Published February 5, 2026 | Version V 1.3.26 E 1.3
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B02: Concise Description of the BRISM-Model (one-pager): The Born Rule as a Necessary Interface Condition.

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Description

This concise one-pager presents the BRane Interface Substrate Model (BRISM), a structural framework in which the Born rule emerges naturally from the way complex quantum states are translated into real measurement outcomes. The bulk is defined as a non‑geometric, complex Hilbert‑space substrate in which amplitudes and phases are ontically realized, while the brane represents the real arena of appearance where measurable, positive, and normalized quantities arise. A linear interface operator connects these two levels and ensures that only one probability structure is compatible with real measurement statistics. The term brane is used purely metaphorically and has no connection to string‑theoretic branes or geometrical extra dimensions. BRISM does not introduce new physics but reorganizes the existing Hilbert‑space formalism to show that the Born rule follows from structural requirements of measurability itself.

In contrast to Everett’s decision‑theoretic approaches or Zurek’s envariance‑based derivations, which rely on agent‑based rationality principles or specific assumptions about system–environment structure, BRISM avoids both conceptual dependencies. It shows that the Born rule already follows from the structural requirements of mapping complex, phase‑bearing bulk states onto a real, phase‑neutral arena of appearance. Thus, BRISM provides a pre‑instrumental, interpretation‑independent justification of quantum probabilities that does not rely on branching worlds, observer rationality, or environment‑induced symmetries.

For a comprehensive treatment, please refer to the main model: BRISM Model V1.3.26, DOI 10.5281/zenodo.18391945.

All BRISM papers on Zenodo  >> Searchlist

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Dates

Created
2026-02-04
one-pager BRISM
Submitted
2026-02-05
one-pager BRISM

References

  • [1] M. Born, Zur Quantenmechanik der Stoßvorgänge, Zeitschrift für Physik 37, 863–867 (1926). [2] A. M. Gleason, Measures on the closed subspaces of a Hilbert space, Journal of Mathematics and Mechanics 6, 885–893 (1957). [3] P. Busch, Quantum states and generalized observables, Physical Review Letters 91, 120403 (2003). [4] P. Busch, Gleason-type derivations of the quantum probability rule, Foundations of Physics 33, 1269–1302 (2003). [5] W. H. Zurek, Probabilities from entanglement: Born's rule from envariance, Physical Review A 71, 052105 (2005). [6] D. Deutsch, Quantum theory of probability and decisions, Proceedings of the Royal Society of London A 455, 3129–3137 (1999). [7] D. Wallace, The Emergent Multiverse: Quantum Theory according to the Everett Interpretation, Oxford University Press, Oxford (2012). [8] M. Schlosshauer, Decoherence and the Quantum-to-Classical Transition, Springer, Berlin (2007). [9] A. Peres, Quantum Theory: Concepts and Methods, Kluwer Academic Publishers, Dordrecht (1995). [10] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge (2000). [11] A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, Edizioni della Normale, Pisa (2011). [12] P. Busch, P. J. Lahti, and P. Mittelstaedt, The Quantum Theory of Measurement, Springer, Berlin (1996). [13] S. Saunders, J. Barrett, A. Kent, and D. Wallace (eds.), Many Worlds? Everett, Quantum Theory, and Reality, Oxford University Press, Oxford (2010). [14] M. Redhead, Incompleteness, Nonlocality, and Realism, Clarendon Press, Oxford (1987). [15] P. Busch, M. Grabowski, and P. J. Lahti, Operational Quantum Physics, Springer, Berlin (1995).