Unit 11. Einstein’s special theory of relativity

Einstein interpreted the failure of the Michelson-Morley experiment to mean that the velocity of light is invariant, that time and distance are relative and that Galilean – Newtonian mechanics must be modified accordingly. Out of these modifications came the theory of relativity.

Relativity is divided into two parts. One part is called the special, or restricted, theory of relativity, and the other is called the general theory. The special theory, developed by Einstein in 1905, deals with observers and their reference frames moving with constant velocities. The mathematics of the special theory is simple enough.

The general theory, proposed by Einstein in 1915, deals with motions of bodies in accelerated frames of reference. The mathematics of the general theory is quite difficult, and the experimental evidence for its validity is not as well founded as for the special theory.

Since the Michelson-Morley experiment fails to provide a fixed frame of reference in space, Einstein’s theory assumes that all such experiments will fail, at that at relatively high speeds the laws of Newton are not valid. Einstein’s special theory of relativity shows that the laws of physics can be restated so that they will apply to any frame of reference, and that at low relative speeds these laws reduce to Newton’s laws of motion.

The first postulate for setting up these equations is: The laws of physics apply equally well for all observers as long as they are moving with constant velocities.

The second postulate follows from the assumption that the velocity of light is invariant.

The velocity of light in free space has the same value regardless of the motion of the source and the motion of the observer. To see the meaning of this statement, consider a reference frame and observer O at rest. A source of light S is set up, and by means of an experiment the velocity of light is measured and found to be 3×10⁸ m/s. Another observer O`, moving with a velocity v with respect to O, allows the light from the same source S to pass through his apparatus. Upon measuring the velocity of this same light in his frame, he too finds 3×10⁸ m/s.

For these two identical results to be consistent, Einstein derived new transformation equations. To do this he assumed that distance and time are relative, i. e., they are not invariant.

Classical laws such as Newton’s laws of motion can be used in most applications of kinematics and dynamics to the motions of macroscopic bodies; but at speeds above 10% the speed of light, the relativistic equations should be used.

Words and word combinations to be remembered

failure – неудача, провал	assume – допускать, предполагать	valid – действительный, имеющий силу
observer – наблюдатель	interpret – объяснять, толковать	low – низкий
reference frames – система отсчёта	use – использовать	free – свободный, незанятый
meaning – значение, смысл	consider – думать, рассматривать	consistent – совместимый, согласующийся
statement – заявление, утверждение	set up – устанавливать, ставить	regardless of – не обращая внимания; невзирая на

Ex. 1. Translate from Russian into English:

Скорость света, низкая скорость, движение тел, закон движения, достоверность, пространство, наблюдатель, предположение, кинематика, неизменный, относительный, постоянный, соответственно, ускорить, применять, в независимости от.

Ex. 2. Make up the word combinations using the words from 2 columns, make up some sentences with these word combinations:

The failure	of this statement
The reference	of experiment
The motion	of light
The speed	frame
The meaning	equations
The transformation	of the observer

Ex. 3. Fill in the blanks:

1. Relativity is divided into … .

2. The special theory, developed by … in … , deals with observers and their reference frames moving with constant velocities.

3. The … theory deals with motions of bodies in accelerated frames of reference.

4. The mathematics of the general theory is … .

5. Einstein’s theory assumes that at relatively high speeds the laws of Newton … .

6. Einstein’s special theory of relativity shows that the laws of physics at low relative speeds reduce to … .

7. The laws of physics apply equally well for all observers as long as they … .

8. The velocity of light in free space has … .

9. Classical laws such as Newton’s laws of motion can be used in most applications of kinematics and dynamics to the motions of macroscopic bodies; but at speeds above 10% … .

Ex.4. Choose the right word:

1. Einstein interpreted (the failure / the success) of the Michelson-Morley experiment to mean that the velocity of light is (relative / invariant), that time and distance are (relative / invariant).

2. The special theory deals with observers and their reference frames moving with (constant / different) velocities.

3. The general theory deals with motions of bodies in (accelerating / accelerated) frames of reference.

4. Einstein’s theory assumes that at relatively (slow / high) speeds the laws of Newton are not valid.

5. The laws of physics apply equally well for all observers as long as they (are moving / move) with constant velocities.

6. The velocity of light in free space has the (some / same) value regardless of the motion of the source and the motion of the observer.

7. At speeds above 10% the speed of light, the (relativism / relativistic) equations should be used.

Ex. 5. Answer the following questions:

1. How did Einstein interpret the failure of the Michelson-Morley experiment? 2. Why must Galilean – Newtonian mechanics be modified? 3. How many parts is theory of relativity divided into? 4. What does special theory of relativity deal with? 5. What does general theory of relativity deal with? 6. What does Einstein’s theory assume? 7. When do the laws of physics apply equally well for all observers? 8. Is the velocity of light invariant? 9. What value does the velocity of light have in free space? 10. Einstein assumed that distance and time are relative. What does it mean? 11. When should the relativistic equations be used?