Many years ago, Ed Tryon suggested that our entire Universe might simply be a fluctuation of the vacuum. The paper appeared in Nature (volume 246, page 396), where he pointed out the curious fact that our Universe contains zero energy — provided it is “flat”, which observations confirm. The point Tryon jumped off from — the secret of making universes out of nothing at all, as vacuum fluctuations — is that the gravitational energy of the Universe is negative.
The way to understand this is that if you think of a collection of matter, such as the atoms that make up a star, or the bricks that make up a pile, the “zero of gravitational energy” associated with those objects is when they are far apart — as far apart as it is possible for them to be. The strange thing is, as the objects fall together under the influence of gravity they lose energy. They start with none, and end up with less. So gravitational energy is negative, from the perspective in which everyday energy (the mc^^2 in those atoms and bricks) is positive. Any object in the Universe, like a planet, or the Sun, which is not spread out as far as possible literally has a negative amount of gravitational energy. And if it shrinks, its gravitational energy becomes more negative.
The reason this was so interesting to Tryon is that the energy of all the matter in the Universe, all the mc^^2, is positive. What’s more, if you take a lump of matter and squeeze it into a singularity, then at the singularity the negative gravitational energy of the mass is exactly equal and opposite to its mass energy.
If this blows your mind, you are in good company. One of my favourite Albert Einstein anecdotes recounts a tale from more than half a century ago, during World War Two, when Einstein acted as a part-time consultant with the US Navy Department, assessing ideas for new weapons. Einstein didn’t actually work in Washington, but every couple of weeks George Gamow, another eminent physicist, would bring a briefcase full of ideas up to Princeton for Einstein to peruse. One day, as Gamow recalled in his book My World Line (Viking, New York, 1970), the two physicists were crossing the road together, on their way from Einstein’s home to the Institute for Advanced Study, when Gamow casually mentioned a new idea that he had heard from another physicist, Pascual Jordan. Jordan had mentioned, tongue in cheek, that a star could be made out of nothing at all, because at the point of zero volume its negative gravitational energy precisely cancels out its positive mass energy.
“Einstein stopped in his tracks,” Gamow tells us, “and, since we were crossing a street, several cars had to stop to avoid running us down.”
Jordan’s idea will not work for the formation of a star, because any star trying to form from a singularity in this way will be inside a black hole, invisible to the Universe at large. But it will work for the creation of an entire universe, within the black hole.
Provided that the Universe is indeed flat, the energy involved in making a universe from a singularity is indeed zero! It is, in the words of Alan Guth, “the ultimate free lunch”.
Adapted from In Search of the Big Bang.