# Define Rest Mass

1. Oct 3, 2014

### avito009

I was remembering the equation E=MC2. So as per me Rest Mass is nothing but Energy that is stationary. Am I right?

2. Oct 3, 2014

### Simon Bridge

The "rest mass" is the mass of an object measured in a frame of reference that is stationary with respect to the object.
The mass may be "moving around" in some other reference frame, but it still has rest mass - therefore rest mass can be energy that is moving around.

Note: $E=mc^2$ just means that mass is a form of energy.

3. Oct 4, 2014

### avito009

Rest mass and rest energy are equivalent and remain proportional to one another. I am not talking about object that is moving here.

Now E=MC2. Energy and mass are equivalent and the "C2" is the conversion factor because the mass has to be converted into units of Energy. Mass is measured in Kilograms and Energy is measured in Joules. So to convert Kilograms to Joules "C2" would be used.

4. Oct 4, 2014

### Simon Bridge

... this is correct. What I want you to realize is that "rest mass" does not refer only to "energy that is stationary". In the context of Einstein's relativity there is no absolute motion, so there is no absolute for "stationary" either. The word "stationary" must be used with a reference frame. Stationary with respect to what? Moving with respect to what? So when you said:
... you forgot to say what it is stationary with respect to.
The statement is correct if you mean "stationary with respect to itself"... suddenly does not sound so profound does it :)

... the kg and the J are the SI units for mass and energy respectively. These are not the only units. Speed is also measured in miles-per-hour, mass in pounds, and energy in ergs, for example.

When you do relativity a lot you will start using "natural" units... these are units chosen so that c=1 - so the equation becomes E=M.
http://en.wikipedia.org/wiki/Natural_units

 The $c^2$ is not there just to convert the units - if unit conversion were the only reason, then any old speed will do. For instance, the mass multiplied by the escape velocity from the surface of the Earth would have units of energy...

Niggle: usually the rest mass m and the invariant speed c are represented in lower-case letters.
The full mass-energy relation is $E=\gamma mc^2$

Last edited: Oct 4, 2014
5. Oct 4, 2014

### Staff: Mentor

Rest mass is also known as invariant mass and is given by $m^2c^2=E^2/c^2-p^2$. So if momentum is 0 then that reduces to the famous $E=mc^2$.

Note that it is a mistake to say "energy is mass" since they differ when momentum is not 0 even in units where c=1 (mass is invariant and energy is not), but when (as you said) the energy is stationary then it is numerically equal to mass in units where c=1.

6. Oct 4, 2014

### Drakkith

Staff Emeritus
Remember that mathematical equations are not definitions. For example, the equation for electric current is I=V/R, or current equals voltage divided by resistance. But this doesn't mean that current is voltage or resistance, or that voltage or resistance is current. Each one has its own definition and all three are related, but they are not the same thing.

Similarly, mass and energy are related by the equation E=MC2, but that doesn't necessarily mean that energy and mass are the same thing. (Of course it doesn't mean that they aren't the same thing either) If I remember correctly, Einstein's original thought process regarding energy and mass was that if a quantity of energy is added or removed from a system, a corresponding amount of mass is added or removed as well, with the amount of mass and energy related by Einstein's equation.

Mass is a complicated concept that has multiple aspects. Wiki lists them here: http://en.wikipedia.org/wiki/Mass#Definitions_of_mass