A transformational approach to collective behavior
This talk presents a revolutionary approach to the characterization, forecast, and control of collective systems. Collective systems are an ensemble of conservatively interacting entities. The evolution of the entities are determined by symmetries of the entities. Collective systems take many different forms. An elementary field is a collective of elementary particles, a plasma is a collective of charged particles, a fluid is a collective of molecules, and a cosmos is a collective of celestial bodies. The new theory builds on the canonical transformation approach to dynamics. This approach recognizes that the symmetry leads to the conservation of a real function, H(p,q), that is the infinitesimal generator of a Lie group. The finite generator of the canonical transformation, S(P;q), is derived from the infinitesimal generator, by the solution of the Hamilton-Jacobi equation. This generating function is also known as the action, the entropy, and the logarithmic likelihood. The new theory generalizes this generating function, S(P,q), to the generating functional of the collective, S(p)[f(x)], where f(x) is the collective field. We call it the Heisenberg Scattering Transformation (HST, because of Heisenberg's invention of the S-matrix), which is the Wigner-Weyl Transformation of the collective field to the individual entity. Practically, this is a localized Fourier Transformation, whose principal components give the singularity spectrums, that is the solution to the Renormalization Group Equations or how the field changes (that is, is correlated) as function of scale and position. This characterization of the topology, allows for the forecast and control (that is, optimization and ponderomotive stabilization) of the collective system. Limitations on the measurement of the system (that is the Born Rule and the Heisenberg Uncertainty Principle) lead to quantization of the stochastic probabilities of the collective field. How different collective systems couple together to form system-of-systems is formalized. This new theory unifies the four elementary fields (strong, weak, EM, and gravity), and constructs a mathematically logical process of renormalization with a physical interpretation.
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For a transcript and slides, many active hyperlinks:
https://doi.org/10.13140/RG.2.2.10730...
Academic paper with the content of this talk:
https://arxiv.org/abs/2410.08558
Academic paper for a general audience discussing the meta-physical philosophy of this theory:
https://arxiv.org/abs/2401.04846