# Re: one question

Kevin C. Houston writes:
> > For example, a device like this:
> >
> >
> >    E/c --v                         :::: p = [ 0 E/(2*c) ]
> > |----------------------------------:::/|
> > |######~~~~~~~~~~~~~~~~~~~~~~~~~~~~::/ |
> > |######~~~~~L~A~S~E~R~~~~~~~~~~~~~~:/  | beam splitter
> > |######~~~~~~~~~~~~~~~~~~~~~~~~~~~~:\  |
> > |######~~~~~~~~~~~~~~~~~~~~~~~~~~~~::\ |
> > |----------------------------------:::\|
> >                                    :::: p = [ 0 -E/(2*c) ]
> >
> > # = laser  ~ = laser light  -- = wires
> >
> > also won't move.  The beam splitter "absorbs momentum" just like
> > the black absorbing plate did, even though it splits the beam
> > into two beams traveling in the +y and -y directions.  This setup
> > also has the advantage of not requiring an unobtainium heat sink,
> > as long as you get a Perfect Mirror (tm) from Acme Physics
> > Warehouse.
>
> So you're saying that the beam splitter above would move at the same
> speed as a absorbtion plate of the same mass?

It would get momentum p from a beam with momentum p just like the
perfect absorber would.  However, over time it would end up at a
higher speed than the absorber because it does not increase in
mass over time like the absorber does.  The absorber develops
momenergy [ m+p p 0 0 ] after absorbing photons with momenergy [
p p 0 0 ], so its mass increases to sqrt(m^2 + 2 * p * m) (if p
<< m, this approximates to m + p), while the beam splitter
develops momenergy [ sqrt(m^2+p^2) p 0 0 ] from splitting the
same beam because its mass remains a constant m.  Hence the
velocity of the absorber after absorbing light with momentum p is
p / sqrt(m^2 + 2*p*m), while the velocity of the beam splitter is
p / sqrt(m^2 + p^2).

> >  > > The wires are indeed under tension, because there is a force
> >  > > between the laser and the plate.  This tension was created in the
> >  > > first instant the laser was turned on, and a small amount of its
> >  > > energy went into stretching the wires before it was all spent on
> >  > > heating the plate.

> I've always been taught to view atomic bonds as tiny springs which obey
> hookes law F=kx  where k is some constant.  this is the force that
> balances the force of the laser / absorber plate.  Is this view correct?
> Doesn't a spring provide a constant force as long as it's stretched from
> it's initial position?

Note that F = k * x means that the force varies linearly with
displacement, so increasing displacement means increasing force.
A spring provides constant force as long as it remains stretched
the same amount.  This may be what you meant above, but you don't
seem to make the distinction that the spring force varies with
displacement.  F = k * x is approximately correct for "ideal"
springs and small displacements and may be valid for normal
materials under small amounts of tension or compression; I don't
know for sure.