# Rest energy of a sample of pure matter

1. Mar 16, 2012

### jaketodd

I am wondering what the rest energy (mc^2) is of 1 cubic meter of pure matter (no empty space).

Thanks,

Jake

2. Mar 16, 2012

### Drakkith

Staff Emeritus
Pure matter? There is no such thing.
You need choose a density of some amount or tell us the mass of the matter.

3. Mar 16, 2012

### jaketodd

I know there's no such thing. Well I was thinking a neutron star would be pure matter, but I'm unsure of that, so I'm asking: Theoretically, how much rest energy would one cubic meter of pure matter have?

Thanks,

Jake

4. Mar 16, 2012

### Drakkith

Staff Emeritus
There is no such thing as "pure matter", not even theoretically. You're taking a few science terms and using them incorrectly.

5. Mar 16, 2012

### Drakkith

Staff Emeritus
Let me put it this way. Matter is composed of quarks, which form into protons and neutrons, and of electrons. Compress matter enough, such as in a neutron star, and you get a superdense material known as neutronium. Compress it even more and the end result is what appears to be a singularity, a region of space where matter is compressed into infinite density. It is unknown whether singularities actually exist or if they are simply artifacts of an incomplete theory. "Pure matter" seems to me to be the infinitely compressed type, which cannot occupy a set volume of space, as it is compressed infinitely small.

6. Mar 16, 2012

### DaveC426913

It should be simple enough to determine the density of neutronium, calculate the mass of a cubic metre of it, then apply E=mc2.

Mass of a cubic metre of neutronium, which is similar to the density of atomic nuclei:
http://en.wikipedia.org/wiki/Neutron_star
and an energy calculator:
http://www.1728.org/einstein.htm

[ EDIT ] you could skip down 2 posts where Pengy does it for you.

Last edited: Mar 16, 2012
7. Mar 16, 2012

### jaketodd

If quarks are the most fundamental units of matter, then it seems all you would need to do is fill a cubic meter with them, with no empty space. This would be more dense than neutronium, as that is formed of neutrons, which are, in turn, formed of quarks. If space is quantized, which I, personally, believe it must be, then you can't form a singularity because that would have more than one quantum's worth of matter occupying the same quantum. I know there is a class of matter that can occupy the same space as other matter within that class, but let's leave that out for now.

8. Mar 16, 2012

### Pengwuino

Let's just decide we're using a neutron star's density of roughly $4.0 \times 10^{17} kg/m^3$. So one cubic meter would have the rest energy of $4.0 \times 10^{17} kg/m^3 \times 9.00 \times 10^{16} m^2/s^2 = 3.6 \times 10^{34} J$. There you go.

9. Mar 16, 2012

### jaketodd

I knew that, but thanks. BTW, is a Pengquino the speed of a neutrino in Antarctica?

Jake

10. Mar 17, 2012

### Staff: Mentor

Then why did you ask the question?

11. Mar 18, 2012

### jaketodd

I asked the question because I thought there might be a more-dense solution, and from the discussion, it seems the answer is quarks.

12. Mar 18, 2012

### yuiop

A Bose-Einstein condensate is effectively a collection of atoms that have formed into a single atom so this is matter with no gaps between its constituent particles. In an alternative model of the black hole called the gravastar, the outer shell is made of a very dense Bose-Einstein condensate type material which is possibly the densest material theorised to exist. In the classic interpretation of black holes there is no upper limit to the density of matter that is compressed to a singularity at the centre.