The concept of matter ought to be more widely known.

You might wonder, did I misunderstand the question? Did I think it was asking, "What scientific term or concept is already widely known?" For if there is any scientific concept that is widely known, then it's the concept of matter, i.e. that stuff from which all things are made.

But no, I didn't misread the question. While every intelligent person has heard of the concept of "matter," few people know the scientific meaning of the word. What we have here is an example of a concept that was first used in ordinary life, but that has come to be explicated in the development of science.

So what does science tell us about matter?

As you probably know, there's an age-old debate about whether things are ultimately made out of particles, or whether things are excitations or waves in some continuous medium. (In fact, the philosopher Immanuel Kant found this debate so tedious that he declared it irresolvable in principle.) But many of us were told that the wave-particle debate was solved by quantum physics, which says that matter has both particle-like and wave-like aspects.

Then things got a bit weird when Niels Bohr said, "there is no quantum reality," and when Eugene Wigner said, "there is no reality without an observer." What the hell is going on here? Has matter disappeared from physics? Has physics really told us that mind-independent matter doesn't exist?

Thank goodness for the renegades of physics. In the 1960s, people like John Bell and David Bohm and Hugh Everett said: "We don't buy the story being told by Bohr, Wigner, and their ilk. In fact, we find this talk of 'observer-created reality' to be confusing and misleading." These physicists then went on to argue that there is a quantum reality, and that it exists whether or not anyone is there to see it.

But what is this quantum reality like? It's here that we have to stretch our imagination to the breaking point. It's here where we have to let science expand our horizon far beyond what our eyes and ears can teach us.

To a first approximation, what really exists, at the very bottom, is quantum wavefunctions. But we must be careful not to confuse an assertion of mathematical existence with an assertion of physical existence. In the first instance, a quantum wavefunction is a mathematical object—a function that takes numbers as inputs, and spits out numbers as outputs.

Thus, to speak accurately, we ought to say that a quantum wavefunction represents matter, not that it is matter. But how does it accomplish that? In other words, what are the things that exist, and what properties are being attributed to them? It's at this point that things become a bit unclear, or a bit scholastic. There are so many questions we could ask about what it means to say that wavefunctions exist. But what's the use—because quantum mechanics isn't really true.

We now know that quantum mechanics is not literally true—at least not if Einstein's relativity theory is true. In the middle of the 20th century, physicists saw that if you combine relativity with quantum mechanics, then wavefunctions cannot be localized—the result is that, strictly speaking, there aren't any localized material objects. But what there are, they said, are quantum fields—these nebulous quantum entities that spread themselves throughout all of space.

But don't get too excited about quantum fields, because they have their own problems. It was already suspected in the 1960s that quantum fields aren't quantum reality in itself—rather, they're a sort of observer-dependent description of that reality in the same way that saying, "that car is moving at 45 miles per hour" is an observer-dependent description of reality. In fact, it was proven by the German physicist Hans-Jürgen Borchers that many distinct and incompatible quantum field descriptions correspond to any one situation. A similar result has recently been demonstrated by the Michigan philosopher David Baker. The upshot is that you've got to take quantum fields with a grain of salt—they're a human contrivance that gives just one perspective on reality itself.

In summary, particles, in the traditional sense of the word, do not exist. Nor do quantum wavefunctions really exist. Nor do fields exist, neither in the traditional sense of the word, nor in the quantum-theoretic sense of the word.

These facts can seem depressing. It seems that matter in itself is always hiding behind the veil of our descriptions of it.

But do not despair. Note what has been happening here. The description of matter as particles was helpful, but not exactly correct. The description of matter as a wavefunction is even more accurate, but it has limitations. Our best current description of matter is in terms of quantum fields, but the quantum fields are not yet the thing in itself.

At each stage, our description of matter has become more nuanced, more widely applicable, and more useful. Will this process come to an end? Will we ever arrive at the one true description of the basic constituents of the universe?

Who's to say? But as long as each generation outdoes the previous one, what more could we want?