[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.