Authors: Stephane H Maes
The principle of least action applies to many domains of Physics. Yet its justifications and derivations usually come from archaic classical principles like the Fermat or Maupertuis principles, or mathematical analytical frameworks used for classical mechanics. As is well known, it is widely applicable to other domains, without necessarily a clear justification for it. In addition, the Feynman Path Integral formulation of Quantum Mechanics gave it a second life. However, the conventional logic to reach these conclusions is at time circular, and the principle is applied without proof that it is applicable: it just works and everybody does it. It is this applicability that led us in the past to treat the Action path integral as God’s equation.The paper justifies the principle of least action and Feynman’s path integrals through different physical reasoning, and on that basis we confirm its validity in most situations, even if Hamiltonians or Lagrangians may be shaky to define, or the system may be dissipative. We also explain when, and why, sometimes, it may not conventionally apply. The derivation uncovers different links between Entropy and Action, which also opens a different way to look at the origin of the probability distribution of even just a single lone particle; especially when complemented with the W-type multi-fold hypothesis, and makes some considerations on Feynman diagrams, instantons, renormalons and resurgence. Also discontinuities in the paths of the path integrals imply that spacetime is discrete, and non-commutative, and supersymmetry in flat spacetime is unphysical. Surfaceology, as optimized computation of the Feynman diagram is shown to trivially predict that all gauge theories double copy dual to gravity share the same forbidden scatterings. We show how the results of the multi-fold theory, in particular the multi-fold space time matter induction and scattering, built explicitly on the path integral formalism, its underlying principles, and the principle of least action, allows recovering almost everything in Today’s physics. It leaves out essentially only some of the coupling constants and mixing angles/parameters. This goes a long way towards the ambition of a Theory Of Everything (TOE). Our justification of the principle of least action, and path integrals, and the multi-fold theory encounters relationships between Entropy and Action. We review these encounters, including that entanglement might be irreversible. Also, from our approach, we obtain a formulation of the evolution of entropy, including for irreversible systems, which matches Onsager and Prigogine’s famous models and principles.
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