9.1.3 Time Dilation

Question 1

Time Dilation

Answer 1

• One of the consequences of Einstein’s postulates is that the concept of simultaneity becomes relative.
• An observer for whom two events occur at different places measures a longer time interval between the events than an observer for whom the events happen in the same place. This is known as time dilation:

Question 2

According to the special theory of relativity, moving clocks slow down. Suppose two spaceships pass each other with a relative speed v. Which of the following statements is incorrect?

Answer 2

As the relative speed v decreases, the time dilation factor increases, and clocks in the moving spaceship slow down further.

Question 3

For non-relativistic phenomena, which are adequately described by Newton’s laws, which of the following happens to the value of gamma?

Answer 3

g = 1

Question 4

A light clock is at rest in an inertial frame S. Relative to another inertial frame S′, S is moving to the right with velocity v. The path of light seen by an observer in S′ is shown in the figure. Which of the following is the roundtrip travel time for the light measured by the observer in S′ ?

Answer 4

2 sqrt(d^2 + l^2) / c

Question 5

Suppose S is the rest frame in which a light clock is at rest. The rest frame is moving to the right with velocity v relative to an observer in S′. According to the special theory of relativity, moving clocks slow down. Which of the following statements is false?

Answer 5

If the clock in S runs twice as slow as the clock in S’, then g = 1/2

Question 6

Which of the following are the units of gamma?

Answer 6

g is a dimensionless quantity, that is, it has no units

Question 7

In the rest frame, a muon’s life is 2.2 × 10−6 s. An observer encounters a muon that is moving with 0.9c. What will the muon’s life be to the observer?

Answer 7

5.1 × 10^−6 s

Question 8

Which of the following happens to the value of gamma if an object moves at a speed greater than the speed of light?

Answer 8

g becomes imaginary

Question 9

Suppose two inertial frames, A and B, are moving at speeds (1/4)c and (1/2)c, respectively, relative to an observer O at rest. Compare the values of the g-factor in the time dilation equation as measure by O for A and B

Answer 9

gA < gB

Question 10

Consider the light clock in the figure; the two mirrors are separated by a distance d. A clock tick consists of a roundtrip travel of a light beam from A to B and back to A. Which of the following is the value of d (in miles or meters) for which a tick equals one second?

Answer 10

93,000 miles