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Reconciling a Reactionless Propulsive Drive with the First Law of Thermodynamics

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 $μ$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.