Why does E=mc² reduce to E=m in natural units?

[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?

 

[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"

http://en.wikipedia.org/wiki/E=mc²

 

[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

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

 

[DaveC426913]

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?

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

 

[DaveC426913]

I guess I'd better laocte the thread and perhaps the thread-poster.

 

[Meir Achuz]

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?

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.

 

[rbj]

In natural units, E and m have the same units.

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.