Monday, 7 January 2013

You can't move


The new Zeno's paradox

Imagine an infinitely long conveyor belt that is one kilometre wide. On each side of the conveyor belt is flat uninterrupted terrain of the same material as  the belt. (The belt is also empty east of where our story is set.) On this conveyor belt we find two twins, (they are each others twin, not one from two pairs of twins.)

They grow up on the conveyor belt until they are twenty-one years old. They are, (by the miracle that improbable does not equal impossible) remain identical to this day. To celebrate their birthday they decide to have a straight line drag-race. They have two almost identical cars, except that one has a maximum speed of 2 kilometres per hour and the other has a maximum of 4 kilometres per hour.
(Not the most exciting of drag-races, but it makes it easier to remember the numbers.)

The starting blocks for these two vehicles is a contraption at the edge of the conveyor belt and suspends the slower car one millimetre above the belt, (no the wheels are not touching the belt), and the other one millimetre above the surrounding flat land. Neither car can turn left or right and the starting contraption, (that will drop both cars at the same time), sends them off parallel to the edge of the belt. (The wheels have been constructed so that they have perfect friction and both will start at their maximum speed.)

The belt is moving east, (always has, always will) at exactly 2 kilometres per hour, (this is the direction of the race).

You are friends with one of the twins and she asks you which car she should pick.

Those of you that know v1+v2 != (v1+v2) will tell her to pick the 4 kilometre per hour car as the 2 kilometre per hour car will be going ever so slightly slower than 4 kilometres per hour car.

So if this happened in a galaxy that is already moving at the speed of light, would they be able to move at all?

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