# How is finite energy spread wholly in the infinite universe

We all know that energy is never lost, but it transforms into another form.
Doesn't that mean that energy is not unlimited? I mean, why is it that way if it was infinite?
However, if energy is spread throughout the whole world, how can something finite fully fill something infinite?

Does that mean that energy isn't finite? Or the universe isn't infinite? Or maybe there are places without any energy at all?
Of course, there is probably something stupid I'm missing, but an answer would hopefully fix that.

Note: sorry if it's a dumb question, I just heard of it and wasn't able to answer it, nor find it on the web.

## 2 Answers

We all know that energy is never lost, but it transforms into another form.

Actually, in General Relativity it is possible for energy to change. But energy is also frame dependent (in any theory) and there is no obvious frame in General Relativity in general.

Doesn't that mean that energy is not unlimited?

No, even if you used Special Relativity (where energy is conserved .... locally) then it is easy to have an unlimited amount of energy in an infinite universe.

I mean, why is it that way if it was infinite?

We do not know if the universe is spatially infinite, and we do not know if it has an infinite amount of energy (or not).

However, if energy is spread throughout the whole world, how can something finite fully fill something infinite?

You can spread a finite amount of energy throughout an infinite universe. An easy example is a charged spherical shell of radius R=1m, charge Q=1 Coulomb, and mass M=1kg. The field is $Q/(4\pi\epsilon_0r^2)$ outside the sphere so the field has an energy density of $\frac{\epsilon_0}{2}\left(\frac{Q}{4\pi\epsilon_0r^2}\right)^2$ outside the sphere. So the energy of the field is

$$\int_R^\infty \frac{\epsilon_0}{2}\left(\frac{Q}{4\pi\epsilon_0r^2}\right)^24\pi r^2dr$$

Which equals $\frac{Q^2}{8\pi\epsilon_0R}.$ And the energy of the shell is $E=Mc^2$ so the total energy is the energy of the shell and the energy of the field which is $\frac{Q^2}{8\pi\epsilon_0R}+Mc^2<\infty.$

If you don't like the shell being empty on the inside, fill it with some mass, then there is still a finite amount of energy but it is filling up the whole infinite amount of space.

How did that work? You simply put less energy in the places that are farther out.

It's like if you had a dollar you wanted to share with an infinite number of friends. You could give half to your best friend, then a quarter to your next best friend then an eighth to the next a sixteenth to the next and so on. As long as you are willing to give ever smaller amounts of it to the next friend it can work out.

Same with that field energy, it puts less and less energy on each shell of space outside the sphere.

Does that mean that energy isn't finite?

We don't know, we don't know if the universe if finite or infinite and we don't know what the universe is like super super far away. We assume it is similar to over here, but we don't know. But we also don't know how much energy there is.

Or the universe isn't infinite?

The universe could be finite, but really really big, or it could be infinite, both are possible, both are consistent with our observations.

Or maybe there are places without any energy at all?

It is hard to have perfectly no energy, since things like electric fields spread out over all space and even if they are quite small that still leads to a tiny tiny amount of energy.

It is indeed possible to both have a infinite universe with finite total energy. Pose that there is only a part of the universe that is occupied with energy. This region will grow at the speed of light but will still be finite.

The other way around (finite universe-infinite energy) is the only combination i find impossible because it implies an infinite energy density

On the question of finite or infinite energy and space short answer is that i don´t know and i´m pretty certain now one really knows.

(The freaky conclusions that one can make discussing the question of infinite or for that matter finite universe Can be found here: http://www.universetoday.com/119553/is-the-universe-finite-or-infinite/ note: the link is a popular science article )