Re: Rigid rod problem


russell@xxxxxxxx wrote:
> russ...@xxxxxxxx wrote:
> > Kim B wrote:
> > > >> Take a look at http://micki.dk/diverse/accel.jpg - it shows 4 points
> > > >> accelerating, which all could belong to the same rigid rod (David, you
> > > >> may have a look too!).

All right, we'll try it your way.

The diagram represents the current and future positions of four marks
or observers on an accelerated rigid rod.

The first thing I notice is that at t=0, at the time when the farthest
portion of the rod is halted, the near edge has already begun to move
to the right. This makes sense, as there would be a time-lag between
the time the near edge was pushed and when the far edge received the
signal.

I presumed that there was no way to keep a physical object from
crossing the light cone from the origin.

Now I'm having second thoughts. As the slope dt/dx of the hyperbola
would be greater than 1 all the way out to infinity, and yet it would
find a way not to cross the line x=t.

If a bear is chasing you through the woods at velocity c, and you run
from him at an increasing velocity less than c, can you keep him from
reaching you forever? Twenty minutes ago, I would have said, obviously
not. But then if I thought about it for twenty minutes, I probably
would have said, yes.

.