What really is mass?

Question

I was always taught that mass was how much matter something is made of, but I recently read that it is how resistant an object is to acceleration; as such, you could add mass to an object by increasing its energy, even though you aren't really adding any matter. Which is correct?

Answer 1

Mass is a constant that relates how momentum and energy are balanced.

In prerelativistic physics, energy is $mc^2+p^2/2m$ and in relativistic physics energy satisfies $E=\sqrt{(cp)^2+(mc^2)^2}$ and the former is approximately equal to the latter when $|pc|\ll mc^2.$

Answer 2

Mass is not the amount of matter present in a body (this is what most books say).

It is actually the measure of inertia of a body.

Therefore, by increasing its energy, you increase inertia. So, mass is also increased, even though there is no exchange of matter.

Hope I helped you.