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Explain to your friend, who is willing to accept that light moves at the same speed in any frame, why clocks on a passing train are not synchronized. If it helps, assume that Anna is at the middle of the train.

Short Answer

Expert verified

Light moves at the same speed at any frame because of inertia reference frames. Clocks are not synchronized as the clocks mainly reads different time frames.

Step by step solution

01

Significance of the special relativity

The special relativity is described as the relationship amongst the time and space. In this, the physics laws are invariant in the inertial reference frame.

02

Determination of the explanation

The light which comes from the train’s front end will eventually arrive according to that friend’s reference frame also at the same exact time. However, in the case of Anna’s reference frame, that light which strikes at the train’s front end that will arrive at the earliest. The reason for this is the clocks of the train are not synchronized together. Hence, the clocks produce difference times for two pulses of light at the rear and also at the train’s front end.

Thus, light moves at the same speed at any frame because of inertia reference frames. Clocks are not synchronized as the clock mainly reads different time frames.

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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?

From the Lorentz transformation equations, show that if time intervals between two events,t andt' , in two frames are of opposite sign, then the events are too far apart in either frame for light to travel from one to the other. Argue that therefore they cannot be casually related.

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