According to present day science what is matter? What constitutes matter? What is non matter? Are waves matter, or only that which is waving is matter? When there is a water wave in an ocean, Is only the water matter or is the wave also matter?
We call "matter" something that we don't know, which therefore may or may not exist as we think of it. Maybe matter is really just another shade of blue. We should also keep in mind that except for our own mind we probably won't get to know anything at all. What's left is explanation. Some have provided "good" explanations. But that's not telling us what matter is. It's telling us instead that matter doesn't exist after all and that something else exist, say, energy for example, or some sort of "waves", whatever. If so, the real question is not "What is matter?" but "What is energy?", or what are "waves" etc. The question therefore is: What is the real stuff that explains everything else which only seems to exist but really doesn't so that the what the real stuff explains is really our impressions that certain things exist, like tables and chairs, matter, or whatever.
So, what is the real stuff?
EB
That depends what you mean by 'real'; and that is a subject for Philosophy, not Natural Science.
In terms of Natural Science, matter is what Quantum Field Theory says it is - and QFT defines what matter 'is' by using mathematics to describe how things interact, in a way that allows us to accurately predict what will happen next, given a particular set of initial conditions. We arbitrarily label some of those descriptions as 'mass' or 'energy'; and we can describe very accurately how those two sets of results in our calculations will relate to one another - and to everything else.
Concepts like 'mass' and 'energy' are useful for making fairly precise predictions about what will happen next. Mathematics is even more useful. But all of these things are mere models of an underlying reality that is, and probably always will be, inaccessible to us. We don't know what 'real' even means; and speculation about it is, in my opinion, futile.
When we use a concept of 'matter' that conforms to the mathematical model called QFT, we are able to very accurately predict how our observations will evolve - ie, what we will see happen next. Those models assign values to a small number of fields (each of which is associated with a particle, which is what we call a local maximum in those fields; it seems that the values for many of these fields are constrained to multiples of a particular minimum quantity, hence the 'quantum' in QFT). Each of these fields has well defined properties, or rules, that specify how they interact. Whether these models represent what is "actually happening" is not a question that can be answered in a scientific way; it is like asking 'What is North of the North Pole?" or "What happened before the start of time?".
Science has the goal of finding out how the universe works. It appears that there are rules, and that everything obeys those rules; Science is the process of writing what we hope will be the definitive rulebook, based solely on observing what happens.
QFT is the best rulebook we have come up with to date; Its predictions match observation as perfectly as we are able to detect, except in its descriptions of gravitation. We have a separate, and almost as effective, rulebook to tell us how to predict what happens when gravity is important; And there are some reasons to think that there may be some underlying rules from which both rulebooks might be derived.
As far as Natural Science is concerned, what matter is, is 'that thing you have when all of the fields at this set of locations in spacetime are interacting in such a way as to give a number for 'mass' that is non-zero'. It is defined - as all other physical entities are defined - in terms of the rules. We know that we know a lot of the rules to a very high degree of precision; So we can be confident to the same high degree that this is a good description of matter.
