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Results · Quantum foundations

The relativistic necessity of the Born rule: uniqueness from Poincaré symmetry and dynamical preservation

Nidhal Mghirbi · International Journal of Quantum Foundations 12 (2026) 1–28 · Zenodo, ; first version · doi:10.5281/zenodo.17580489

In plain wordsFor massive spin-1/2 particles, only one quadratic expression in the wave function respects relativity, stays positive and is conserved, and it becomes the familiar squared wave function at low speeds; in pilot-wave theory, a distribution matching it at one time keeps matching it.

The result

As the paper states it, in briefFrom the symmetries of the Klein–Gordon and Dirac equations and the representation theory of the Poincaré group, the paper derives their conserved currents and argues that, for spin-1/2 particles, the probability density is the unique admissible form, reducing to |ψ|2 in the non-relativistic limit; within de Broglie–Bohm theory it proves that this distribution is preserved by the dynamics.

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Peer review
Published in the International Journal of Quantum Foundations 12 (2026) 1–28: received 10 October 2025, accepted 31 October 2025, as the journal’s page and the published paper record.

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Novelty and credit

Novelty
Synthesis of prior work (credited): in its own words, “a pedagogical and rigorous synthesis of prior foundational works” that “deliberately avoids claims of a first-principles derivation from nothing.”
Reach
Our most-read work on Zenodo: 1,793 unique views and 411 unique downloads across its versions, as of 30 October 2026.

Versionstwo, each with its own DOI

Every archived version, newest first. Dates are Zenodo publication dates. All versions: 10.5281/zenodo.17153428, which always resolves to the newest.
VersionDateDOINotes
—10.5281/zenodo.17580489
first10.5281/zenodo.17153429Titled “The Relativistic Necessity of the Born Rule: Uniqueness from Symmetry and Dynamics”.

Paper, code and links

Paper

On Zenodo: doi:10.5281/zenodo.17580489. No copy is hosted here.

Journal

International Journal of Quantum Foundations 12 (2026) 1–28; received 10 October 2025, accepted 31 October 2025.

Corrections

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All corrections, and what counts as one.

Cite

@article{mghirbi2025bornrule,
  author  = {Mghirbi, Nidhal},
  title   = {The relativistic necessity of the {B}orn rule: uniqueness from {P}oincaré symmetry and dynamical preservation},
  journal = {International Journal of Quantum Foundations},
  volume  = {12},
  pages   = {1--28},
  year    = {2026},
  doi     = {10.5281/zenodo.17580489},
  url     = {https://doi.org/10.5281/zenodo.17580489}
}

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