# What is the right name for the 'mass' increased with heat?

The term 'relativistic mass' is superseded and many answers in this site often state that the term mass ought to be used ony for rest(/invariant) mass.

John Rennie explains that :

... but you need to be clear that the relativistic mass is a computational device and it does not mean the mass is changing. Nothing happens to the gold. If I am sitting by the gold while you speed off in your spaceship I will see nothing happen to it.

But he adds that:

the key point. When we heat the gold all observers, no matter what their speed, will agree that the gold has changed because we all see it absorbing the light from the IR lamp

So, it is intended that the mass of the gold has indeed changed, is that so? If that is the case, besides rest mass there is something more, but John Rennie does not specify how the gold has changed and if we are allowed to call the increased entity mass in which case maybe thermal mass is the correct term? If it is mass, in what way is it different from the mass of an electron?

Do you happen to know if there are any theories explaining what really is going on: how does the gold change and 'mass' increases?

Suppose we consider a single gold atom. It has some mass $m$, and there is an associated energy given by Einstein's famous equation:

$$E = mc^2$$

But the gold atom can absorb energy and transform into an excited state. It can do this because it has an internal structure, i.e. electrons surrounding a nucleus, and it can absorb energy by rearranging its electrons. But suppose it absorbs some extra energy $\Delta E$ then its total energy has increased, and equation (1) tells us the mass must increase as well:

$$E + \Delta E = m'c^2$$

where $m'$ is the (increased) mass of the excited state.

And this means the mass of the gold atom isn't a constant. To specify the mass we also have to say whether the gold atom is in an excited state or not. In practice when we talk about the mass of a gold atom we mean the mass of a gold atom in its ground state ($3.92484812 \times 10^{-24}$ kg according to Wikipedia).

If instead of a gold atom we consider an elementary particle like an electron then it has no internal structure so it cannot absorb energy like an atom can. That means the energy of a stationary electron has a constant value and it cannot changed as the energy of an atom can. So the mass of the electron:

$$m_e = \frac{E_\text{electron}}{c^2}$$

is a universal constant. This is what we call the rest mass or invariant mass of the electron.

Strictly speaking we can't talk about the rest mass of a gold atom, or anything else that isn't an elementary particle, without giving extra information e.g. rest mass of the gold atom in its ground state. In practice we're lazy and use the term rest mass for composite systems and just assume everyone knows we mean in the ground state.

There isn't a specific term for the mass of a composite system in an excited state - we just use the term mass.

To beginners in relativity it seems odd that mass can change, but this is one of the things about relativity you just have to get used to. Einstein's mass-energy equation isn't just some mathematical toy and the rest mass of relativistic systems can and does depend on their energy.

• @user157860: Everything above is in the centre of mass frame so the average velocity of the system as a whole is zero. The separate parts of the system will have non-zero kinetic and potential energy, and both of these contribute to the gravitational mass. – John Rennie Jun 3 '17 at 8:23
• @user157860: Energy can be turned into mass and vice versa - the LHC does this all the time. See for example my answer to What keeps mass from turning into energy?. – John Rennie Jun 3 '17 at 10:59
• @user157860: the mass of any interacting system, like a lump of gold, is not simply the sum of the masses of its components. It is the mass of the components plus the net interaction energy of those components. That interaction energy is the sum of the (positive) kinetic energy and the (negative) potential energy. When you heat a lump of gold you make the kinetic energy of the gold atoms more positive and the potential energy less negative. Both of these increase the mass. – John Rennie Jun 3 '17 at 11:16