest in it wa heightened as the result of investigations into the phenomena of electricity, mag netism, and light. A long series of careful studies of these phenomena by many people culminated in Maxwells equations of the electromagnetic field, which Maxwell equations did not seem to obey the principle of relativity. That ss/ the describe electricity, magnetism, and light in one uniform system. However, tI transform Maxwells equations by the substitution of equations 15.2, their form does not remain the same, therefore, in a moving space ship the electrical and optical phenomena should be different from those in a stationary ship Thus one could use these optical phenomena to determine the speed of the ship; in particular, one could determine the absolute speed of the ship by making suitab optical or electrical measurements. One of the consequences of Maxwells equa- tions is that if there is a disturbance in the field such that light is generated, these electromagnetic waves go out in all directions equally and at the same speed c, or 186,000 mi/sec. Another consequence of the equations is that If the source of the disturbance is moving, the light emitted goes through space at the same speed c. This is analogous to the case of sound, the speed of sound waves being likewise independent of the motion of the source This independence of the motion of the source, in the case of light, brings up an interesting problem Suppose we are riding in a car that is going at a speed u, and light from the rear is going past the car with speed c. Differentiating the first equation in (15.2) gives x'/dt= dx/dt -u, which means that according to the galilean transformation the apparent the passing light, as we measure it in the car, should not be c but should be For instance, if the car is going 100,000 mi /sec, and the light is going mi/sec, then apparently the light going past the car should go 86,000 mi/sec. In any case, by measuring the speed of the light going past the car(if the galilean transformation is correct for light), one could determine the speed of the car. A number of experiments based on this general idea were performed to determine the velocity of the earth, but they all failed-they gave no velocity at all. We shall discuss one of these experiments in detail, to show exactly what was done wrong with the equations of physics. What could it be?