## SpecialRelativity

This directory wil contain a variety of problems in special relativity. Particular attention is given to the postulates set forth by Albert Einstein. The wording of these postulates used here are from Elementary Modern Physics written by Weidner and Sells and published by Allyn and Bacon, Inc. 1973

### Postulate I.

The Principle of Relativity: The laws of physics are the same, or invariant, in all inertial systems -- that is, the mathematical form of the law remains the same.

This postulate implies such things as:

• What is, is.
• What is not, is not.
• There is no such thing as a free lunch.
• There is no preferred inertial system.
• What will be, will be.
• Que sera, que sera.
• The universe works.

It will be referred to in the problem solutions as:
The common sense postulate.

### Postulate II.

The speed of light in a vacuum is a constant, independant of the inertial system, the source, and the observer.

The Lorentz transformations relate the space and time intervals between two events observed in one inertial systems to the space and time intervals observed in another inertial system. These intervals are related by the following pair of equations.

The important thing to note about these equations is that they are two simultaneous equations. Well known methods of solving simultaneous equations are then applicable.

There are are 6 parameters, v and c, and the 4 space/time intervals. To solve an equation pair with 6 parameters requires 4 additional values (equations). The known value of c provides one equation. The value of v, the velocity of S' relative to S is normally given. Thus, in the typical problems only two additional equations are needed to solve the equation pair. These are values of any two of the space/time intervals. The other two space/space time intervals can then be determined. Dealing with special relativity problems then requires no more mathematical abilty than that needed to solve simultaneous equations. The method of elimation by substitution is the common way of doing this. This is simply a mechnical process.

The most common difficulty the novice encounters is deducing the value of the two needed values from the problem statement. As will be shown in the problems, the common sense postulate forms a powerful guide to understanding how to proceed and understanding the solution.

Two conditions that are frequently useful are:

• The space interval (the distance) between two events that occur at the same place is zero.
• The time interval between two events that occur at the same time is zero.

Failure to recognize these two ideas is rather common among those learning this subject.

Familiarity with the common terminology of special relativity will be assumed in the following problems. This includes such terms as length contraction, time dilation, proper length, simultaneity, space interval, time interval and inertial system.

The Mighty Rod Grabber 8/28/96