Relativity: Know all about special theory, general theory and more

A general theory of Physics, primarily conceived by Albert Einstein, which involves a profound analysis of time and space, leading to a generalization of physical law, with far-reaching implications in important branching of physics and in cosmology is what we know as relativity.

A general theory of Physics, primarily conceived by Albert Einstein, which involves a profound analysis of time and space, leading to a generalization of physical law, with far-reaching implications in important branching of physics and in cosmology is what we know as relativity.

History of Relativity

Historically, the theory developed in two stages. Einstein’s initial formulation in 1905,(which is now known as the special, or restricted, theory of relativity) does not treat gravitation, and one of the two principles on which it is based, the principle of relativity(the other being the principle of the constancy of the speed of light), stipulates the form in variance of physical laws only for inertial reference systems. Both restrictions were removed by Einstein in his general theory of relativity developed in 1915, which exploits a deep seated equivalence between inertial and gravitational effects, and leads to a successful relativistic generalization of Isaac Newton’s theory of gravitation.

Special theory: The key feature of the Theory of Special relativity is the elimination of an absolute notion of simultaneity in favor of the notion that all observers always measure light to have the same velocity in vacuum, c, independent of their own motion. The impetus for the development of the theory arose from the theory of electricity and magnetism developed by J.C Maxwell. This theory accounted for all observed phenomena involving electric and magnetic fields and also predicted that disturbances in these fields would propagate as waves with definite speed, c, in vacuum. These electromagnetic waves predicted in Maxwell’s theory successfully accounted for the existence of light and other forms of electromagnetic radiation. However, the presence of a definite speed, c, posed a difficulty, since if one velocity c, it would be expected that another inertial observer, moving toward the light ray with velocity v with respect to the first, would measure the light to have velocity c+v. Hence, it initially was taken for granted that there must be a preferred rest frame in which Maxwell’s equations would be valid, and only in that frame would light be seen to travel with velocity c.
However, this viewpoint was greatly shaken by the 1887 experiment of A.A. Michelson and E. W Morley, which failed to detect any motion of the Earth through the ether. By radically altering some previously held beliefs concerning the structure of space and time, the theory of special relativity allows Maxwell’s equations to hold, and light to propagate with velocity c, in all frames reference, thereby making Maxwell’s theory consistent with the null result of Michelson and Morley.

Simultaneity in relativity Physics: The most dramatic aspect of the theory of special relativity is its overflowing of the notion that there is a well – defined, observer independent meaning to the notion of simultaneity. To explain more precisely what it means by absolute simultaneity, the following terminology will be introduced. An event is a point of space at an instant of time. Since it takes four numbers to specify an event- one for the time at which the event occurred and three for its spatial position- it follows that the set of all events constitutes a four dimensional continuum, which is referred to as space-time.

General Theory: General relativity is the geometric theory of gravitation developed by Albert Einstein in 1915. It is a generalization of special relativity, and includes the classical gravitational theory of Newton as the limiting case when the gravitational fields involved are weak and the velocities of all the bodies involved are small compared to the speed of light c. The most important applications of the theory are to the structure of neutron stars and black holes, the large –scale cosmological description of the universe, and the motion of the bodies in the solar system.

Need for relativistic theory: One of the basic tenets of special relativity is that no physical effect can propagate with a velocity greater than the speed of light, c, which represents a universal speed limit.
On the other hand, classical gravitational theory describes the gravitational field of a body throughout space as a function of its instantaneous position which is equivalent to the assumption that gravitational effects propagate with an infinite velocity. Thus, special relativity and classical gravitational theory of gravity is necessary.

Principle of Equivalence: It had long been considered a fundamental question why bodies of different mass fall with the same acceleration in a gravitational field. This situation was explained by Sir Isaac Newton with the statement that both the gravitational force on a body and its inertial resistance to acceleration are proportional to its mass. Thus the mass cancels out of the mathematical description of the motion. Experiments confirm this cancellation to any accuracy of a few parts in 1012.

Newton’s explanation is more in the nature of an ad hoc description. A deeper and more natural explanation occured to Albert Einstein. There are numerous forces other than gravity which are mass- proportional. These generally arise due to the use of accelerated coordinate systems to describe the motion, for example, the centrifugal force encountered in a rotating coordinate system. If an observer in the gravitational fields of the Earth and another in an accelerating elevator or rocket in free space both observe it to accelerate relative to the floor. According to classical theory, the Earth-based observer would attribute it to the accelerated floor overtaking the uniformly moving body. In both cases the motion is identical, and in particular the acceleration is independent of the mass of the test body.

Einstein elevated this fact to a general principle, the principle of equivalence; the principal states that on a local scale all physical effects of a gravitational field are indistinguishable from the physical effects of an accelerated coordinate system. This profound principle is the physical cornerstone of the theory of general relativity. From the point of view of the principle of equivalence, it is obvious why the motion of a test body in a gravitational field is independent of its mass. But the principle applies not only to mechanics but to all physical phenomena and thereby has profound consequences for electromagnetic and other mechanical phenomena.

First Published:May 30, 2020, 11:48 a.m.