Physics 11 – Relativity of TIME

According to the special theory of relativity, time is not an absolute quantity.

A great example of Special Relativity in action is the idea of Simultaneity. This is based on the

idea of different frames of reference and the speed of light remaining the same speed.

Simultaneity: (passing train video clip example)

Events that are observed to be simultaneous in one inertial frame of reference may not

be observed to be simultaneous when observed from a different inertial frame of

reference

Observations:

– Observer 2 on the platform will see the 2 events (lightning strike 1 & 2) at the

same time

– Observer 1 in the train will see the lightning strike at the front before the

lightning strike at the back.

Speed of light is constant in both frames of reference.

Time Dilation: Time Dilation occurs due to the special property of light having a constant maximum speed of 3.0 x 108 m/s in a vacuum. The result is that time is not absolute. (video clip - YouTube - Time Dilation - Albert Einstein and the Theory of Relativity) As an object approaches the speed of light, time relative to other frames of reference slows down. One of the odd results of this it that anyone on the fast moving object and anyone in a different frame of reference will feel time pass at a natural rate. However, it also appears that time slows down for the other frame of reference. This is tricky to understand but is based on both time and space not being absolute. In two different frames of reference (with different velocities), each person feels that his/her progressionthrough time is natural. It therefore appears that time slows down for the other person. This is time dilation. (video clip - YouTube - Time Travel Einstein's big idea (Theory of Relativity))

Scientists have confirmed that time dilation exists by placing a very precise atomic clock

on a jet plane and flying it for a period of time, while placing an identical clock in a stationary

lab. (video clip - YouTube - Time dilation experiment)

• The clock on the aircraft had lost a bit of time compared to the clock left in the

stationary lab.

• Time Dilation Formula:

• t = the dilated time interval is measured by the observer that is in motion with respect

to the event = this observer views the event (the fast moving object) from a different

place.

• t0 = the proper time interval is measured by the observer at rest with respect to the

event = this observer views the event (the fast moving object) from the same place.

Examples:

1. An astronaut is travelling at a constant speed of 2.7 x 108 m/s relative to the Earth toward a

distant star. If this trip takes 25 years as measured by an observer on Earth, how long does it

take relative to the observer on the space vehicle?

2. An astronaut is travelling at a constant speed of 2.95 x 108 m/s relative to the Earth through

space. According to the time devices on the space vehicle, her trip lasted 0.500 years. How

long did this trip last relative to an observer on Earth?

3. You take a trip through space and when you return to Earth you have aged 4.0 years. Your

friend who remained on Earth has aged 11.0 years. How fast was your spaceship travelling

on your trip?

Time Dilation Problems

1. An astronaut is traveling at a constant speed of 2.40 x 108 m/s relative to Earth through

space. According to timing devices aboard the space vehicle, the trip took 1.25 years. How

long did the trip take if measured relative to Earth? (2.08 years)

2. An astronaut is travelling at a constant speed of 7.50 x 107 m/s through space relative to

Earth. According to timing devices aboard the space vehicle the trip lasted 3.00 years. How

long did the trip take is measured relative to Earth? (3.10 years)

3. An astronaut is traveling at a constant speed of 2.80 x 108 m/s measured relative to Earth

through space. If this trip takes 50.0 years as measured on Earth, how long does it take

relative to the space vehicle? (18.0 years)

4. A student on earth sees a spacecraft leaving the earth at a constant speed of 0.95c to

reach a star that is 38 light-years from earth. (One light-year is the distance that light travels in

one year. It is a measure of distance.)

If the student and an astronaut in the spacecraft are looking at a clock on the wall of the

spacecraft (assuming the student had a way to see it), which of them measures the proper

time interval? Explain your answer

5. You are traveling through space at a constant speed of 2.90 x 108 m/s relative to Earth. If

your friend who stayed back on Earth aged 35.0 years during the time of your trip, how many

years did you age? (8.96 years)

6. In the above problem, if you aged 10.0 years and your friend aged 18.0 years, how fast

was your space vehicle traveling through space relative to Earth? (2.49 x 108 m/s)

7. Your teacher is taking your class on a field trip to a distant planet. The space bus is

traveling at a constant speed of 0.96c relative to the Earth. Your teacher prepared an exam

before leaving the Earth that was set to take 2.5 hours. If the students complete this exam

while on the field trip, how much time passes for those that have stayed behind at the

school on Earth while those on the space bus write it? (8.9 hours)

8. Two children with toy laser guns fire a laser beam at the ends A and B of a moving train as

shown in the diagram. Two observers are mid-way between points A and B. The observer

standing on the ground says that the laser beam was fired at the same time.

a. What would the observer sitting on the

train say concerning the two firings? You

must explain your answer.

b. What observer is correct concerning the

two firings? You must explain your

answer.