Thursday, May 18, 2023

Maximally symmetric Universe, self-organized quantum criticality, and symmetry between order and disorder

This post was inspired by the Big Think article "A surprise new “theory of everything” involves the symmetry between order and disorder" (see this). The article relates to the book "The language of symmetry" edited by Rattigan, Noble and Hatta, which can be found at Amazon. Two ideas considered in the article, maximal symmetries and self-organized criticality, define two key principles of TGD. Also the third, rather paradoxical idea that symmetry breaking leads to a generation of symmetry, has a precise meaning in the TGD Universe. Consider first the maximization of symmetries as a fundamental principle.
  1. In the TGD framework, the fundamental principle determining physics as geometry is that the infinite-dimensional geometry of the "world of classical worlds" (WCW) exists mathematically. Physics is unique because of its mathematical existence and has maximal symmetries. Freed demonstrated that for the loop spaces this geometry is unique and indeed has an infinite-D group of isometries (Kac-Moody symmetries).
  2. 4-D general coordinate invariance is essential in TGD and implies holography in reducing to a generalization of 2-D holomorphy to 4-D case, which in turn corresponds to 4-D quantum criticality.
    1. The first guess would be that WCW consists of 3-D surfaces in M4×CP2: M4×CP2 is indeed unique by several mathematical arguments and also by standard model symmetries. 3-surface generalizes the notion of a point-like particle.
    2. 4-D general coordinate invariance requires that a given 3-surface corresponds to a nearly unique 4-surface in M4×CP2. This means holography, or equivalently, Bohr orbitology. WCW also has interpretation as a space of 4-D analogs of Bohr orbits. Quantum TGD becomes the analogue of wave mechanics in WCW.

      Note that in atomic physics this would mean the replacement of electrons configuration space E3 with the space of its Bohr orbits: this would be fiber space over E3 with fiber at given point consisting of Bohr orbits through it.

Consider next self-organized criticality as a basic principle. In TGD quantum criticality is behind the analogous principle.
  1. For 2-D systems conformal invariance implying holomorphy of string orbits extends to 4-D analog of holomorphy, which realizes quantum criticality in 4-D case. Holomorphy implies holography! Field equations reduce to a purely algebraic form, having no dependence on the coupling parameters of the action as long as it is general coordinate invariant and constructible using the induced geometry.
  2. This happens outside 3-D and lower-D singularities. Space-time surface is a minimal surface, analog of a soap film spanned by frames. Minimal surface property is analog of massless field equations at field level and analog of massless geodesic property at particle level. The classical and quantum dynamics distinguishes between different actions only at the frames, which can depend on action.
To understand the self-organized quantum criticality, quantum TGD is required.
  1. In Quantum TGD, wave functions of the ordinary wave mechanics are replaced with analogs of wave functions in WCW (WCW spinor fields as many-fermion states as WCW spinors) consisting of analogs of Bohr orbits. This forces a new ontology: I call it zero energy ontology (ZEO) forcing a new view of quantum measurement.
  2. In state function reduction (SFR) this kind of superposition inside quantization volume (causal diamond (CD) is replaced with a new one, and also the size and other parameters characterizing the CD can change. The standard paradox of quantum measurement theory disappears.
  3. There are two kinds of SFRs.
    1. In small SFRs (SSFRs), the boundary of CD is stationary and states at it are not affected but the active boundary is shifted and CD tends to increase. The sequences of SSFRs correspond to Zeno effect, having no effect in standard QM, and give rise to a conscious entity, self for which subjective time as sequence of SSFRs correlates with the increase of the distance between tips of CD.
    2. In big SFRs (BSFRs), the arrow of time changes so that the active boundary of the CD becomes passive and vice versa. BSFRS correspond to ordinary SFRs. BSFR means "death" of self and reincarnation with an opposite arrow of time. Even small perturbations can induce BSFR by affecting the set of the observables measured in SSFR: if the new set does not commute with those defining the passive states, BSFR unavoidably occurs.
    3. BSFRs give rise to self-organized quantum criticality. Self lives at criticality against death! As a consequence, the flow of consciousness of self has gaps with a distribution of gap durations. This is known for human consciousness.
  4. Paradoxically, this continual short term dying in BSFRs makes it possible for the system able to survive and correct behaviors. Self can also learn of avoidable behaviors by trial and error. Self can learn moral and ethical rules: do not do anything destroying quantum coherence! Perhaps most of the learning is by this method. Homeostasis is a basic implication. The system is at quantum criticality at the top of a hill and unstable. When it starts to fall down, it makes BSFR in some scale and changes the arrow of time and returns back near criticality. Self-organization, say spontaneous generation of molecules from their building bricks, can be understood as a time reversed dissipation.
The third topic discussed relates to the paradoxical creation of symmetries by symmetry breaking. The emerging vision indeed is that symmetry breaking paradoxically leads to the emergence of a deeper symmetry. This is what the TGD view of the realization of the isometries of WCW as symmetries of the physical system indeed predicts.
  1. The half Virasoro algebra V with non-negative conformal weights serves as a simplified example. V contains an infinite set of sub-algebras Vk for which conformal weights are divisible by integer k=1,2,,... One also obtains inclusion hierarchies ⊂ Vk(n) ⊂ Vk(n+1) ⊂ .. such that k(n) divides k(n+1), whose generalizations are very relevant to quantum TGD.
  2. The ordinary realization of conformal symmetries is as a gauge symmetry for which the generators Ln, n> 0, annihilate the physical states. One can however generalize this and only assume that Vk and [Vk,V] annihilate the physical states. In this case, the generators Ln , n<k do not annihilate the states and act as genuine symmetries. Gauge symmetries are broken but have transformed to genuine physical symmetries! This removes the paradox from the idea of emergence of symmetries by symmetry breaking!
These kinds of mathematical structures is the cornerstone of quantum TGD. Virasoro algebra is replaced with the isometry algebra of WCW and associated algebra but completely analogous conditions hold true. This mechanism would not hold true for the isometry algebra of WCW only.

See for instance the article TGD view of Michael Levin's work .

For a summary of earlier postings see Latest progress in TGD.

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