A Universe From Nothing: Why There Is Something Rather Than Nothing by Lawrence M. Krauss & Richard Dawkins

Author:Lawrence M. Krauss & Richard Dawkins
Language: eng
Format: mobi
Tags: Philosophy & Social Aspects, Science, Cosmology, Time, General, Physics
ISBN: 9781451624458
Publisher: Free Press
Published: 2012-01-10T00:00:00+00:00

If the region is large enough but not too large, then the galaxies at the edge of the region will be receding from us uniformly due to the Hubble expansion, but their speeds will be far less than the speed of light. In this case, the laws of Newton apply, and we can ignore the effects of special and general relativity. In other words, every object is governed by physics that is identical to that which describes the balls that I have just imagined trying to eject from the Earth.

Consider the galaxy shown above, moving away from the center of the distribution as shown. Now, just as for the ball from the Earth, we can ask whether the galaxy will be able to escape from the gravitational pull of all the other galaxies within the sphere. And the calculation we would perform to determine the answer is precisely the same as the calculation we performed for the ball. We simply calculate the total gravitational energy of the galaxy, based on its motion outward (giving it positive energy), and the gravitational pull of its neighbors (providing a negative energy piece). If its total energy is greater than zero, it will escape to infinity, and if less than zero, it will stop and fall inward.

Now, remarkably, it is possible to show that we can rewrite the simple Newtonian equation for the total gravitational energy of this galaxy in a way that reproduces exactly Einstein’s equation from general relativity for an expanding universe. And the term that corresponds to the total gravitational energy of the galaxy becomes, in general relativity, the term that describes the curvature of the universe.

So what do we then find? In a flat universe, and only in a flat universe, the total average Newtonian gravitational energy of each object moving with the expansion is precisely zero!

This is what makes a flat universe so special. In such a universe the positive energy of motion is exactly canceled by the negative energy of gravitational attraction.

When we begin to complicate things by allowing for empty space to have energy, the simple Newtonian analogy to a ball being thrown up in the air becomes incorrect, but the conclusion remains essentially the same. In a flat universe, even one with a small cosmological constant, as long as the scale is small enough that velocities are much less than the speed of light, the Newtonian gravitational energy associated with every object in the universe is zero.

In fact, with a vacuum energy, Guth’s “free lunch” becomes even more dramatic. As each region of the universe expands to ever larger size, it becomes closer and closer to being flat, so that the total Newtonian gravitational energy of everything that results after the vacuum energy during inflation gets converted to matter and radiation becomes precisely zero.

But you can still ask, Where does all the energy come from to keep the density of energy constant during inflation, when the universe is expanding exponentially? Here, another remarkable aspect of general relativity does the trick.

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