9.2.1 The Lorentz Transformation Equations

Question 1

The Lorentz Transformation Equations

Answer 1

• The Galilean transformation equations of classical relativity apply only at nonrelativistic speeds.
• The Lorentz transformation equations of special relativity apply at all speeds. They relate the coordinates of an event in one frame to the coordinates of the event in another frame:
• The relativistic velocity addition formula relates the velocity of an object in one frame to the object’s velocity in another frame:

Question 2

delta t’ = g(delta t - v delta x / c^2)

Which of the following shows how to derive the time dilation relationship from the above relationship?

Answer 2

delta x = 0

Question 3

In an inertial frame, Spaceship A is moving to the left with speed 0.6 c and Spaceship B is moving to the right with speed 0.6 c. Based on the special theory of relativity, which of the following is the relative speed of the two spaceships?

Answer 3

0.88 c

Question 4

True or false?
When v is very small compared to the speed of light, the Lorentz transformations reduce to Galilean transformations. This is a necessary property of Lorentz transformations.

Answer 4

true

Question 5

Suppose an object is moving in two-dimensional space, with coordinates (x, y, t). The figure shows the object’s velocity vector at a particular instant as viewed from two inertial frames with relative motion along the x-axis only; that is delta y’ = delta y. In S’ the x-component of the velocity is give by
u’x = ux - v/(1- uxv/c^2)
Which of the following is the transformation equation in S’ for the y-component, u’y?

Answer 5

uy’ = uy/g(1-uxv/c^2)

Question 6

Which of the following variables denotes the velocity of the reference frame?

Answer 6

v

Question 7

Which of the following is the unit of the term vx’/c^2?

Answer 7

Unit of time

Question 8

An observer in an inertial frame O’ sees another intertial frame O moving to the right as speed (1/2)c. An observer in O sees light moving to the right with speed c. Which of the following is the speed of the object as measured by the observer in O’? Use the relativistic equation for addition of velocities.

Answer 8

c

Question 9

An observer in an inertial frame O’ sees another intertial frame O moving to the right as speed (1/4)c. An observer in O sees light moving to the right with speed (1/4)c. Which of the following is the speed of the object as measured by the observer in O’?

Answer 9

The speed measured by the observer in O’ is less than (1/2)c

Question 10

Evaluate the following as true or false.
An intertial frame S’ is moving with velocity v to the right relative to an inertial frame S. Two events occur and an observer in S measures their coordinates and calculates delta x and delta t. If the two events occur at the same position in S, then they also occur at the same position in S’’.

Answer 10

false