[danbruc]

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.

[tsimionescu]

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.

[kgwgk]

Other people may say that photons are just mathematical tools that we use to describe fields. :-)

[danbruc]

The fact that gauge fields have redundant degrees of freedom should at least be a strong hint that the fields are not the fundamental description. ;)

[carlob]

I don't think you are correct: you can view the extra degrees of freedom as just a symmetry

[danbruc]

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.

[mokus]

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.

[danbruc]

Gauge symmetries are local symmetries. In case of the complex temperature field you can change the imaginary part of the temperature at each point independently without any physical effect. Global symmetries on the other hand are meaningful, for example spatial translation and rotations and time translations in Newtonian spacetime are associated with the isotropy and homogenity of space and time and also the related conservation of momentum, angular momentum, and energy. And of course your example of changinging the reference potential is also a global symmetry, not a gauge symmetry.

[dschuetz]

Oh yes, quantum electromagnetic quantum field. Just add "quantum" and the discussion is over.