Question: You are gliding over Earth's surface at a high speed, carrying your high-precision clock. At points and on the ground are similar clocks, synchronized in the ground frame of reference. As you pass overclock. it and your clock both read . (a) According to you, do clocksand advance slower or faster than yours? (b) When you pass overclock , does it read the same time. an earlier time, or later time than yours? (Make sure your answer agrees with what ground observers should sec.) (c) Reconcile any seeming contradictions between your answers to parts (a) and (b).

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Answer

(a) The clocks and are advanced slower than you clock.

(b) The time in the clockread slower than yours.

(c)There is no contradiction between parts (a) and (b).

Step by step solution

01

What is relativity?

The special relativity theory defines the relationship between space and time.According to Einstein, the speed of light in a vacuum is the same in any other space. General relativity talks about the gravitation force and its relation to the other force.

02

Determine if the clocks and are the advance slower

According to Einstein, if a person travels very high speed, then the events occurring in the inertial frame appear much slower than the event relative to his frame. This is happening because time in the inertial frame is going much slower than the time in the person frame. Therefore, the clock of the inertial frame would advance slower.

Hence the clocks and are advance slower than you clock.

03

Determine if the clock read the same time when you pass overclock .

The clock is still on the inertial frame and will still be slower than your clock when you pass it. Therefore, the clock is slower than your clock.

Hence the time on the clock read slower than yours.

04

Determine any contradiction in parts (a) and (b).

When the ground observer sees your clock is going faster than his clock, you see the distance between the and length contracted, and it looks like you have a shorter length to travel. Therefore, there is no contract between parts (a) and (b).

Hence there is no contradiction between parts (a) and (b).

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Most popular questions from this chapter

In Example 2.5, we noted that Anna could go wherever she wished in as little time as desired by going fast enough to length-contract the distance to an arbitrarily small value. This overlooks a physiological limitation. Accelerations greater than about 30gare fatal, and there are serious concerns about the effects of prolonged accelerations greater than 1g. Here we see how far a person could go under a constant acceleration of 1g, producing a comfortable artificial gravity.

(a) Though traveller Anna accelerates, Bob, being on near-inertial Earth, is a reliable observer and will see less time go by on Anna's clock (dt')than on his own (dt).Thus, dt'=(1/γ)dt, where u is Anna's instantaneous speed relative to Bob. Using the result of Exercise 117(c),with g replacing F/m, substitute for u,then integrate to show that

t=cgsinhgt'c

(b) How much time goes by for observers on Earth as they “see” Anna age 20 years?

(c) Using the result of Exercise 119, show that when Anna has aged a time t’, she is a distance from Earth (according to Earth observers) of

x=c2g(coshgt'c-1)

(d) If Anna accelerates away from Earth while aging 20 years and then slows to a stop while aging another 20. How far away from Earth will she end up and how much time will have passed on Earth?

You stand at the center of your 100m spaceship and watch Anna's identical ship pass at 0.6c. At t=0 on your wristwatch, Anna, at the center of her ship, is directly across you and her wristwatch also reads 0.

(a) A friend on your ship,24m from you in a direction towards the tail of the ship, looks at a clock directly across from him on Anna's ship. What does it read?

(b) Your friend now steps onto Anna's ship. By this very act he moves from a frame where Anna is one age to a frame where she is another. What is the difference in these ages? Explain.

(c) Answer parts (a) and (b) for a friend 24m from you but in a direction toward the front of Anna's passing ship.

(d) What happens to the reading on a clock when you accelerate toward it? Away from it?

Radiant energy from the Sun, approximately1.5×1011maway, arrives at Earth with an intensity of1.5kW/m2. At what rate is mass being converted in the Sun to produce this radiant energy?

A typical household uses 500 kWh of energy in I month. How much mass is convened to produce this energy?

According to Bob, on Earth, it is 20ly to Planet Y. Anna has just passed Earth, moving at a constant speed υ in a spaceship, When Anna passes Planet Y. She is 20years older than when she passed Earth. Calculate ν.

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