Chapter 27: Relativity

Relativity

The study of objects and phenomena in one reference frame as seen from another reference frame that is moving with respect to the first.

Galilean Relativity

The principle that the laws of mechanics are the same in non-accelerating reference frames.

Inertial Reference Frame

A reference frame that is not accelerating.

Looking at Relativity

• The speed of a moving object seems to vary depending on the observer.
• A variety of answers can all be correct, relative to various observers.
• Relativity applies to all areas of physics.
• Galileo Galilei applied relativity to mechanics.

Galileo’s Observations

• Followers of Copernicus debated where a dropped ball ought to land.
• Galileo responded that the laws of mechanics are the same in steadily moving reference frames as they are in resting reference frames.
• A dropped object on a moving ship obeyed Galileo’s prediction.
• The apparent velocity of a person walking on a moving ship, from the perspective of a person on shore, depends on the velocities of the ship and the person.

Galilean Transformations

• Two different observers can be thought to be using two different coordinate systems.
• It may be possible to convert one coordinate system to another.

Example: Galilean Transformation Equations

At t_i = 0 s, a ship traveling at 5.0 m/s north passes 1.0 × 10³ m east of a 75 m tall lighthouse. The origin of the ship’s coordinate system is located at the ship, and the origin of the lighthouse’s system is at the top of the lighthouse.

What are the equations to complete a Galilean transformation from the coordinates in the ship’s system (x′, y′, z′, t′) to the lighthouse’s system (x, y, z, t)?

At the initial time, the ship is located at (1.0 × 10³ m, 0 m, –75 m) in the lighthouse’s coordinate system.

x = x′ + 1.0 × 10³ m

y = y′ + (5.0 m/s)Δt

z = z′ – 75 m

t = t′

Inertial Reference Frames

• The laws of mechanics have the same mathematical form in every reference frame that does not accelerate.
• No mechanical experiment can determine absolute motion, only relative motion.

Problems Arising from Galilean Relativity

• Scientists in the nineteenth century hypothesized the existence of a luminiferous ether that was completely at rest.
• Michelson used an interferometer to test predictions about the ether.
• His experiments provided no evidence that the ether existed.

Questions for Students

1. Define relativity and Galilean relativity. How do they differ?
2. What is an inertial reference frame?
3. Explain Galileo’s observations about objects on a moving ship.
4. What are Galilean transformations and how are they used?
5. Describe the problems that arose from Galilean relativity and how they were addressed.