The parliament of observers - Against the observable axiom of quantum mechanics
Abstract
The 'unreasonable effectiveness of mathematics in the natural sciences' may at times give the impression that natural science, especially modern theoretical physics, is all but a formal apparatus. However, a key challenge of physics remains to align everyday notions of experience -- be it directly or mediated through instruments of arbitrary sophistication -- with their mathematical formalisation. This applies in particular to quantum theory, arguably the most successful theory of physics ever invented. One of its core assumptions postulates: Observables correspond with self−adjoint operators. Here, we argue that already this most basic premise about the quantum formalism falls apart under careful scrutiny, at least when understood for all observables at once. In other words, we challenge the role of the noncommutative algebra of bounded operators as an adequate formalisation of the 'algebra of observables', understood as (equivalence classes of) measurement procedures that admit a coherent empirical interpretation.
Related
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BibTeX
@misc{frembs2026parliament,
title = {{The parliament of observers - Against the observable axiom of quantum mechanics}},
author = {Markus Frembs and Andreas Döring},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07254},
eprint = {2610.07254},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07254},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The parliament of observers - Against the observable axiom of quantum mechanics
AU - Markus Frembs
AU - Andreas Döring
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07254
UR - https://arxiv.org/abs/2610.07254
AB - The 'unreasonable effectiveness of mathematics in the natural sciences' may at times give the impression that natural science, especially modern theoretical physics, is all but a formal apparatus. However, a key challenge of physics remains to align everyday notions of experience -- be it directly or mediated through instruments of arbitrary sophistication -- with their mathematical formalisation. This applies in particular to quantum theory, arguably the most successful theory of physics ever invented. One of its core assumptions postulates: Observables correspond with self−adjoint operators. Here, we argue that already this most basic premise about the quantum formalism falls apart under careful scrutiny, at least when understood for all observables at once. In other words, we challenge the role of the noncommutative algebra of bounded operators as an adequate formalisation of the 'algebra of observables', understood as (equivalence classes of) measurement procedures that admit a coherent empirical interpretation.
ER -