E=mc^2 in natural units

1. Nov 14, 2006

DaveC426913

Somewhere a month or two ago, there was a discussion about E=mc^2 and the question of what the c^2 represents.

The answer was that c^2 was simply a conversion unit, to put it in more common units of kg, m and s. That, if the formula were considered in more natural distance units of light seconds, it resolves to simply E=m.

Could someone elaborate?

Does it mean that, say, one gram of mass, if converted to energy, could apply a force that would move a gram of mass one light-second per second squared? Or some such?

Last edited: Nov 14, 2006
2. Nov 14, 2006

drphysic

A quick look at Wikipedia gives an example of:

E (joules or kg·m²/s²) = m (kilograms) multiplied by (299,792,458 m/s)²

Is this the type of answer you were looking for?

The relevant page is: http://en.wikipedia.org/wiki/E%3Dmc%C2%B2" [Broken]

http://en.wikipedia.org/wiki/E=mc²

Last edited by a moderator: May 2, 2017
3. Nov 15, 2006

rbj

also take a look at Wikipedia articles on Natural units and Planck units.

http://en.wikipedia.org/wiki/Natural_units
http://en.wikipedia.org/wiki/Planck_units

not all natural unit systems define the unit velocity to be the speed of light $c$ (such as atomic units). but then the unit velocity is $\alpha c$. in those units then the speed of light is not 1 but is $1/ \alpha$ and it comes out as

$$E = m \frac{1}{\alpha^2}$$.

4. Nov 15, 2006

DaveC426913

No. All you've shown is what the units are.

5. Nov 15, 2006

DaveC426913

6. Nov 15, 2006

Meir Achuz

In natural units, E and m have the same units. You can pick any common unit you want. The most common choice for nuclear physics is MeV.
The mass of an electron is .511 Mev.

7. Nov 15, 2006

rbj

which is dimensionless for both. they are the ratio of the energy (or mass) in units of any consistent system of units to the quantity of energy (or mass) of the corresponding natural unit as measured in the same consistent system of units. in natural units, physical quantities are dimesionless.