The Cosmic Background Radiation Space Drive

A Physics Puzzle

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.

Cosmic Background Radiation Space Drive

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”?

Why It Doesn't Work

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?

Hypothesis 1: Radiation pressure drag.

(This is what I think is happening.) The fallacy lies in assuming the ship is moving inertially through empty space. The ship is in fact traversing a diffuse photon gas (the CBR), which creates a drag force counter to the direction of motion. An object at rest with respect to the CBR feels no net force, since photons impinge upon it with the same energy from all directions. An object moving with respect to the CBR feels an increased radiation pressure from the blueshifted photons coming from the direction of motion, and decreased radiation pressure in the opposite direction, resulting in a net force opposite to the velocity vector. This CBR drag decelerates the ship. Using the Doppler shift temperature difference to extract work and propel the ship cannot accelerate the ship or even fully counter the CBR drag, since no heat engine can be 100% efficient. The problem is thus equivalent to a perpetual motion airplane which uses the relative wind to drive a windmill which drives a pusher propeller.

Hypothesis 2: Not a cycle.

This can be argued entirely from the ship frame. There is no violation of the second law since no closed cycle exists, any more than exploiting geothermal energy resulting from gravitational contraction, or driving a turbine from a pressurised reservoir of gas. The ship's heat engine is pumping heat from a hot source to a cold sink and, in doing so equalising the temperature difference between them. When the the source and sink temperatures become equal, the engine will stop. Fortunately a half-universe is a pretty big heat source and sink, so there's no near-term risk of running out.

Seems reasonable, doesn't it? But if this argument were correct, consider what we'd observe from the laboratory frame. As before, the ship would be accelerating while creating an anisotropy in the CBR from which an observer in the laboratory frame could extract work. Two ships accelerating in opposite directions could then cancel the effect on the CBR while both continuing to accelerate.

Consequences

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

C-ship: Relativistic ray-traced images

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