When does it make sense to use "energy density" to describe traditional density (mass/volume)?

Question

I was just listening to an NPR story where an astrophysicist is describing empty space as a [volume having the] state of "zero energy density". I would have thought he would describe it as a place with the absence of mass (which, from junior-high-school general science, I've always defined as "the number and kinds of atoms" -- though obviously sub-atomic particles have mass).

Does the lack of energy density in a particular space necessarily imply that there is no mass (or matter?) there (à la E=mc²)?

Answer 1

I suppose he's referring to vacuum energy, which is a kind of zero point energy, that is, the energy of the vacuum ground state (the ground state of a quantum mechanical system is its lowest-energy state, and this lowest energy is never zero). See the Wikipedia articles for more information.

In general, you shouldn't think of physical vacuum as some absolutely empty void: see the answers of this question to learn more about vacuum. Also, this John Baez article can be helpful.

Answer 2

In general relativity the curvature is related to an object called the stress-energy tensor, and as normally written one entry in this is the energy density. In GR the energy density counts both things like dark energy and also the contribution from matter, where the matter density is converted to energy density using the famous equation $E=mc^2$.

So general relativity doesn't care whether the energy comes from energy or from matter. It treats the two as identical apart from the factor of $c^2$. In fact relativists usually work in geometrical units where the speed of light is one, and in those units energy and matter densities are equal.

And that's why the astrophysicist is referring to energy density. Firstly it would be tedious to have to keep referring to both energy density and matter density, and secondly GR doesn't care anyway.