This is related to this:
differentiation emerge from a state of uniformity — JuanZu
Reading your post again, it does sound like you are stressing that my view would be based on immanence rather than transcendence in terms of any "first cause" or first symmetry breaking. And that would be right.
And between Plato and Aristotle, this would be more Aristotle (although the Timaeus tantalises us with its notion of chora, or the "receptacle" that the forms need to become actualised in material being).
So in this thread, I have argued for the immanent and hylomorphic view of causality. The systems science view. And that is a metaphysics that has even come into vogue – because of gauge symmetry – in recent philosophy as Ontic Structural Realism. It has also come into vogue in fundamental physics as more and more is understood about the maths of topological order – and so how the gauge physics of quantum field theory can be properly generalised to cover, for instance, condensed matter and other emergent material phenomena.
Likewise, the idea of dimensionality as it might account for a hot Big Bang is leading to a dissipative structure approach – as first pushed in cosmology by David Layzer. So a thermodynamics, but one more appropriate to a cosmos as a self-organising structure of dissipation. One that gets beyond the roadblock of the Second Law and its world built on systems already gone to the equilibrium of a Heat Death. Again a tale of immanence where even "entropy" emerges or evolves in topological fashion.
So it is all about symmetry and symmetry-breaking. But then also about that as itself an evolving hierarchy of topological order.
Our current universe is in its very complex – and yet also very simple – state. This seems an odd thing to say, but that itself stresses we are dealing with a logic of dichotomies. Things start to happen when two complementary things are happening at once. This is the thought that breaks the logjam of metaphysics. And has done so ever since Anaximander figured out the logic of the Apeiron split by the dichotomising action of apokrisis.
Anyway, our current universe has achieved a state that is matter dominated – as the radiation background has already cooled itself to causal irrelevance. The CMB has been redshifted out of sight and may as well be a literal a-causal void of Newtonian fancy. And also, all the anti-matter that did exist has been almost completely annihilated – fizzled to join that CMB because of a charge-parity violation buried in the fine print of gauge symmetry and the Standard Model hierarchy of particles it produced.
So as I said, SU(3) exists but is balled up into protons and neutrons and doesn't organise the universe at any more general level than being the strong nuclear force making atomic-level matter possible. SU(2) hangs around as the weak force which allows Standard Model particles to rotate their way down its thermal ladder and become the final most massless versions of their type. Pretty much everything has degenerated to up and down quarks, electrons and neutrinos, by now.
And U(1) runs the show in conjunction with the gravitational degrees of freedom embodied in this simple collection of Dirac particles. Charge is permanently broken as protons and electrons can't be rotated into each other anymore. As quark matter and lepton matter, the temperature of the Universe is too cold and they are now locked into that final lowest level slot on the Standard Model's gauge structure.
So charge is permanently broken, but then also permanently in a dynamical state of dichotomised balance. Protons and electrons have to be arranged into neutralising atomic forms just to settle things down enough for matter to be locally electrostatically bound and globally gravitationally organised as the stars and galaxies of the great Cosmic Web of dynamically swirling mass.
It is dances within dances. Symmetries broken at one level that need to be healed to create the symmetry to be broken the next. The story of topological order. First the universe breaks everything down so that all that seems to be left in the void is a residual dust of positive protons and negative electrons. But then that broken charge must restore its lost symmetry however it can. Hence the emergence of what we actually call matter. Atoms of hydrogen, helium and lithium.
And then because these atoms have mass as well, you get the clumping of clouds that reheats this dusty matter to the point it catches fired and becomes a star. A fusion furnace that is self-organisd for longevity as it exists as a yo-yo balance of gravity and its heat. Its own weight collapses it, but its own heat expands it. And so it can hang in space, radiating into the void, neatly balanced at its critical point.
A lucky fact as fusion starts making heavier elements. And then the exhaustion of the fuel and final collapse of the star is an explosion that loads up every possible slot of the periodic table with all the atoms its symmetries represent. The symmetries determined now by electron shells or orbitals.
And so it goes on. Dichotomies all the way up and so all the way back down. Simplicity creating complexity. Symmetries get broken and create some new brand of complexity. That in itself is the cause for some new re-simplification which fixes what just got broken. In a world broken by U(1) charge, structure must arise that can neutralise that destabilising fact. Order must be restored. Protons and electrons must get bound into neutrons.
If no charge symmetry had been broken, then the Cosmos could have rested its self-organising immanence right there. The only matter to talk of would be dark matter – cold clouds of non-interacting particles just dancing the dance of a gravitating dust. And too cold to even make interesting emergent patterns doing that.
The Big Bang might be a fireball – for quantum uncertainty reasons, as Planck hot as it was Planck small – but most of that disorganised potential got spent quickly under the doubling~halving expansion and cooling of a Minkowski spacetime metric – the Poincare group organisation of Special Relativity.
