Chapter 36 Relativity

A photograph of the Compact Muon Solenoid detector at the Large Hadron Collider.

The Compact Muon Solenoid detector at the Large Hadron Collider, where protons are accelerated to 99.999999% of the speed of light.

In This Chapter, you will learn how relativity changes our concepts of space and time.

What is an inertial reference frame?

Inertial reference frames are reference frames that move relative to each other with constant velocity.

  • You’ll learn to work with the positions and times of events.

  • All the clocks in an inertial reference frame are synchronized.

《 LOOKING BACK Section 4.3 Relative motion

The figure illustrates graphical representation of an Inertial reference frame.

What is relativity about?

Einstein’s theory of relativity is based on a simple-sounding principle: The laws of physics are the same in all inertial reference frames. This leads to these conclusions:

  • Light travels at the same speed c in all inertial reference frames.

  • No object or information can travel faster than the speed of light.

    The figure illustrates graphical representation of Einstein's theory of relativity.

How does relativity affect time?

Time is relative. Two reference frames moving relative to each other measure different time intervals between two events.

  • Time dilation is the idea that moving clocks run slower than clocks at rest.

  • We’ll examine the famous twin paradox.

    The figure illustrates two clocks placed in a reference frame.

How does relativity affect space?

Distances are also relative. Two reference frames moving relative to each other find different distances between two events.

  • Length contraction is the idea that the length of an object is less when the object is moving than when it is at rest.

    The figure illustrates how relativity affects space.

How does relativity affect mass and energy?

Einstein’s most famous equation, E=mc2, says that mass can be transformed into energy, and energy into mass, as long as the total energy is conserved.

  • Nuclear fission converts mass into energy.

  • Collisions between high-speed particles create new particles from energy.

    The figure illustrates the equivalence of mass and energy theory of Einstein.

Does relativity have applications?

Abstract though it may seem, relativity is important in technologies such as medical PET scans (positron-emission tomography) and nuclear energy. And the global GPS system, a technology we use every day, functions only when the signals from precision clocks in orbiting satellites are corrected for relativistic time dilation.

A photograph of an electronic pad showing GPS.

Learning Objectives

After studying this chapter, you should be able to

  1. 36.1 Work with reference frames and Galilean relativity.

  2. 36.2 Explain the principle of relativity.

  3. 36.3 Work with events and measurements.

  4. 36.4 Solve problems about simultaneity.

  5. 36.5 Calculate proper time and time dilation.

  6. 36.6 Solve relativity problems using the Lorentz transformations.

  7. 36.7 Calculate relativistic momentum.

  8. 36.8 Calculate relativistic energy and apply mass-energy equivalence.