The Total Energy

The total energy in the observable universe can be shown to be zero by adding the total mass energy in matter and radiation to the total gravitational potential energy. That is: energy total = mass energy + gravitational energy. Does this result mean that the creation of matter out of nothing contradicts no physical conservation law?

Answer

Yes, there can be the creation of matter out of nothing with no violation of conservation laws! First proposed in 1958 by H. Margenau and later recalculated in more detail by N. Rosen and others in 1994, the gravitational energy cancels the mass energy in a closed, homogeneous universe.

The simplest general approach was done by Margenau. Consider a finite spherical universe of radius R filled with matter and radiation of equivalent total mass M. The gravitational potential energy is the negative quantity –kGM²/R, where G is the gravitational constant and k is a positive numerical factor not greatly different from 1. The total energy E in the universe is then E =Mc² – kGM²/R. Using representative values such as R = 1.3 × 10²⁶ m and a mass density of 8 × 10^–27 kg/m³, we estimate k ~ 2.4 when E = 0. Nathan Rosen and others showed that the gravitational energy cancels out the mass energy without resorting to numerical estimates.