Richard Muller, Professor of Physics, U. Calif. Berkeley, coFounder of Berkeley Earth
I have an unorthodox approach, but it is correct, and it helps students visualize what is happening.
When I was a student I was very bothered by people who told me that light was a wave, but couldn’t answer my question, “What is waving?” They had been taught that the old idea of an “aether” had been discredited. The first professor to set this straight for me was the great theorist at Berkeley, Eyvind Wichmann, who explained in the advanced graduate course I took that the aether had never been proven to not exist. The aether had been shown to be undetectable by the Michael-Morley “aether wind” experiments, but it was never gone from physics. It was just renamed “the vacuum”.
Many people think of the vacuum as “empty”, but in modern physics, there are chapters of advanced books written about the properties of the vacuum. It can be polarized; it contains a Higgs field and dark energy; it is full of virtual particles. In general relativity a small region can contain huge amounts of volume, described by the “metric tensor” of the vacuum.
But for the introductory student, just think of it as a “thing”. But it isn’t “matter”. Matter is a vibration of the vacuum. Some top theorist have told me that they think of the vacuum as a stretched membrane, and when that membrane vibrates, then there is energy and matter. It’s only an analogy, but that’s what they visualize. Me too.
This membrane can vibrate in many different ways. One is to vibrate from a value of zero electric field to a positive field and then back to a negative field. It can vibrate, but that vibration can also propagate like a wave. Think of a stretched piece of thin rubber, and you shake one end, and a wave travels across it. We now know that the wave consists of both an electric and a magnetic field. (Each field is a kind of membrane stretch.) This is what we call an “electromagnetic wave”. Visible light is one form; radio waves are a lower frequency form.
The vacuum can vibrate in many different ways. Physicists think of these as extra dimensions, but they are not spatial dimensions. You can describe the vacuum at a location by it position, but also by the strength of electric field there; technically, that is another “dimension” but it doesn’t count as a spatial dimension.
Quantum waves are the same. An electron consists of a vibration of the vacuum that contains an electron field. That field is NOT an electric field; it is the electron field. That is the field that moves according to the Schrodinger equation (or, more precisely, the Dirac equation).
What is this membrane we call the vacuum? It clearly can’t be described in terms of ordinary matter, because ordinary matter is described in terms of it. So there is nothing that we can reduce it to. Imagine some very highly intelligent water waves, with their entire civilization consisting of complex water waves, pondering the question of “What is waving?” They are not aware of the water because their reality consists only of waves.