Honest question: aren't radio waves "physical objects" that represent oscillations of an electro-magnetic field, to the best of our current understanding?
There is an agreement in physics that low energy EM fields are called waves, such as radio waves, and high energy EM fields are called photons or even particles. In any case they are actually both. If they are physical objects I don't know. I think, I wouldn't go that far.
Sure, they are both, but my point was - if they have wave-like characteristics, they must be a wave of/in something; if we can have experimental evidence that the wave exists, I would consider that experimental evidence that the field the wave is a wave of must also exist, to the same extent.
Radio waves are streams of photons, the fields are just a mathematical tool we use to describe this. And there are several of them, the classical electromagnetic field but also an entire set of fields involved in the quantum version.
My understanding was that some kind of wave-particle dualism was well accepted. It's exact physical meaning may not be understood, but isn't there experimental evidence that photons, even individual ones, behave as waves in some circumstances (as does as any other 'particle', in fact)?
I've seen this dualism claimed pretty recently by Leonard Susskind.
It is usually called a gauge symmetry but it is kind of a misnomer and should better be called a gauge redundancy. It is artifical and only due to the mathematical formalism we are using. As an analogy, probably not a really good one, is that you could decide to describe temperatures with a complex number and just say temperature is invariant under translation along the imaginary axis. Sure, the symmetry is in your mathematics but it doesn't really tell you anything new or interesting. Besides of course that the imaginary part is actually redundant and you better described temperature with a real number instead.
That would not work in the same way as a typical gauge theory though - typically the symmetry of a gauge is for shifts of the entire system along the gauge - changes along the gauge locally do have physical meaning. For example, in an electrical diagram you can arbitrarily shift every voltage in the system by a billion Volts (ground rail is 1b Volts, 5V rail is 1b+5V, etc) and the system will behave identically. The gauge quantity is real and not redundant, it’s just that it doesn’t have a known meaningful absolute reference point.