So the spacetime container that emerges from relativistic symmetry was disposing of the heat as fast as it could run. And running at the speed of light – in being at first just a ball of radiation, a chaotic soup of relativistic excitations – that was so fast it would have gone to zero about now. Or as the CMB, it has now fallen to 2.7 degrees K, and will halve that temperature once again in another 14 billion years.
(Or in fact 10 billion years, as dark energy has shown up to hurry things along. A further topological complication to add to the long list of things that are immanently emergent due to symmetry breakings we still need to figure out.)
One final point to toss in – as I was trying to give a feeling for why gauge symmetry-breaking is the cause of the "complex simplicity" which is our current "atoms in a void" universe – is that it should be noted how the symmetries are (dichotomously) divided between the real number symmetries of relativity and the complex number symmetries of quantum theory.
The U in the SU(3)xSU(2)xU(1) formula means a unitary matrix. A matrix description in which rotation and translation can be entangled. Or indeed, re-entangled. The view of reality as it was before rotation and translation got broken and so what it looks like again when that symmetry is restored.
Likewise the key symmetry at the heart of relativity is the Lorentz group SO(3,1). An orthogonal matrix group – orthogonal meaning it is fully broken at a dimensional level and so described in disentangled real number values. No complex number mixing. Just the three orthogonal rotations of the 3D spin group SO(3). But with the addition of a time~energy conservation "direction" that is created by the speed of light as the universal limit on interactions with directions. This then makes it the 4D spacetime group of SO(3,1).
The Poincare group is then this 4D Lorentz group of relativistic "boosts" added to the standard 3+3D standard symmetries of 3D space to construct the 10D Poincare group – not literally ten dimensional, but that is how many degrees of freedom you have to package together in a self-constraining fashion where you have 6 Euclidean or flat space degrees of freedom (three translations/three rotations) being traded off against the contractions and dilations demanded to make the resulting metric properly Minkowski and speed of light restricted.
Phew. So gauge symmetry comes in forms that are real number to speak to the globally-broken symmetry of spacetime as the dimensional container. And then also that are the complex number or unitary gauge symmetries to describe what remains as the open freedoms to be expressed at every point of this spacetime container. Just by constraining the metric to a collection of points itself sets up an "inner space" of intrinsic quantum spin that has now been set free to to add its topological order to the whole mix. You get all the possible kinds of local excitations or particles that become possible under the hierarchy of SU(3)xSU(2)xU(1).
At least once inflation is over and has dumped a load of reheated vector particles into the vacuum. Which also must have the different thing of a scalar Higgs field – although that has to be SU(2) to later mix quantumly with the electroweak force and thus break it to become the weak force plus electromagnetism.
Then dark matter could be anything. Black holes, a condensed matter effect that results in "2D" anyon particles, all sorts of exotic stuff – which would somehow have to also be explained in Platonic structural terms. There are always more symmetry groups to be pulled out of the maths bag.
And dark energy! If it exists as some kind of quantum uncertainty effect within dimensionality itself and isn't just an optical effect of viewing the universe from some locally underdense "gravitational well".
But immanence rules. And it rules as possibility can't help but stumble its way into orderly patterns. And it doesn't do this just once. Order always creates its own new possibilities which then have to stumble into new patterns.
Symmetry thinking is then just the way to discover this kind of immanent pattern making. The invariant structures that can't help but emerge when everything is trying to happen all together and all at once.
Shake up possibility and it settles down into whatever conformity that is its stable equilibrium state. A state where differences can no longer make a difference as the same old pattern just keeps re-emerging. The pattern that was immanent and then emerged dynamically to become something that looked permanent and even fore-destined.
But every such pattern then becomes its own state of free possibility. A higher level symmetry to be broken at a higher level – shaken and shaken until it to settles into its own dynamical balance.
A Cosmos is more complex from the start as it has to be symmetry-breaking in two complementary directions at once. It is itself already a symmetry-breaking in progress. A Big Bang that is a mix of its relativistic metric doing the expanding and a hot quantum content doing the other thing of a cooling. A plasma fireball that is turning itself from a radiation soup into a matter dust via a series of topological phase transitions as the container expands and the contents spread out and dilute.
So good job we have both the real number matrices and the complex number matrices to keep track of both sides of this symmetry equation. Poincare invariance married to gauge invariance by little particle creating tricks such as that SU(2) is the double cover of SO(3). A Minkowski metric point can harbour the further inner complexity of a half-spin fermion that has to rotate 720 degrees to look like a 360 degree revolution. The mirror reflection trick that allows fermions to come as the creation~annihilation pairs of matter and antimatter.
The symmetry that gets broken to arrive at a world made of just matter and a void of long-spent radiation. The relic antimatter gone to join all dark matter and other stuff like neutrinos that has become causally irrelevant in this ruthless game of cosmic Darwinism. Or self-organising immanence.
And so it goes on. And on. Symmetry-breaking out to the furthest horizon.
:wink: