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*This thread is a direct shoot-off of this post from the thread Atiyah's arithmetic physics.*

Manasson V. 2008, Are Particles Self-Organized Systems?

Abstract said:Elementary particles possess quantized values of charge and internal angular momentum or spin. These characteristics do not change when the particles interact with other particles or fields as long as they preserve their entities. Quantum theory does not explain this quantization. It is introduced into the theory a priori. An interacting particle is an open system and thus does not obey conservation laws. However, an open system may create dynamically stable states with unchanged dynamical variables via self-organization. In self-organized systems stability is achieved through the interplay of nonlinearity and dissipation. Can self-organization be responsible for particle formation? In this paper we develop and analyze a particle model based on qualitative dynamics and the Feigenbaum universality. This model demonstrates that elementary particles can be described as self-organized dynamical systems belonging to a wide class of systems characterized by a hierarchy of period-doubling bifurcations. This semi-qualitative heuristic model gives possible explanations for charge and action quantization, and the origination and interrelation between the strong, weak, and electromagnetic forces, as well as SU(2) symmetry. It also provides a basis for particle taxonomy endorsed by the Standard Model. The key result is the discovery that the Planck constant is intimately related to elementary charge.

The author convincingly demonstrates that practically everything known about particle physics, including the SM itself, can be derived from first principles by treating the electron as an evolved self-organized open system in the context of dissipative nonlinear systems. Moreover, the dissipative structure gives rise to discontinuities within the equations and so unintentionally also gives an actual prediction/explanation of state vector reduction, i.e. it offers an actual resolution of the measurement problem of QT.

However, this paper goes much further: quantization itself, which is usually assumed a priori as fundamental, is here on page 6 shown to originate naturally as a dissipative phenomenon emerging from the underlying nonlinear dynamics of the system being near stable superattractors, i.e. the origin of quantization is a limiting case of interplay between nonlinearity and dissipation.

Furthermore, using standard tools from nonlinear dynamics and chaos theory, in particular period doubling bifurcations and the Feigenbaum constant ##\delta##, the author then goes on to derive:

- the origin of spin half and other SU(2) symmetries

- the origin of the quantization of action and charge

- the coupling constants for strong, weak and EM interactions

- the number and types of fields

- a explanation of the fine structure constant ##\alpha##:

$$ \alpha = (2\pi\delta^2) \cong \frac {1} {137}$$

- a relationship between ##\hbar## and ##e##:$$ \hbar = \frac {\delta^2 e^2} {2} \sqrt {\frac {\mu_0} {\epsilon_0}}$$

In particular the above equation suggests a great irony about the supposed fundamentality of quantum theory itself; as the author puts it himself:

Suffice to say, this paper is a must-read. Many thanks to @mitchell porter for linking it and to Sir Michael Atiyah for reigniting the entire discussion in the first place.page 10 said:Ironically, the two most fundamentalquantum constants, ##\hbar## and ##e##, are linked through the Feigenbaum ##\delta##, a constant that belongs to the physics of deterministic chaos and is thus exclusivelynon-quantum.

Our results are assonant with ’t Hooft’s proposal that the theory underlying quantum mechanics may be dissipative [15]. They also suggest that quantum theory, albeit being both powerful and beautiful, may be just a quasi-linear approximation to a deeper theory describing the non-linear world of elementary particles. As one of the founders of quantum theory, Werner Heisenberg once stated, “. . . it may be that. . . the actual treatment of nonlinear equations can be replaced by the study of infinite processes concerning systems of linear differential equations with an arbitrary number of variables, and the solution of the nonlinear equation can be obtained by a limiting process from the solutions of linear equations. This situation resembles the other one. . . where by an infinite process one can approach the nonlinear three-body problem in classical mechanics from the linear three-body problem of quantum mechanics.”[11]