- #36
apeiron
Gold Member
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arivero said:
This wasn't quite what I meant. Again, what Marcus finds troubling and paradoxical (his comments on how what "exists" as 1D might percolate upwards to construct a higher-D effect) is a natural part of a systems approach to causality.
So I am not arguing that there is spin as the lowest, most fundamental, form of existence. Instead, that it represents the limit of a process of dimensional constraint.
When you have asked every other question about a location (removed all its degrees of freedom for spatial motion) you still do not yet know if it spins. At 0D, there is still that open question.
Now if we are asking that question from the perspective of a 3D world, then spin can have three orientations (or the answer could also be that there is no spin).
And then the gauge point, asking from a 3D realm is not enough to prevent higher dimensional varieties of spin. For all we know, the spin may be a rotation through 720 degrees, not 360 - the double cover of SO(3). If I understand gauge symmetry correctly (OK, long shot
) then you would have to be making measurements from the perspective of a higher dimensional realm to pin down all the potential facets of a spin.Yes, I am making spin sound literal - a rotation. But that is just because I do mean to remind that spin judgements do require a context, a realm from which measurements are being made, questions are being asked, as so constraints on localised freedoms are being imposed.
"Spin" itself could be considered as a raw or vague potential. So it is not a particular state of rotation but the general possibility of an irreducible local symmetry - which gains a definite character in a definite measuring context. So a standard gauge view as I understand it.
To answer your question on why SO(3)? A constraints based approach (as in condensed matter physics) says that as dimensionality cools, it becomes dimensionally reduced. So higher, more complex, spin can only be seen from a hotter perspective.
Early in the big bang, SO(3) would be a symmetry still found "everywhere". Now it is only expressed at certain "hot locations" - certain massive particles, certain energetic events.
If the universe did cool to a 1D dust, then even 3D polarised spin could not be observed. There would be no reference frame to ask the proper questions. How we would describe spin in such a reduced world is another question. It would not be an actual rotation clearly (how could that be defined?).
But as I said, my own view is that extended spatial degrees of freedom - the freedoms of linear motion, of positional uncertainty - cannot be reduced to less that three. Which is why we find ourselves in a 3D realm as the result of sliding all the way to the bottom of a process of dimensional reduction.
Now CDT and other attempts to marry GR to QFT do seem to give a picture of actual further dimensional reduction. It is as if they are finding a way to cool reality further. New constraints spontaneously appear.
But no! In fact, I am arguing, these models are reheating spacetime. They are selectively melting the background (the other other degrees of freedom that make up the other spatial directions are being melted and rendered vague) while preserving (keeping cool) other remaining degrees of freedom (the naked spatial action of a vector - and as Marcus was worrying about, the open question of what kind of spin might remain for a 1D vector no longer able to rotate in the framework of some crystalised set of dimensions, but instead "rotate" in some co-ordinateless version of space).
This is why I say the current dimensional reduction is smuggling in the Planck scale, rather than generating it as an output of the modelling. You get apparent further dimensional reduction because the Planck machinery melts your backdrop. And melting the backdrop makes if vague - returns it to a "higher" state of dimensional indeterminacy.
Perhaps someone will show me that I'm wrong in my view that dimensional reduction approaches achieve their results in this fashion. Marcus did not in the end contradict me the last time I argued the case.
I'm not saying models like CDT are bad or deceptive. But I do believe their intent is misguided.
The view I am arguing towards (supported by arguments I have only hinted at here - such as the lessons of network theory) is that 3+1D is the "coldest possible state of dimensionality" if reality arises as a condensation, a self-organising phase transition, from a potential infinity of degrees of freedom to a lowest entropy balance of degrees of freedom.
If this is correct, then it seems to me that collapsing GR to QFT is doomed to failure (so long as it is framed as the job of collapsing the state of things past 3+1D).
Fundamental theories are seeking a big reason why reality is bounded by limits (such as the Planck scale). And just here - taking a constraints-based approach to the self-organisation of dimensionality - is where we can already find some natural arguments as to why a dimensional reduction does not just go all the way and shrivel into a dust of nothingness.
Luckily for us, there was an irreducible limit on constraint. The 0D story of spin is just one aspect of it (and yes, the irreducibility of spin is dependent on the irreducibility of the other dimensions in which spin as a property is embedded).
So get down to 1D dust, and spin as we know it can't be found. But as a question to be asking, a way to be thinking, I believe it is subtle and profound.
Arivero, I've enjoyed very much your two papers on ancient greek metaphysics and you will know from Rhythmos, Diathige, Trope in particular how the question of irreducible properties is a very old and established one. Need we mention platonic solids?
So this is exactly that approach applied in a modern setting - where we now know about higher-D symmetries and gauge spin, where the question becomes what is irreducible about dimensionality, physical degrees of freedom, itself.