- #1
Hiero
- 322
- 68
The problem goes:
‘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 L0 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:
But if we find the time in the wall’s frame of reference with relativistic accuaracy, it gives:
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.
‘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 L0 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.