# Special Relativity

## Connection for AP® Courses

In this chapter you will be introduced to the theory of special relativity, which was first described by Albert Einstein in the year 1905. The chapter opens with a discussion of Einstein’s postulates that form the basis of special relativity. You will learn about an essential physics framework that is used to describe the observations and measurements made by an observer in what is called the “inertial frame of reference” (Enduring Understanding 3.A). Special relativity is a universally accepted theory that defines a relationship between space and time (Essential Knowledge 1.D.3). When the speed of an object approaches the speed of light, Newton’s laws no longer hold, which means that classical (Newtonian) mechanics (Enduring Understanding 1.D) is not sufficient to define the physical properties of such a system. This is where special relativity comes into play. Many interesting and counterintuitive physical results follow from the theory of special relativity. In this chapter we will explore the concepts of simultaneity, time dilation, and length contraction.
Further into the chapter you will find information that supports the concepts of relativistic velocity addition, relativistic momentum, and energy (Enduring Understanding 4.C). Learning these concepts will help you understand how the mass (Enduring Understanding 1.C and Essential Knowledge 4.C.4) of an object can appear to be different for different observers and how matter can be converted into energy and then back to matter so that the energy of the system remains conserved. (Essential Knowledge 1.C.4 and Enduring Understanding 5.B). The information and examples presented in the chapter support Big Ideas 1, 3, 4, and 5 of the AP® Physics Curriculum Framework.
The content of this chapter supports:
Big Idea 1 Objects and systems have properties such as mass and charge. Systems may have internal structure.
Enduring Understanding 1.C Objects and systems have properties of inertial mass and gravitational mass that are experimentally veriﬁed to be the same and that satisfy conservation principles.
Essential Knowledge 1.C.4 In certain processes, mass can be converted to energy and energy can be converted to mass according to 
 
, the equation derived from the theory of special relativity.
Enduring Understanding 1.D Classical mechanics cannot describe all properties of objects.
Essential Knowledge 1.D.3 Properties of space and time cannot always be treated as absolute.
Big Idea 3 The interactions of an object with other objects can be described by forces.
Enduring Understanding 3.A All forces share certain common characteristics when considered by observers in inertial reference frames.
Essential Knowledge 3.A.1 An observer in a particular reference frame can describe the motion of an object using such quantities as position, displacement, distance, velocity, speed, and acceleration.
Big Idea 4 Interactions between systems can result in changes in those systems.
Enduring Understanding 4.C Interactions with other objects or systems can change the total energy of a system.
Essential Knowledge 4.C.4 Mass can be converted into energy and energy can be converted into mass.
Big Idea 5 Changes that occur as a result of interactions are constrained by conservation laws.
Enduring Understanding 5.B The energy of a system is conserved.
Essential Knowledge 5.B.11 Beyond the classical approximation, mass is actually part of the internal energy of an object or system with 
 
.
It is important to note that although classical mechanic, in general, and classical relativity, in particular, are limited, they are extremely good approximations for large, slow-moving objects. Otherwise, we could not use classical physics to launch satellites or build bridges. In the classical limit (objects larger than submicroscopic and moving slower than about 1% of the speed of light), relativistic mechanics becomes the same as classical mechanics. This fact will be noted at appropriate places throughout this chapter.