2014 04 22

Mike Polioudakis

Potential energy of the universe and the mass of the universe

I have always been uneasy with the idea of potential energy. I have no trouble with some aspects of the idea, and I do not have trouble putting it into the appropriate equations. I have trouble because the idea didn’t make sense in some situations and I could not see where the potential energy was stored in some situations. This note is an example of both issues on the cosmic level.

My problems might arise because I don’t understand well enough the idea of a gravity field as a field of negative energy. I do understand the idea, just maybe not well enough. If so, please correct me. To the extent that I do understand the idea, I still don’t understand why the energy-mass in the total gravity field of the universe has to equal, or nearly equal, the total energy-mass of everything else in the universe. It seems clear to me that there is more positive energy-mass in the universe than negative energy-mass. If so, then the universe likely began with a big amount of positive energy-mass. I do understand theories in which the universe began with a small amount of positive energy-mass (1 ounce) and then grew both as a result of inflation. I just don’t agree, or I don’t agree that the resulting positive energy-mass growth is almost totally offset by the resulting negative energy-mass. I understand it is useful for an Omega value (ratio of positive-energy mass to produce a nearly-flat universe) if the total positive energy-mass nearly equals the negative energy-mass; and, for that, it is useful if the universe began with only a small amount of positive energy-mass, then the universe inflated with negative and positive energy-mass nearly equal. But I still don’t like it. For here, I assume a significant amount of positive energy-mass, and the storing of some of it in a gravity field. I might get back to these issues in another note.

Begin with two standard examples. First, take a spring. Stretch it and lock it. Now the spring has some potential energy. The kinetic energy of stretching the spring was converted to potential energy, and the potential energy is stored in the spring. When you release the spring, potential energy turns to kinetic energy again as the spring contracts. One kind of kinetic energy (stretching) is converted to potential energy, stored, and then converted back to another kind of kinetic energy (contracting). Second, grab a big rock. Climb up a building, or up a cliff, off which you can drop the rock. Carrying the rock upward converts kinetic energy to potential energy and stores the potential energy. When you drop the rock, the potential energy becomes kinetic energy as the rock falls. One kind of kinetic energy (lifting the rock) was converted to potential energy, stored, and then converted back to another kind of kinetic energy (falling). This is all high school stuff.

Where is the energy stored? It is stored in the spring and it is stored in the gravitation field that is made up of the Earth and the rock.

According to Einstein, stored energy should show up as mass. The stretched spring should be slightly more massive (heavier) than the un-stretched spring. I think this effect has been verified, although I am not sure. I would appreciate references to simple clear empirical studies.

In the case of the spring, it is not too hard to imagine the energy is stored in the spring, although exactly where in the spring might take a little thinking out. In the case of the Earth, the rock, and the gravity field, I am not sure where the energy is stored. I think it is stored primarily in the gravity fields of the Earth and the rock, mostly in the gravity field of the Earth. If they have a single gravity field between them, then the energy is stored in that combined field. I don’t think the rock becomes more massive. I don’t think the Earth becomes more massive. The combination of the Earth and the rock might get more massive. I am not sure if the gravity field of the Earth, the rock, or their combination, gets more massive. You can make up your own mind where the energy is stored.

Now imagine two large rocks out in space far away from any other gravitational field. At first the rocks touch each other. Then a space traveler moves the rocks far apart and holds them apart. In theory, I think, the combination of the two rocks and the gravity field between them should get more massive. I don’t know if this idea is correct according to theory, or if it has been verified experimentally.

Now imagine the universe when it was young and small. It might be easier to think of what happens after the universe has inflated. The universe expands. Space expands. As the universe expands, everything gets farther apart. For here, I think it does not matter if everything gets farther apart because space itself expands or because some genie pushes everything apart through space that is pre-existing. See below.

As everything gets farther apart, everything has more potential energy between everything else. If the forced expansion were to stop, everything would come back together. The coming back together would convert potential energy into kinetic energy. Everything could come back together only if everything had potential energy in relation to everything else.

OK. So where is the potential energy of the universe’s expansion stored? Is it stored in a giant gravity field for the whole universe?

If the potential energy of the universe is stored in a giant gravity field, then that field should be getting more massive as a result of the expansion of the universe. How do we measure that mass? Where is that mass?

What is the energy that drives the expansion of the universe? Where is the energy coming from for the expansion of the universe? It does no good simply to say “there is a repulsive force” if there is no energy to drive the force (Einstein’s mysterious “cosmological constant”). If there were no energy to drive the force, then the force would not force.

Suppose one kind of energy is being converted to the energy for expansion of the universe, which source energy then resides in the potential energy of the universe. What was that original source energy that was converted to the energy that drives the expansion of the universe?

If the expansion force had (has) energy, then it also had (has) mass. Where is (was) that mass? Is some of the mass of the universe being converted to expansion energy to drive the expansion of the rest of the mass? Is the original energy (some of the original mass) of the universe being converted first to driving energy, then to potential energy, and is converted to mass-as-stored-potential-energy as the universe expands?

If some mass is being converted to potential energy, and the stored potential energy shows up as mass, then where is the final energy-mass exactly? Is it spread evenly throughout the universe? Is it more evident in places where there is more mass that is going apart, as for example, in galaxies, or between galaxies?

I am not saying this potential-energy-as-mass is the source of some dark matter or some dark energy. If it is the source of dark matter and dark energy, great, and I hope to collect my Nobel because my wife and I really need the money. I just would like some good answers.

If the universe has to have energy to drive expansion, how can we tell if that energy is being expended? Again, I am not claiming to have uncovered a (the) source of dark energy but will happily take the money if I have. I just would like some easily-understood answers.

If the energy that drives the universe was originally in some kind of mass, or had some kind of mass, then the expansion of the universe is the conversion from that kind of mass to expansion energy (kinetic energy), and then to potential energy, and so to another kind of mass. If that kind of original energy for expansion has mass (it should), even un-localized, and the resultant potential energy has mass (it should), even un-localized, then the expansion of the universe is also the conversion of one kind of mass, via energy, to another kind of mass. Again, I would like some clear answers.

There is a difference between moving apart as the result of moving apart through space (what we see in everyday life) versus moving apart as the result of space expanding. All pop books on cosmology make a big point of this difference. I am happy to grant the difference. Still, after the moving apart, however it is done, there is stored potential energy (and its attendant mass) where before there was not. Either we get rid of the law of conservation of energy, or we grant that the potential energy of the gravitational field of the universe got its energy from somewhere. The potential energy had to come from other energy or from some mass.

If some energy is driving the expansion of the universe, I would like to know what energy that is, where it is stored before it drives the expansion, and how it drives the expansion. If the energy is stored in mass before it drives the expansion, I would like to know what that mass is, and how it is converted to energy to drive the expansion. I have already said I would like to know how and where the potential energy of the expansion of the universe is stored; I assume in the total gravity field of the universe.

A lot of this can be calculated out. I don’t have the data, but, to a cosmologist who does have the data, the figuring should not be hard.