```Timothy van der Linden writes:
> Am I right saying the following:
>
> Photons loose energy because they accelerate the car. Only because of that
> acceleration their frequency is lowered.
> Because it takes more energy to transfer the same amount of momentum to a
> faster moving car (E=v^2 versus p=v) the frequency is lowered even more.

There is one important constraint in this situation:  photons
_always_ have equal momentum and energy; hence a photon
reflecting off a moving object must impart equal amounts of
momentum and energy to it.

A photon has less energy when seen from the frame of a
fast-moving object moving in the same direction as the photon, so
in the object frame the photon imparts less momentum to the
object.  Seen from the observer's frame, the photon loses more
momentum to a receding fast-moving object than a slow-moving one.

Remember that reflecting objects moving opposite to the direction
of the incident photons actually impart energy and momentum to
the photons; in the object frame the photon has more energy and
momentum.

> After all this, can we conclude a charged battery is heavier than an
> uncharged battery?

Yes, this is also true.  Hot objects are heavier than cold ones
(although not by an amount we have equipment to measure).  A
mirrored box full of photons is heavier than the empty box.

> Steve writes:
> >The reality that static stress does not continue to dissipate
> >energy over time is not intuitive, because our muscles aren't
> >static structures like boards or rods or wires; they must
> >dissipate energy even to hold a weight motionless above your
> >head, while a table holding the same weight does not dissipate
> >energy.
>
> Yes, in fact is does not take any energy to keep floating a few metres above
> Earth's surface.

Well, it depends on how you make the object float.

```