Entangled Pairs: What Co-location Can and Cannot Explain

When one particle of an entangled pair is measured, the joint state of the pair changes at once, however far apart the particles are. In the laboratory's description that update is non-local. The paper formalizes a conjecture about it: that the non-locality belongs to the laboratory's description, not to the particles. Each particle gets one extra coordinate, a label. In coordinates adapted to the pair, the two partners sit at the same place while they are entangled, so the update at measurement happens at a single point and in a definite order.

Key results

The central result is negative and exact. A rule acting where the partners meet could produce correlations stronger than quantum mechanics allows. So co-location explains neither the strength of quantum correlations nor the impossibility of signaling. Both have to be imported from quantum mechanics.
What it does deliver is a place and an order. The construction moves the puzzle of entanglement rather than removing it. It makes progress on the distance in "spooky action at a distance", not on the action.
It agrees with quantum mechanics. The mechanism is stated in four postulates and proved empirically equivalent to the nonrelativistic quantum mechanics of distinguishable massive particles, for spin measurements that do not couple spin to position.
A relativistic version orders the measurements invariantly. In 1 + 1 dimensions, a pair's measurements get a strict Lorentz-invariant partial order carried by the events themselves.
The claim is validity, not correctness. The account reproduces established results without contradiction. Its only empirical rivals are dynamical-collapse models, and it predicts zero collapse noise, as every no-collapse account does.

Read

Every numerical claim in the paper is backed by a unit test in the released code.

Preprint

A label-coordinate bookkeeping for entangled pairs: what co-location can and cannot explain

30 pages · 3 figures · 5 tables · PDF, 1.4 MB

The full paper: the frame construction, the contact-rule test, many-particle states and entanglement swapping, the relativistic variant, and the comparison with dynamical collapse.

Read the paper (PDF) doi:10.5281/zenodo.23249337

Verification code

Python package and test suite

Python / NumPy · 198 tests · MIT license · release v1.2.2

The frame maps, the locality-graph rules, the covariant variant and its ordering rule, and the numerical checks behind each proposition. Each numbered claim in the paper has a matching test.

View on GitHub doi:10.5281/zenodo.22820042

How to cite

Fischer, V. (2026). A label-coordinate bookkeeping for entangled pairs: What co-location can and cannot explain [Preprint]. Zenodo. https://doi.org/10.5281/zenodo.23249337

BibTeX

@misc{fischer2026labelcoordinate,
  author    = {Fischer, Verlyn},
  title     = {A label-coordinate bookkeeping for entangled
               pairs: what co-location can and cannot explain},
  year      = {2026},
  publisher = {Zenodo},
  note      = {Preprint},
  doi       = {10.5281/zenodo.23249337},
  url       = {https://doi.org/10.5281/zenodo.23249337}
}

@software{fischer2026labelcoordinatecode,
  author    = {Fischer, Verlyn},
  title     = {Verification code for "A label-coordinate
               bookkeeping for entangled pairs"},
  year      = {2026},
  publisher = {Zenodo},
  version   = {v1.2.2},
  doi       = {10.5281/zenodo.22820042},
  url       = {https://doi.org/10.5281/zenodo.22820042}
}

The paper is licensed under CC BY 4.0 and the code under the MIT license.