Merlyn wrote:
Having loads of fun here
<my email truncated the interesting and relevant parts
of the previuos messages, so no quote possible>
Horace, your gedanken experiment involving the dropped
rock neglects the fact that light carries momentum.
In order for the rock to be turned into light
ttraveling the opposite direction, a force must be
applied to reverse its momentum. Equally, Einstein at
the top of the ladder must apply a force when he
catches the light to stop it and turn it into a
stationary rock.
Actually it was my gedanken, or rather my quote of Einstein's gedanken
experiment. But you're right, force is necessary to change the momentum
of the rock/photon.
But we can deal with the momentum issue. The rock can exchange momentum
with the person who catches it _without_ exchanging more than a
negligible amount of energy, and it's the total energy we were concerned
with. Just make the planet on which the person who catches it is
sitting sufficiently massive, so that the planet's motion, and by
extension the motion of the person, is negligible.
We see this effect all the time in real life. Bounce a ball off a hard,
solid wall. The ball's momentum reverses, which implies the wall gained
momentum equal to twice what the ball had to start with, but if it's a
good hard rubber ball and the wall is good and solid, the ball loses
almost none of its energy. The wall gains momentum but (almost) no energy.
A massive mirror, for another example, will flip the momentum vector of
a beam of light very nicely while absorbing essentially none of the energy.
The reason is that "net impulse" -- transfer of momentum -- depends only
on the duration of the applied force, while "work" -- energy transfer --
depends on the force and the distance the body it acts on moves during
the application of the force. If the body is massive and hence doesn't
move more than a miniscule amount during application of the force, only
a negligible amount of energy will be transfered.
Finally, if you throw a _sticky_ ball at a wall, and it sticks but
doesn't bounce off, _and_ if the wall is good and solid (and massive),
you find that the wall gains momentum equal to what the ball had, _but_
it still gains almost no kinetic energy. Instead, the ball's kinetic
energy (almost) all turns into heat.
