Special Theory of Relativity

Being teacher i want to discus these facts about physics to you guys .
It was found that there was no displacement of the interference fringes, so that the result of the experiment was negative and would, therefore, show that there is still a difficulty in the theory itself. . . .Albert Michelson
One of the great theories of physics appeared early in the twentieth century when Albert Einstein presented his special theory of relativity in 1905. We learned in introductory physics that Newton’s laws of motion must be measured relative to some reference frame. A reference frame is called an inertial frame if Newton’s laws are valid in that frame. If a body subject to no net external force moves in a straight line with constant velocity, then the coordinate system attached to that body defi nes an inertial frame. If Newton’s laws are valid in one reference frame, then they are also valid in a reference frame moving at a uniform velocity relative to the first system. This is known as the Newtonian principle of relativity or Galilean invariance. Newton showed that it was not possible to determine absolute motion in space by any experiment, so he decided to use relative motion. In addition, the Newtonian concepts of time and space are completely separable. Consider two inertial reference frames, K and K, that move along their x and x œ axes, respectively, with uniform relative velocity v as shown in Figure 2.1. We show system K moving to the right with velocity v with respect to system K, which is fixed or stationary somewhere.

One result of the relativity theory is that there are no fixed, absolute frames of reference. We use the term fixed to refer to a system that is fixed on a particular object, such as a planet, star, or spaceship that itself is moving in space. The transformation of the coordinates of a point in one system to the other system is given by x œ x vt yœ y (2.1) zœ z Similarly, the inverse transformation is given by x x œ vt y yœ (2.2) z zœ where we have set t t œ because Newton considered time to be absolute. Equations (2.1) and (2.2) are known as the Galilean transformation. Newton’s laws of motion are invariant under a Galilean transformation; that is, they have the same form in both systems K and K. In the late nineteenth century Albert Einstein was concerned that although Newton’s laws of motion had the same form under a Galilean transformation, Maxwell’s equations did not. Einstein believed so strongly in Maxwell’s equations that he showed there was a significant problem in our understanding of the Newtonian principle of relativity. In 1905 he published ideas that rocked the very foundations of physics and science. He proposed that space and time are not separate and that Newton’s laws are only an approximation. This special theory of relativity and its ramifications are the subject of this chapter. We begin by presenting the experimental situation historically—showing why a problem existed and what was done to try to rectify the situation. Then we discuss Einstein’s two postulates on which the special theory is based. The interrelation of space and time is discussed, and several amazing and remarkable predictions based on the new theory are shown. As the concepts of relativity became used more often in everyday research and development, it became essential to understand the transformation of momentum, force, and energy. Here we study relativistic dynamics and the relationship between mass and energy, which leads to one of the most famous equations in physics and a new conservation law of mass-energy. Finally, we return to electromagnetism to investigate the effects of relativity. We learn that Maxwell’s equations don’t require change, and electric and magnetic effects are relative, depending on the observer. We leave until Chapter 15 our discussion of Einstein’s general theory of relativity.