LHC and fictions

[Ignacio Añón]

M. Dowd wrote:

"The issue of mathematical formalizabiliy arises well before
electroweak theory.  A useful discussion of one example can be found
at https://physics.stackexchange.com/questions/314061/on-the-state-of-quantum-electrodynamics

In general, the relationship of mathematical formalizability to
fictionalism is of interest.  Mathematicians feel gratified by
successful formalization, whether or not it makes the theory "less
fictional" in any sense."

As you say, issues of formlizability arise quite early, at the most
primitive level. But they are determined, hierarchically, by a
preeminent framework, which is still faintly understood(M-theory or
QCD). Historically, the Lagrangian simplification of the Newtonian
model, allowed the Hamilton, Faraday, and maxwell, simplification,
without which, special relativity, general relativity, and the
copenhagen model, are hardly imaginable, This is said to underline,
that attempting to tackle the primitive issues, might block the
possible next synthesis, already latent in Supersymmetry, M-theory and
QCD. Primitive first principles must be guided by sophisticated ideas,
otherwise a regression, instead of a simplification, is possible...

Originally, even Newtonian gravity, was criticized by Leibniz and
Huygens, as an obscurantist fiction. You also make the correct point,
that rigorous mathematical models for physics, can be held independent
of their fictitious character, although some link between mathematical
rigour, and physical reality, might exist, despite our being, as of
2021, unable to understand what it is. A formal mathematical model,
where the parity of subatomic particles is conserved, can easily be
built, and yet we know by experiment, that it is not...

The third question in the Stack exchange post is quite interesting:
mathematically, you can actually simplify and reduce any quantum
electro dynamical, or even any string theory framework, into a lattice
computation. But if you want to understand its structure, and isolate
its topological invariant elements, you need to add a color variable,
and you also need to be careful, when reducing the invariant
structure, to its Lie group. The continuous symmetry of the invariant
structure, has a dimensionless fourier layer, linking the Lattice
space, to its differential hamiltonian. This is very important at high
energies, and is the only framework that allows you to count the "flux
vacua", occurring in any global physical theory aiming to include all
the forces...




El mar, 30 mar 2021 a las 22:43, <martdowd at aol.com> escribió:
>
> Ignacio Anon wrote:
>
>
> If the LHC(large hadron collider) ends up confirming that the Higgs boson, has such a low mass, because some aspect of the field structure surrounding it, can be described by a lagrangian, this might give us some sense about how "fictional", certain formulations are in quantum field theory.
>
> The issue of mathematical formalizabiliy arises well before electroweak theory.  A useful discussion of one example can be found at https://physics.stackexchange.com/questions/314061/on-the-state-of-quantum-electrodynamics
>
> In general, the relationship of mathematical formalizability to fictionalism is of interest.  Mathematicians feel gratified by successful formalization, whether or not it makes the theory "less fictional" in any sense.
>
> Martin Dowd
>
>
> -----Original Message-----
> From: Ignacio Añón <ianon at latahona.com.uy>
> To: Foundations of Mathematics <fom at cs.nyu.edu>
> Sent: Mon, Mar 29, 2021 3:29 pm
> Subject: LHC and fictions
>
> Vaughan Pratt <pratt at cs.stanford.edu>:
>
> While I'm sympathetic to the point of view of mathematical fictionalism, I'd be interested in hearing from any FOM participants about physics fictionalism.
>
> Whereas Bohmian mechanics maintains that particles such as electrons move continuously, the Copenhagen Interpretation maintains that electrons in orbitals only exist as distributions and not as actual continuously moving particles.
>
> These being contradictory points of view, must we infer that at least one of them is fictional?
>
> Vaughan Pratt
>
>
> If the LHC(large hadron collider) ends up confirming that the Higgs boson, has such a low mass, because some aspect of the field structure surrounding it, can be described by a lagrangian, this might give us some sense about how "fictional", certain formulations are in quantum field theory.
>
> We already know, that either Quantum chromodynamics(QCD), as formulated in the Bardeem style interpretation("technicolor"), or M-theory, will be shown to be correct. This will give us some way of grasping how "fictional", certain ideas are in physics...
>
> It looks like the invariant topology engulfing the elements of QCD, will be shown to be less fictional than M-theory, and include within their invariant spaces, certain string membranes, whose subtle logic is governed by the asymptotically free and complex, lagrangian dynamics of the QCD, generated, as a puppet by a puppetier, by an invariant topological structure, within which QCD and M-theory are just layers.
>
> Forming the topology, locking the invariant subtleties of its structure, precision electroweak measurments have shown an asymptotically free logic, which is enriching the invariance of the topology: almost nothing is understood today of it, and the formalism to tackle it, is not yet there, although the physical ideas are all in the air.
>
> The fascinating thing, is that this asymptotically free logic, seems to be less fictional, than any topological, geometric, Langlands style theory: this will revolutionize math and FOM, since they will be shown to be a tiny fraction of a larger field, fusing our notion of number, space, and physics, into a subtler, non-asymptotic, logic...
>
>
>