Mass matter, energy and "massless matter"

Question

This is perhaps a rather silly question, or rather a matter of convention, but I would like to hear arguments about the appropriateness of certain definitions.

Traditionally, in chemistry and in pre-relativistic physics, matter was called mass matter that occupied a volume in space and was formed by atoms. However, in some informal uses, any physical entity that fulfills either of the following two properties is called matter:

1. It interacts gravitationally and, therefore, contributes to the curvature of space-time.
2. It can produce a signal in a physical subatomic particle detector.

Obviously, photons or electromagnetic radiation satisfy both conditions, so in a sense photons are "massless matter". However, some authors follow somewhat the traditional definition of matter by restricting the term to fermionic matter (which satisfies the Pauli principle and, therefore, is matter that somehow "occupies a volume"). However, the gluons themselves, which are responsible for most of the mass of ordinary matter, would not be matter but only a field of forces. It seems to me a bit arbitrary and unsatisfactory the restrictive definition of matter that applies it only to fermions with mass (especially when we know that the mass of elementary fermions does not indicate a "quantity of something" but only the intensity of the coupling with the Higgs field.

My question is: Are there any arguments of convenience that exclude that massless bosons or dark energy can be considered just exotic forms of matter? (I do not go into dark matter, because it could turn out that it is formed by mass fermions, although its nature at the moment is an open problem).

Answer 1

In cosmology, matter dilutes with the expansion of the universe as the scale factor $a^{-3}$. That can serve as a definition of matter. In this definition, photons and other radiation is not matter, as it scales with $a^{-4}$. Note that most neutrinos are relativistic and thus, according to this cosmological definition, also wouldn't be considered matter. Finally, dark energy also isn't matter because it doesn't scale with $a$ (it's constant). In addition, dark energy is a property of space itself, not something moving around in space.

In particle physics, matter is fermions and, because of the Pauli exclusion principle, therefore takes up space. Again, gauge bosons or photons are not considered matter either, but in this definition, neutrinos are matter.

If you are in a chemistry context, you might even say that alpha or beta radiation is not matter, but radiation and thus distinct - as a chemist you can't put that on a balance, or bottle it up.

You see, with semantics, context "matters".

Answer 2

The real problem with a definition of matter is that it strongly depends on the conceptual frame one uses. In contemporary Physics, we are used to working with general theories that in some well definite limits may reduce to special cases. The definitions useful at a specialized level may not be relevant at a more general level.

This is the case with the concept of matter. At the scale of distances, speeds, and energies relevant to chemistry, the matter may coincide with atoms. In a more general conceptual frame, such simple identification is blurred.

Using the property of having mass to distinguish between matter and not-matter is simple at the non-relativistic level, it becomes questionable, once we realize that mass is not an additive property in SR (one photon has zero mass, the system of two photons moving in opposite directions has non-zero mass).

Therefore, the real question is at what level of theory the concept of matter is useful?

I think that contemporary Physics's answer is that it is approximately the level of Chemistry.