Moving Clocks - Examples

Moving Clocks

































Suppose that the transverse dimensions of a moving object always shrink.

In the reference frame of the wall, the ball goes through the hole.


In the reference frame of the ball, it does not make it.

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A light pulse bounces back and forth between two mirrors.

In the rest-frame of the mirrors, the crossing time T is just T = D/c.


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Everyone agrees that the pulse travels at speed c in any reference frame.



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One half cycle of the clock

"Tick - Tock".



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The pulse reflects off the other mirror and heads back to the first.



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A space ship leaves the earth and accelerates to 4/5 the speed of light. The ship and the earth exchange regular radio messages so that the earth-bound observer can figure out (by correcting for message-travel time) the earth-times of events on the spaceship.

Two events on the ship are separated by three years of ship-time. How many earth-years separate the events?


Shortcut method using triangles.




A space ship leaves the earth and accelerates to 12/13 the speed of light. The ship and the earth exchange regular radio messages so that the earth-bound observer can figure out (by correcting for message-travel time) the earth-times of events on the spaceship.

Two events on the ship are separated by five years of ship-time. How many earth-years separate the events?


Shortcut method using triangles.

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A spaceship travels from the earth to the star, alpha centauri which is 4 light-years away. If the ship reaches alpha centauri 5 years later (earth-time), how much time has elapsed on board?


so

Shortcut method using triangles.






A spaceship travels from the earth to a star which is 12 light years away. If the ship reaches the star 13 years later (earth-time), how much time has elapsed on board?


so

Shortcut method using triangles.

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