Einstein Postulates for special theory of relativity

THE POSTULATES OF SPECIAL RELATIVITY

A scientific theory usually begins with general statements called postulates, which attempt to provide a basis for the theory. From these postulates we can obtain a set of mathematical laws in the form of equations that relate physical variables. Finally, we test the predictions of the equations in the laboratory. The theory stands until contradicted by experiment, after which the postulates may be modified or replaced, and the cycle is repeated.

In his 1905 paper, entitled "On the Electrodynamics of Moving Bodies," Einstein offered two postulates that form the basis of his special theory of relativity. We can rephrase his postulates as follows:

The principle of relativity: 

1. The laws of physics are the same in all inertial reference frames.
2. The principle of the constancy of the speed of light: The speed of light in free space has the same value c in all inertial reference frames.

The first postulate declares that the laws of physics are absolute, universal, and the same for all inertial observers. Laws that hold for one inertial observer cannot be violated for any inertial observer.

The second postulate is much more difficult to accept, because it violates our "common sense," which is firmly grounded in the Galilean kinematics that we have learned from everyday experiences. Consider three observers A, B, and C, each of whom is at rest in a different inertial reference frame. A flash of light is emitted by observer A, who observes the light to travel at speed c. The frame of observer B is moving away from A at a speed of c/4; Galilean kinematics predicts that B measures the value c c/4 3c/4 for the speed of the light emitted by A. Observer C is in a frame that is moving toward A with speed c/4; according to Galileo, observer C measures a speed of c +c/4 = 5c/4 for the speed of the light emitted by A. Einstein's second postulate, on the other hand, as sets that all three observers measure the same speed c for the light pulse!

This is of course not the way ordinary objects behave. A projectile fired from a moving car has a velocity relative to the ground determined by the vector sum of the velocity of the projectile relative to the car and the velocity of the car relative to the ground. However, the velocities of light waves and particles moving at speeds close to c do not behave in this way. 

Einstein put forth these postulates at a time when experimental tests were difficult or impossible. During the following decades, the development of high-energy particle accelerators made possible the study of the motions of particles at speeds close to c. In 1964, for example, an experiment was performed at CERN, the European high energy particle physics laboratory near Geneva, Switzer land. The proton accelerator at CERN was used to pro duce a beam of particles called neutral pions (°), which decay rapidly (with an average lifetime of about (10-16 s) to two gamma rays:

Gamma rays are electromagnetic radiations that travel at the speed of light. The experimenters measured directly the speed of the gamma rays emitted by the decaying pions, which were moving at a speed of 0.99975c. According to Galileo, gamma rays emitted in the direction of motion of the pions should have a speed of c+0.99975c 1.99975c in the laboratory frame of reference. According to Einstein, they should have a speed of c. The measured speed was 2.9977 X 10 m/s, equal to c to within 1 part in 104, thus providing direct verification of the second postulate.

The two postulates taken together have another consequence: they imply that it is impossible to accelerate a particle to a speed greater than c, no matter how much kinetic energy we give it. This is also a prediction that can be tested in the laboratory, and one that brings out another difference between the postulates of relativity and those of classical physics. Classical physics places no upper limit on the speed that an object may attain; relativity does impose such a limiting speed, which, by the first postulate, must be the same for all frames of reference.

In another experiment done in 1964, electrons were accelerated by a large voltage difference (up to 15 million volts), and the speed of the electrons was directly determined.

Figure  shows the measured speeds as a function of the kinetic energy acquired by the electrons. No matter how much the accelerating voltage is increased, the speed never quite reaches or exceeds c. Once again, experiments at high speeds are inconsistent with predictions based on the kinematics of Galileo and Newton but instead confirm the postulates of special relativity.