Explain the two theories of relativity in a simplified form.

Question:

Explain the two theories of relativity in a simplified form.

The Special and the General Theory of Relativity

At the turn of the twentieth century, classical physics had two eminently successful theories. One was Newtonian mechanics which dealt with matter and the other was Maxwell's theory of the electromagnetic field. Newtonian mechanics gives the correct particle dynamics in any inertial frame of reference. To translate the data obtained in one frame of reference to the variables used in the other frame the Galilean transformation equations are used. The Newtonian theory is Galilean invariant. That is, Newton's law has the same mathematical structure in all inertial frames. Next, consider maxwell's equations. The entire gamut of known electromagnetic phenomena falls within its ambit. But there is one problem. Maxwell's equations are not Galilean invariant. The mathematical structure changes from one inertial frame to another when Galilean transformation equations are applied. The humongous success of the Newtonian theory and the relative newness of maxwell's equations prompted a modification of the Maxwellian theory in order to make it Galilean invariant. New terms were appended to Maxwell's equations. But this predicted new electromagnetic phenomena which failed to show up under rigorous experimental conditions. In the meantime, Lorentz worked out the transformation equations that rendered Maxwell's equations invariant under translation from one inertial frame to another. So now classical physics had to face the conundrum of having to deal with two eminently successful theories each with its own transformation relation but apparently not in conformity with each other.

Answer and Explanation:

Enter Albert Einstein. This patent clerk had no qualms in summarily dismissing the Newtonian theory as incomplete and suggesting that Maxwell's equations with its attendant Lorentz transformations should be given primacy over the Newtonian theory and the related Galilean transformations. Thus it is the Newtonian theory that is in need of modification. The basic conceptions of mechanics namely mass, length and time all undergo drastic changes once they are made Lorentz compliant. The first casualty is the concept of simultaneity. Two events that are simultaneous in one frame of reference need not be simultaneous in other frames. Next comes the concept of length. The length of an object measured in its rest frame is always greater than the length as determined in a frame in which the object is moving. Similarly, the lifetime of a particle in its own rest frame is less than the lifetime as determined in a frame in which it is moving. The mass of a particle in its own rest frame is less than the mass it would have in a frame in which it is moving.

These counter-intuitive phenomena follow from the postulates of the special theory of relativity as stated by Einstein. There are two postulates. The postulate of relativity states that the laws of physics should have the same mathematical structure in all inertial frames. The correct transformation equations from one frame to the other are the Lorentz transformations. The second postulate is called the postulate of the constancy of the speed of light. It states that the speed of light is the same in all inertial frames. The results of the Michelson- Morley experiment and Fizeau's experiment can easily be explained with the special theory of relativity. With the advent of elementary particle experiments, the theory of relativity has been borne out innumerable times.

Einstein further generalized his theory to the case of non-inertial or accelerated frames. This is called the general theory of relativity (GTR). It is constructed on the premise that the inertial mass and the gravitational mass of an object are always numerically equal. In no experiment will these attributes show a numerical difference. This is called the principle of equivalence. In other words, GTR maintains that gravity is nothing but acceleration. The mass and energy at a locality determine the metric structure of that space-time region. Gravitation is simply a manifestation of the geometry. It is the curvature in the space-time brought about by the mass of the sun that forces the planets to travel through their particular trajectories in the space-time interval minimizing grooves offered by the fabric of space-time. With this picture, Einstein accurately explained the observed perihelion precession of mercury. He also made a prediction that starlight would bend due to the mass of the sun and this was indeed observed during the 1919 solar eclipse in the celebrated experiment undertaken by Eddington.


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General and Special Relativity: Theory and Examples

from CLEP Natural Sciences: Study Guide & Test Prep

Chapter 5 / Lesson 6
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