Would you agree that degrees of freedom are more fundamental than properties? The Higgs mechanism works on a mathematical level by making an extra degree of freedom available to the elementary particles, and this degree of freedom manifests itself as mass. (There are also extra degrees of freedom left over known as Goldstone bosons; the Higgs particle itself is an example of a Goldstone boson.)
The physical interpretation of that math would go like this: the "massless" elementary particles are coupled to the Higgs field, which "dresses" the particles in a cloak of virtual Higgs particles, and it is this cloak that plays the role of mass. The stronger the coupling, the heavier the cloak.
I might agree if I knew what you meant.
The physical interpretation of that math would go like this: the "massless" elementary particles are coupled to the Higgs field, which "dresses" the particles in a cloak of virtual Higgs particles, and it is this cloak that plays the role of mass. The stronger the coupling, the heavier the cloak.
Hmm... I think I see what you are getting at. The Higgs mechanism is a mathematical concept that may be interpreted physically. Degrees of freedom would also be a mathematical concept.
Allow me to try to explain the difficulty I had with your original statement. It is not that I think it was incorrect; but rather, it reflects a way of looking at the world that is different from the way that I, as an engineer, view it.
Consider gravitational mass. Everyone has an idea, acquired by direct experience, that massive objects are attracted to the earth. Since Newton's time, we have written F = mg. But does this equation "explain" or "account for" gravitational mass? My contention is no: F = mg is a convenient mathematical description of what we observe to happen (at least in most everyday applications).
Put it another way, does nature obey our mathematics? Or do we hope our mathematics describes nature? My impression is the mathematician or mathematically inclined physicist considers the equations more real than nature. Thus, Goldstone bosons are not objects but degrees of freedom.