Mindbender: Double speed

A silly one! There is a drain-pipe lying in the road. It is fifteen feet long. A squirrel pokes its head in at one end and then runs around and pokes its head in at the other end. If this takes six seconds and it doubles in speed each trip, how many trips will it have to make before it is poking its head into each end of the drainpipe at the same time?

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ANSWER

Actually it's not as silly as it sounds (well maybe it is) but in the world of mathematics and physics (to which the real world is only a close approximation) this puzzle is actually possible and I remember answering similar questions in my first year of phyiscs at university. If the question is actually taken literally the squirrel would be looking at himself after its 30th trip at which point it will be travelling at 408021893.12m/s (if I've done my maths correctly). It is during the squirrel's 30th trip that it has reached the speed of light and time would quite literally have stood still. By the time it reached the end of the pipe the sqirrel would have succeeded in travelling back in time and be looking at him or her self in the past. Or to think of it another way, the squirrel would have literally overtaken the light rays which are travelling through the pipe and if it stuck its head in the pipe after its 30th run the image hitting its eyes would be of itself sticking its head into the other end of the pipe. In theory it would then also be possible to take a photo of the event where the squirrel is sitting at both ends of the pipe at the same time. Of course it is quite debatable whether such time travel really is possible or whether the squirrel would have survived breaking the sound barrier or whether the squirrel could even find the end of the pipe while travelling at those speeds because any image that actually enters its eyes would be highly distorted (kind of like watching the starship enterprise engaging its warp drive) or whether the squirrel would not have escaped the earth's gravitational pull.

Sent in by Jörg Ernst, UniSA Chaplain

Question 32; The answer given to this question states that "in the world of mathematics and physics (to which the real world is only a close approximation) this puzzle is actually possible." I would like to point out that in the "world of physics" it is not possible for a body with finite mass to travel at the speed of light without having an infinite amount of energy. To travel at speeds greater than the speed of light would require an even greater amount of energy, which is just not possible. Therefore, the squirrel can not be going faster than the speed of light and so cannot be at both ends of the drain pipe at the same time.

Sent in by D Judson, University of Brighton

The question clearly states that the condition to be satisfied is that the squirrels head is poking into both ends of the pipe at the same time. This condition can not be satisfied even if it were possible to be travelling faster than the speed of light, because travelling faster that the speed of light does not stop or reverse time. In the case that the squirrel can travel faster than the speed of light, his head only appears to be poking into the other end of the drain pipe, but it isn't really there. Its the same as when we are looking at stars in the sky. The stars we see may not actually be there. The light which shows their destruction may not have reached us yet, but this doesn't affect whether or not at this instant the star exists.

Sent in by Stuart Herring, London

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