Particle vs Wave Interpretations of QM

[jeffn1]

Sure, classical physics also contains different interacting entities.

My point was not that interactions are mysterious or impossible. Rather, the history of physics contains several examples where entities initially regarded as distinct turned out to be different aspects of a more unified structure.

For example, electric and magnetic fields were once viewed as separate entities and are now understood as components of the electromagnetic tensor.

So when I see several fundamental fields interacting with each other, I naturally wonder whether they are truly fundamental and distinct, or whether a more economical underlying description might exist.

For what its worth, Art Hobson states, in Fields and Their Quanta, "The universe is a set of at least 25 fields, each of which fills the entire universe. These fields are probably facets of a single universal field." (P. 183)

 

[Matterwave]

For what its worth, Art Hobson states, in Fields and Their Quanta, "The universe is a set of at least 25 fields, each of which fills the entire universe. These fields are probably facets of a single universal field." (P. 183)

I wonder how he counts 25.

 

[PeterDonis]

I wonder how he counts 25.

6 leptons, 6 quarks, 12 gauge bosons, and the Higgs in the Standard Model. Of course this counting leaves out a lot of things. Hobson does say "at least", which might be a gesture in the direction of those things.

 

[Matterwave]

6 leptons, 6 quarks, 12 gauge bosons, and the Higgs in the Standard Model. Of course this counting leaves out a lot of things. Hobson does say "at least", which might be a gesture in the direction of those things.

What is the reason to count only 6 quarks? We count only the doublet from the weak SU(2) interaction and not the triplet from the strong SU(3) interaction? Naively I would have thought 18 -- 3 generations by SU(2) doublet by SU(3) triplet. And this is not even getting into chirality and spin.

Or do you think something like this is what Hobson was trying to account for with "at least"?

 

[PeterDonis]

What is the reason to count only 6 quarks?

Up, down, strange, charm, top, bottom.

Yes, that counting leaves out the quarks' color charge. But note that, for example, when we say the proton and neutron are each made of 3 quarks, that's how we're counting. We're not taking into account the color degrees of freedom, because hadrons are colorless, and the valence quarks inside them are not in any particular color eigenstate. Nor are there multiple different kinds of protons and neutrons with different color mixtures among the quarks.

We count only the doublet from the weak SU(2) interaction

No, we're not really counting that way. The leptons are the electron, muon, tauon and their neutrinos. But the electron, muon, and tauon aren't just their parts of the left-handed SU(2) weak doublet; they're also the right-handed SU(2) singlet. Similar remarks apply to the quarks. That's one of the reasons I said the counting I gave leaves out a lot of things.

And this is not even getting into chirality and spin.

Yes, that's not really taken into account, just as color charge on the quarks is not. Again, I said the counting I gave leaves a lot out. But it is one that appears in a lot of pop science sources, and even some not so pop science sources.

 

[Matterwave]

I'm going to have to think on this more but it seems highly non-trivial to me to even count the number of fields.

 

[PeterDonis]

I'm going to have to think on this more but it seems highly non-trivial to me to even count the number of fields.

Yes, it is. Hobson did say "at least" 25 fields.

 

[Matterwave]

Yes, it is. Hobson did say "at least" 25 fields.

Semantic question -- when you say "yes it is", you are saying it's trivial to count or it's not trivial to count?

I might have phrased my point better as it's not trivial what you count as distinct fields.

 

[PeterDonis]

Semantic question -- when you say "yes it is", you are saying it's trivial to count or it's not trivial to count?

Yes, it is not trivial. As in, yes, we have no bananas:

https://en.wikipedia.org/wiki/Yes!_We_Have_No_Bananas

 

[Roberto Pavani]

Isn't the counting somewhat convention-dependent? Maxwell's electromagnetic field already incorporates electric charge via its sources, and GR incorporates mass-energy via the stress-energy tensor. What is the criterion for counting these as separate fields rather than aspects of a more unified structure?

 

[Matterwave]

Isn't the counting somewhat convention-dependent?

"The counting" that I was referring to was the one in Art Hobson's quote mentioned in post #241 which I assumed was meant for fields in QFT.

Indeed, even Hobson himself said "at least 25", suggesting ambiguity.

What is the criterion for counting these as separate fields rather than aspects of a more unified structure?

In relativity, the electric and magnetic fields of Maxwell were unified into the electromagnetic field via the Faraday tensor $F_{ab}$ which is an antisymmetric (0,2) tensor. This tensor has 6 independent components which account for the 3 components of the electric field and 3 components of the magnetic field.

What is called "the electric field" in one reference frame may show up in another as part of "the magnetic field" and vice versa.

 

[Roberto Pavani]

$E$ and $B$ mix under Lorentz transformations.
However, for a Coulomb field generated by an electric charge, there is always a rest frame in which $B=0$, whereas $E$ cannot be transformed away.
For a free electromagnetic wave, neither field can be eliminated by any physical Lorentz transformation; doing so would require moving at $c$.