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Chapter 12: Q22 P (page 532)

(a) Draw a space-time diagram representing a game of catch (or a conversation) between two people at rest, apart. How is it possible for them to communicate, given that their separation is spacelike?

(b) There's an old limerick that runs as follows:

There once was a girl named Ms. Bright,

Who could travel much faster than light.

She departed one day,

The Einsteinian way,

And returned on the previous night.

What do you think? Even if she could travel faster than light, could she return before she set out? Could she arrive at some intermediate destination before she set out? Draw a space-time diagram representing this trip.

Short Answer

Expert verified

(a) Draw a space-time diagram between two people at rest, 10 ft apart.


The conversation is not instantaneous because as sound wave need time to travel.

(b) Draw a space-time diagram representing this trip.

She will be returning late as the time required by her is more.

Step by step solution

01

Write the given data from the question.

Consider a space-time diagram representing a game of catch (or a conversation) between two people at rest, 10 ft apart.

02

(a) Draw a space-time diagram between two people at rest, 10ft apart.

Draw a space-time diagram between two people at rest, 10 ft apart.

Fig. 1

According to the circumstances, it is impossible for player to connect with player . Instead, player communicates with the player who receives the message later and learns of the answer from player when he is older.

03

(b) Draw a space-time diagram representing this trip.

Draw a space-time diagram representing this trip.

Fig. 2

For a moving observer, it could be feasible to claim that she arrived at B before she left A, but for a circuitous route, it is unavoidable that one must concede that she returns later than when she started.

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Define proper acceleration in the obvious way:

伪渭=d畏渭d蟿=d2x渭d蟿2

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(b) This same wave is observed from an inertial system S鈫�moving in thexdirection with speed vrelative to the original system S. Find the electric and magnetic fields in S鈫�, and express them in terms of the role="math" localid="1658134499928" S鈫�coordinates: E(x鈫�,y鈫�,z鈫�,t鈫�)and B(x鈫�,y鈫�,z鈫�,t鈫�). [Again, be sure to define any auxiliary quantities you introduce.]

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(d) What is the ratio of the intensity in to the intensity in? As a youth, Einstein wondered what an electromagnetic wave would like if you could run along beside it at the speed of light. What can you tell him about the amplitude, frequency, and intensity of the wave, as approaches ?

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