Is there really such a thing as rest mass?

Question

Given that everything is always moving, stars, planets, solar systems, galaxies, etc. is there really such a thing as a rest mass?

Of course some things are stationary relative to each other, but nothing is truly at rest, is it?

Answer 1

The total energy of a relativistic object is:

$$ E^2 = p^2c^2 + m^2c^4 $$

where $p$ is the momentum, $c$ is the speed of light and $m$ is a property of the object called the invariant mass or rest mass. This invariant mass is the same for all observers no matter how they are moving, so it is a fundamental property of the object. In the rest frame of the object the momentum is zero and the expression simplifies to:

$$ E = mc^2 $$

which should be familiar :-)

The key point about the invariant/rest mass of an object is that it doesn't depend on whether the observer and the object are moving relative to each so it is always well defined, and that's why we use it.

I would guess you are asking because you have heard that the mass of an object changes with its speed. There is a property called the relativistic mass that does increase with speed, however no modern physicist uses this precisely because it is observer dependent.

Answer 2

Of course there is. Rest mass is defined as the mass measured from a reference frame where the particle is at rest. You can see it as a number attached to the particle invariant of reference frame.