In article , "Ed Keane III" writes:

Geoffrey A. Landis wrote in message
. com...

When the sail is moving, then the reflected photons are Doppler
shifted, and leave the sail with lower energy than they arrived. This
loss of energy exactly equals the energy imparted to the sail, a fact
which can be trivially verified by using Newton's laws, the Doppler
formula, and the Einstein equation for photon momentum p=E/c


Doppler shift is caused by relative velocity and has nothing
to do with acceleration or deceleration. Any energy imparted
to the motion of the sail will cause a change in velocity and
will be indicated by a change in Doppler shift.

If the sail is not moving, there is no Doppler shift. However, note
that since energy is proportional to momentum squared, the derivative
of energy with respect to momentum is zero for a non-moving sail.
Thus, when the sail is stationary, it can reflect photons with perfect
efficiency and still gain momentum at no energy cost.


This is exactly what Gold argues. Except he points out, correctly,
that if there is no energy lost from the photons it violates the laws
of thermodynamics, or more simply conservation of energy, by
getting something for nothing if the sail gains momentum.

But there is energy lost from the photons. Do the math. That's where
the Doppler shift matters.

Mati Meron | "When you argue with a fool,
| chances are he is doing just the same"