Critical emergence of quantum theory, spacetime and gravity from generalised trace dynamics
Abstract
Generalized trace dynamics (GTD) is a deterministic dynamics of aikyons (atoms of space-time-matter) whose near-equilibrium statistical mechanics yields quantum dynamics, while large anti-self-adjoint fluctuations drive spontaneous localisation and emergent classical spacetime. We separate two independent large limits: long-Connes-time coarse-graining of a finite system, which conditionally yields the quantum Ward identities, and the extensive many-aikyon/large-matrix limit required for a collective singularity. We turn the condensed-matter analogy of the E8 x omega E8 programme into a quantitative, falsifiable effective framework. Four coupled composite channels (bifermionic localisation, geometric soldering/Lorentz-Higgs, gauge-invariant electroweak, and matrix-valued flavour) define an exact susceptibility matrix and Legendre effective action, giving zero-mode and free-energy criteria for a common continuous or first-order transition. We pose the nonequilibrium problem in Schwinger-Keldysh form, define a projected fluctuation-dissipation defect and the martingale condition for Born probabilities, identify Newton's constant with the stiffness of the ordered geometric phase, and give conditions under which the Sakharov, constrained-BF, Jacobson, Padmanabhan and Verlinde descriptions of gravity are limits of one substrate. A regulated two-sector surrogate ensemble (a Myers-deformed geometric triple coupled to a matter matrix, with a Grassmann-regulated fermionic extension) shows that selected diagnostics are calculable: exact Adler-Millard charge conservation, a multi-channel first-order jump, a verified fluctuation-dissipation relation and its quench defect, and a fermionic spectral dimension d_s = 1.96 on the emergent two-sphere. The result is a calculational programme, not a completed derivation; the next step is the many-aikyon composite two-point matrix for GTD itself.
Related
- Quantum Tunneling and the Emergence of Classical Spacetime in Einstein-Æther Quantum Cosmology
- Conformal Anomalies and Generalised Energy Conservation in De Sitter Spacetime
- Quantum Dynamics of Probe Particles in Thermal Fields and the Emergence of Stochastic Dynamics
- Classical and Quantum Dynamics in State Space: Projective Hilbert Space, Measurement, and Classical Emergence
- Spacetime Emergence in the Memory of a Learning Agent
BibTeX
@misc{singh2026critical,
title = {{Critical emergence of quantum theory, spacetime and gravity from generalised trace dynamics}},
author = {Tejinder P. Singh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10571},
eprint = {2609.10571},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10571},
}
RIS
TY - UNPB
TI - Critical emergence of quantum theory, spacetime and gravity from generalised trace dynamics
AU - Tejinder P. Singh
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.10571
UR - https://arxiv.org/abs/2609.10571
AB - Generalized trace dynamics (GTD) is a deterministic dynamics of aikyons (atoms of space-time-matter) whose near-equilibrium statistical mechanics yields quantum dynamics, while large anti-self-adjoint fluctuations drive spontaneous localisation and emergent classical spacetime. We separate two independent large limits: long-Connes-time coarse-graining of a finite system, which conditionally yields the quantum Ward identities, and the extensive many-aikyon/large-matrix limit required for a collective singularity. We turn the condensed-matter analogy of the E8 x omega E8 programme into a quantitative, falsifiable effective framework. Four coupled composite channels (bifermionic localisation, geometric soldering/Lorentz-Higgs, gauge-invariant electroweak, and matrix-valued flavour) define an exact susceptibility matrix and Legendre effective action, giving zero-mode and free-energy criteria for a common continuous or first-order transition. We pose the nonequilibrium problem in Schwinger-Keldysh form, define a projected fluctuation-dissipation defect and the martingale condition for Born probabilities, identify Newton's constant with the stiffness of the ordered geometric phase, and give conditions under which the Sakharov, constrained-BF, Jacobson, Padmanabhan and Verlinde descriptions of gravity are limits of one substrate. A regulated two-sector surrogate ensemble (a Myers-deformed geometric triple coupled to a matter matrix, with a Grassmann-regulated fermionic extension) shows that selected diagnostics are calculable: exact Adler-Millard charge conservation, a multi-channel first-order jump, a verified fluctuation-dissipation relation and its quench defect, and a fermionic spectral dimension d_s = 1.96 on the emergent two-sphere. The result is a calculational programme, not a completed derivation; the next step is the many-aikyon composite two-point matrix for GTD itself.
ER -