A Branching structure of Decoherent Quantum histories

J. Weyers

Philipp Strasberg, Joseph Schindler

Within the many worlds interpretation (MWI) it is believed that, as time passes on, the linearity of the Schrödinger equation together with decoherence generate an exponentially growing tree of branches where "everything happens", provided the branches are defined for a decohering basis. By studying an example, using exact numerical diagonalization of the Schrödinger equation to compute the decoherent histories functional, we find that this picture needs revision. Our example shows decoherence for histories defined at a few times, but a significant fraction (often the vast majority) of branches shows strong interference effects for histories of many times. In a sense made precise below, the histories independently sample an equilibrated quantum process, and, remarkably, we find that only histories that sample frequencies in accordance with Born's rule remain decoherent. Our results suggest that there is more structure in the many worlds tree than previously anticipated, influencing arguments of both proponents and opponents of the MWI.

Jeffrey Satinover

Everettian branch multiplicity is often discussed as though it were a count of wavefunction terms or decoherent alternatives. This paper argues that the relevant object is an algebra-relative packing number on physically admissible history classes. Candidate histories, already assumed to belong to a decoherent or approximately decoherent family, are first quotiented by exact physical symmetries and then compared only through distinctions visible in a specified operator system of admissible effects. The resulting effective branch packing number \( N_{\mathrm{eff}}(t;{\mathcal A},\varepsilon) \) is the maximal number of mutually \( \varepsilon \)-distinguishable symmetry classes of histories relative to \( \mathcal A \). The paper proves a sequence of structural results: an orbit-packing reduction theorem; monotonicity under refinement of the admissible operator system; metric packing bounds; polynomial and, under the natural affine-rank condition, sharp asymptotic record-compression theorems for collective linear records of identical bosonic qudits; contraction of channel distinguishability under recovery; and a logical cluster theorem for recovered channels. In particular, \( r_0 \) independent collective record directions give \( \Theta(N^{r_0}) \) record growth rather than the labeled \( d^N \) growth; and separated clusters of recovered logical channels, rather than microscopic histories, determine logical branch multiplicity. Applications include the three-qubit bit-flip code, bosonic qudit occupation sectors, and a formal orbit-record model for dipositronium annihilation histories. The framework relates decoherent histories, Quantum Darwinism, exchange symmetry, and quantum error correction without asserting literal merger of globally orthogonal branches.

J. J. Halliwell

Mohammad Radfar

This working paper introduces the Fractal Decision-Branching Framework (FDBF), a conceptual framework for representing human decision histories as branching structures and for examining possible structural correspondences between decision-tree geometry, fractal or scale-dependent branching, and Everettian interpretations of quantum mechanics. FDBF distinguishes three epistemic levels: (1) established physical concepts such as quantum superposition and decoherence, (2) interpretive claims associated with the Everett/Many-Worlds family of quantum interpretations, and (3) new speculative hypotheses proposed by the framework. The model does not claim that conscious human decisions create new universes, nor does it treat fractal or branching structures observed in nature as evidence for the existence of a multiverse. Instead, it proposes that macroscopic decision points may be interpreted as observable markers of diverging histories within a branching description of reality. The paper develops a formal representation of decision branching, examines the conditions under which such structures could meaningfully be described as fractal or scale-dependent, discusses the relationship between decision histories and Everettian branching, and addresses falsifiability, epistemic limitations, and possible directions for future empirical development. FDBF is presented as a conceptual and interdisciplinary working framework spanning decision theory, philosophy of physics, complex systems, fractal geometry, and foundational questions in quantum mechanics. Author: Mohammad RadfarCorresponding author: m.raadfar@gmail.com

J. J. Halliwell