Unlike in wave mechanics, chaos is possible in quantum TGD
Sabine Hossenfelder has an interesting Youtube video about chaos titled “Scientists Uncover Hidden Pattern in Quantum Chaos” (see this).
Standard Quantum Mechanics cannot describe chaos. TGD view allows its description. In the geometric degrees of freedom, quantums states correspond to quantum superpositions of space-time surfaces in H=M4×CP2 satisfying holography which makes it possible to avoid path integral spoiled by horrible divergences. Holography= holomorphy principle allows to construct space-time surfaces as roots of a pair (f1,f2) of analytic functions of 3 complex coordinates and one hypercomplex coordinate. These surfaces are minimal surfaces and satisfy field equations for any general coordinate invariant action constructible in terms of induced gauge fields and metric.
The iterations of (f1,f2)–> (g1(f1,f2),g2(f1,f2)) give rise to transition to chaos in 2 complex-D sense and as a special case one obtains analogs of Julia and Mandelbrot fractals when assumes that only g1 differs from identity. Hence chaos emerges because point-like particles are replaced with 3-surfaces in turn replaced by space-time surfaces obeying holography=holomorphy principle.
See for instance the articles About some number theoretical aspects of TGD and About Langlands correspondence in the TGD framework .
Source: https://matpitka.blogspot.com/2024/12/unlike-in-wave-mechanics-chaos-is.html
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