Re: Rigid rod problem

Spoonfed wrote:
> russ...@xxxxxxxx wrote:
> > Kim B wrote:
> >
> > [snip]
> >
> > > If you choose a point on the rod a use its current speed as your FOR,
> > > the the rest of the rod will fit nicely in this FOR (along the FOR's
> > > line of simultaneity) ... with the same speed all along and the
> > > correct proper length, exactly as it fits in our "rest" frame at the
> > > base line ... all frames are equal, assuming the rod has accelerated
> > > and will accelerate forever.
> >
> > Thanks. Of course you are quite right about that, and I
> > apologize for my many mistakes here.
>
> I believe it when I hear it, but it's a little tricky to figure out.
>
> It seems surprising that no matter what reference frame you are in, all
> parts of the rod will pass v=0 at the same time. I'm not in the mood
> to develop a proof, but it seems right.

I won't prove it here either; I'll just give some
further motivation.

If you imagine Born-rigid acceleration over a finite
time, and then ending, it must be the case that in the
end, no part of the rod is moving relative to any other
part (otherwise the rod would not be rigid). So, in
that sense it's not a surprising result at all.

On the other hand, given the complications that occur
with acceleration, I agree it's a bit surprising that
Born-rigid acceleration is possible at all, even in
theory.

You can see what's happening if you take Kim B's
diagram and, say, pick some point on the leftmost
hyperbola and draw the tangent there. Then draw
parallel tangents on the other hyperbolas, at whatever
points are determined by the parallel requirement.
Then notice that the points you have picked all lie
on the same straight line, tilted slightly upward to
the right. This is a line of simultaneity in the
frame that is moving at the speed given by the tangent
slope, and (recognizing that our diagram is drawn in
Euclidean rather than Minkowskian space) we see that
this line would actually be perpendicular to the tangent
if we redrew the diagram in the coordinates of that
frame. Thus, as Kim B says, the diagram looks the same
no matter what frame we draw it in.

.

Relevant Pages

  • Re: Rigid rod problem
    ... >>>part (otherwise the rod would not be rigid). ... >>>You can see what's happening if you take Kim B's ... >>>diagram and, say, pick some point on the leftmost ... >>>hyperbola and draw the tangent there. ...
    (sci.physics.relativity)
  • Re: Rigid rod problem
    ... >Kim B wrote: ... If the rod is 100 meters in length when I do this, ... >> Acceleration is certainly not intuitive and has a few surprises ... e.g. an event horizon and varying clock and acceleration ...
    (sci.physics.relativity)
  • Re: Rigid rod problem
    ... Kim B wrote: ... >>/ second, will the rod break? ... > Acceleration is certainly not intuitive and has a few surprises ... e.g. an event horizon and varying clock and acceleration ...
    (sci.physics.relativity)
  • Re: Rigid rod problem
    ... Yes, and by rigid, we mean Born-rigid, i.e. the rod keeps ... Please note that the time axis in the diagram is vertical, ... the specified acceleration to take place, ... > from him at an increasing velocity less than c, ...
    (sci.physics.relativity)
  • Re: Rigid rod problem
    ... >> The diagram represents the current and future positions of four marks ... >> or observers on an accelerated rigid rod. ... >the specified acceleration to take place, ... >how far away the bear is from you when you start. ...
    (sci.physics.relativity)