How heavy is the universe? It鈥檚 a tantalising question, and now it has an astonishing answer. In cosmic terms, weight just doesn鈥檛 add up in the normal way.
We can measure the density of the universe near to us 鈥� it is about 10-26 kilograms per cubic metre 鈥� but weighing the whole thing is difficult. 鈥淥ur universe is supposed to be infinite and expanding,鈥� says astrophysicist Andrew Jaffe at Imperial College London. Einstein鈥檚 general theory of relativity tells us that the expansion affects how we measure both distance and mass, so you can鈥檛 just multiply the volume by the density.
That did not deter Hans Fahr at the University of Bonn, Germany, and Michael Heyl at the German Aerospace Centre, also in Bonn, who have devised an equation to calculate the total mass of the universe within any given radius of Earth. Allowing for relativistic effects, Fahr and Heyl find that when they calculate the mass out to a great distance from Earth, the universe is much lighter than expected. The mass appears not to increase in proportion to volume, but in proportion to radius (Astronomical Notes, vol 327, p 383).
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鈥淭he universe turns out to be just a little lighter than a black hole of the same size鈥�
This startling result is reminiscent of the strange behaviour of black holes. The radius of a black hole鈥檚 event horizon, within which all matter and radiation inevitably fall into the hole, is also proportional to its mass. So although small black holes are incredibly dense and heavy, very large ones are proportionately much lighter. At any radius from Earth, the universe turns out to be just a little lighter than a black hole of the same size, Fahr and Heyl say.
鈥淲hat鈥檚 interesting is that they have managed to reproduce this physical correspondence with black holes just by starting from an essentially philosophical question: what does it even mean to ask about the mass of the universe?鈥� says Jaffe.
The new result also agrees with a controversial solution for the universe鈥檚 mass that was predicted almost a century ago. In 1918, Austrian physicist Hans Thirring reasoned that our Earth rotating in one direction in the stationary universe should be physically equivalent to a stationary Earth with the universe rotating around it in the opposite direction. After all, it鈥檚 impossible to tell the difference by observation. Thirring calculated that for this equivalence to be true, the universe鈥檚 mass must be directly proportional to its radius.
Until now, cosmologists have had difficulty reconciling this requirement with general relativity (New 杏吧原创, 17 May 2003, p 30). But it鈥檚 exactly the relationship Fahr and Heyl found. 鈥淲e were astonished,鈥� says Fahr.
They are now trying to work out the physical significance of their peculiar mass-radius relationship. For example, does it have any implications for dark energy, the repulsive stuff that is thought to make up most of the universe鈥檚 mass?
Jaffe is impressed, but cautious. 鈥淭his is just one way to define the mass of the universe,鈥� he says. 鈥淭here鈥檚 room for different definitions 鈥� and they may not give the same answer.鈥�
