
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.

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.

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

One half cycle of the clock
"Tick - Tock".

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

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.

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.