• W assemble in the earth's center into a tiny sphere, one wave length of light in diameter. Some very in teresting things could begin to hap pen by then. Remember that space is curved by mass. Oh, very little. But on the mass surface, this effect is in inverse proportion to the radius of that mass. And I have postu lated a very, very small size of ex traordinarily high density. By the time our small but enormously heavy mass has reached a wave length of light in diameter, it has almost wrapped its own space around itself, and has become very close to what I would call a gravi tational "crit." I believe we are about to have a gravitational ex plosion. Before it is too late, let us review our calculations. Take a certain mass and distribute it in the physi cal space of a universe which has the shape of a three-dimensional spherical bubble within a fourdimensional cosmos. Then stipu late that the total mass-energy of the system, which is equal to the initial mass-energy plus the relativistic increase due to the speed of expansion, is also equal to its total negative gravitational energy. This is the same as stipulating that the total energy of the system is zero, and no simpler stipulation can be made. Write this down as an equa tion, for which we need only the initial mass, the gravitational con stant, and the speed of light. Solve this equation and examine the solution you obtain (1.). This solu tion represents an explosion which proceeds with nearly the speed of light, with a continuously increasing mass but also a continuously de creasing density. And if you sub stitute the age of the universe today for the time appearing explicitly in this solution you obtain a density of the order of 10"30 gram per cc. This is the density of our present uni verse, within the margin of obser vational error. And if you like, make the initial mass from which you started, zero, and the solution is hardly affected. No known physical law has been violated in this calculation, but a yet unknown mechanism has been postulated for the trade of positive mass-energy for negative gravitational energy. This is an intriguing result, which
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