Here's a puzzle I first thought of in the mid-1980s, which I don't recall having seen discussed. Included is my (non-rigorous) solution, as well as another proposed solution that contains a nasty booby trap.
Define the laboratory frame to be at rest with regard to the cosmic background radiation (CBR) (e.g. no dipole temperature component). Now imagine a spaceship in motion relative to the laboratory frame, its nosecone pointed in the direction of motion. An observer on the spaceship measuring the cosmic background will see a dipole variation, with maximum blueshift in the direction of travel relative to the laboratory frame and maximum redshift in the opposite direction.
Thus, at the ship's nose we measure a higher temperature (due to blueshift) than we do at the ship's tail, where the CBR is redshifted. Given the temperature difference, can we not extract work with a heat engine, using a collector at the ship's nose as the high temperature heat source and a radiator at the ship's tail as the low temperature heat sink?
The work extracted by the heat engine can then be converted to electricity which, connected to a flashlight mounted in the ship's tail, accelerates the ship, as its momentum must increase in a direction opposite that carried away by the photons ejected.
As the ship is accelerated by the photon drive, the blueshift and redshift increase as velocity does, and so consequently does the temperature difference between the source and sink, increasing the amount of work extracted by the heat engine and the power of the photon drive.
Why is this not a “free energy star drive”?
It can't work. It might seem fine from the standpoint of an engineer on the ship, who simply observes different temperatures fore and aft and hooks up an engine between them, but from the laboratory frame the ship appears to be committing a serious moving violation. It's gaining energy (whether kinetic energy resulting from the photon drive, or just by charging a capacitor with the electricity generated from the heat engine), doing so by pumping energy from a source to a sink at the same (laboratory frame) temperature. Bzzzt—second law violation! So what have we overlooked?
I thought of this puzzle in 1985 while musing about the fact that the universe could be said to possess a preferred rest frame defined by the CBR, and thinking through what consequences that might have on the general assumption that all inertial frames are equivalent. I thought it was really cool to encounter a puzzling interaction between the Doppler effect and the second law of thermodynamics.
It's also amusing to note that the phenomenon of CBR drag would argue for highly-streamlined ultrarelativistic spaceships which minimised frontal area subject to blueshifted radiation pressure. Thus pokey interstellar transports may look like flying junkyards, but intergalactic fighters will be sleek enough even for Hollywood.
by John Walker
February 23rd, 1994