The Special Theory of Relativity

The theory of space and time developed by Albert Einstein that has become one of the foundations of modern physics. Einstein’s theory of relativity often is discussed in two general categories: the special theory of relativity, which he first proposed in 1905, and the general theory of relativity, which he presented in 1915. The special theory of relativity is concerned with the laws of physics as seen by observers moving relative to one another at constant velocity—that is, by observers in non-accelerating or inertial reference frames. Special relativity has been well demonstrated and verified by many types of experiments and observations.

Einstein proposed two fundamental postulates in formulating special relativity: (1) First postulate of special relativity: The speed of light (c) has the same value for all (inertial-reference-frame) observers, regardless and independent of the motion of the light source or the observers. (2) Second postulate of special relativity: All physical laws are the same for all observers moving at constant velocity with respect to one another.

The first postulate appears contrary to our everyday “Newtonian mechanics” experience, yet the principles of special relativity have been more than adequately validated in experiments. Using special relativity, scientists can now predict the space-time behavior of objects traveling at speeds from essentially zero up to those approaching that of light itself. At lower velocities the predictions of special relativity become identical with classical Newtonian mechanics.

There are some interesting consequences of the Theory of Relativity:

• The first interesting relativistic effect is called time dilation. Simply stated—with respect to a stationary observer/ clock—time moves more slowly on a moving clock system.

• Another interesting effect of relativistic travel is length contraction. We first define an object’s proper length (Lp) as its length measured in a reference frame in which the object is at rest. Then, the length of the object when it is moving (L) - as measured by a stationary observeris always smaller, or contracted. This apparent shortening, or contraction, of a rapidly moving object is seen by an external observer (in a different inertial reference frame) only in the object’s direction of motion.

Special relativity also influences the field of dynamics. Although the rest mass (mo) of a body is invariant, its “relative” mass increases as the speed of the object increases with respect to an observer in another fixed or inertial reference frame. An object’s relative mass is given by

 m = (1 / β) m_o

This simple equation has far-reaching consequences. As an object approaches the speed of light, its mass increases and eventually becomes infinite. Since things cannot have infinite masses, physicists conclude that material objects cannot reach the speed of light. This is basically the speed-of-light barrier, which appears to limit the speed at which interstellar travel can occur. From the theory of special relativity, scientists now conclude that only a “zero- rest-mass” particle, such as a Photon, can travel at the speed of light. There is one other major consequence of special relativity that has greatly affected our daily lives - the equivalence of mass and energy from Einstein’s very famous formula:

E = Δm c² 

where E is the energy equivalent of an amount of matter (?m) that is annihilated, or converted completely into pure energy, and c is the speed of light. This simple yet powerful equation explains where all the energy in nuclear fission or nuclear fusion comes from. The complete annihilation of just one gram of matter releases about 9 × 1013 joules of energy.

Questions to Ponder

• If 2 objects are moving in the opposite directions at the speed of light, what is their relative velocity?
• Does gravity travel faster than the speed of light?
• Why do the laws of physics break down in singularities?