  A "space drive" is a hypothetical device that generates a propulsive force in
free space using an input of power without the need for a reaction mass. Any
device that generates photons (e.g., a laser) would qualify as a propellantless
"photon rocket," but the force generated by emitting photons per power input
(3.33 $\mu$N/kW) is too small to be a practical propulsion device. The ability
to generate greater force per power input would be highly desirable, but, as
demonstrated in this paper, such a device would be able to operate as a
perpetual motion machine of the first kind. Since applying a constant force
results in a constant acceleration, the kinetic energy of a mass driven by such
a device increases quadratically with time, while the energy input increases
only linearly with time. Thus, at some point, the kinetic energy of the
device-driven mass exceeds the energy input, and if this energy is collected
via decelerating the mass (via regenerative electromagnetic braking, for
example), then there would be a net gain in energy. For devices with
thrust-to-power ratios on the order of 1 N/kW that have been discussed recently
in connection with the so-called EM drive, this breakeven occurs at velocities
low enough to be feasible with current technology, clearly demonstrating the
absurdity of such a device. When relativistic effects are taken into account,
it is shown that the photon rocket can only reach energy breakeven as the
accelerated mass asymptotically approaches the speed of light. Thus, any device
with a thrust-to-power ratio greater than the photon rocket would be able to
operate as a perpetual motion machine of the first kind, and thus should be
excluded by the First Law of Thermodynamics.
