- #1

Hiero

- 322

- 68

‘One end of a rubber band is attached to a wall. The free end is stretched away from the wall at a rate v. At time zero the band is length L

_{0}and a bug starts crawling along, from the wall, at rate u. How long until the bug reaches the free end?’

(Typically u << v for dramatic effect.)

The classical solution is:

## t = (L_0/v)(e^{v/u}-1) ##

But if we find the time in the wall’s frame of reference with relativistic accuaracy, it gives:

##t = (L_0/v)(\frac{(1+v/c)^{0.5(c/u-1)}}{(1-v/c)^{0.5(c/u+1)}}-1) ##

The exact form is strange but interesting. I’m just posting this in case anyone has any comments on the form of it. It seems vaguely familiar.