Crank mail is an occupational hazard for cosmologists. Einstein wanna-bes, convinced they’ve developed deep new theories, occasionally send their crabbed jottings to the professionals. Edward Harrison, an astronomer at the University of Massachusetts, is no stranger to such odd correspondence, and he might have dismissed a letter that crossed his desk recently had he not noticed that it was from a retired chemistry professor named Charles Leffert. One gets lots of crackpot mail, says Harrison. This was one that was not quite so crackpot.
Leffert posed this question: What happens to two bodies--planets, stars, galaxies, or what have you--in an expanding universe if you join them with a string? This query, silly as it sounds, raises some knotty issues, says Harrison. In particular, it seems to show that one of the most fundamental principles of physics--the conservation of energy--is inconsistent with an expanding universe.
Cosmologists take the expanding universe for granted almost as much as physicists do the conservation of energy. It’s the best explanation they have for the observation that the light from distant galaxies is stretched toward the long-wavelength, red end of the spectrum, which seems to indicate that the galaxies are receding from our own Milky Way. Cosmologists say the galaxies are being carried along by the expansion of space itself, which began with the explosive birth of the universe in the Big Bang.
But in the June issue of the Astrophysical Journal, a leading forum for noncrank astronomers, Harrison shows in mathematical detail how the thought experiment prompted by Leffert’s question seems to produce a conflict between cosmic expansion and energy conservation. Harrison is quick to point out that the idea of joining two widely separated bodies in the universe is wildly impractical. So he ignores details like the mass of the connecting rope and what material it might be made from. Physicists often use such simplified models, eschewing realism in order to concentrate on the underlying principles.
Just imagine two celestial bodies, says Harrison, one much larger than the other. (You could think of the bodies as stars, but stars have their own motions that have nothing to do with cosmic expansion.) On the larger body place a winch. Pay out some line from the winch and attach it to the smaller body light-years away. What happens? As space expands between the two bodies, they will recede from each other, and the smaller body will start to pull rope from the winch. The winch will unwind.
Clear enough--but there’s a problem here. Harrison says this simple system is a perpetual motion machine: it generates energy forever. As the universe keeps expanding, the winch keeps spinning, and the system never runs down. In principle, says Harrison, you could attach a few cogs to the winch and mine energy from the expansion of the universe. The energy would seem to come from nowhere--whereas the essence of the energy conservation principle is that energy must always come from somewhere.
It would be coming from somewhere, of course, if the tethered bodies were actually to slow the expansion of the whole universe, by however tiny an amount, the way a cart slows down a horse. That is what Cambridge University astronomer Martin Rees thinks is happening: the energy gained by the winch, he says, comes at the expense of the expansion. If Harrison’s saying it’s paradoxical, then I think he’s wrong, says Rees.
But Harrison thinks Rees hasn’t considered the issue carefully enough. Far from slowing down, he says, cosmic expansion actually speeds up, according to his calculations, the more bodies you string together. Harrison doesn’t doubt that the universe is expanding. But he thinks it’s possible that the thought experiment is pointing to the existence of some hidden source of energy in the universe.
Another possibility, says Harrison, is that energy conservation just doesn’t apply to the universe as a whole. All our notions of energy are derived from an acquaintance with local phenomena, he says. And in the laboratory we can certainly define energy in such a way that it is conserved. But the moment we start applying everyday concepts to the universe as a whole, we’re in trouble.
