Physics Guy wrote: ↑Tue Apr 05, 2022 11:39 am
The structure of natural law as we have always known it so far has three tiers, sort of analogous to constitutional law, statute law, and precedent from court rulings, in human law.
At the bottom there is one fundamental equation, like F = ma (in its day) or the Schrödinger equation (which is far more general than the simple case of a single particle which is usually presented). This bottom-level equation is kind of like a grammatical rule, rather than a statement. F = ma, for instance, doesn't tell you anything at all until you fill in some kind of law for the force. The Schrödinger equation says little more than that probability will always total to one, until you specify exactly what the Hamiltonian operator is.
Then there are the laws that specify what things actually exist and what forces act among them. Currently we have the so-called Standard Model of particle physics, which states a specific (rather large and complicated) Hamiltonian operator for the universe, modulo lots of ways of re-writing it into equivalent forms. In particular the Standard Model Hamiltonian contains a couple of dozen quantum field operators, which create and destroy the elementary particles that we know. The Standard Model stipulates three fundamental forces and three different families of matter particles (counting the Higgs). It also specifies as natural constants the masses of the particles and how much they have of various kinds of charge. And then as an afterthought we have gravity.
Finally there are initial conditions, which as far as the theory is concerned could have been absolutely anything, and simply happen to have been whatever they were, that led to how things are now.
We've collected a lot of light emitted billions of years ago from stars billions of years away, and the sets of frequencies emitted by those ancient, distant stars look just like the patterns we see emitted and absorbed by hydrogen and helium and other elements in our labs here on Earth, except for the whole intricate pattern being uniformly shifted to lower frequency, because of Doppler shifts and the continuous expansion of space. This is a huge amount of data that really strongly indicates that the same laws we see in our labs also applied a long, long time ago in all those far, far distant galaxies. As far as the entire visible universe is concerned, the constitutional and statute laws seem to be fixed and universal, with differences between here and there, and now and then, determined entirely by initial conditions.
We know we can't see all of the universe, though. Most of it has expanded too far and too fast for light from it ever to reach us. So conceivably some of those basic laws can actually vary, presumably under some deeper set of meta-laws that we don't yet know, and we are simply in a big blob of space where one phase of laws apply, while other versions rule elsewhere, kind of how the oceans are full of water while the mountains are bare. Or conceivably there are many universes within some larger multiverse, and individual universes can have all different laws.
On the one hand we have no scrap of evidence, so far, for anything like that. And presumably if it were true that the laws we now know are only one of the many possibilities that apply in other places and times, there would still be some deeper set of laws that really were universal, that we just haven't found yet. Our basic guess, that is, is that the triple structure of natural law must always apply, though the dividing lines between the different levels might vary.
Maybe the Standard Model is just due to our local initial conditions. It contains a bunch of magic numbers, some of which are tantalisingly close to simple fractions (the fine structure constant is close to 1/137) while others are bizarrely tiny (all the elementary particle masses, in units of the Planck mass). It's kind of weird to think that God just picked all those weird numbers off the top of her head for no reason, but no theory we now have says anything at all about why any of those numbers should be anything in particular. (No theory that works, anyway. All the so-called Grand Unified Theories are attempts to put a backstory behind some of the magic numbers.) If the process of determining some of those numbers were pushed back into the initial conditions, instead of having to be part of the set-up of the laws themselves ... well, I guess we'd count that as explaining the magic numbers a little better, somehow, at least, even though they'd still ultimately be arbitrary. Sigh.
Or maybe some of what we now think are arbitrary initial conditions actually had to be that way because of some law we don't know. The boundaries between fundamental grammar, basic content, and initial conditions may well all shift up or down in the future, if we learn enough more.