Collapse and causality in generalised trace dynamics: record selection in Connes time and the causal consistency of emergent records
Abstract
Dynamical wave-function collapse must not violate causality: a record selected "now" has no frame-independent meaning, and a nonlinear law can let distant observers signal. We ask whether this conflict is avoided when classical spacetime, with its causal structure, itself arises from localisation, as proposed in generalized trace dynamics (GTD), where the fluctuations that select a record come from unresolved pregeometric degrees of freedom ordered by Connes time, not by a spacetime coordinate. The hypersurface question is then not posed where selection happens; it returns as the requirement that emergent records do not signal. We apply the standard no-signalling theorem to an effective collapse law of CSL type. The norm-preserving, response-free law of a naive coarse-graining never selects. In history form, record weights are martingales only if the fluctuation history leans towards the leading record with gain twice its own diffusion and, for operators with three or more collinear eigenvalues, the linear law carries its counter-term, which a smooth coefficient drive gives with the wrong sign; any other gain signals. For an equilibrium sea the fluctuation-dissipation relation fixes the gain, so the Born gain is an Einstein relation between coupling, temperature and correlation time. A rate that reads the entanglement of the conditioned state signals; enhancement must sit in fixed collective operators. Positive states annihilate the Grassmann bilinear carrying the collapse coefficient, so the physical block is a reconstruction with positive kinetic form. The coefficient noise is evaluated for the Sutherland texture of GTD's relational master matrix: a block coupled to its local strain acquires an Ohmic spectral density with computed friction, continuum criterion and recurrence, while a kinetic cross-coupling yields none. What remains is the projection supplying counter-term and gain.
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BibTeX
@misc{singh2026collapse,
title = {{Collapse and causality in generalised trace dynamics: record selection in Connes time and the causal consistency of emergent records}},
author = {Tejinder P. Singh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10569},
eprint = {2610.10569},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10569},
}
RIS
TY - UNPB
TI - Collapse and causality in generalised trace dynamics: record selection in Connes time and the causal consistency of emergent records
AU - Tejinder P. Singh
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.10569
UR - https://arxiv.org/abs/2610.10569
AB - Dynamical wave-function collapse must not violate causality: a record selected "now" has no frame-independent meaning, and a nonlinear law can let distant observers signal. We ask whether this conflict is avoided when classical spacetime, with its causal structure, itself arises from localisation, as proposed in generalized trace dynamics (GTD), where the fluctuations that select a record come from unresolved pregeometric degrees of freedom ordered by Connes time, not by a spacetime coordinate. The hypersurface question is then not posed where selection happens; it returns as the requirement that emergent records do not signal. We apply the standard no-signalling theorem to an effective collapse law of CSL type. The norm-preserving, response-free law of a naive coarse-graining never selects. In history form, record weights are martingales only if the fluctuation history leans towards the leading record with gain twice its own diffusion and, for operators with three or more collinear eigenvalues, the linear law carries its counter-term, which a smooth coefficient drive gives with the wrong sign; any other gain signals. For an equilibrium sea the fluctuation-dissipation relation fixes the gain, so the Born gain is an Einstein relation between coupling, temperature and correlation time. A rate that reads the entanglement of the conditioned state signals; enhancement must sit in fixed collective operators. Positive states annihilate the Grassmann bilinear carrying the collapse coefficient, so the physical block is a reconstruction with positive kinetic form. The coefficient noise is evaluated for the Sutherland texture of GTD's relational master matrix: a block coupled to its local strain acquires an Ohmic spectral density with computed friction, continuum criterion and recurrence, while a kinetic cross-coupling yields none. What remains is the projection supplying counter-term and gain.
ER -