You are standing on a train platform watching a high-speed train pass by. A light inside one of the train cars is turned on and then a little later it is turned off. (a) Who can measure the proper time interval for the duration of the light: you or a passenger on the train? (b) Who can measure the proper length of the train car: you or a passenger on the train? (c) Who can measure the proper length of a sign attached to a post on the train platform: you or a passenger on the train? In each case explain your answer.

Question

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Answer 1

Textbook Question

Chapter 37, Problem Q37.1DQ

You are standing on a train platform watching a high-speed train pass by. A light inside one of the train cars is turned on and then a little later it is turned off. (a) Who can measure the proper time interval for the duration of the light: you or a passenger on the train? (b) Who can measure the proper length of the train car: you or a passenger on the train? (c) Who can measure the proper length of a sign attached to a post on the train platform: you or a passenger on the train? In each case explain your answer.

(a)

Expert Solution

To determine

Whether passenger on train or observer in platform measures Proper time

Explanation of Solution

The relative velocity between passenger and train is zero, time measured by passenger in train is the proper time.

Conclusion: The time measured from frame where the relative velocity between two events is zero is called the proper time. Proper time is measured from frame where there is no relative motion between events.

(b)

Expert Solution

To determine

Passenger on train or observer in platform measures the proper length.

Explanation of Solution

The Proper length is the length measured by observer at rest in his own frame. The relative velocity between passenger and train is zero, time measured by passenger in train is the proper time Since the passenger in train is at rest in his own frame, he can measure proper length of train Since the sign is attached to ground ,relative velocity between observer in platform and ground is zero, he measures the proper length of sign.

Conclusion: Proper length is measured from frame where there is no relativity between events.

(c)

Expert Solution

To determine

Whether observer on platform or passenger on train measures proper length of sign post attached to ground.

Explanation of Solution

The time measured from frame where the relative velocity between two events is zero is called the proper time. The relative velocity between observer on platform and sign post is zero, time measured by observer on platform is the proper time.

Conclusion: Proper length is measured from frame where there is no relative motion between events.

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Answer 2

Textbook Question

Chapter 37, Problem Q37.1DQ

You are standing on a train platform watching a high-speed train pass by. A light inside one of the train cars is turned on and then a little later it is turned off. (a) Who can measure the proper time interval for the duration of the light: you or a passenger on the train? (b) Who can measure the proper length of the train car: you or a passenger on the train? (c) Who can measure the proper length of a sign attached to a post on the train platform: you or a passenger on the train? In each case explain your answer.

(a)

Expert Solution

To determine

Whether passenger on train or observer in platform measures Proper time

Explanation of Solution

The relative velocity between passenger and train is zero, time measured by passenger in train is the proper time.

Conclusion: The time measured from frame where the relative velocity between two events is zero is called the proper time. Proper time is measured from frame where there is no relative motion between events.

(b)

Expert Solution

To determine

Passenger on train or observer in platform measures the proper length.

Explanation of Solution

The Proper length is the length measured by observer at rest in his own frame. The relative velocity between passenger and train is zero, time measured by passenger in train is the proper time Since the passenger in train is at rest in his own frame, he can measure proper length of train Since the sign is attached to ground ,relative velocity between observer in platform and ground is zero, he measures the proper length of sign.

Conclusion: Proper length is measured from frame where there is no relativity between events.

(c)

Expert Solution

To determine

Whether observer on platform or passenger on train measures proper length of sign post attached to ground.

Explanation of Solution

The time measured from frame where the relative velocity between two events is zero is called the proper time. The relative velocity between observer on platform and sign post is zero, time measured by observer on platform is the proper time.

Conclusion: Proper length is measured from frame where there is no relative motion between events.

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Answer 3

Textbook Question

Chapter 37, Problem Q37.1DQ

You are standing on a train platform watching a high-speed train pass by. A light inside one of the train cars is turned on and then a little later it is turned off. (a) Who can measure the proper time interval for the duration of the light: you or a passenger on the train? (b) Who can measure the proper length of the train car: you or a passenger on the train? (c) Who can measure the proper length of a sign attached to a post on the train platform: you or a passenger on the train? In each case explain your answer.

(a)

Expert Solution

To determine

Whether passenger on train or observer in platform measures Proper time

Explanation of Solution

The relative velocity between passenger and train is zero, time measured by passenger in train is the proper time.

Conclusion: The time measured from frame where the relative velocity between two events is zero is called the proper time. Proper time is measured from frame where there is no relative motion between events.

(b)

Expert Solution

To determine

Passenger on train or observer in platform measures the proper length.

Explanation of Solution

The Proper length is the length measured by observer at rest in his own frame. The relative velocity between passenger and train is zero, time measured by passenger in train is the proper time Since the passenger in train is at rest in his own frame, he can measure proper length of train Since the sign is attached to ground ,relative velocity between observer in platform and ground is zero, he measures the proper length of sign.

Conclusion: Proper length is measured from frame where there is no relativity between events.

(c)

Expert Solution

To determine

Whether observer on platform or passenger on train measures proper length of sign post attached to ground.

Explanation of Solution

The time measured from frame where the relative velocity between two events is zero is called the proper time. The relative velocity between observer on platform and sign post is zero, time measured by observer on platform is the proper time.

Conclusion: Proper length is measured from frame where there is no relative motion between events.

