[HarHarVeryFunny]

But of course one can then question why are there exactly N different types of fields, with their specific types of interaction (at least in our universe)? Why should we suppose that this is the most fundamental description of reality, rather than being emergent from something else?

[frutiger]

> But of course one can then question why are there exactly N different types of fields, with their specific types of interaction (at least in our universe)?

Even that has a (still unsatisfactory) answer.

Poincaré symmetry imposes constraints on the kinds of fields we can have. Gauge symmetry shows us how they may couple.

There are still some arbitrary selections of the possible permutations that nature has “picked”.

[HarHarVeryFunny]

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.

[behringer]

You might not want to visit because it's probable you would explode or have some other horrific death due to incompatibility between your fields and theirs.

[skirmish]

See "Schild's Ladder" by Greg Egan: a science experiment creates a bubble of new physics expanding at 0.5 c, and humanity is forced to flee the expansion while some stay right next to the expanding boundary to investigate the inside.

[HarHarVeryFunny]

Yes, probably would not turn out well. Will put it on my bucket list next to "visit black hole event horizon".

[jerf]

I completely agree that's a reasonable question.

I'd also observe that between dark matter and dark energy, there's good reason to believe that we may not have a full accounting of all fields.

I am just observing that if you have a non-scientist asking the question "how many fundamental particles are there", with the expectation that "995.5" is not really the right answer, "the number of fields" is a reasonable response that probably gets closer to what they are looking for. Even if someday someone does get them to all be some manifestations of a single field it would arguably still be the case that people are more interested in the answer of the current number of fields then being told "1", because "1" is in many ways not a helpful answer to "how many types of things are there". Even if there is a profound sense in which it was true, there would still be a profound sense in which it was false, too.

[tsimionescu]

Well, why would there be fewer than N? There is no general principle that we can impose on the world, it just is, we can only discover what the laws and components of the world are (hopefully). I'm not claiming it's impossible for there to be fewer fields than we think right now. But there is no reason to believe there should be.

[GistNoesis]

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.

[tsimionescu]

Occam's razor has nothing to do with this, it only applies once you have multiple competing theories - you can't use Occam's razor to decide that a theory "should" exist.

Currently, we don't have any theory that works that's any simpler than the SM. So that's the theory that Occam's razor currently tells us must be true, as it's the simplest alternative that actually works.

[HarHarVeryFunny]

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.

[tsimionescu]

I think it's very obvious no such answer is even possible in principle. Mathematics has no limits, you can describe anything you like by picking some axioms. Do you want to make sense of the expression 1+1=3? I can find axioms in which this is true.

So, there is no way to start from mathematics and find something that must exist in some way, such as "there can only be 100 types of universe". Any such discovery is contingent upon some arbitrary choice of axioms. You can choose axioms that appeal to some ultimately esthetic sense of elegance or simplicity, and that can explain our universe more or less uniquely, but this doesn't mean that they are right to any extent more than the SM is.

[antonvs]

We can certainly imagine part of what the GP comment described being true: "a more fundamental substrate to reality than fields that fields emerge from." In fact, many physicists assume that's the case with the Standard Model - that e.g. the similarities between generations of quantum particle are explained by some deeper and (hopefully) simpler construct.

Similarly, "Maybe the N fields are just vibrational modes or attractor dynamics of something simpler" could also be true - Calibi-Yau manifolds in string theory are essentially one such attempt to unify the similar and repetitive aspects of QFT that currently have no theoretically-justified connection in the theory.

Sure, at some level you presumably hit a wall - e.g. "why are there Calabi Yau manifolds?" But I don't think that's what the GP was referring to.

> Any such discovery is contingent upon some arbitrary choice of axioms.

This is true, but we see some wonderful examples of this in the real universe, producing laws that must be true in all universes that satisfy the axioms (assuming we believe that mathematical proofs aren't somehow tied to our universe.)

For example, Noether's theorem tells us mathematically when and why conservation laws, like conservation of energy and momentum, exist (i.e., for any continuous symmetry of the action of a physical system with conservative forces.)

Similarly, the inverse square law applies to anything that propagates, with no losses, outwards from a point in all directions in locally flat three-dimensional space. Again, we expect this to be true in any universe with these properties.

There are quite a number of other examples of this.

[api]

To me it looks like the periodic table. There's an underlying set of levers in terms of quantum characteristics of fields, but not all settings of these levers are stable. This is just like how only atoms with certain combos of protons and neutrons and electrons are neutral and stable.

If you look at histogram plots of protons, neutrons, and stability, it's not a perfectly idealized form. It's a rocky plot. This emerges from the quantized nature of reality.

So a periodic table of particles (fields) that looks kind of weird and ad-hoc to us is the expected result.

What we don't yet fully understand is really two things as far as I know. First, we know less about why these particular values are special. For the periodic table we actually understand this pretty well. Second, we do not know if there are other islands of stability or particles-fields we cannot see (e.g. WIMPS). For the periodic table we are pretty sure there are no large islands of stability at higher weights. Not 100% sure, but if they do exist there's probably only a few exotic mega-atoms that could be stable, not many.