How has Einstein derived special relativity? Explain.
The Special Theory Of Relativity:
There are two postulates of the special theory of relativity. The first postulate states that the laws of physics should have the same mathematical structure in all inertial frames. The correct transformation equations connecting inertial frames are the Lorentz transformations. The second postulate is 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 are successfully explained using the special theory of relativity.
Answer and Explanation:
Classical physics had two successful theories capable of describing all observed phenomena at the time they were constructed.
One was Newtonian mechanics. It dealt with the matter. The other was Maxwell's theory of the electromagnetic field.
In any inertial frame of reference Newtonian mechanics gives the correct particle dynamics. To connect the different inertial frames of reference the Galilean transformation equations are used. The Newtonian theory is Galilean invariant. This means that Newton's laws possess the same mathematical structure in all inertial frames.
All the known electromagnetic phenomena can be described using Maxwell's Equations. But Maxwell's equations are not Galilean invariant. When new terms were added to Maxwell's equations to make them Galilean invariant, they predicted new electromagnetic phenomena. These phenomena are not observed in nature.
At that time Lorentz developed the correct transformation equations which made the Maxwell equations invariant under change of frames.
Thus classical physics now had two eminently successful theories each with its own transformation equations.
It was Albert Einstein, the patent office clerk, who showed the courage to dismiss the Newtonian theory as incomplete. He suggested that Maxwell's equations were correct and complete. Again, he proposed that the correct transformation equations for both mechanics and electrodynamics are the Lorentz Transformation equations. This meant that it is the Newtonian theory that needed modification. Thus was born special relativity.
Once Newton's Law is made Lorentz invariant, the basic conceptions of mechanics which are the mass, length and time -undergo drastic changes. Now two events that are simultaneous in one frame of reference need not be simultaneous in other inertial frames. Again, the length of an object is measured to be contracted in a moving frame as compared to one in which it is at rest. Similarly, the lifetime of a particle as measured in a moving frame is greater than that in its rest frame. Also, the mass of a particle is measured to be greater in a moving frame as compared to that in its rest frame.
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from Remedial Algebra IChapter 25 / Lesson 1