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Paper CCI: The Quantum Wave Function as a Brane Displacement Field: Deriving the Schrödinger Equation Without Quantization Postulates embedded in a five-dimensional anti-de Sitter space, the quantum wave function arises as the brane

Bharathi Jagadeesan

Published May 19, 2026• 0 citations
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Abstract

Part of the One-Octonion Brane-Bulk Framework paper series. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.
DOI
10.5281/zenodo.20300348

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J. W. G. Wignall

The one-particle Schrödinger and Dirac equations are derived, without making any quantization hypothesis, from the postulate that an elementary particle is a physical wave packet of dynamically varying form and size, rather than a pointlike object located somewhere within the support of a wavefunction that serves only as a mathematical probability amplitude. An isolated multiparticle system can, similarly, be described in principle as a set of interacting wave packets governed by coupled one-particle equations, a picture from which, in the nonrelativistic limit, the multiparticle Schrödinger equation can be obtained as a sufficiency condition for the system to have a conserved total energy equal to a particular value E .

Journal of Physics A Mathematical and General•May 25, 2005•1 citation
A series of successive quantizations is considered, starting with the quantization of a non-relativistic or relativistic point particle: (1) quantization of a particle’s position, (2) quantization of wave function, (3) quantization of wave functional. The latter step implies that the wave packet profiles forming the states of quantum field theory are themselves quantized, which gives new physical states that are configurations of configurations. In the procedure of quantization, instead of the Schrödinger first-order equation in time derivative for complex wave function (or functional), the equivalent second-order equation for its real part was used. In such a way, at each level of quantization, the equation a quantum state satisfies is just like that of a harmonic oscillator, and wave function(al) is composed in terms of the pair of its canonically conjugated variables.
We present a structural framework in which quantum mechanics emerges from the B7/B13 wave duality on a discrete cubic lattice with step l_P. Main findings: (A) The complex wave function arises from two real bases: Psi = psi_B7 + i·psi_B13, where B7 is the closed wave (0-form) and B13 is the flowing wave (1-form). The complex nature of the wave function is not postulated — it is derived from octahedral geometry. (B) Mass is the average energy of B7/B13 sites: m = N_p(n)^2 [1 - eta/(7C)] × m_pi/4, where N_p(n) = 3(16 + n·2^{n-1}), eta is the B7/B13 equilibrium parameter, and C = 35.325 is the cyclic constant. (C) The potential consists of two sources: V(x) = V_source(x) + V_background(x), where V_source is the Coulomb/gravity potential and V_background comes from rho_V modulation. (D) Multi-particle formalism follows from B7/B13: bosons are B7⊗B7 + B13⊗B13 (symmetric), fermions are B7⊗B13 - B13⊗B7 (antisymmetric), and the Pauli principle follows from Psi_A(1,1) = 0. (E) Decoherence is the loss of B7/B13 phase coherence; measurement is the B13 → B7 transition; the Born rule follows from decoherence. All five quantum mechanical postulates (complex wave function, Schrödinger equation, Born rule, measurement collapse, Pauli principle) become derivations from a single geometric structure. The document is not a proven theory. It is an invitation to further research within any theoretical framework capable of pursuing these directions. We present what we have found, mark what is proven versus hypothesized, and identify concrete predictions: decoherence time ~10^{-17} s for molecules, rho_V effects on atomic spectra in galactic centers, and quantum Zeno effect dependence on eta_eq. Notes:This document is part of the Matrix Theory (MT) series. It presents the complete derivation of quantum mechanics from B7/B13 wave duality, covering five steps: (1) B7/B13 wave duality, (2) mass from B7/B13, (3) potential from rho_V modulation, (4) multi-particle formalism, (5) decoherence model. It should be read alongside the B7/B13 Wave Duality paper (DOI: 10.5281/zenodo.23111157), which establishes the common core. Working protocol documents (MT_ANNIHILATION v3.6, MT_ROADMAP v3.0, MT_ID_GRADIENT v3.0) are available as supplementary materials. Contributors:Olbiks, Algis — Conceptualization, Methodology, Validation, Writing - original draftDeepSeek (AI) — Formal analysis, Investigation, Writing - review & editing
Moon, Schindler et al. (Nat. Phys. 21, 1813-1819, 2025) demonstrate a time rondeau crystal in 13C nuclear spins: long-range stroboscopic DTC order coexisting with short-range micromotion disorder. We identify this as the mesoscopic realisation of brane-bulk transit disorder. The transit-to-period ratio t/tau_pi = 4.685 (PDG) is irrational, involving sqrt(3). f_bulk = 3.691% is transcendental. The n-RMD multipole spectrum maps to G2 permutohedron eigenvalues. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.
The one-particle Schrödinger and Dirac equations are derived, without making any quantization hypothesis, from the postulate that an elementary particle is a physical wave packet of dynamically varying form and size, rather than a pointlike object located somewhere within the support of a wavefunction that serves only as a mathematical probability amplitude. An isolated multiparticle system can, similarly, be described in principle as a set of interacting wave packets governed by coupled one-particle equations, a picture from which, in the nonrelativistic limit, the multiparticle Schrödinger equation can be obtained as a sufficiency condition for the system to have a conserved total energy equal to a particular value E .