# Rest mass and apparent mass

1. Jul 15, 2011

### hanii

hey guys ...i've got a doubt..
when there is no absolute rest in the universe...how is rest mass defined?

2. Jul 15, 2011

### Staff: Mentor

There's always a frame in which the body (or its center of mass) is at rest. Nothing 'absolute' needed.

3. Jul 15, 2011

### Staff: Mentor

You can also calculate the "rest mass" (more properly called "invariant mass") using the energy and momentum as measured in any inertial reference frame, by solving the following equation for m:

$$E^2 = (pc)^2 + (mc^2)^2$$

In different reference frames you measure different values for E and p, but they always give you the same value for m.

4. Jul 15, 2011

### CJames

A non-accelerating object is always at rest with respect to itself.

5. Jul 15, 2011

### ZealScience

Yes there is no absolute rest, because particles are all moving fast. Unless reach absolute zero which would break the second law of thermodynamics or the uncertainty principle. But discussing relativity, I think, we talk more generally about macroscopic objects in reference frames.

6. Jul 15, 2011

### bcrowell

Staff Emeritus
"Absolute rest" in this context means being able to define whether an object is at rest without reference to anything external. Even if we could cool an object down to absolute zero, it wouldn't be at "absolute rest" in this sense.

7. Jul 15, 2011

### chogg

Let me add that the motion of the particles that make up a macroscopic object actually does increase the (rest) mass of that object. This blew my mind as a beginning grad student. A hot potato weighs more than a cold potato (though not much more!).

8. Jul 15, 2011

### ZealScience

Of course it depends on reference frames, but with temperature particles are moving fast! The mass of electron that measured by scientists is the mass of moving electrons. They are not interested in inertial mass of electrons.

9. Jul 15, 2011

### bcrowell

Staff Emeritus
Yes, but that has nothing to do with what people mean when they refer to "absolute rest" in the context of SR.

10. Jul 16, 2011

### hanii

so...we should be at rest relative to the frame of reference in which the object is...to find the rest mass of that object

11. Jul 16, 2011

### hanii

how is this equation derived? could u please explain me..

12. Jul 16, 2011

### Staff: Mentor

Do you mean this one?

Here's one way to derive it: start with the equations for relativistic momentum and energy:

$$p = \frac {mv}{\sqrt{1 - v^2/c^2}}$$

$$E = \frac {mc^2}{\sqrt{1 - v^2/c^2}}$$

Solve them together to eliminate v. For example, by solving one equation for v and substituting it into the other one.