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Answer 4

Textbook Question

Chapter 37, Problem Q37.1DQ

You are standing on a train platform watching a high-speed train pass by. A light inside one of the train cars is turned on and then a little later it is turned off. (a) Who can measure the proper time interval for the duration of the light: you or a passenger on the train? (b) Who can measure the proper length of the train car: you or a passenger on the train? (c) Who can measure the proper length of a sign attached to a post on the train platform: you or a passenger on the train? In each case explain your answer.

(a)

Expert Solution

To determine

Whether passenger on train or observer in platform measures Proper time

Explanation of Solution

The relative velocity between passenger and train is zero, time measured by passenger in train is the proper time.

Conclusion: The time measured from frame where the relative velocity between two events is zero is called the proper time. Proper time is measured from frame where there is no relative motion between events.

(b)

Expert Solution

To determine

Passenger on train or observer in platform measures the proper length.

Explanation of Solution

The Proper length is the length measured by observer at rest in his own frame. The relative velocity between passenger and train is zero, time measured by passenger in train is the proper time Since the passenger in train is at rest in his own frame, he can measure proper length of train Since the sign is attached to ground ,relative velocity between observer in platform and ground is zero, he measures the proper length of sign.

Conclusion: Proper length is measured from frame where there is no relativity between events.

(c)

Expert Solution

To determine

Whether observer on platform or passenger on train measures proper length of sign post attached to ground.

Explanation of Solution

The time measured from frame where the relative velocity between two events is zero is called the proper time. The relative velocity between observer on platform and sign post is zero, time measured by observer on platform is the proper time.

Conclusion: Proper length is measured from frame where there is no relative motion between events.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(a)

Expert Solution

To determine

Whether passenger on train or observer in platform measures Proper time

Explanation of Solution

The relative velocity between passenger and train is zero, time measured by passenger in train is the proper time.

Conclusion: The time measured from frame where the relative velocity between two events is zero is called the proper time. Proper time is measured from frame where there is no relative motion between events.

(b)

Expert Solution

To determine

Passenger on train or observer in platform measures the proper length.

Explanation of Solution

The Proper length is the length measured by observer at rest in his own frame. The relative velocity between passenger and train is zero, time measured by passenger in train is the proper time Since the passenger in train is at rest in his own frame, he can measure proper length of train Since the sign is attached to ground ,relative velocity between observer in platform and ground is zero, he measures the proper length of sign.

Conclusion: Proper length is measured from frame where there is no relativity between events.

(c)

Expert Solution

To determine

Whether observer on platform or passenger on train measures proper length of sign post attached to ground.

Explanation of Solution

The time measured from frame where the relative velocity between two events is zero is called the proper time. The relative velocity between observer on platform and sign post is zero, time measured by observer on platform is the proper time.

Conclusion: Proper length is measured from frame where there is no relative motion between events.

Answer 8

(a)

Expert Solution

To determine

Whether passenger on train or observer in platform measures Proper time

Explanation of Solution

The relative velocity between passenger and train is zero, time measured by passenger in train is the proper time.

Conclusion: The time measured from frame where the relative velocity between two events is zero is called the proper time. Proper time is measured from frame where there is no relative motion between events.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Whether passenger on train or observer in platform measures Proper time

Answer 13

Explanation of Solution

The relative velocity between passenger and train is zero, time measured by passenger in train is the proper time.

Conclusion: The time measured from frame where the relative velocity between two events is zero is called the proper time. Proper time is measured from frame where there is no relative motion between events.

Answer 14

(b)

Expert Solution

To determine

Passenger on train or observer in platform measures the proper length.

Explanation of Solution

The Proper length is the length measured by observer at rest in his own frame. The relative velocity between passenger and train is zero, time measured by passenger in train is the proper time Since the passenger in train is at rest in his own frame, he can measure proper length of train Since the sign is attached to ground ,relative velocity between observer in platform and ground is zero, he measures the proper length of sign.

Conclusion: Proper length is measured from frame where there is no relativity between events.

Answer 15

(b)

Expert Solution

Answer 16

(b)

Expert Solution

Answer 17

Expert Solution

Answer 18

To determine

Passenger on train or observer in platform measures the proper length.

Answer 19

Explanation of Solution

The Proper length is the length measured by observer at rest in his own frame. The relative velocity between passenger and train is zero, time measured by passenger in train is the proper time Since the passenger in train is at rest in his own frame, he can measure proper length of train Since the sign is attached to ground ,relative velocity between observer in platform and ground is zero, he measures the proper length of sign.

Conclusion: Proper length is measured from frame where there is no relativity between events.

Answer 20

(c)

Expert Solution

To determine

Whether observer on platform or passenger on train measures proper length of sign post attached to ground.

Explanation of Solution

The time measured from frame where the relative velocity between two events is zero is called the proper time. The relative velocity between observer on platform and sign post is zero, time measured by observer on platform is the proper time.

Conclusion: Proper length is measured from frame where there is no relative motion between events.

Answer 21

(c)

Expert Solution

Answer 22

(c)

Expert Solution

Answer 23

Expert Solution

Answer 24

To determine

Whether observer on platform or passenger on train measures proper length of sign post attached to ground.

Answer 25

Explanation of Solution

The time measured from frame where the relative velocity between two events is zero is called the proper time. The relative velocity between observer on platform and sign post is zero, time measured by observer on platform is the proper time.

Conclusion: Proper length is measured from frame where there is no relative motion between events.