Interesting, but (way out of my depth here) why do these symmetries have to exist?

It would be much more satisfying (not that nature exists to be satisfying) if we could explain our universe starting from some universal constraints on things that must be true of any non-random mechanistic universe, plus some set of (< N) non-forced "it must be A or B" additional constraints, then be able to derive everything known about our universe - fields and symmetries etc - (& ideally predict something unknown) as resulting from some particular selection of those additional constraints.

This seems about as close as we could get to explaining our universe... Basically saying that god flipped a coin marked A and B, and it come down A so here we are. Maybe god kept on flipping sets of coins and created a whole bunch of other universes too, whose physics we could also derive.... and maybe one day visit and confirm.

Elegance. It's Occam's razor. If we can do with only one field, it's probably it.

It's inductive and abductive reasoning. The one field, and it has lot of mathematical characteristics which makes it unique on its own, and also it is the only one that has a chance to fit, is the e8 field popularized by Garrett Lisi.

If a universe were to be designed based using the e8 Lie algebra as an elemental field, it would look a lot like our universe.

Currently the standard model is a patchwork of field added as experiments for observing particles were possible to realize. The big picture's view is a unified theory which fits perfectly all existing data.

I'm not saying fewer fields, but perhaps a more fundamental substrate to reality than fields that fields emerge from. Maybe the N fields are just vibrational modes or attractor dynamics of something simpler.

It seems there has to be a reason WHY there are exactly N fields, and WHY they interact in the ways they do.

Edit: As I noted in another comment, the best explanation may come down to "there are only 100 viable types of universe, and ours is type 42". I'd be happy with that.

Where are you getting 37? The standard model has 17 fields.

If you pick and choose which properties to select as unique fields, maybe you can get the number 37, but at that point why not 118 fields?

I am not sure there’s any breakthrough here, but this article is about a different QM interpretation (as opposed to Copenhagen or Many Worlds). Interesting but seems irrelevant to the discussion here of particles and fields.

Yes, the field is the substrate.

"I insist upon the view that 'all is waves'."

    Letter to John Lighton Synge (9 November 1959), as quoted by Walter Moore in Schrödinger: Life and Thought (1989) ISBN 0521437679 

"All is a wave" is the unifying principle. I am no mathematician, but the math needs to start with that fundamental principle.

The very notion of calling it "qunatum" physics is probably wrong since quantum is "a discrete quantity of energy proportional in magnitude to the frequency of the radiation it represents."

And if everything is a wave there are no discrete quantities beyond our definition of what constitutes the end, or borders, of the wave.

Yes, very messy and ultimately unknowable.

First, just to clarify - there are different ways to count the quantum fields, just as there are different ways to count particles, as the article points out. You really need to specify the premises you're using to count them. But either 17 or 37 are natural counts. 17 is a somewhat simplified version, which ignores quark color charges and groups the W and Z bosons together.

Here's how the list of 37 typically breaks down:

18 quark fields: 6 flavors x 3 colors

3 charged leptons: electron, muon, tau

3 neutral leptons: neutrinos corresponding to the charged leptons

12 gauge bosons: 1 photon, 3 electroweak bosons (Z, W+, W-), 8 gluons

1 Higgs boson

(Note: this refers to fields as we observe them today, essentially counting what are known as Dirac fields. These are not the more fundamental fields that were present before the electromagnetic force separated from the weak nuclear force in the early universe, a process known as electroweak symmetry breaking. More on this below.)

In writing that list out, I realized that it skips one of the properties the article mentioned: chirality. If we take that into account, the number of charged lepton fields doubles to 6, and we have 40 fundamental quantum fields.

The reason that distinction is often ignored is that at everyday energies, the left- and right-handed components of particles are essentially blended together, so experiments don’t see them as separate particle types. Treating left- and right-handed chirality as a single field is a simplification of the underlying electroweak theory. Treating them as distinct particles, as the article does, is actually a bit dubious.

Re electroweak symmetry breaking, if we're really looking for "fundamental", then it makes sense to look at the fields before symmetry breaking. In a very real sense, these are more fundamental, because they give rise to the fields we observe.

But, that gets into fields that most non-physicists won't recognize, and that don't even have good names: the weak isospin gauge fields W^1_\mu,\; W^2_\mu,\; W^3_\mu,\; and the hypercharge field B_\mu.

In that scenario, there are 4 Higgs fields, which brings the total field count to 43. After symmetry breaking, those extra 3 Higgs fields became longitudinal polarization modes of the electroweak bosons, which are not counted as extra fields. The article mentions this, "the W+, W−, and Z bosons have a third, “longitudinal” polarization state as well," and adds them to its particle count.

We can relate this all back to the article as follows:

1. To count antiparticles, group the quarks and leptons into fermions - 18 + 3 + 3 = 24, and double that to count antiparticles, giving 48. Bosons are their own antiparticles, so their count doesn't change. The total particle count is now 48 fermions + 12 gauge bosons + 1 Higgs = 61.

2. For spin/polarization, double the number of fermions again to 96, double the number of gluons from to 16, multiply photons by 2, multiply the 3 electroweak bosons by 3 giving 9. This gives 96 fermions + 2 photons + 16 gluons + 9 electroweak bosons + 1 Higgs boson = 124 particles.

That 124 is 6 more than the 118 mentioned in the article, but again it depends on exactly what you're counting. Chirality in particular complicates things, because of the blending issue I mentioned earlier.